Z3---4.15.1.UNS-Prf.s

View TPTP
Problem Process solution in
SystemOnTSTP Download .tgz
%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : SYN036-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% Computer : n005.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sat Jun 21 05:37:59 AM UTC 2025

% Result   : Unsatisfiable 22.55s 22.72s
% Output   : Proof 22.77s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : SYN036-1 : TPTP v9.0.0. Released v1.0.0.
% 0.04/0.12  % Command    : run_E %s %d THM
% 0.11/0.33  % Computer : n005.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 300
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Fri Jun 20 12:26:20 EDT 2025
% 0.11/0.33  % CPUTime    : 
% 22.55/22.72  % SZS status Unsatisfiable
% 22.55/22.72  % SZS output start Proof
% 22.55/22.72  tff(big_q_type, type, (
% 22.55/22.72     big_q: $i > $o)).
% 22.55/22.72  tff(c20_type, type, (
% 22.55/22.72     c20: $i)).
% 22.55/22.72  tff(big_p_type, type, (
% 22.55/22.72     big_p: $i > $o)).
% 22.55/22.72  tff(c15_type, type, (
% 22.55/22.72     c15: $i)).
% 22.55/22.72  tff(c11_type, type, (
% 22.55/22.72     c11: $i)).
% 22.55/22.72  tff(f4_type, type, (
% 22.55/22.72     f4: $i > $i)).
% 22.55/22.72  tff(elem_0_type, type, (
% 22.55/22.72     elem_0: $i)).
% 22.55/22.72  tff(c16_type, type, (
% 22.55/22.72     c16: $i)).
% 22.55/22.72  tff(f1_type, type, (
% 22.55/22.72     f1: $i > $i)).
% 22.55/22.72  tff(c6_type, type, (
% 22.55/22.72     c6: $i)).
% 22.55/22.72  tff(c3_type, type, (
% 22.55/22.72     c3: $i)).
% 22.55/22.72  tff(f2_type, type, (
% 22.55/22.72     f2: $i > $i)).
% 22.55/22.72  tff(c4_type, type, (
% 22.55/22.72     c4: $i)).
% 22.55/22.72  tff(c9_type, type, (
% 22.55/22.72     c9: $i)).
% 22.55/22.72  tff(c8_type, type, (
% 22.55/22.72     c8: $i)).
% 22.55/22.72  tff(c14_type, type, (
% 22.55/22.72     c14: $i)).
% 22.55/22.72  tff(f3_type, type, (
% 22.55/22.72     f3: $i > $i)).
% 22.55/22.72  tff(c19_type, type, (
% 22.55/22.72     c19: $i)).
% 22.55/22.72  tff(c7_type, type, (
% 22.55/22.72     c7: $i)).
% 22.55/22.72  tff(c2_type, type, (
% 22.55/22.72     c2: $i)).
% 22.55/22.72  tff(c1_type, type, (
% 22.55/22.72     c1: $i)).
% 22.55/22.72  tff(1,assumption,(~big_p(c11)), introduced(assumption)).
% 22.55/22.72  tff(2,assumption,(~big_q(c16)), introduced(assumption)).
% 22.55/22.72  tff(3,assumption,(~big_p(elem!0)), introduced(assumption)).
% 22.55/22.72  tff(4,assumption,(big_p(c6)), introduced(assumption)).
% 22.55/22.72  tff(5,assumption,(~big_q(elem!0)), introduced(assumption)).
% 22.55/22.72  tff(6,assumption,(big_p(c11)), introduced(assumption)).
% 22.55/22.72  tff(7,assumption,(big_p(c3)), introduced(assumption)).
% 22.55/22.72  tff(8,assumption,(~big_q(f2(elem!0))), introduced(assumption)).
% 22.55/22.72  tff(9,plain,
% 22.55/22.72      (^[W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : refl(((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y)) <=> ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y)))),
% 22.55/22.72      inference(bind,[status(th)],[])).
% 22.55/22.72  tff(10,plain,
% 22.55/22.72      (![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y)) <=> ![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))),
% 22.55/22.72      inference(quant_intro,[status(thm)],[9])).
% 22.55/22.72  tff(11,plain,
% 22.55/22.72      (![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y)) <=> ![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))),
% 22.55/22.72      inference(rewrite,[status(thm)],[])).
% 22.55/22.72  tff(12,plain,
% 22.55/22.72      (^[W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(c3)) | big_p(Y)) <=> ((~big_p(c3)) | big_p(Y))), ((((~big_p(c3)) | big_p(Y)) | big_q(c4)) <=> (((~big_p(c3)) | big_p(Y)) | big_q(c4)))), rewrite((((~big_p(c3)) | big_p(Y)) | big_q(c4)) <=> ((~big_p(c3)) | big_q(c4) | big_p(Y))), ((((~big_p(c3)) | big_p(Y)) | big_q(c4)) <=> ((~big_p(c3)) | big_q(c4) | big_p(Y)))), (((((~big_p(c3)) | big_p(Y)) | big_q(c4)) | big_p(X3)) <=> (((~big_p(c3)) | big_q(c4) | big_p(Y)) | big_p(X3)))), rewrite((((~big_p(c3)) | big_q(c4) | big_p(Y)) | big_p(X3)) <=> ((~big_p(c3)) | big_p(X3) | big_q(c4) | big_p(Y))), (((((~big_p(c3)) | big_p(Y)) | big_q(c4)) | big_p(X3)) <=> ((~big_p(c3)) | big_p(X3) | big_q(c4) | big_p(Y)))), ((((((~big_p(c3)) | big_p(Y)) | big_q(c4)) | big_p(X3)) | big_q(f2(W))) <=> (((~big_p(c3)) | big_p(X3) | big_q(c4) | big_p(Y)) | big_q(f2(W))))), rewrite((((~big_p(c3)) | big_p(X3) | big_q(c4) | big_p(Y)) | big_q(f2(W))) <=> ((~big_p(c3)) | big_p(X3) | big_q(c4) | big_q(f2(W)) | big_p(Y))), ((((((~big_p(c3)) | big_p(Y)) | big_q(c4)) | big_p(X3)) | big_q(f2(W))) <=> ((~big_p(c3)) | big_p(X3) | big_q(c4) | big_q(f2(W)) | big_p(Y)))), (((((((~big_p(c3)) | big_p(Y)) | big_q(c4)) | big_p(X3)) | big_q(f2(W))) | big_q(W)) <=> (((~big_p(c3)) | big_p(X3) | big_q(c4) | big_q(f2(W)) | big_p(Y)) | big_q(W)))), rewrite((((~big_p(c3)) | big_p(X3) | big_q(c4) | big_q(f2(W)) | big_p(Y)) | big_q(W)) <=> ((~big_p(c3)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))), (((((((~big_p(c3)) | big_p(Y)) | big_q(c4)) | big_p(X3)) | big_q(f2(W))) | big_q(W)) <=> ((~big_p(c3)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y)))), ((((((((~big_p(c3)) | big_p(Y)) | big_q(c4)) | big_p(X3)) | big_q(f2(W))) | big_q(W)) | (~big_p(X1))) <=> (((~big_p(c3)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y)) | (~big_p(X1))))), rewrite((((~big_p(c3)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y)) | (~big_p(X1))) <=> ((~big_p(c3)) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))), ((((((((~big_p(c3)) | big_p(Y)) | big_q(c4)) | big_p(X3)) | big_q(f2(W))) | big_q(W)) | (~big_p(X1))) <=> ((~big_p(c3)) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y)))), (((((((((~big_p(c3)) | big_p(Y)) | big_q(c4)) | big_p(X3)) | big_q(f2(W))) | big_q(W)) | (~big_p(X1))) | big_q(X2)) <=> (((~big_p(c3)) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y)) | big_q(X2)))), rewrite((((~big_p(c3)) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y)) | big_q(X2)) <=> ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))), (((((((((~big_p(c3)) | big_p(Y)) | big_q(c4)) | big_p(X3)) | big_q(f2(W))) | big_q(W)) | (~big_p(X1))) | big_q(X2)) <=> ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))))),
% 22.55/22.72      inference(bind,[status(th)],[])).
% 22.55/22.72  tff(13,plain,
% 22.55/22.72      (![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((((((((~big_p(c3)) | big_p(Y)) | big_q(c4)) | big_p(X3)) | big_q(f2(W))) | big_q(W)) | (~big_p(X1))) | big_q(X2)) <=> ![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))),
% 22.55/22.72      inference(quant_intro,[status(thm)],[12])).
% 22.55/22.72  tff(14,axiom,(![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((((((((~big_p(c3)) | big_p(Y)) | big_q(c4)) | big_p(X3)) | big_q(f2(W))) | big_q(W)) | (~big_p(X1))) | big_q(X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_33')).
% 22.55/22.72  tff(15,plain,
% 22.55/22.72      (![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))),
% 22.55/22.72      inference(modus_ponens,[status(thm)],[14, 13])).
% 22.55/22.72  tff(16,plain,
% 22.55/22.72      (![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))),
% 22.55/22.72      inference(modus_ponens,[status(thm)],[15, 11])).
% 22.55/22.72  tff(17,plain,(
% 22.55/22.72      ![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))),
% 22.55/22.72      inference(skolemize,[status(sab)],[16])).
% 22.55/22.72  tff(18,plain,
% 22.55/22.72      (![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))),
% 22.55/22.72      inference(modus_ponens,[status(thm)],[17, 10])).
% 22.55/22.72  tff(19,plain,
% 22.55/22.72      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | ((~big_p(c3)) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(elem!0))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | (~big_p(c3)) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(elem!0))),
% 22.55/22.72      inference(rewrite,[status(thm)],[])).
% 22.55/22.72  tff(20,plain,
% 22.55/22.72      (((~big_p(c3)) | big_q(elem!0) | (~big_p(c3)) | big_p(elem!0) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(elem!0)) <=> ((~big_p(c3)) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(elem!0))),
% 22.55/22.72      inference(rewrite,[status(thm)],[])).
% 22.55/22.72  tff(21,plain,
% 22.55/22.72      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | ((~big_p(c3)) | big_q(elem!0) | (~big_p(c3)) | big_p(elem!0) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(elem!0))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | ((~big_p(c3)) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(elem!0)))),
% 22.55/22.73      inference(monotonicity,[status(thm)],[20])).
% 22.55/22.73  tff(22,plain,
% 22.55/22.73      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | ((~big_p(c3)) | big_q(elem!0) | (~big_p(c3)) | big_p(elem!0) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(elem!0))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | (~big_p(c3)) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(elem!0))),
% 22.55/22.73      inference(transitivity,[status(thm)],[21, 19])).
% 22.55/22.73  tff(23,plain,
% 22.55/22.73      ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | ((~big_p(c3)) | big_q(elem!0) | (~big_p(c3)) | big_p(elem!0) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(elem!0))),
% 22.55/22.73      inference(quant_inst,[status(thm)],[])).
% 22.55/22.73  tff(24,plain,
% 22.55/22.73      ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | (~big_p(c3)) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(elem!0)),
% 22.55/22.73      inference(modus_ponens,[status(thm)],[23, 22])).
% 22.55/22.73  tff(25,plain,
% 22.55/22.73      (big_q(c4)),
% 22.55/22.73      inference(unit_resolution,[status(thm)],[24, 18, 5, 3, 8, 7])).
% 22.55/22.73  tff(26,plain,
% 22.55/22.73      (^[X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : refl(((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9)) <=> ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9)))),
% 22.55/22.73      inference(bind,[status(th)],[])).
% 22.55/22.73  tff(27,plain,
% 22.55/22.73      (![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9)) <=> ![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))),
% 22.55/22.73      inference(quant_intro,[status(thm)],[26])).
% 22.55/22.73  tff(28,plain,
% 22.55/22.73      (![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9)) <=> ![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))),
% 22.55/22.73      inference(rewrite,[status(thm)],[])).
% 22.55/22.73  tff(29,plain,
% 22.55/22.73      (^[X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) <=> ((~big_q(X8)) | (~big_p(X7)) | big_p(c11))), ((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) <=> (((~big_q(X8)) | (~big_p(X7)) | big_p(c11)) | big_p(X9)))), rewrite((((~big_q(X8)) | (~big_p(X7)) | big_p(c11)) | big_p(X9)) <=> ((~big_q(X8)) | (~big_p(X7)) | big_p(c11) | big_p(X9))), ((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) <=> ((~big_q(X8)) | (~big_p(X7)) | big_p(c11) | big_p(X9)))), (((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | (~big_q(X13))) <=> (((~big_q(X8)) | (~big_p(X7)) | big_p(c11) | big_p(X9)) | (~big_q(X13))))), rewrite((((~big_q(X8)) | (~big_p(X7)) | big_p(c11) | big_p(X9)) | (~big_q(X13))) <=> ((~big_q(X8)) | (~big_q(X13)) | (~big_p(X7)) | big_p(c11) | big_p(X9))), (((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | (~big_q(X13))) <=> ((~big_q(X8)) | (~big_q(X13)) | (~big_p(X7)) | big_p(c11) | big_p(X9)))), ((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | (~big_q(X13))) | big_q(c16)) <=> (((~big_q(X8)) | (~big_q(X13)) | (~big_p(X7)) | big_p(c11) | big_p(X9)) | big_q(c16)))), rewrite((((~big_q(X8)) | (~big_q(X13)) | (~big_p(X7)) | big_p(c11) | big_p(X9)) | big_q(c16)) <=> ((~big_q(X8)) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | big_p(X9))), ((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | (~big_q(X13))) | big_q(c16)) <=> ((~big_q(X8)) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | big_p(X9)))), (((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | (~big_q(X13))) | big_q(c16)) | (~big_p(X14))) <=> (((~big_q(X8)) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | big_p(X9)) | (~big_p(X14))))), rewrite((((~big_q(X8)) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | big_p(X9)) | (~big_p(X14))) <=> ((~big_q(X8)) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))), (((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | (~big_q(X13))) | big_q(c16)) | (~big_p(X14))) <=> ((~big_q(X8)) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9)))), ((((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | (~big_q(X13))) | big_q(c16)) | (~big_p(X14))) | big_q(X15)) <=> (((~big_q(X8)) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9)) | big_q(X15)))), rewrite((((~big_q(X8)) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9)) | big_q(X15)) <=> ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))), ((((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | (~big_q(X13))) | big_q(c16)) | (~big_p(X14))) | big_q(X15)) <=> ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))))),
% 22.55/22.73      inference(bind,[status(th)],[])).
% 22.55/22.73  tff(30,plain,
% 22.55/22.73      (![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : (((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | (~big_q(X13))) | big_q(c16)) | (~big_p(X14))) | big_q(X15)) <=> ![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))),
% 22.55/22.73      inference(quant_intro,[status(thm)],[29])).
% 22.55/22.73  tff(31,axiom,(![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : (((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | (~big_q(X13))) | big_q(c16)) | (~big_p(X14))) | big_q(X15))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_81')).
% 22.55/22.73  tff(32,plain,
% 22.55/22.73      (![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))),
% 22.55/22.73      inference(modus_ponens,[status(thm)],[31, 30])).
% 22.55/22.73  tff(33,plain,
% 22.55/22.73      (![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))),
% 22.55/22.73      inference(modus_ponens,[status(thm)],[32, 28])).
% 22.55/22.73  tff(34,plain,(
% 22.55/22.73      ![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))),
% 22.55/22.73      inference(skolemize,[status(sab)],[33])).
% 22.55/22.73  tff(35,plain,
% 22.55/22.73      (![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))),
% 22.55/22.73      inference(modus_ponens,[status(thm)],[34, 27])).
% 22.55/22.73  tff(36,plain,
% 22.55/22.73      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c3)) | big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(c4)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_p(c3)) | big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(c4)))),
% 22.55/22.73      inference(rewrite,[status(thm)],[])).
% 22.55/22.73  tff(37,plain,
% 22.55/22.73      (((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | (~big_p(c3)) | big_q(c16) | big_p(c11) | (~big_p(c3)) | big_p(elem!0)) <=> ((~big_p(c3)) | big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(c4)))),
% 22.55/22.73      inference(rewrite,[status(thm)],[])).
% 22.55/22.73  tff(38,plain,
% 22.55/22.73      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | (~big_p(c3)) | big_q(c16) | big_p(c11) | (~big_p(c3)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c3)) | big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(c4))))),
% 22.55/22.73      inference(monotonicity,[status(thm)],[37])).
% 22.55/22.73  tff(39,plain,
% 22.55/22.73      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | (~big_p(c3)) | big_q(c16) | big_p(c11) | (~big_p(c3)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_p(c3)) | big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(c4)))),
% 22.55/22.73      inference(transitivity,[status(thm)],[38, 36])).
% 22.55/22.73  tff(40,plain,
% 22.55/22.73      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | (~big_p(c3)) | big_q(c16) | big_p(c11) | (~big_p(c3)) | big_p(elem!0))),
% 22.55/22.73      inference(quant_inst,[status(thm)],[])).
% 22.55/22.73  tff(41,plain,
% 22.55/22.73      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_p(c3)) | big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(c4))),
% 22.55/22.73      inference(modus_ponens,[status(thm)],[40, 39])).
% 22.55/22.73  tff(42,plain,
% 22.55/22.73      (big_p(c11)),
% 22.55/22.73      inference(unit_resolution,[status(thm)],[41, 35, 5, 3, 2, 7, 25])).
% 22.55/22.73  tff(43,plain,
% 22.55/22.73      (^[X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : refl(((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9)) <=> ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9)))),
% 22.55/22.73      inference(bind,[status(th)],[])).
% 22.55/22.73  tff(44,plain,
% 22.55/22.73      (![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9)) <=> ![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))),
% 22.55/22.73      inference(quant_intro,[status(thm)],[43])).
% 22.55/22.73  tff(45,plain,
% 22.55/22.73      (![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9)) <=> ![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))),
% 22.55/22.73      inference(rewrite,[status(thm)],[])).
% 22.55/22.73  tff(46,plain,
% 22.55/22.73      (^[X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(c11)) | big_p(X7)) <=> (big_p(X7) | (~big_p(c11)))), ((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) <=> ((big_p(X7) | (~big_p(c11))) | (~big_q(X8))))), rewrite(((big_p(X7) | (~big_p(c11))) | (~big_q(X8))) <=> ((~big_q(X8)) | big_p(X7) | (~big_p(c11)))), ((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) <=> ((~big_q(X8)) | big_p(X7) | (~big_p(c11))))), (((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) <=> (((~big_q(X8)) | big_p(X7) | (~big_p(c11))) | big_p(X9)))), rewrite((((~big_q(X8)) | big_p(X7) | (~big_p(c11))) | big_p(X9)) <=> ((~big_q(X8)) | big_p(X7) | (~big_p(c11)) | big_p(X9))), (((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) <=> ((~big_q(X8)) | big_p(X7) | (~big_p(c11)) | big_p(X9)))), ((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | (~big_q(X13))) <=> (((~big_q(X8)) | big_p(X7) | (~big_p(c11)) | big_p(X9)) | (~big_q(X13))))), rewrite((((~big_q(X8)) | big_p(X7) | (~big_p(c11)) | big_p(X9)) | (~big_q(X13))) <=> ((~big_q(X8)) | (~big_q(X13)) | big_p(X7) | (~big_p(c11)) | big_p(X9))), ((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | (~big_q(X13))) <=> ((~big_q(X8)) | (~big_q(X13)) | big_p(X7) | (~big_p(c11)) | big_p(X9)))), (((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | (~big_q(X13))) | big_q(c16)) <=> (((~big_q(X8)) | (~big_q(X13)) | big_p(X7) | (~big_p(c11)) | big_p(X9)) | big_q(c16)))), rewrite((((~big_q(X8)) | (~big_q(X13)) | big_p(X7) | (~big_p(c11)) | big_p(X9)) | big_q(c16)) <=> ((~big_q(X8)) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | big_p(X9))), (((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | (~big_q(X13))) | big_q(c16)) <=> ((~big_q(X8)) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | big_p(X9)))), ((((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | (~big_q(X13))) | big_q(c16)) | (~big_p(X14))) <=> (((~big_q(X8)) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | big_p(X9)) | (~big_p(X14))))), rewrite((((~big_q(X8)) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | big_p(X9)) | (~big_p(X14))) <=> ((~big_q(X8)) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))), ((((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | (~big_q(X13))) | big_q(c16)) | (~big_p(X14))) <=> ((~big_q(X8)) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9)))), (((((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | (~big_q(X13))) | big_q(c16)) | (~big_p(X14))) | big_q(X15)) <=> (((~big_q(X8)) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9)) | big_q(X15)))), rewrite((((~big_q(X8)) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9)) | big_q(X15)) <=> ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))), (((((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | (~big_q(X13))) | big_q(c16)) | (~big_p(X14))) | big_q(X15)) <=> ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))))),
% 22.55/22.73      inference(bind,[status(th)],[])).
% 22.55/22.73  tff(47,plain,
% 22.55/22.73      (![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | (~big_q(X13))) | big_q(c16)) | (~big_p(X14))) | big_q(X15)) <=> ![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))),
% 22.55/22.73      inference(quant_intro,[status(thm)],[46])).
% 22.55/22.73  tff(48,axiom,(![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | (~big_q(X13))) | big_q(c16)) | (~big_p(X14))) | big_q(X15))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_65')).
% 22.55/22.73  tff(49,plain,
% 22.55/22.73      (![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))),
% 22.55/22.73      inference(modus_ponens,[status(thm)],[48, 47])).
% 22.55/22.73  tff(50,plain,
% 22.55/22.73      (![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))),
% 22.55/22.73      inference(modus_ponens,[status(thm)],[49, 45])).
% 22.55/22.73  tff(51,plain,(
% 22.55/22.73      ![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))),
% 22.55/22.73      inference(skolemize,[status(sab)],[50])).
% 22.55/22.73  tff(52,plain,
% 22.55/22.73      (![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))),
% 22.55/22.73      inference(modus_ponens,[status(thm)],[51, 44])).
% 22.55/22.73  tff(53,plain,
% 22.55/22.73      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c3)) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(elem!0) | (~big_q(c4)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c3)) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(elem!0) | (~big_q(c4)))),
% 22.55/22.73      inference(rewrite,[status(thm)],[])).
% 22.55/22.73  tff(54,plain,
% 22.55/22.73      (((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | big_p(elem!0) | big_q(c16) | (~big_p(c11)) | (~big_p(c3)) | big_p(elem!0)) <=> ((~big_p(c3)) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(elem!0) | (~big_q(c4)))),
% 22.55/22.73      inference(rewrite,[status(thm)],[])).
% 22.55/22.73  tff(55,plain,
% 22.55/22.73      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | big_p(elem!0) | big_q(c16) | (~big_p(c11)) | (~big_p(c3)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c3)) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(elem!0) | (~big_q(c4))))),
% 22.55/22.73      inference(monotonicity,[status(thm)],[54])).
% 22.55/22.73  tff(56,plain,
% 22.55/22.73      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | big_p(elem!0) | big_q(c16) | (~big_p(c11)) | (~big_p(c3)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c3)) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(elem!0) | (~big_q(c4)))),
% 22.55/22.73      inference(transitivity,[status(thm)],[55, 53])).
% 22.55/22.73  tff(57,plain,
% 22.55/22.73      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | big_p(elem!0) | big_q(c16) | (~big_p(c11)) | (~big_p(c3)) | big_p(elem!0))),
% 22.55/22.73      inference(quant_inst,[status(thm)],[])).
% 22.55/22.73  tff(58,plain,
% 22.55/22.73      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c3)) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(elem!0) | (~big_q(c4))),
% 22.55/22.73      inference(modus_ponens,[status(thm)],[57, 56])).
% 22.55/22.73  tff(59,plain,
% 22.55/22.73      ($false),
% 22.55/22.73      inference(unit_resolution,[status(thm)],[58, 52, 5, 3, 2, 42, 7, 25])).
% 22.55/22.73  tff(60,plain,((~big_p(c3)) | big_q(elem!0) | big_p(elem!0) | big_q(c16) | big_q(f2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 22.55/22.73  tff(61,plain,
% 22.55/22.73      (~big_p(c3)),
% 22.55/22.73      inference(unit_resolution,[status(thm)],[60, 8, 3, 2, 5])).
% 22.55/22.73  tff(62,plain,
% 22.55/22.73      (^[W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : refl((big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y))) <=> (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y))))),
% 22.55/22.73      inference(bind,[status(th)],[])).
% 22.55/22.73  tff(63,plain,
% 22.55/22.73      (![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y))) <=> ![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))),
% 22.55/22.73      inference(quant_intro,[status(thm)],[62])).
% 22.55/22.73  tff(64,plain,
% 22.55/22.73      (![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y))) <=> ![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))),
% 22.55/22.73      inference(rewrite,[status(thm)],[])).
% 22.55/22.73  tff(65,plain,
% 22.55/22.73      (^[W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(c3) | (~big_p(Y))) | big_q(c4)) <=> (big_p(c3) | big_q(c4) | (~big_p(Y)))), ((((big_p(c3) | (~big_p(Y))) | big_q(c4)) | big_p(X3)) <=> ((big_p(c3) | big_q(c4) | (~big_p(Y))) | big_p(X3)))), rewrite(((big_p(c3) | big_q(c4) | (~big_p(Y))) | big_p(X3)) <=> (big_p(c3) | big_p(X3) | big_q(c4) | (~big_p(Y)))), ((((big_p(c3) | (~big_p(Y))) | big_q(c4)) | big_p(X3)) <=> (big_p(c3) | big_p(X3) | big_q(c4) | (~big_p(Y))))), (((((big_p(c3) | (~big_p(Y))) | big_q(c4)) | big_p(X3)) | big_q(f2(W))) <=> ((big_p(c3) | big_p(X3) | big_q(c4) | (~big_p(Y))) | big_q(f2(W))))), rewrite(((big_p(c3) | big_p(X3) | big_q(c4) | (~big_p(Y))) | big_q(f2(W))) <=> (big_p(c3) | big_p(X3) | big_q(c4) | big_q(f2(W)) | (~big_p(Y)))), (((((big_p(c3) | (~big_p(Y))) | big_q(c4)) | big_p(X3)) | big_q(f2(W))) <=> (big_p(c3) | big_p(X3) | big_q(c4) | big_q(f2(W)) | (~big_p(Y))))), ((((((big_p(c3) | (~big_p(Y))) | big_q(c4)) | big_p(X3)) | big_q(f2(W))) | big_q(W)) <=> ((big_p(c3) | big_p(X3) | big_q(c4) | big_q(f2(W)) | (~big_p(Y))) | big_q(W)))), rewrite(((big_p(c3) | big_p(X3) | big_q(c4) | big_q(f2(W)) | (~big_p(Y))) | big_q(W)) <=> (big_p(c3) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))), ((((((big_p(c3) | (~big_p(Y))) | big_q(c4)) | big_p(X3)) | big_q(f2(W))) | big_q(W)) <=> (big_p(c3) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y))))), (((((((big_p(c3) | (~big_p(Y))) | big_q(c4)) | big_p(X3)) | big_q(f2(W))) | big_q(W)) | (~big_p(X1))) <=> ((big_p(c3) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y))) | (~big_p(X1))))), rewrite(((big_p(c3) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y))) | (~big_p(X1))) <=> (big_p(c3) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))), (((((((big_p(c3) | (~big_p(Y))) | big_q(c4)) | big_p(X3)) | big_q(f2(W))) | big_q(W)) | (~big_p(X1))) <=> (big_p(c3) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y))))), ((((((((big_p(c3) | (~big_p(Y))) | big_q(c4)) | big_p(X3)) | big_q(f2(W))) | big_q(W)) | (~big_p(X1))) | big_q(X2)) <=> ((big_p(c3) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y))) | big_q(X2)))), rewrite(((big_p(c3) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y))) | big_q(X2)) <=> (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))), ((((((((big_p(c3) | (~big_p(Y))) | big_q(c4)) | big_p(X3)) | big_q(f2(W))) | big_q(W)) | (~big_p(X1))) | big_q(X2)) <=> (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))))),
% 22.55/22.73      inference(bind,[status(th)],[])).
% 22.55/22.73  tff(66,plain,
% 22.55/22.73      (![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (((((((big_p(c3) | (~big_p(Y))) | big_q(c4)) | big_p(X3)) | big_q(f2(W))) | big_q(W)) | (~big_p(X1))) | big_q(X2)) <=> ![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))),
% 22.55/22.73      inference(quant_intro,[status(thm)],[65])).
% 22.55/22.73  tff(67,axiom,(![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (((((((big_p(c3) | (~big_p(Y))) | big_q(c4)) | big_p(X3)) | big_q(f2(W))) | big_q(W)) | (~big_p(X1))) | big_q(X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_49')).
% 22.55/22.73  tff(68,plain,
% 22.55/22.73      (![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))),
% 22.55/22.73      inference(modus_ponens,[status(thm)],[67, 66])).
% 22.55/22.73  tff(69,plain,
% 22.55/22.73      (![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))),
% 22.55/22.73      inference(modus_ponens,[status(thm)],[68, 64])).
% 22.55/22.73  tff(70,plain,(
% 22.55/22.73      ![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))),
% 22.55/22.73      inference(skolemize,[status(sab)],[69])).
% 22.55/22.73  tff(71,plain,
% 22.55/22.73      (![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))),
% 22.55/22.73      inference(modus_ponens,[status(thm)],[70, 63])).
% 22.55/22.73  tff(72,plain,
% 22.55/22.73      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(c4) | (~big_p(c11)) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(elem!0))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | big_p(c3) | big_q(c4) | (~big_p(c11)) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(elem!0))),
% 22.55/22.73      inference(rewrite,[status(thm)],[])).
% 22.55/22.73  tff(73,plain,
% 22.55/22.73      ((big_p(c3) | big_q(elem!0) | (~big_p(c11)) | big_p(elem!0) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(c11))) <=> (big_p(c3) | big_q(c4) | (~big_p(c11)) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(elem!0))),
% 22.55/22.73      inference(rewrite,[status(thm)],[])).
% 22.55/22.73  tff(74,plain,
% 22.55/22.73      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(elem!0) | (~big_p(c11)) | big_p(elem!0) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(c11)))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(c4) | (~big_p(c11)) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(elem!0)))),
% 22.55/22.73      inference(monotonicity,[status(thm)],[73])).
% 22.55/22.73  tff(75,plain,
% 22.55/22.73      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(elem!0) | (~big_p(c11)) | big_p(elem!0) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(c11)))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | big_p(c3) | big_q(c4) | (~big_p(c11)) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(elem!0))),
% 22.55/22.74      inference(transitivity,[status(thm)],[74, 72])).
% 22.55/22.74  tff(76,plain,
% 22.55/22.74      ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(elem!0) | (~big_p(c11)) | big_p(elem!0) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(c11)))),
% 22.55/22.74      inference(quant_inst,[status(thm)],[])).
% 22.55/22.74  tff(77,plain,
% 22.55/22.74      ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | big_p(c3) | big_q(c4) | (~big_p(c11)) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(elem!0)),
% 22.55/22.74      inference(modus_ponens,[status(thm)],[76, 75])).
% 22.55/22.74  tff(78,plain,
% 22.55/22.74      (big_q(c4)),
% 22.55/22.74      inference(unit_resolution,[status(thm)],[77, 71, 5, 3, 8, 6, 61])).
% 22.55/22.74  tff(79,plain,
% 22.55/22.74      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(elem!0) | (~big_q(c4)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(elem!0) | (~big_q(c4)))),
% 22.55/22.74      inference(rewrite,[status(thm)],[])).
% 22.55/22.74  tff(80,plain,
% 22.55/22.74      (((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | big_p(elem!0) | big_q(c16) | (~big_p(c11)) | (~big_p(c11)) | big_p(elem!0)) <=> (big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(elem!0) | (~big_q(c4)))),
% 22.55/22.74      inference(rewrite,[status(thm)],[])).
% 22.55/22.74  tff(81,plain,
% 22.55/22.74      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | big_p(elem!0) | big_q(c16) | (~big_p(c11)) | (~big_p(c11)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(elem!0) | (~big_q(c4))))),
% 22.55/22.74      inference(monotonicity,[status(thm)],[80])).
% 22.55/22.74  tff(82,plain,
% 22.55/22.74      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | big_p(elem!0) | big_q(c16) | (~big_p(c11)) | (~big_p(c11)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(elem!0) | (~big_q(c4)))),
% 22.55/22.74      inference(transitivity,[status(thm)],[81, 79])).
% 22.55/22.74  tff(83,plain,
% 22.55/22.74      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | big_p(elem!0) | big_q(c16) | (~big_p(c11)) | (~big_p(c11)) | big_p(elem!0))),
% 22.55/22.74      inference(quant_inst,[status(thm)],[])).
% 22.55/22.74  tff(84,plain,
% 22.55/22.74      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(elem!0) | (~big_q(c4))),
% 22.55/22.74      inference(modus_ponens,[status(thm)],[83, 82])).
% 22.55/22.74  tff(85,plain,
% 22.55/22.74      ($false),
% 22.55/22.74      inference(unit_resolution,[status(thm)],[84, 52, 5, 3, 2, 6, 78])).
% 22.55/22.74  tff(86,plain,((~big_p(c11)) | big_q(elem!0) | big_p(elem!0) | big_q(c16) | big_q(f2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 22.55/22.74  tff(87,plain,
% 22.55/22.74      (~big_p(c11)),
% 22.55/22.74      inference(unit_resolution,[status(thm)],[86, 8, 3, 2, 5])).
% 22.55/22.74  tff(88,assumption,(~big_p(f1(elem!0))), introduced(assumption)).
% 22.55/22.74  tff(89,assumption,(big_p(c9)), introduced(assumption)).
% 22.55/22.74  tff(90,plain,
% 22.55/22.74      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_p(c9)))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | big_p(c3) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_p(c9)))),
% 22.55/22.74      inference(rewrite,[status(thm)],[])).
% 22.55/22.74  tff(91,plain,
% 22.55/22.74      ((big_p(c3) | big_q(elem!0) | (~big_p(c9)) | big_p(elem!0) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(c9))) <=> (big_p(c3) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_p(c9)))),
% 22.55/22.74      inference(rewrite,[status(thm)],[])).
% 22.55/22.74  tff(92,plain,
% 22.55/22.74      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(elem!0) | (~big_p(c9)) | big_p(elem!0) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(c9)))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_p(c9))))),
% 22.55/22.74      inference(monotonicity,[status(thm)],[91])).
% 22.55/22.74  tff(93,plain,
% 22.55/22.74      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(elem!0) | (~big_p(c9)) | big_p(elem!0) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(c9)))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | big_p(c3) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_p(c9)))),
% 22.55/22.74      inference(transitivity,[status(thm)],[92, 90])).
% 22.55/22.74  tff(94,plain,
% 22.55/22.74      ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(elem!0) | (~big_p(c9)) | big_p(elem!0) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(c9)))),
% 22.55/22.74      inference(quant_inst,[status(thm)],[])).
% 22.55/22.74  tff(95,plain,
% 22.55/22.74      ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | big_p(c3) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_p(c9))),
% 22.55/22.74      inference(modus_ponens,[status(thm)],[94, 93])).
% 22.55/22.74  tff(96,plain,
% 22.55/22.74      (big_q(c4)),
% 22.55/22.74      inference(unit_resolution,[status(thm)],[95, 71, 5, 3, 8, 89, 61])).
% 22.55/22.74  tff(97,plain,
% 22.55/22.74      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(c9)) | (~big_q(c4)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(c9)) | (~big_q(c4)))),
% 22.55/22.74      inference(rewrite,[status(thm)],[])).
% 22.55/22.74  tff(98,plain,
% 22.55/22.74      (((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | (~big_p(c9)) | big_q(c16) | big_p(c11) | (~big_p(c9)) | big_p(elem!0)) <=> (big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(c9)) | (~big_q(c4)))),
% 22.55/22.74      inference(rewrite,[status(thm)],[])).
% 22.55/22.74  tff(99,plain,
% 22.55/22.74      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | (~big_p(c9)) | big_q(c16) | big_p(c11) | (~big_p(c9)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(c9)) | (~big_q(c4))))),
% 22.55/22.74      inference(monotonicity,[status(thm)],[98])).
% 22.55/22.74  tff(100,plain,
% 22.55/22.74      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | (~big_p(c9)) | big_q(c16) | big_p(c11) | (~big_p(c9)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(c9)) | (~big_q(c4)))),
% 22.55/22.74      inference(transitivity,[status(thm)],[99, 97])).
% 22.55/22.74  tff(101,plain,
% 22.55/22.74      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | (~big_p(c9)) | big_q(c16) | big_p(c11) | (~big_p(c9)) | big_p(elem!0))),
% 22.55/22.74      inference(quant_inst,[status(thm)],[])).
% 22.55/22.74  tff(102,plain,
% 22.55/22.74      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(c9)) | (~big_q(c4))),
% 22.55/22.74      inference(modus_ponens,[status(thm)],[101, 100])).
% 22.55/22.74  tff(103,plain,
% 22.55/22.74      ($false),
% 22.55/22.74      inference(unit_resolution,[status(thm)],[102, 35, 5, 3, 2, 89, 1, 96])).
% 22.55/22.74  tff(104,plain,((~big_p(c9)) | big_q(elem!0) | big_p(elem!0) | big_q(c16) | big_p(c11) | big_q(f2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 22.55/22.74  tff(105,plain,
% 22.55/22.74      (~big_p(c9)),
% 22.55/22.74      inference(unit_resolution,[status(thm)],[104, 1, 3, 2, 5, 8])).
% 22.55/22.74  tff(106,assumption,(~big_p(f1(c3))), introduced(assumption)).
% 22.55/22.74  tff(107,assumption,(~big_p(c9)), introduced(assumption)).
% 22.55/22.74  tff(108,plain,
% 22.55/22.74      (^[V: $i, Z: $i, U: $i, X: $i, X5: $i] : refl(((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X)) <=> ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X)))),
% 22.55/22.74      inference(bind,[status(th)],[])).
% 22.55/22.74  tff(109,plain,
% 22.55/22.74      (![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X)) <=> ![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))),
% 22.55/22.74      inference(quant_intro,[status(thm)],[108])).
% 22.55/22.74  tff(110,plain,
% 22.55/22.74      (![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X)) <=> ![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))),
% 22.55/22.74      inference(rewrite,[status(thm)],[])).
% 22.55/22.74  tff(111,plain,
% 22.55/22.74      (^[V: $i, Z: $i, U: $i, X: $i, X5: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(X) | big_p(f1(X))) | (~big_q(U))) <=> ((~big_q(U)) | big_p(f1(X)) | big_p(X))), ((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) <=> (((~big_q(U)) | big_p(f1(X)) | big_p(X)) | big_p(V)))), rewrite((((~big_q(U)) | big_p(f1(X)) | big_p(X)) | big_p(V)) <=> (big_p(V) | (~big_q(U)) | big_p(f1(X)) | big_p(X))), ((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) <=> (big_p(V) | (~big_q(U)) | big_p(f1(X)) | big_p(X)))), (((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) | big_q(Z)) <=> ((big_p(V) | (~big_q(U)) | big_p(f1(X)) | big_p(X)) | big_q(Z)))), rewrite(((big_p(V) | (~big_q(U)) | big_p(f1(X)) | big_p(X)) | big_q(Z)) <=> (big_p(V) | big_q(Z) | (~big_q(U)) | big_p(f1(X)) | big_p(X))), (((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) | big_q(Z)) <=> (big_p(V) | big_q(Z) | (~big_q(U)) | big_p(f1(X)) | big_p(X)))), ((((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) | big_q(Z)) | (~big_q(c8))) <=> ((big_p(V) | big_q(Z) | (~big_q(U)) | big_p(f1(X)) | big_p(X)) | (~big_q(c8))))), rewrite(((big_p(V) | big_q(Z) | (~big_q(U)) | big_p(f1(X)) | big_p(X)) | (~big_q(c8))) <=> ((~big_q(c8)) | big_p(V) | big_q(Z) | (~big_q(U)) | big_p(f1(X)) | big_p(X))), ((((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) | big_q(Z)) | (~big_q(c8))) <=> ((~big_q(c8)) | big_p(V) | big_q(Z) | (~big_q(U)) | big_p(f1(X)) | big_p(X)))), (((((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) | big_q(Z)) | (~big_q(c8))) | big_p(c9)) <=> (((~big_q(c8)) | big_p(V) | big_q(Z) | (~big_q(U)) | big_p(f1(X)) | big_p(X)) | big_p(c9)))), rewrite((((~big_q(c8)) | big_p(V) | big_q(Z) | (~big_q(U)) | big_p(f1(X)) | big_p(X)) | big_p(c9)) <=> ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | (~big_q(U)) | big_p(f1(X)) | big_p(X))), (((((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) | big_q(Z)) | (~big_q(c8))) | big_p(c9)) <=> ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | (~big_q(U)) | big_p(f1(X)) | big_p(X)))), ((((((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) | big_q(Z)) | (~big_q(c8))) | big_p(c9)) | big_q(X5)) <=> (((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | (~big_q(U)) | big_p(f1(X)) | big_p(X)) | big_q(X5)))), rewrite((((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | (~big_q(U)) | big_p(f1(X)) | big_p(X)) | big_q(X5)) <=> ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))), ((((((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) | big_q(Z)) | (~big_q(c8))) | big_p(c9)) | big_q(X5)) <=> ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))))),
% 22.55/22.74      inference(bind,[status(th)],[])).
% 22.55/22.74  tff(112,plain,
% 22.55/22.74      (![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (((((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) | big_q(Z)) | (~big_q(c8))) | big_p(c9)) | big_q(X5)) <=> ![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))),
% 22.55/22.74      inference(quant_intro,[status(thm)],[111])).
% 22.55/22.74  tff(113,axiom,(![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (((((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) | big_q(Z)) | (~big_q(c8))) | big_p(c9)) | big_q(X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_7')).
% 22.55/22.74  tff(114,plain,
% 22.55/22.74      (![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))),
% 22.55/22.74      inference(modus_ponens,[status(thm)],[113, 112])).
% 22.55/22.74  tff(115,plain,
% 22.55/22.74      (![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))),
% 22.55/22.74      inference(modus_ponens,[status(thm)],[114, 110])).
% 22.55/22.74  tff(116,plain,(
% 22.55/22.74      ![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))),
% 22.55/22.74      inference(skolemize,[status(sab)],[115])).
% 22.55/22.74  tff(117,plain,
% 22.55/22.74      (![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))),
% 22.55/22.74      inference(modus_ponens,[status(thm)],[116, 109])).
% 22.55/22.74  tff(118,plain,
% 22.55/22.74      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_p(c3) | (~big_q(c8)) | big_p(c9) | big_q(c16) | big_q(elem!0) | big_p(elem!0) | big_p(f1(c3)))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | big_p(c3) | (~big_q(c8)) | big_p(c9) | big_q(c16) | big_q(elem!0) | big_p(elem!0) | big_p(f1(c3)))),
% 22.55/22.74      inference(rewrite,[status(thm)],[])).
% 22.55/22.74  tff(119,plain,
% 22.55/22.74      (((~big_q(c8)) | big_p(elem!0) | big_q(c16) | big_p(c9) | big_q(elem!0) | (~big_q(c8)) | big_p(f1(c3)) | big_p(c3)) <=> (big_p(c3) | (~big_q(c8)) | big_p(c9) | big_q(c16) | big_q(elem!0) | big_p(elem!0) | big_p(f1(c3)))),
% 22.55/22.74      inference(rewrite,[status(thm)],[])).
% 22.55/22.74  tff(120,plain,
% 22.55/22.74      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | ((~big_q(c8)) | big_p(elem!0) | big_q(c16) | big_p(c9) | big_q(elem!0) | (~big_q(c8)) | big_p(f1(c3)) | big_p(c3))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_p(c3) | (~big_q(c8)) | big_p(c9) | big_q(c16) | big_q(elem!0) | big_p(elem!0) | big_p(f1(c3))))),
% 22.55/22.74      inference(monotonicity,[status(thm)],[119])).
% 22.55/22.74  tff(121,plain,
% 22.55/22.74      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | ((~big_q(c8)) | big_p(elem!0) | big_q(c16) | big_p(c9) | big_q(elem!0) | (~big_q(c8)) | big_p(f1(c3)) | big_p(c3))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | big_p(c3) | (~big_q(c8)) | big_p(c9) | big_q(c16) | big_q(elem!0) | big_p(elem!0) | big_p(f1(c3)))),
% 22.55/22.74      inference(transitivity,[status(thm)],[120, 118])).
% 22.55/22.74  tff(122,plain,
% 22.55/22.74      ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | ((~big_q(c8)) | big_p(elem!0) | big_q(c16) | big_p(c9) | big_q(elem!0) | (~big_q(c8)) | big_p(f1(c3)) | big_p(c3))),
% 22.55/22.74      inference(quant_inst,[status(thm)],[])).
% 22.55/22.74  tff(123,plain,
% 22.55/22.74      ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | big_p(c3) | (~big_q(c8)) | big_p(c9) | big_q(c16) | big_q(elem!0) | big_p(elem!0) | big_p(f1(c3))),
% 22.55/22.74      inference(modus_ponens,[status(thm)],[122, 121])).
% 22.55/22.74  tff(124,plain,
% 22.55/22.74      (big_p(c3) | (~big_q(c8)) | big_p(c9) | big_q(c16) | big_q(elem!0) | big_p(elem!0) | big_p(f1(c3))),
% 22.55/22.74      inference(unit_resolution,[status(thm)],[123, 117])).
% 22.55/22.74  tff(125,plain,
% 22.55/22.74      (~big_q(c8)),
% 22.55/22.74      inference(unit_resolution,[status(thm)],[124, 107, 3, 5, 2, 61, 106])).
% 22.55/22.74  tff(126,assumption,(~big_p(c3)), introduced(assumption)).
% 22.55/22.74  tff(127,plain,
% 22.55/22.74      (~big_q(c8)),
% 22.55/22.74      inference(unit_resolution,[status(thm)],[124, 126, 3, 5, 2, 107, 106])).
% 22.55/22.74  tff(128,plain,
% 22.55/22.74      (^[V: $i, Z: $i, U: $i, X: $i, X5: $i] : refl((big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X)) <=> (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X)))),
% 22.55/22.74      inference(bind,[status(th)],[])).
% 22.55/22.74  tff(129,plain,
% 22.55/22.74      (![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X)) <=> ![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))),
% 22.55/22.74      inference(quant_intro,[status(thm)],[128])).
% 22.55/22.74  tff(130,plain,
% 22.55/22.74      (![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X)) <=> ![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))),
% 22.55/22.74      inference(rewrite,[status(thm)],[])).
% 22.55/22.74  tff(131,plain,
% 22.55/22.74      (^[V: $i, Z: $i, U: $i, X: $i, X5: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(X) | big_p(f1(X))) | (~big_q(U))) <=> ((~big_q(U)) | big_p(f1(X)) | big_p(X))), ((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) <=> (((~big_q(U)) | big_p(f1(X)) | big_p(X)) | big_p(V)))), rewrite((((~big_q(U)) | big_p(f1(X)) | big_p(X)) | big_p(V)) <=> (big_p(V) | (~big_q(U)) | big_p(f1(X)) | big_p(X))), ((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) <=> (big_p(V) | (~big_q(U)) | big_p(f1(X)) | big_p(X)))), (((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) | (~big_q(Z))) <=> ((big_p(V) | (~big_q(U)) | big_p(f1(X)) | big_p(X)) | (~big_q(Z))))), rewrite(((big_p(V) | (~big_q(U)) | big_p(f1(X)) | big_p(X)) | (~big_q(Z))) <=> (big_p(V) | (~big_q(Z)) | (~big_q(U)) | big_p(f1(X)) | big_p(X))), (((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) | (~big_q(Z))) <=> (big_p(V) | (~big_q(Z)) | (~big_q(U)) | big_p(f1(X)) | big_p(X)))), ((((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) | (~big_q(Z))) | big_q(c8)) <=> ((big_p(V) | (~big_q(Z)) | (~big_q(U)) | big_p(f1(X)) | big_p(X)) | big_q(c8)))), rewrite(((big_p(V) | (~big_q(Z)) | (~big_q(U)) | big_p(f1(X)) | big_p(X)) | big_q(c8)) <=> (big_q(c8) | big_p(V) | (~big_q(Z)) | (~big_q(U)) | big_p(f1(X)) | big_p(X))), ((((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) | (~big_q(Z))) | big_q(c8)) <=> (big_q(c8) | big_p(V) | (~big_q(Z)) | (~big_q(U)) | big_p(f1(X)) | big_p(X)))), (((((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) | (~big_q(Z))) | big_q(c8)) | big_p(c9)) <=> ((big_q(c8) | big_p(V) | (~big_q(Z)) | (~big_q(U)) | big_p(f1(X)) | big_p(X)) | big_p(c9)))), rewrite(((big_q(c8) | big_p(V) | (~big_q(Z)) | (~big_q(U)) | big_p(f1(X)) | big_p(X)) | big_p(c9)) <=> (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | (~big_q(U)) | big_p(f1(X)) | big_p(X))), (((((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) | (~big_q(Z))) | big_q(c8)) | big_p(c9)) <=> (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | (~big_q(U)) | big_p(f1(X)) | big_p(X)))), ((((((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) | (~big_q(Z))) | big_q(c8)) | big_p(c9)) | big_q(X5)) <=> ((big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | (~big_q(U)) | big_p(f1(X)) | big_p(X)) | big_q(X5)))), rewrite(((big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | (~big_q(U)) | big_p(f1(X)) | big_p(X)) | big_q(X5)) <=> (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))), ((((((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) | (~big_q(Z))) | big_q(c8)) | big_p(c9)) | big_q(X5)) <=> (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))))),
% 22.55/22.74      inference(bind,[status(th)],[])).
% 22.55/22.74  tff(132,plain,
% 22.55/22.74      (![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (((((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) | (~big_q(Z))) | big_q(c8)) | big_p(c9)) | big_q(X5)) <=> ![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))),
% 22.55/22.74      inference(quant_intro,[status(thm)],[131])).
% 22.55/22.74  tff(133,axiom,(![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (((((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) | (~big_q(Z))) | big_q(c8)) | big_p(c9)) | big_q(X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_5')).
% 22.55/22.74  tff(134,plain,
% 22.55/22.74      (![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))),
% 22.55/22.74      inference(modus_ponens,[status(thm)],[133, 132])).
% 22.55/22.74  tff(135,plain,
% 22.55/22.74      (![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))),
% 22.55/22.74      inference(modus_ponens,[status(thm)],[134, 130])).
% 22.55/22.74  tff(136,plain,(
% 22.55/22.74      ![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))),
% 22.55/22.74      inference(skolemize,[status(sab)],[135])).
% 22.55/22.74  tff(137,plain,
% 22.55/22.74      (![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))),
% 22.55/22.74      inference(modus_ponens,[status(thm)],[136, 129])).
% 22.55/22.74  tff(138,plain,
% 22.55/22.74      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_q(c8) | big_p(c9) | big_q(elem!0) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(f4(elem!0))))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | big_q(c8) | big_p(c9) | big_q(elem!0) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(f4(elem!0))))),
% 22.55/22.74      inference(rewrite,[status(thm)],[])).
% 22.55/22.74  tff(139,plain,
% 22.55/22.74      ((big_q(c8) | big_p(elem!0) | (~big_q(f4(elem!0))) | big_p(c9) | big_q(elem!0) | (~big_q(f4(elem!0))) | big_p(f1(elem!0)) | big_p(elem!0)) <=> (big_q(c8) | big_p(c9) | big_q(elem!0) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(f4(elem!0))))),
% 22.55/22.74      inference(rewrite,[status(thm)],[])).
% 22.55/22.74  tff(140,plain,
% 22.55/22.74      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_q(c8) | big_p(elem!0) | (~big_q(f4(elem!0))) | big_p(c9) | big_q(elem!0) | (~big_q(f4(elem!0))) | big_p(f1(elem!0)) | big_p(elem!0))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_q(c8) | big_p(c9) | big_q(elem!0) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(f4(elem!0)))))),
% 22.55/22.74      inference(monotonicity,[status(thm)],[139])).
% 22.55/22.74  tff(141,plain,
% 22.55/22.74      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_q(c8) | big_p(elem!0) | (~big_q(f4(elem!0))) | big_p(c9) | big_q(elem!0) | (~big_q(f4(elem!0))) | big_p(f1(elem!0)) | big_p(elem!0))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | big_q(c8) | big_p(c9) | big_q(elem!0) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(f4(elem!0))))),
% 22.55/22.74      inference(transitivity,[status(thm)],[140, 138])).
% 22.55/22.74  tff(142,plain,
% 22.55/22.74      ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_q(c8) | big_p(elem!0) | (~big_q(f4(elem!0))) | big_p(c9) | big_q(elem!0) | (~big_q(f4(elem!0))) | big_p(f1(elem!0)) | big_p(elem!0))),
% 22.55/22.74      inference(quant_inst,[status(thm)],[])).
% 22.55/22.75  tff(143,plain,
% 22.55/22.75      ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | big_q(c8) | big_p(c9) | big_q(elem!0) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(f4(elem!0)))),
% 22.55/22.75      inference(modus_ponens,[status(thm)],[142, 141])).
% 22.55/22.75  tff(144,plain,
% 22.55/22.75      (big_q(c8) | big_p(c9) | big_q(elem!0) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(f4(elem!0)))),
% 22.55/22.75      inference(unit_resolution,[status(thm)],[143, 137])).
% 22.55/22.75  tff(145,plain,
% 22.55/22.75      (~big_q(f4(elem!0))),
% 22.55/22.75      inference(unit_resolution,[status(thm)],[144, 127, 3, 5, 88, 107])).
% 22.55/22.75  tff(146,assumption,(~big_q(c14)), introduced(assumption)).
% 22.55/22.75  tff(147,assumption,(big_p(c19)), introduced(assumption)).
% 22.55/22.75  tff(148,plain,
% 22.55/22.75      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_p(c19)))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | big_p(c3) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_p(c19)))),
% 22.55/22.75      inference(rewrite,[status(thm)],[])).
% 22.55/22.75  tff(149,plain,
% 22.55/22.75      ((big_p(c3) | big_q(elem!0) | (~big_p(c19)) | big_p(elem!0) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(c19))) <=> (big_p(c3) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_p(c19)))),
% 22.55/22.75      inference(rewrite,[status(thm)],[])).
% 22.55/22.75  tff(150,plain,
% 22.55/22.75      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(elem!0) | (~big_p(c19)) | big_p(elem!0) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(c19)))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_p(c19))))),
% 22.55/22.75      inference(monotonicity,[status(thm)],[149])).
% 22.55/22.75  tff(151,plain,
% 22.55/22.75      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(elem!0) | (~big_p(c19)) | big_p(elem!0) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(c19)))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | big_p(c3) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_p(c19)))),
% 22.55/22.75      inference(transitivity,[status(thm)],[150, 148])).
% 22.55/22.75  tff(152,plain,
% 22.55/22.75      ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(elem!0) | (~big_p(c19)) | big_p(elem!0) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(c19)))),
% 22.55/22.75      inference(quant_inst,[status(thm)],[])).
% 22.55/22.75  tff(153,plain,
% 22.55/22.75      ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | big_p(c3) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_p(c19))),
% 22.55/22.75      inference(modus_ponens,[status(thm)],[152, 151])).
% 22.55/22.75  tff(154,plain,
% 22.55/22.75      (big_q(c4)),
% 22.55/22.75      inference(unit_resolution,[status(thm)],[153, 71, 147, 5, 3, 8, 126])).
% 22.55/22.75  tff(155,plain,
% 22.55/22.75      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(c19)) | (~big_q(c4)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(c19)) | (~big_q(c4)))),
% 22.55/22.75      inference(rewrite,[status(thm)],[])).
% 22.55/22.75  tff(156,plain,
% 22.55/22.75      (((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | (~big_p(c19)) | big_q(c16) | big_p(c11) | (~big_p(c19)) | big_p(elem!0)) <=> (big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(c19)) | (~big_q(c4)))),
% 22.55/22.75      inference(rewrite,[status(thm)],[])).
% 22.55/22.75  tff(157,plain,
% 22.55/22.75      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | (~big_p(c19)) | big_q(c16) | big_p(c11) | (~big_p(c19)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(c19)) | (~big_q(c4))))),
% 22.55/22.75      inference(monotonicity,[status(thm)],[156])).
% 22.55/22.75  tff(158,plain,
% 22.55/22.75      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | (~big_p(c19)) | big_q(c16) | big_p(c11) | (~big_p(c19)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(c19)) | (~big_q(c4)))),
% 22.55/22.75      inference(transitivity,[status(thm)],[157, 155])).
% 22.55/22.75  tff(159,plain,
% 22.55/22.75      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | (~big_p(c19)) | big_q(c16) | big_p(c11) | (~big_p(c19)) | big_p(elem!0))),
% 22.55/22.75      inference(quant_inst,[status(thm)],[])).
% 22.55/22.75  tff(160,plain,
% 22.55/22.75      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(c19)) | (~big_q(c4))),
% 22.55/22.75      inference(modus_ponens,[status(thm)],[159, 158])).
% 22.55/22.75  tff(161,plain,
% 22.55/22.75      (big_p(c11)),
% 22.55/22.75      inference(unit_resolution,[status(thm)],[160, 35, 147, 5, 3, 2, 154])).
% 22.55/22.75  tff(162,plain,
% 22.55/22.75      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(elem!0) | (~big_p(c19)) | (~big_q(c4)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(elem!0) | (~big_p(c19)) | (~big_q(c4)))),
% 22.55/22.75      inference(rewrite,[status(thm)],[])).
% 22.55/22.75  tff(163,plain,
% 22.55/22.75      (((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | big_p(elem!0) | big_q(c16) | (~big_p(c11)) | (~big_p(c19)) | big_p(elem!0)) <=> (big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(elem!0) | (~big_p(c19)) | (~big_q(c4)))),
% 22.55/22.75      inference(rewrite,[status(thm)],[])).
% 22.55/22.75  tff(164,plain,
% 22.55/22.75      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | big_p(elem!0) | big_q(c16) | (~big_p(c11)) | (~big_p(c19)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(elem!0) | (~big_p(c19)) | (~big_q(c4))))),
% 22.55/22.75      inference(monotonicity,[status(thm)],[163])).
% 22.55/22.75  tff(165,plain,
% 22.55/22.75      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | big_p(elem!0) | big_q(c16) | (~big_p(c11)) | (~big_p(c19)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(elem!0) | (~big_p(c19)) | (~big_q(c4)))),
% 22.55/22.75      inference(transitivity,[status(thm)],[164, 162])).
% 22.55/22.75  tff(166,plain,
% 22.55/22.75      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | big_p(elem!0) | big_q(c16) | (~big_p(c11)) | (~big_p(c19)) | big_p(elem!0))),
% 22.55/22.75      inference(quant_inst,[status(thm)],[])).
% 22.55/22.75  tff(167,plain,
% 22.55/22.75      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(elem!0) | (~big_p(c19)) | (~big_q(c4))),
% 22.55/22.75      inference(modus_ponens,[status(thm)],[166, 165])).
% 22.55/22.75  tff(168,plain,
% 22.55/22.75      ($false),
% 22.55/22.75      inference(unit_resolution,[status(thm)],[167, 52, 147, 5, 3, 2, 161, 154])).
% 22.55/22.75  tff(169,plain,((~big_p(c19)) | big_q(elem!0) | big_p(elem!0) | big_q(c16) | big_q(f2(elem!0)) | big_p(c3)), inference(lemma,lemma(discharge,[]))).
% 22.55/22.75  tff(170,plain,
% 22.55/22.75      (~big_p(c19)),
% 22.55/22.75      inference(unit_resolution,[status(thm)],[169, 126, 3, 2, 8, 5])).
% 22.55/22.75  tff(171,plain,
% 22.55/22.75      (^[X11: $i, X17: $i, X10: $i, X16: $i] : refl((big_q(c14) | big_q(X16) | big_q(X17) | big_p(X10) | big_p(X11) | big_p(c19) | big_p(f3(X10)) | big_q(f4(X16))) <=> (big_q(c14) | big_q(X16) | big_q(X17) | big_p(X10) | big_p(X11) | big_p(c19) | big_p(f3(X10)) | big_q(f4(X16))))),
% 22.55/22.75      inference(bind,[status(th)],[])).
% 22.55/22.75  tff(172,plain,
% 22.55/22.75      (![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | big_p(X10) | big_p(X11) | big_p(c19) | big_p(f3(X10)) | big_q(f4(X16))) <=> ![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | big_p(X10) | big_p(X11) | big_p(c19) | big_p(f3(X10)) | big_q(f4(X16)))),
% 22.55/22.75      inference(quant_intro,[status(thm)],[171])).
% 22.55/22.75  tff(173,plain,
% 22.55/22.75      (![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | big_p(X10) | big_p(X11) | big_p(c19) | big_p(f3(X10)) | big_q(f4(X16))) <=> ![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | big_p(X10) | big_p(X11) | big_p(c19) | big_p(f3(X10)) | big_q(f4(X16)))),
% 22.55/22.75      inference(rewrite,[status(thm)],[])).
% 22.55/22.75  tff(174,plain,
% 22.55/22.75      (^[X11: $i, X17: $i, X10: $i, X16: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(X10) | big_p(f3(X10))) | big_q(c14)) <=> (big_q(c14) | big_p(X10) | big_p(f3(X10)))), ((((big_p(X10) | big_p(f3(X10))) | big_q(c14)) | big_p(X11)) <=> ((big_q(c14) | big_p(X10) | big_p(f3(X10))) | big_p(X11)))), rewrite(((big_q(c14) | big_p(X10) | big_p(f3(X10))) | big_p(X11)) <=> (big_q(c14) | big_p(X10) | big_p(X11) | big_p(f3(X10)))), ((((big_p(X10) | big_p(f3(X10))) | big_q(c14)) | big_p(X11)) <=> (big_q(c14) | big_p(X10) | big_p(X11) | big_p(f3(X10))))), (((((big_p(X10) | big_p(f3(X10))) | big_q(c14)) | big_p(X11)) | big_q(f4(X16))) <=> ((big_q(c14) | big_p(X10) | big_p(X11) | big_p(f3(X10))) | big_q(f4(X16))))), rewrite(((big_q(c14) | big_p(X10) | big_p(X11) | big_p(f3(X10))) | big_q(f4(X16))) <=> (big_q(c14) | big_p(X10) | big_p(X11) | big_p(f3(X10)) | big_q(f4(X16)))), (((((big_p(X10) | big_p(f3(X10))) | big_q(c14)) | big_p(X11)) | big_q(f4(X16))) <=> (big_q(c14) | big_p(X10) | big_p(X11) | big_p(f3(X10)) | big_q(f4(X16))))), ((((((big_p(X10) | big_p(f3(X10))) | big_q(c14)) | big_p(X11)) | big_q(f4(X16))) | big_q(X16)) <=> ((big_q(c14) | big_p(X10) | big_p(X11) | big_p(f3(X10)) | big_q(f4(X16))) | big_q(X16)))), rewrite(((big_q(c14) | big_p(X10) | big_p(X11) | big_p(f3(X10)) | big_q(f4(X16))) | big_q(X16)) <=> (big_q(c14) | big_q(X16) | big_p(X10) | big_p(X11) | big_p(f3(X10)) | big_q(f4(X16)))), ((((((big_p(X10) | big_p(f3(X10))) | big_q(c14)) | big_p(X11)) | big_q(f4(X16))) | big_q(X16)) <=> (big_q(c14) | big_q(X16) | big_p(X10) | big_p(X11) | big_p(f3(X10)) | big_q(f4(X16))))), (((((((big_p(X10) | big_p(f3(X10))) | big_q(c14)) | big_p(X11)) | big_q(f4(X16))) | big_q(X16)) | big_p(c19)) <=> ((big_q(c14) | big_q(X16) | big_p(X10) | big_p(X11) | big_p(f3(X10)) | big_q(f4(X16))) | big_p(c19)))), rewrite(((big_q(c14) | big_q(X16) | big_p(X10) | big_p(X11) | big_p(f3(X10)) | big_q(f4(X16))) | big_p(c19)) <=> (big_q(c14) | big_q(X16) | big_p(X10) | big_p(X11) | big_p(c19) | big_p(f3(X10)) | big_q(f4(X16)))), (((((((big_p(X10) | big_p(f3(X10))) | big_q(c14)) | big_p(X11)) | big_q(f4(X16))) | big_q(X16)) | big_p(c19)) <=> (big_q(c14) | big_q(X16) | big_p(X10) | big_p(X11) | big_p(c19) | big_p(f3(X10)) | big_q(f4(X16))))), ((((((((big_p(X10) | big_p(f3(X10))) | big_q(c14)) | big_p(X11)) | big_q(f4(X16))) | big_q(X16)) | big_p(c19)) | big_q(X17)) <=> ((big_q(c14) | big_q(X16) | big_p(X10) | big_p(X11) | big_p(c19) | big_p(f3(X10)) | big_q(f4(X16))) | big_q(X17)))), rewrite(((big_q(c14) | big_q(X16) | big_p(X10) | big_p(X11) | big_p(c19) | big_p(f3(X10)) | big_q(f4(X16))) | big_q(X17)) <=> (big_q(c14) | big_q(X16) | big_q(X17) | big_p(X10) | big_p(X11) | big_p(c19) | big_p(f3(X10)) | big_q(f4(X16)))), ((((((((big_p(X10) | big_p(f3(X10))) | big_q(c14)) | big_p(X11)) | big_q(f4(X16))) | big_q(X16)) | big_p(c19)) | big_q(X17)) <=> (big_q(c14) | big_q(X16) | big_q(X17) | big_p(X10) | big_p(X11) | big_p(c19) | big_p(f3(X10)) | big_q(f4(X16)))))),
% 22.55/22.75      inference(bind,[status(th)],[])).
% 22.55/22.75  tff(175,plain,
% 22.55/22.75      (![X11: $i, X17: $i, X10: $i, X16: $i] : (((((((big_p(X10) | big_p(f3(X10))) | big_q(c14)) | big_p(X11)) | big_q(f4(X16))) | big_q(X16)) | big_p(c19)) | big_q(X17)) <=> ![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | big_p(X10) | big_p(X11) | big_p(c19) | big_p(f3(X10)) | big_q(f4(X16)))),
% 22.55/22.75      inference(quant_intro,[status(thm)],[174])).
% 22.55/22.75  tff(176,axiom,(![X11: $i, X17: $i, X10: $i, X16: $i] : (((((((big_p(X10) | big_p(f3(X10))) | big_q(c14)) | big_p(X11)) | big_q(f4(X16))) | big_q(X16)) | big_p(c19)) | big_q(X17))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_101')).
% 22.55/22.75  tff(177,plain,
% 22.55/22.75      (![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | big_p(X10) | big_p(X11) | big_p(c19) | big_p(f3(X10)) | big_q(f4(X16)))),
% 22.55/22.75      inference(modus_ponens,[status(thm)],[176, 175])).
% 22.55/22.75  tff(178,plain,
% 22.55/22.75      (![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | big_p(X10) | big_p(X11) | big_p(c19) | big_p(f3(X10)) | big_q(f4(X16)))),
% 22.55/22.75      inference(modus_ponens,[status(thm)],[177, 173])).
% 22.55/22.75  tff(179,plain,(
% 22.55/22.75      ![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | big_p(X10) | big_p(X11) | big_p(c19) | big_p(f3(X10)) | big_q(f4(X16)))),
% 22.55/22.75      inference(skolemize,[status(sab)],[178])).
% 22.55/22.75  tff(180,plain,
% 22.55/22.75      (![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | big_p(X10) | big_p(X11) | big_p(c19) | big_p(f3(X10)) | big_q(f4(X16)))),
% 22.55/22.75      inference(modus_ponens,[status(thm)],[179, 172])).
% 22.55/22.75  tff(181,plain,
% 22.55/22.75      (((~![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | big_p(X10) | big_p(X11) | big_p(c19) | big_p(f3(X10)) | big_q(f4(X16)))) | (big_q(c14) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(f3(elem!0)) | big_p(elem!0))) <=> ((~![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | big_p(X10) | big_p(X11) | big_p(c19) | big_p(f3(X10)) | big_q(f4(X16)))) | big_q(c14) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(f3(elem!0)) | big_p(elem!0))),
% 22.55/22.75      inference(rewrite,[status(thm)],[])).
% 22.55/22.75  tff(182,plain,
% 22.55/22.75      ((big_q(c14) | big_q(elem!0) | big_q(elem!0) | big_p(elem!0) | big_p(elem!0) | big_p(c19) | big_p(f3(elem!0)) | big_q(f4(elem!0))) <=> (big_q(c14) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(f3(elem!0)) | big_p(elem!0))),
% 22.55/22.75      inference(rewrite,[status(thm)],[])).
% 22.55/22.75  tff(183,plain,
% 22.55/22.75      (((~![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | big_p(X10) | big_p(X11) | big_p(c19) | big_p(f3(X10)) | big_q(f4(X16)))) | (big_q(c14) | big_q(elem!0) | big_q(elem!0) | big_p(elem!0) | big_p(elem!0) | big_p(c19) | big_p(f3(elem!0)) | big_q(f4(elem!0)))) <=> ((~![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | big_p(X10) | big_p(X11) | big_p(c19) | big_p(f3(X10)) | big_q(f4(X16)))) | (big_q(c14) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(f3(elem!0)) | big_p(elem!0)))),
% 22.55/22.75      inference(monotonicity,[status(thm)],[182])).
% 22.55/22.75  tff(184,plain,
% 22.55/22.75      (((~![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | big_p(X10) | big_p(X11) | big_p(c19) | big_p(f3(X10)) | big_q(f4(X16)))) | (big_q(c14) | big_q(elem!0) | big_q(elem!0) | big_p(elem!0) | big_p(elem!0) | big_p(c19) | big_p(f3(elem!0)) | big_q(f4(elem!0)))) <=> ((~![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | big_p(X10) | big_p(X11) | big_p(c19) | big_p(f3(X10)) | big_q(f4(X16)))) | big_q(c14) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(f3(elem!0)) | big_p(elem!0))),
% 22.55/22.75      inference(transitivity,[status(thm)],[183, 181])).
% 22.55/22.75  tff(185,plain,
% 22.55/22.75      ((~![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | big_p(X10) | big_p(X11) | big_p(c19) | big_p(f3(X10)) | big_q(f4(X16)))) | (big_q(c14) | big_q(elem!0) | big_q(elem!0) | big_p(elem!0) | big_p(elem!0) | big_p(c19) | big_p(f3(elem!0)) | big_q(f4(elem!0)))),
% 22.55/22.75      inference(quant_inst,[status(thm)],[])).
% 22.55/22.75  tff(186,plain,
% 22.55/22.75      ((~![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | big_p(X10) | big_p(X11) | big_p(c19) | big_p(f3(X10)) | big_q(f4(X16)))) | big_q(c14) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(f3(elem!0)) | big_p(elem!0)),
% 22.55/22.75      inference(modus_ponens,[status(thm)],[185, 184])).
% 22.55/22.75  tff(187,plain,
% 22.55/22.75      (big_q(c14) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(f3(elem!0)) | big_p(elem!0)),
% 22.55/22.75      inference(unit_resolution,[status(thm)],[186, 180])).
% 22.55/22.75  tff(188,plain,
% 22.55/22.75      (big_p(f3(elem!0))),
% 22.55/22.75      inference(unit_resolution,[status(thm)],[187, 170, 5, 146, 145, 3])).
% 22.55/22.75  tff(189,plain,
% 22.55/22.75      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(c4) | big_p(c19) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f3(elem!0))))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | big_p(c3) | big_q(c4) | big_p(c19) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f3(elem!0))))),
% 22.55/22.75      inference(rewrite,[status(thm)],[])).
% 22.55/22.75  tff(190,plain,
% 22.55/22.75      ((big_p(c3) | big_q(elem!0) | (~big_p(f3(elem!0))) | big_p(c19) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f3(elem!0)))) <=> (big_p(c3) | big_q(c4) | big_p(c19) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f3(elem!0))))),
% 22.55/22.75      inference(rewrite,[status(thm)],[])).
% 22.55/22.75  tff(191,plain,
% 22.55/22.75      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(elem!0) | (~big_p(f3(elem!0))) | big_p(c19) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f3(elem!0))))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(c4) | big_p(c19) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f3(elem!0)))))),
% 22.55/22.75      inference(monotonicity,[status(thm)],[190])).
% 22.55/22.75  tff(192,plain,
% 22.55/22.75      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(elem!0) | (~big_p(f3(elem!0))) | big_p(c19) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f3(elem!0))))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | big_p(c3) | big_q(c4) | big_p(c19) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f3(elem!0))))),
% 22.55/22.75      inference(transitivity,[status(thm)],[191, 189])).
% 22.55/22.75  tff(193,plain,
% 22.55/22.75      ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(elem!0) | (~big_p(f3(elem!0))) | big_p(c19) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f3(elem!0))))),
% 22.55/22.75      inference(quant_inst,[status(thm)],[])).
% 22.55/22.75  tff(194,plain,
% 22.55/22.75      ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | big_p(c3) | big_q(c4) | big_p(c19) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f3(elem!0)))),
% 22.55/22.75      inference(modus_ponens,[status(thm)],[193, 192])).
% 22.55/22.75  tff(195,plain,
% 22.55/22.75      (big_q(c4)),
% 22.55/22.75      inference(unit_resolution,[status(thm)],[194, 71, 170, 5, 188, 8, 126])).
% 22.55/22.75  tff(196,plain,
% 22.55/22.75      (^[X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : refl(((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16))) <=> ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16))))),
% 22.55/22.75      inference(bind,[status(th)],[])).
% 22.55/22.75  tff(197,plain,
% 22.55/22.75      (![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16))) <=> ![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))),
% 22.55/22.75      inference(quant_intro,[status(thm)],[196])).
% 22.55/22.75  tff(198,plain,
% 22.55/22.75      (![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16))) <=> ![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))),
% 22.55/22.75      inference(rewrite,[status(thm)],[])).
% 22.55/22.75  tff(199,plain,
% 22.55/22.75      (^[X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) <=> ((~big_q(X8)) | (~big_p(X7)) | big_p(c11))), ((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) <=> (((~big_q(X8)) | (~big_p(X7)) | big_p(c11)) | big_p(X9)))), rewrite((((~big_q(X8)) | (~big_p(X7)) | big_p(c11)) | big_p(X9)) <=> ((~big_q(X8)) | big_p(X9) | (~big_p(X7)) | big_p(c11))), ((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) <=> ((~big_q(X8)) | big_p(X9) | (~big_p(X7)) | big_p(c11)))), (((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | big_q(f4(X16))) <=> (((~big_q(X8)) | big_p(X9) | (~big_p(X7)) | big_p(c11)) | big_q(f4(X16))))), rewrite((((~big_q(X8)) | big_p(X9) | (~big_p(X7)) | big_p(c11)) | big_q(f4(X16))) <=> ((~big_q(X8)) | big_p(X9) | (~big_p(X7)) | big_p(c11) | big_q(f4(X16)))), (((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | big_q(f4(X16))) <=> ((~big_q(X8)) | big_p(X9) | (~big_p(X7)) | big_p(c11) | big_q(f4(X16))))), ((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | big_q(f4(X16))) | big_q(X16)) <=> (((~big_q(X8)) | big_p(X9) | (~big_p(X7)) | big_p(c11) | big_q(f4(X16))) | big_q(X16)))), rewrite((((~big_q(X8)) | big_p(X9) | (~big_p(X7)) | big_p(c11) | big_q(f4(X16))) | big_q(X16)) <=> ((~big_q(X8)) | big_p(X9) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_q(f4(X16)))), ((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | big_q(f4(X16))) | big_q(X16)) <=> ((~big_q(X8)) | big_p(X9) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_q(f4(X16))))), (((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | big_q(f4(X16))) | big_q(X16)) | big_p(c19)) <=> (((~big_q(X8)) | big_p(X9) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_q(f4(X16))) | big_p(c19)))), rewrite((((~big_q(X8)) | big_p(X9) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_q(f4(X16))) | big_p(c19)) <=> ((~big_q(X8)) | big_p(X9) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))), (((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | big_q(f4(X16))) | big_q(X16)) | big_p(c19)) <=> ((~big_q(X8)) | big_p(X9) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16))))), ((((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | big_q(f4(X16))) | big_q(X16)) | big_p(c19)) | big_q(X17)) <=> (((~big_q(X8)) | big_p(X9) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16))) | big_q(X17)))), rewrite((((~big_q(X8)) | big_p(X9) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16))) | big_q(X17)) <=> ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))), ((((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | big_q(f4(X16))) | big_q(X16)) | big_p(c19)) | big_q(X17)) <=> ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))))),
% 22.55/22.75      inference(bind,[status(th)],[])).
% 22.55/22.75  tff(200,plain,
% 22.55/22.75      (![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : (((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | big_q(f4(X16))) | big_q(X16)) | big_p(c19)) | big_q(X17)) <=> ![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))),
% 22.55/22.75      inference(quant_intro,[status(thm)],[199])).
% 22.55/22.75  tff(201,axiom,(![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : (((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | big_q(f4(X16))) | big_q(X16)) | big_p(c19)) | big_q(X17))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_85')).
% 22.55/22.75  tff(202,plain,
% 22.55/22.75      (![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))),
% 22.55/22.75      inference(modus_ponens,[status(thm)],[201, 200])).
% 22.55/22.75  tff(203,plain,
% 22.55/22.75      (![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))),
% 22.55/22.75      inference(modus_ponens,[status(thm)],[202, 198])).
% 22.55/22.75  tff(204,plain,(
% 22.55/22.75      ![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))),
% 22.55/22.75      inference(skolemize,[status(sab)],[203])).
% 22.55/22.75  tff(205,plain,
% 22.55/22.75      (![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))),
% 22.55/22.75      inference(modus_ponens,[status(thm)],[204, 197])).
% 22.55/22.75  tff(206,plain,
% 22.55/22.75      (((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))) | (big_p(c11) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_p(f3(elem!0))) | (~big_q(c4)))) <=> ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))) | big_p(c11) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_p(f3(elem!0))) | (~big_q(c4)))),
% 22.55/22.75      inference(rewrite,[status(thm)],[])).
% 22.55/22.75  tff(207,plain,
% 22.55/22.75      (((~big_q(c4)) | big_p(c19) | big_q(elem!0) | big_q(elem!0) | (~big_p(f3(elem!0))) | big_p(c11) | big_p(c19) | big_q(f4(elem!0))) <=> (big_p(c11) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_p(f3(elem!0))) | (~big_q(c4)))),
% 22.55/22.75      inference(rewrite,[status(thm)],[])).
% 22.55/22.75  tff(208,plain,
% 22.55/22.75      (((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))) | ((~big_q(c4)) | big_p(c19) | big_q(elem!0) | big_q(elem!0) | (~big_p(f3(elem!0))) | big_p(c11) | big_p(c19) | big_q(f4(elem!0)))) <=> ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))) | (big_p(c11) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_p(f3(elem!0))) | (~big_q(c4))))),
% 22.55/22.76      inference(monotonicity,[status(thm)],[207])).
% 22.55/22.76  tff(209,plain,
% 22.55/22.76      (((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))) | ((~big_q(c4)) | big_p(c19) | big_q(elem!0) | big_q(elem!0) | (~big_p(f3(elem!0))) | big_p(c11) | big_p(c19) | big_q(f4(elem!0)))) <=> ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))) | big_p(c11) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_p(f3(elem!0))) | (~big_q(c4)))),
% 22.55/22.76      inference(transitivity,[status(thm)],[208, 206])).
% 22.55/22.76  tff(210,plain,
% 22.55/22.76      ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))) | ((~big_q(c4)) | big_p(c19) | big_q(elem!0) | big_q(elem!0) | (~big_p(f3(elem!0))) | big_p(c11) | big_p(c19) | big_q(f4(elem!0)))),
% 22.55/22.76      inference(quant_inst,[status(thm)],[])).
% 22.55/22.76  tff(211,plain,
% 22.55/22.76      ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))) | big_p(c11) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_p(f3(elem!0))) | (~big_q(c4))),
% 22.55/22.76      inference(modus_ponens,[status(thm)],[210, 209])).
% 22.55/22.76  tff(212,plain,
% 22.55/22.76      (big_p(c11)),
% 22.55/22.76      inference(unit_resolution,[status(thm)],[211, 205, 170, 5, 145, 188, 195])).
% 22.55/22.76  tff(213,plain,
% 22.55/22.76      (^[X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : refl(((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16))) <=> ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16))))),
% 22.55/22.76      inference(bind,[status(th)],[])).
% 22.55/22.76  tff(214,plain,
% 22.55/22.76      (![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16))) <=> ![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))),
% 22.55/22.76      inference(quant_intro,[status(thm)],[213])).
% 22.55/22.76  tff(215,plain,
% 22.55/22.76      (![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16))) <=> ![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))),
% 22.55/22.76      inference(rewrite,[status(thm)],[])).
% 22.55/22.76  tff(216,plain,
% 22.55/22.76      (^[X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(c11)) | big_p(X7)) <=> (big_p(X7) | (~big_p(c11)))), ((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) <=> ((big_p(X7) | (~big_p(c11))) | (~big_q(X8))))), rewrite(((big_p(X7) | (~big_p(c11))) | (~big_q(X8))) <=> ((~big_q(X8)) | big_p(X7) | (~big_p(c11)))), ((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) <=> ((~big_q(X8)) | big_p(X7) | (~big_p(c11))))), (((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) <=> (((~big_q(X8)) | big_p(X7) | (~big_p(c11))) | big_p(X9)))), rewrite((((~big_q(X8)) | big_p(X7) | (~big_p(c11))) | big_p(X9)) <=> ((~big_q(X8)) | big_p(X9) | big_p(X7) | (~big_p(c11)))), (((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) <=> ((~big_q(X8)) | big_p(X9) | big_p(X7) | (~big_p(c11))))), ((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | big_q(f4(X16))) <=> (((~big_q(X8)) | big_p(X9) | big_p(X7) | (~big_p(c11))) | big_q(f4(X16))))), rewrite((((~big_q(X8)) | big_p(X9) | big_p(X7) | (~big_p(c11))) | big_q(f4(X16))) <=> ((~big_q(X8)) | big_p(X9) | big_p(X7) | (~big_p(c11)) | big_q(f4(X16)))), ((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | big_q(f4(X16))) <=> ((~big_q(X8)) | big_p(X9) | big_p(X7) | (~big_p(c11)) | big_q(f4(X16))))), (((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | big_q(f4(X16))) | big_q(X16)) <=> (((~big_q(X8)) | big_p(X9) | big_p(X7) | (~big_p(c11)) | big_q(f4(X16))) | big_q(X16)))), rewrite((((~big_q(X8)) | big_p(X9) | big_p(X7) | (~big_p(c11)) | big_q(f4(X16))) | big_q(X16)) <=> ((~big_q(X8)) | big_p(X9) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_q(f4(X16)))), (((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | big_q(f4(X16))) | big_q(X16)) <=> ((~big_q(X8)) | big_p(X9) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_q(f4(X16))))), ((((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | big_q(f4(X16))) | big_q(X16)) | big_p(c19)) <=> (((~big_q(X8)) | big_p(X9) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_q(f4(X16))) | big_p(c19)))), rewrite((((~big_q(X8)) | big_p(X9) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_q(f4(X16))) | big_p(c19)) <=> ((~big_q(X8)) | big_p(X9) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))), ((((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | big_q(f4(X16))) | big_q(X16)) | big_p(c19)) <=> ((~big_q(X8)) | big_p(X9) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16))))), (((((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | big_q(f4(X16))) | big_q(X16)) | big_p(c19)) | big_q(X17)) <=> (((~big_q(X8)) | big_p(X9) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16))) | big_q(X17)))), rewrite((((~big_q(X8)) | big_p(X9) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16))) | big_q(X17)) <=> ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))), (((((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | big_q(f4(X16))) | big_q(X16)) | big_p(c19)) | big_q(X17)) <=> ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))))),
% 22.55/22.76      inference(bind,[status(th)],[])).
% 22.55/22.76  tff(217,plain,
% 22.55/22.76      (![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | big_q(f4(X16))) | big_q(X16)) | big_p(c19)) | big_q(X17)) <=> ![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))),
% 22.55/22.76      inference(quant_intro,[status(thm)],[216])).
% 22.55/22.76  tff(218,axiom,(![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | big_q(f4(X16))) | big_q(X16)) | big_p(c19)) | big_q(X17))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_69')).
% 22.55/22.76  tff(219,plain,
% 22.55/22.76      (![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))),
% 22.55/22.76      inference(modus_ponens,[status(thm)],[218, 217])).
% 22.55/22.76  tff(220,plain,
% 22.55/22.76      (![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))),
% 22.55/22.76      inference(modus_ponens,[status(thm)],[219, 215])).
% 22.55/22.76  tff(221,plain,(
% 22.55/22.76      ![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))),
% 22.55/22.76      inference(skolemize,[status(sab)],[220])).
% 22.55/22.76  tff(222,plain,
% 22.55/22.76      (![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))),
% 22.55/22.76      inference(modus_ponens,[status(thm)],[221, 214])).
% 22.55/22.76  tff(223,plain,
% 22.55/22.76      (((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | ((~big_p(c11)) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_q(c4)))) <=> ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | (~big_p(c11)) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_q(c4)))),
% 22.55/22.76      inference(rewrite,[status(thm)],[])).
% 22.55/22.76  tff(224,plain,
% 22.55/22.76      (((~big_q(c4)) | big_p(c19) | big_q(elem!0) | big_q(elem!0) | big_p(c19) | (~big_p(c11)) | big_p(c19) | big_q(f4(elem!0))) <=> ((~big_p(c11)) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_q(c4)))),
% 22.55/22.76      inference(rewrite,[status(thm)],[])).
% 22.55/22.76  tff(225,plain,
% 22.55/22.76      (((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | ((~big_q(c4)) | big_p(c19) | big_q(elem!0) | big_q(elem!0) | big_p(c19) | (~big_p(c11)) | big_p(c19) | big_q(f4(elem!0)))) <=> ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | ((~big_p(c11)) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_q(c4))))),
% 22.55/22.76      inference(monotonicity,[status(thm)],[224])).
% 22.55/22.76  tff(226,plain,
% 22.55/22.76      (((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | ((~big_q(c4)) | big_p(c19) | big_q(elem!0) | big_q(elem!0) | big_p(c19) | (~big_p(c11)) | big_p(c19) | big_q(f4(elem!0)))) <=> ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | (~big_p(c11)) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_q(c4)))),
% 22.55/22.76      inference(transitivity,[status(thm)],[225, 223])).
% 22.55/22.76  tff(227,plain,
% 22.55/22.76      ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | ((~big_q(c4)) | big_p(c19) | big_q(elem!0) | big_q(elem!0) | big_p(c19) | (~big_p(c11)) | big_p(c19) | big_q(f4(elem!0)))),
% 22.55/22.76      inference(quant_inst,[status(thm)],[])).
% 22.55/22.76  tff(228,plain,
% 22.55/22.76      ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | (~big_p(c11)) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_q(c4))),
% 22.55/22.76      inference(modus_ponens,[status(thm)],[227, 226])).
% 22.55/22.76  tff(229,plain,
% 22.55/22.76      ($false),
% 22.55/22.76      inference(unit_resolution,[status(thm)],[228, 222, 170, 5, 145, 212, 195])).
% 22.55/22.76  tff(230,plain,(big_p(c3) | big_q(elem!0) | big_q(f2(elem!0)) | big_q(c14) | big_p(elem!0) | big_q(c16) | big_p(f1(elem!0)) | big_p(c9) | big_p(f1(c3))), inference(lemma,lemma(discharge,[]))).
% 22.55/22.76  tff(231,plain,
% 22.55/22.76      (big_q(c14)),
% 22.55/22.76      inference(unit_resolution,[status(thm)],[230, 107, 8, 5, 3, 2, 88, 61, 106])).
% 22.55/22.76  tff(232,plain,
% 22.55/22.76      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_p(c3) | big_q(c8) | big_p(c9) | big_q(elem!0) | big_p(elem!0) | big_p(f1(c3)) | (~big_q(c14)))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | big_p(c3) | big_q(c8) | big_p(c9) | big_q(elem!0) | big_p(elem!0) | big_p(f1(c3)) | (~big_q(c14)))),
% 22.55/22.76      inference(rewrite,[status(thm)],[])).
% 22.55/22.76  tff(233,plain,
% 22.55/22.76      ((big_q(c8) | big_p(elem!0) | (~big_q(c14)) | big_p(c9) | big_q(elem!0) | (~big_q(c14)) | big_p(f1(c3)) | big_p(c3)) <=> (big_p(c3) | big_q(c8) | big_p(c9) | big_q(elem!0) | big_p(elem!0) | big_p(f1(c3)) | (~big_q(c14)))),
% 22.55/22.76      inference(rewrite,[status(thm)],[])).
% 22.55/22.76  tff(234,plain,
% 22.55/22.76      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_q(c8) | big_p(elem!0) | (~big_q(c14)) | big_p(c9) | big_q(elem!0) | (~big_q(c14)) | big_p(f1(c3)) | big_p(c3))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_p(c3) | big_q(c8) | big_p(c9) | big_q(elem!0) | big_p(elem!0) | big_p(f1(c3)) | (~big_q(c14))))),
% 22.55/22.76      inference(monotonicity,[status(thm)],[233])).
% 22.55/22.76  tff(235,plain,
% 22.55/22.76      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_q(c8) | big_p(elem!0) | (~big_q(c14)) | big_p(c9) | big_q(elem!0) | (~big_q(c14)) | big_p(f1(c3)) | big_p(c3))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | big_p(c3) | big_q(c8) | big_p(c9) | big_q(elem!0) | big_p(elem!0) | big_p(f1(c3)) | (~big_q(c14)))),
% 22.55/22.76      inference(transitivity,[status(thm)],[234, 232])).
% 22.55/22.76  tff(236,plain,
% 22.55/22.76      ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_q(c8) | big_p(elem!0) | (~big_q(c14)) | big_p(c9) | big_q(elem!0) | (~big_q(c14)) | big_p(f1(c3)) | big_p(c3))),
% 22.55/22.76      inference(quant_inst,[status(thm)],[])).
% 22.55/22.76  tff(237,plain,
% 22.55/22.76      ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | big_p(c3) | big_q(c8) | big_p(c9) | big_q(elem!0) | big_p(elem!0) | big_p(f1(c3)) | (~big_q(c14))),
% 22.55/22.76      inference(modus_ponens,[status(thm)],[236, 235])).
% 22.55/22.76  tff(238,plain,
% 22.55/22.76      (big_p(c3) | big_q(c8) | big_p(c9) | big_q(elem!0) | big_p(elem!0) | big_p(f1(c3)) | (~big_q(c14))),
% 22.55/22.76      inference(unit_resolution,[status(thm)],[237, 137])).
% 22.55/22.76  tff(239,plain,
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% 22.55/22.76  tff(240,plain,(big_p(c9) | big_p(elem!0) | big_q(elem!0) | big_p(f1(c3)) | big_q(f2(elem!0)) | big_q(c16) | big_p(f1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 22.55/22.76  tff(241,plain,
% 22.55/22.76      (big_p(f1(c3))),
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% 22.55/22.76  tff(242,plain,
% 22.55/22.76      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_p(c9) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f1(c3))))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | big_p(c3) | big_p(c9) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f1(c3))))),
% 22.55/22.76      inference(rewrite,[status(thm)],[])).
% 22.55/22.76  tff(243,plain,
% 22.55/22.76      ((big_p(c3) | big_q(elem!0) | (~big_p(f1(c3))) | big_p(c9) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f1(c3)))) <=> (big_p(c3) | big_p(c9) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f1(c3))))),
% 22.55/22.76      inference(rewrite,[status(thm)],[])).
% 22.55/22.76  tff(244,plain,
% 22.55/22.76      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(elem!0) | (~big_p(f1(c3))) | big_p(c9) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f1(c3))))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_p(c9) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f1(c3)))))),
% 22.55/22.76      inference(monotonicity,[status(thm)],[243])).
% 22.55/22.76  tff(245,plain,
% 22.55/22.76      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(elem!0) | (~big_p(f1(c3))) | big_p(c9) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f1(c3))))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | big_p(c3) | big_p(c9) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f1(c3))))),
% 22.55/22.76      inference(transitivity,[status(thm)],[244, 242])).
% 22.55/22.76  tff(246,plain,
% 22.55/22.76      ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(elem!0) | (~big_p(f1(c3))) | big_p(c9) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f1(c3))))),
% 22.55/22.76      inference(quant_inst,[status(thm)],[])).
% 22.55/22.76  tff(247,plain,
% 22.55/22.76      ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | big_p(c3) | big_p(c9) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f1(c3)))),
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% 22.55/22.76  tff(248,plain,
% 22.55/22.76      (big_q(c4)),
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% 22.55/22.76  tff(249,plain,
% 22.55/22.76      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(c4)) | (~big_p(f1(c3))))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(c4)) | (~big_p(f1(c3))))),
% 22.55/22.76      inference(rewrite,[status(thm)],[])).
% 22.55/22.76  tff(250,plain,
% 22.55/22.76      (((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | (~big_p(f1(c3))) | big_q(c16) | big_p(c11) | (~big_p(f1(c3))) | big_p(elem!0)) <=> (big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(c4)) | (~big_p(f1(c3))))),
% 22.55/22.76      inference(rewrite,[status(thm)],[])).
% 22.55/22.76  tff(251,plain,
% 22.55/22.76      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | (~big_p(f1(c3))) | big_q(c16) | big_p(c11) | (~big_p(f1(c3))) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(c4)) | (~big_p(f1(c3)))))),
% 22.55/22.76      inference(monotonicity,[status(thm)],[250])).
% 22.55/22.76  tff(252,plain,
% 22.55/22.76      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | (~big_p(f1(c3))) | big_q(c16) | big_p(c11) | (~big_p(f1(c3))) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(c4)) | (~big_p(f1(c3))))),
% 22.55/22.76      inference(transitivity,[status(thm)],[251, 249])).
% 22.55/22.76  tff(253,plain,
% 22.55/22.76      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | (~big_p(f1(c3))) | big_q(c16) | big_p(c11) | (~big_p(f1(c3))) | big_p(elem!0))),
% 22.55/22.76      inference(quant_inst,[status(thm)],[])).
% 22.55/22.76  tff(254,plain,
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% 22.55/22.76  tff(257,plain,
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% 22.55/22.76  tff(258,plain,
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% 22.55/22.76      inference(rewrite,[status(thm)],[])).
% 22.55/22.76  tff(259,plain,
% 22.55/22.76      ((big_p(c3) | big_q(elem!0) | (~big_p(f1(elem!0))) | big_p(c11) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f1(elem!0)))) <=> (big_p(c3) | big_q(c4) | big_p(c11) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f1(elem!0))))),
% 22.55/22.76      inference(rewrite,[status(thm)],[])).
% 22.55/22.76  tff(260,plain,
% 22.55/22.76      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(elem!0) | (~big_p(f1(elem!0))) | big_p(c11) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f1(elem!0))))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(c4) | big_p(c11) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f1(elem!0)))))),
% 22.55/22.76      inference(monotonicity,[status(thm)],[259])).
% 22.55/22.76  tff(261,plain,
% 22.55/22.76      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(elem!0) | (~big_p(f1(elem!0))) | big_p(c11) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f1(elem!0))))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | big_p(c3) | big_q(c4) | big_p(c11) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f1(elem!0))))),
% 22.55/22.76      inference(transitivity,[status(thm)],[260, 258])).
% 22.55/22.76  tff(262,plain,
% 22.55/22.76      ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(elem!0) | (~big_p(f1(elem!0))) | big_p(c11) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f1(elem!0))))),
% 22.55/22.76      inference(quant_inst,[status(thm)],[])).
% 22.55/22.76  tff(263,plain,
% 22.55/22.76      ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | big_p(c3) | big_q(c4) | big_p(c11) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f1(elem!0)))),
% 22.55/22.76      inference(modus_ponens,[status(thm)],[262, 261])).
% 22.55/22.76  tff(264,plain,
% 22.55/22.76      (big_q(c4)),
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% 22.55/22.76  tff(265,plain,
% 22.55/22.76      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(f1(elem!0))) | (~big_q(c4)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(f1(elem!0))) | (~big_q(c4)))),
% 22.55/22.76      inference(rewrite,[status(thm)],[])).
% 22.55/22.76  tff(266,plain,
% 22.55/22.76      (((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | (~big_p(f1(elem!0))) | big_q(c16) | big_p(c11) | (~big_p(f1(elem!0))) | big_p(elem!0)) <=> (big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(f1(elem!0))) | (~big_q(c4)))),
% 22.55/22.76      inference(rewrite,[status(thm)],[])).
% 22.55/22.76  tff(267,plain,
% 22.55/22.76      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | (~big_p(f1(elem!0))) | big_q(c16) | big_p(c11) | (~big_p(f1(elem!0))) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(f1(elem!0))) | (~big_q(c4))))),
% 22.55/22.76      inference(monotonicity,[status(thm)],[266])).
% 22.55/22.76  tff(268,plain,
% 22.55/22.76      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | (~big_p(f1(elem!0))) | big_q(c16) | big_p(c11) | (~big_p(f1(elem!0))) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(f1(elem!0))) | (~big_q(c4)))),
% 22.55/22.77      inference(transitivity,[status(thm)],[267, 265])).
% 22.55/22.77  tff(269,plain,
% 22.55/22.77      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | (~big_p(f1(elem!0))) | big_q(c16) | big_p(c11) | (~big_p(f1(elem!0))) | big_p(elem!0))),
% 22.55/22.77      inference(quant_inst,[status(thm)],[])).
% 22.55/22.77  tff(270,plain,
% 22.55/22.77      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(f1(elem!0))) | (~big_q(c4))),
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% 22.55/22.77  tff(271,plain,
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% 22.55/22.77  tff(272,plain,(big_q(f2(elem!0)) | big_q(elem!0) | big_p(elem!0) | big_q(c16)), inference(lemma,lemma(discharge,[]))).
% 22.55/22.77  tff(273,plain,
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% 22.55/22.77  tff(274,plain,
% 22.55/22.77      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(elem!0) | (~big_q(f2(elem!0))))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(elem!0) | (~big_q(f2(elem!0))))),
% 22.55/22.77      inference(rewrite,[status(thm)],[])).
% 22.55/22.77  tff(275,plain,
% 22.55/22.77      (((~big_q(f2(elem!0))) | big_q(elem!0) | (~big_q(f2(elem!0))) | big_p(elem!0) | big_q(c16) | (~big_p(c11)) | (~big_p(c11)) | big_p(elem!0)) <=> (big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(elem!0) | (~big_q(f2(elem!0))))),
% 22.55/22.77      inference(rewrite,[status(thm)],[])).
% 22.55/22.77  tff(276,plain,
% 22.55/22.77      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(elem!0))) | big_q(elem!0) | (~big_q(f2(elem!0))) | big_p(elem!0) | big_q(c16) | (~big_p(c11)) | (~big_p(c11)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(elem!0) | (~big_q(f2(elem!0)))))),
% 22.55/22.77      inference(monotonicity,[status(thm)],[275])).
% 22.55/22.77  tff(277,plain,
% 22.55/22.77      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(elem!0))) | big_q(elem!0) | (~big_q(f2(elem!0))) | big_p(elem!0) | big_q(c16) | (~big_p(c11)) | (~big_p(c11)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(elem!0) | (~big_q(f2(elem!0))))),
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% 22.55/22.77      inference(quant_inst,[status(thm)],[])).
% 22.55/22.77  tff(279,plain,
% 22.55/22.77      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(elem!0) | (~big_q(f2(elem!0)))),
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% 22.55/22.77  tff(280,plain,
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% 22.55/22.77  tff(281,plain,((~big_p(c11)) | big_q(elem!0) | big_p(elem!0) | big_q(c16)), inference(lemma,lemma(discharge,[]))).
% 22.55/22.77  tff(282,plain,
% 22.55/22.77      (~big_p(c11)),
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% 22.55/22.77      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c3)) | big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(f2(elem!0))))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_p(c3)) | big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(f2(elem!0))))),
% 22.55/22.77      inference(rewrite,[status(thm)],[])).
% 22.55/22.77  tff(284,plain,
% 22.55/22.77      (((~big_q(f2(elem!0))) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(c3)) | big_q(c16) | big_p(c11) | (~big_p(c3)) | big_p(elem!0)) <=> ((~big_p(c3)) | big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(f2(elem!0))))),
% 22.55/22.77      inference(rewrite,[status(thm)],[])).
% 22.55/22.77  tff(285,plain,
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% 22.55/22.77      inference(monotonicity,[status(thm)],[284])).
% 22.55/22.77  tff(286,plain,
% 22.55/22.77      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(elem!0))) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(c3)) | big_q(c16) | big_p(c11) | (~big_p(c3)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_p(c3)) | big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(f2(elem!0))))),
% 22.55/22.77      inference(transitivity,[status(thm)],[285, 283])).
% 22.55/22.77  tff(287,plain,
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% 22.55/22.77      inference(quant_inst,[status(thm)],[])).
% 22.55/22.77  tff(288,plain,
% 22.55/22.77      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_p(c3)) | big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(f2(elem!0)))),
% 22.55/22.77      inference(modus_ponens,[status(thm)],[287, 286])).
% 22.55/22.77  tff(289,plain,
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% 22.55/22.77      inference(unit_resolution,[status(thm)],[288, 35, 5, 3, 273, 2, 282, 7])).
% 22.55/22.77  tff(290,plain,((~big_p(c3)) | big_q(elem!0) | big_p(elem!0) | big_q(c16)), inference(lemma,lemma(discharge,[]))).
% 22.55/22.77  tff(291,plain,
% 22.55/22.77      (~big_p(c3)),
% 22.55/22.77      inference(unit_resolution,[status(thm)],[290, 2, 3, 5])).
% 22.55/22.77  tff(292,assumption,(big_p(f1(c3))), introduced(assumption)).
% 22.55/22.77  tff(293,plain,
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% 22.55/22.77      inference(rewrite,[status(thm)],[])).
% 22.55/22.77  tff(294,plain,
% 22.55/22.77      (((~big_q(f2(elem!0))) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(f1(c3))) | big_q(c16) | big_p(c11) | (~big_p(f1(c3))) | big_p(elem!0)) <=> (big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(f2(elem!0))) | (~big_p(f1(c3))))),
% 22.55/22.77      inference(rewrite,[status(thm)],[])).
% 22.55/22.77  tff(295,plain,
% 22.55/22.77      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(elem!0))) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(f1(c3))) | big_q(c16) | big_p(c11) | (~big_p(f1(c3))) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(f2(elem!0))) | (~big_p(f1(c3)))))),
% 22.55/22.77      inference(monotonicity,[status(thm)],[294])).
% 22.55/22.77  tff(296,plain,
% 22.55/22.77      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(elem!0))) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(f1(c3))) | big_q(c16) | big_p(c11) | (~big_p(f1(c3))) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(f2(elem!0))) | (~big_p(f1(c3))))),
% 22.55/22.77      inference(transitivity,[status(thm)],[295, 293])).
% 22.55/22.77  tff(297,plain,
% 22.55/22.77      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(elem!0))) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(f1(c3))) | big_q(c16) | big_p(c11) | (~big_p(f1(c3))) | big_p(elem!0))),
% 22.55/22.77      inference(quant_inst,[status(thm)],[])).
% 22.55/22.77  tff(298,plain,
% 22.55/22.77      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(f2(elem!0))) | (~big_p(f1(c3)))),
% 22.55/22.77      inference(modus_ponens,[status(thm)],[297, 296])).
% 22.55/22.77  tff(299,plain,
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% 22.55/22.77      inference(unit_resolution,[status(thm)],[298, 35, 5, 3, 273, 2, 1, 292])).
% 22.55/22.77  tff(300,plain,((~big_p(f1(c3))) | big_q(elem!0) | big_p(elem!0) | big_q(c16) | big_p(c11)), inference(lemma,lemma(discharge,[]))).
% 22.55/22.77  tff(301,plain,
% 22.55/22.77      (~big_p(f1(c3))),
% 22.55/22.77      inference(unit_resolution,[status(thm)],[300, 1, 3, 2, 5])).
% 22.55/22.77  tff(302,plain,
% 22.55/22.77      (~big_q(c8)),
% 22.55/22.77      inference(unit_resolution,[status(thm)],[124, 106, 3, 5, 2, 126, 107])).
% 22.55/22.77  tff(303,plain,
% 22.55/22.77      (~big_q(f4(elem!0))),
% 22.55/22.77      inference(unit_resolution,[status(thm)],[144, 302, 3, 5, 88, 107])).
% 22.55/22.77  tff(304,plain,
% 22.55/22.77      (~big_q(c14)),
% 22.55/22.77      inference(unit_resolution,[status(thm)],[238, 302, 3, 5, 107, 126, 106])).
% 22.55/22.77  tff(305,assumption,(big_q(f2(elem!0))), introduced(assumption)).
% 22.55/22.77  tff(306,assumption,(~big_q(f4(elem!0))), introduced(assumption)).
% 22.55/22.77  tff(307,assumption,(~big_p(c19)), introduced(assumption)).
% 22.55/22.77  tff(308,plain,
% 22.55/22.77      (big_p(f3(elem!0))),
% 22.55/22.77      inference(unit_resolution,[status(thm)],[187, 307, 5, 146, 306, 3])).
% 22.55/22.77  tff(309,plain,
% 22.55/22.77      (((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))) | (big_q(c14) | big_p(c11) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_q(f2(elem!0))) | (~big_p(f3(elem!0))))) <=> ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))) | big_q(c14) | big_p(c11) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_q(f2(elem!0))) | (~big_p(f3(elem!0))))),
% 22.55/22.77      inference(rewrite,[status(thm)],[])).
% 22.55/22.77  tff(310,plain,
% 22.55/22.77      (((~big_q(f2(elem!0))) | big_p(elem!0) | big_q(c14) | big_q(elem!0) | (~big_p(f3(elem!0))) | big_p(c11) | big_p(c19) | big_q(f4(elem!0))) <=> (big_q(c14) | big_p(c11) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_q(f2(elem!0))) | (~big_p(f3(elem!0))))),
% 22.55/22.77      inference(rewrite,[status(thm)],[])).
% 22.55/22.77  tff(311,plain,
% 22.55/22.77      (((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))) | ((~big_q(f2(elem!0))) | big_p(elem!0) | big_q(c14) | big_q(elem!0) | (~big_p(f3(elem!0))) | big_p(c11) | big_p(c19) | big_q(f4(elem!0)))) <=> ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))) | (big_q(c14) | big_p(c11) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_q(f2(elem!0))) | (~big_p(f3(elem!0)))))),
% 22.55/22.77      inference(monotonicity,[status(thm)],[310])).
% 22.55/22.77  tff(312,plain,
% 22.55/22.77      (((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))) | ((~big_q(f2(elem!0))) | big_p(elem!0) | big_q(c14) | big_q(elem!0) | (~big_p(f3(elem!0))) | big_p(c11) | big_p(c19) | big_q(f4(elem!0)))) <=> ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))) | big_q(c14) | big_p(c11) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_q(f2(elem!0))) | (~big_p(f3(elem!0))))),
% 22.55/22.77      inference(transitivity,[status(thm)],[311, 309])).
% 22.55/22.77  tff(313,plain,
% 22.55/22.77      ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))) | ((~big_q(f2(elem!0))) | big_p(elem!0) | big_q(c14) | big_q(elem!0) | (~big_p(f3(elem!0))) | big_p(c11) | big_p(c19) | big_q(f4(elem!0)))),
% 22.55/22.77      inference(quant_inst,[status(thm)],[])).
% 22.55/22.77  tff(314,plain,
% 22.55/22.77      ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))) | big_q(c14) | big_p(c11) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_q(f2(elem!0))) | (~big_p(f3(elem!0)))),
% 22.55/22.77      inference(modus_ponens,[status(thm)],[313, 312])).
% 22.55/22.77  tff(315,plain,
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% 22.55/22.77  tff(316,plain,(big_p(c19) | big_q(c14) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_q(f2(elem!0))) | big_p(c11)), inference(lemma,lemma(discharge,[]))).
% 22.55/22.77  tff(317,plain,
% 22.55/22.77      (big_p(c19)),
% 22.55/22.77      inference(unit_resolution,[status(thm)],[316, 304, 5, 303, 3, 273, 1])).
% 22.55/22.77  tff(318,plain,
% 22.55/22.77      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c14) | big_q(c16) | big_p(c11) | big_p(elem!0) | (~big_q(f2(elem!0))) | (~big_p(c19)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c14) | big_q(c16) | big_p(c11) | big_p(elem!0) | (~big_q(f2(elem!0))) | (~big_p(c19)))),
% 22.55/22.77      inference(rewrite,[status(thm)],[])).
% 22.55/22.77  tff(319,plain,
% 22.55/22.77      (((~big_q(f2(elem!0))) | big_q(c14) | (~big_q(f2(elem!0))) | (~big_p(c19)) | big_q(c16) | big_p(c11) | (~big_p(c19)) | big_p(elem!0)) <=> (big_q(c14) | big_q(c16) | big_p(c11) | big_p(elem!0) | (~big_q(f2(elem!0))) | (~big_p(c19)))),
% 22.55/22.77      inference(rewrite,[status(thm)],[])).
% 22.55/22.77  tff(320,plain,
% 22.55/22.77      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(elem!0))) | big_q(c14) | (~big_q(f2(elem!0))) | (~big_p(c19)) | big_q(c16) | big_p(c11) | (~big_p(c19)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c14) | big_q(c16) | big_p(c11) | big_p(elem!0) | (~big_q(f2(elem!0))) | (~big_p(c19))))),
% 22.55/22.77      inference(monotonicity,[status(thm)],[319])).
% 22.55/22.77  tff(321,plain,
% 22.55/22.77      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(elem!0))) | big_q(c14) | (~big_q(f2(elem!0))) | (~big_p(c19)) | big_q(c16) | big_p(c11) | (~big_p(c19)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c14) | big_q(c16) | big_p(c11) | big_p(elem!0) | (~big_q(f2(elem!0))) | (~big_p(c19)))),
% 22.55/22.77      inference(transitivity,[status(thm)],[320, 318])).
% 22.55/22.77  tff(322,plain,
% 22.55/22.77      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(elem!0))) | big_q(c14) | (~big_q(f2(elem!0))) | (~big_p(c19)) | big_q(c16) | big_p(c11) | (~big_p(c19)) | big_p(elem!0))),
% 22.55/22.77      inference(quant_inst,[status(thm)],[])).
% 22.55/22.77  tff(323,plain,
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% 22.55/22.77      inference(quant_inst,[status(thm)],[])).
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% 22.55/22.78      inference(bind,[status(th)],[])).
% 22.55/22.78  tff(349,plain,
% 22.55/22.78      (![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | big_q(X13)) | (~big_q(c16))) | (~big_p(X14))) | big_q(X15)) <=> ![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))),
% 22.55/22.78      inference(quant_intro,[status(thm)],[348])).
% 22.55/22.78  tff(350,axiom,(![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | big_q(X13)) | (~big_q(c16))) | (~big_p(X14))) | big_q(X15))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_67')).
% 22.55/22.78  tff(351,plain,
% 22.55/22.78      (![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))),
% 22.55/22.78      inference(modus_ponens,[status(thm)],[350, 349])).
% 22.55/22.78  tff(352,plain,
% 22.55/22.78      (![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))),
% 22.55/22.78      inference(modus_ponens,[status(thm)],[351, 347])).
% 22.55/22.78  tff(353,plain,(
% 22.55/22.78      ![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))),
% 22.55/22.78      inference(skolemize,[status(sab)],[352])).
% 22.55/22.78  tff(354,plain,
% 22.55/22.78      (![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))),
% 22.55/22.78      inference(modus_ponens,[status(thm)],[353, 346])).
% 22.55/22.78  tff(355,plain,
% 22.55/22.78      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | (~big_q(c16)) | big_q(elem!0) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_q(elem!0) | big_p(elem!0))),
% 22.55/22.78      inference(rewrite,[status(thm)],[])).
% 22.55/22.78  tff(356,plain,
% 22.55/22.78      (((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | big_p(elem!0) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c11)) | big_p(elem!0)) <=> ((~big_p(c11)) | (~big_q(c16)) | big_q(elem!0) | big_p(elem!0))),
% 22.55/22.78      inference(rewrite,[status(thm)],[])).
% 22.55/22.78  tff(357,plain,
% 22.55/22.78      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | big_p(elem!0) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c11)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | (~big_q(c16)) | big_q(elem!0) | big_p(elem!0)))),
% 22.55/22.78      inference(monotonicity,[status(thm)],[356])).
% 22.55/22.78  tff(358,plain,
% 22.55/22.78      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | big_p(elem!0) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c11)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_q(elem!0) | big_p(elem!0))),
% 22.55/22.78      inference(transitivity,[status(thm)],[357, 355])).
% 22.55/22.78  tff(359,plain,
% 22.55/22.78      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | big_p(elem!0) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c11)) | big_p(elem!0))),
% 22.55/22.78      inference(quant_inst,[status(thm)],[])).
% 22.55/22.78  tff(360,plain,
% 22.55/22.78      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_q(elem!0) | big_p(elem!0)),
% 22.55/22.78      inference(modus_ponens,[status(thm)],[359, 358])).
% 22.55/22.78  tff(361,plain,
% 22.55/22.78      ($false),
% 22.55/22.78      inference(unit_resolution,[status(thm)],[360, 354, 5, 3, 344, 6])).
% 22.55/22.78  tff(362,plain,((~big_p(c11)) | big_q(elem!0) | big_p(elem!0)), inference(lemma,lemma(discharge,[]))).
% 22.55/22.78  tff(363,plain,
% 22.55/22.78      (~big_p(c11)),
% 22.55/22.78      inference(unit_resolution,[status(thm)],[362, 5, 3])).
% 22.55/22.78  tff(364,plain,
% 22.55/22.78      (^[X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : refl(((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9)) <=> ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9)))),
% 22.55/22.78      inference(bind,[status(th)],[])).
% 22.55/22.78  tff(365,plain,
% 22.55/22.78      (![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9)) <=> ![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))),
% 22.55/22.78      inference(quant_intro,[status(thm)],[364])).
% 22.55/22.78  tff(366,plain,
% 22.55/22.78      (![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9)) <=> ![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))),
% 22.55/22.78      inference(rewrite,[status(thm)],[])).
% 22.55/22.78  tff(367,plain,
% 22.55/22.78      (^[X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) <=> ((~big_q(X8)) | (~big_p(X7)) | big_p(c11))), ((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) <=> (((~big_q(X8)) | (~big_p(X7)) | big_p(c11)) | big_p(X9)))), rewrite((((~big_q(X8)) | (~big_p(X7)) | big_p(c11)) | big_p(X9)) <=> ((~big_q(X8)) | (~big_p(X7)) | big_p(c11) | big_p(X9))), ((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) <=> ((~big_q(X8)) | (~big_p(X7)) | big_p(c11) | big_p(X9)))), (((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | big_q(X13)) <=> (((~big_q(X8)) | (~big_p(X7)) | big_p(c11) | big_p(X9)) | big_q(X13)))), rewrite((((~big_q(X8)) | (~big_p(X7)) | big_p(c11) | big_p(X9)) | big_q(X13)) <=> ((~big_q(X8)) | big_q(X13) | (~big_p(X7)) | big_p(c11) | big_p(X9))), (((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | big_q(X13)) <=> ((~big_q(X8)) | big_q(X13) | (~big_p(X7)) | big_p(c11) | big_p(X9)))), ((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | big_q(X13)) | (~big_q(c16))) <=> (((~big_q(X8)) | big_q(X13) | (~big_p(X7)) | big_p(c11) | big_p(X9)) | (~big_q(c16))))), rewrite((((~big_q(X8)) | big_q(X13) | (~big_p(X7)) | big_p(c11) | big_p(X9)) | (~big_q(c16))) <=> ((~big_q(X8)) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | big_p(X9))), ((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | big_q(X13)) | (~big_q(c16))) <=> ((~big_q(X8)) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | big_p(X9)))), (((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | big_q(X13)) | (~big_q(c16))) | (~big_p(X14))) <=> (((~big_q(X8)) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | big_p(X9)) | (~big_p(X14))))), rewrite((((~big_q(X8)) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | big_p(X9)) | (~big_p(X14))) <=> ((~big_q(X8)) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))), (((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | big_q(X13)) | (~big_q(c16))) | (~big_p(X14))) <=> ((~big_q(X8)) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9)))), ((((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | big_q(X13)) | (~big_q(c16))) | (~big_p(X14))) | big_q(X15)) <=> (((~big_q(X8)) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9)) | big_q(X15)))), rewrite((((~big_q(X8)) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9)) | big_q(X15)) <=> ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))), ((((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | big_q(X13)) | (~big_q(c16))) | (~big_p(X14))) | big_q(X15)) <=> ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))))),
% 22.55/22.78      inference(bind,[status(th)],[])).
% 22.55/22.78  tff(368,plain,
% 22.55/22.78      (![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : (((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | big_q(X13)) | (~big_q(c16))) | (~big_p(X14))) | big_q(X15)) <=> ![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))),
% 22.55/22.78      inference(quant_intro,[status(thm)],[367])).
% 22.55/22.78  tff(369,axiom,(![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : (((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | big_q(X13)) | (~big_q(c16))) | (~big_p(X14))) | big_q(X15))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_83')).
% 22.55/22.78  tff(370,plain,
% 22.55/22.78      (![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))),
% 22.55/22.78      inference(modus_ponens,[status(thm)],[369, 368])).
% 22.55/22.78  tff(371,plain,
% 22.55/22.78      (![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))),
% 22.55/22.78      inference(modus_ponens,[status(thm)],[370, 366])).
% 22.55/22.78  tff(372,plain,(
% 22.55/22.78      ![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))),
% 22.55/22.78      inference(skolemize,[status(sab)],[371])).
% 22.55/22.78  tff(373,plain,
% 22.55/22.78      (![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))),
% 22.55/22.78      inference(modus_ponens,[status(thm)],[372, 365])).
% 22.55/22.78  tff(374,plain,
% 22.55/22.78      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(f1(c3))))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(f1(c3))))),
% 22.55/22.78      inference(rewrite,[status(thm)],[])).
% 22.55/22.78  tff(375,plain,
% 22.55/22.78      (((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | (~big_p(f1(c3))) | (~big_q(c16)) | big_p(c11) | (~big_p(f1(c3))) | big_p(elem!0)) <=> ((~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(f1(c3))))),
% 22.55/22.78      inference(rewrite,[status(thm)],[])).
% 22.55/22.78  tff(376,plain,
% 22.55/22.78      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | (~big_p(f1(c3))) | (~big_q(c16)) | big_p(c11) | (~big_p(f1(c3))) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(f1(c3)))))),
% 22.55/22.78      inference(monotonicity,[status(thm)],[375])).
% 22.55/22.78  tff(377,plain,
% 22.55/22.78      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | (~big_p(f1(c3))) | (~big_q(c16)) | big_p(c11) | (~big_p(f1(c3))) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(f1(c3))))),
% 22.55/22.78      inference(transitivity,[status(thm)],[376, 374])).
% 22.55/22.78  tff(378,plain,
% 22.55/22.78      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | (~big_p(f1(c3))) | (~big_q(c16)) | big_p(c11) | (~big_p(f1(c3))) | big_p(elem!0))),
% 22.55/22.78      inference(quant_inst,[status(thm)],[])).
% 22.55/22.78  tff(379,plain,
% 22.55/22.78      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(f1(c3)))),
% 22.55/22.78      inference(modus_ponens,[status(thm)],[378, 377])).
% 22.55/22.78  tff(380,plain,
% 22.55/22.78      ($false),
% 22.55/22.78      inference(unit_resolution,[status(thm)],[379, 373, 5, 3, 344, 1, 292])).
% 22.55/22.78  tff(381,plain,((~big_p(f1(c3))) | big_q(elem!0) | big_p(elem!0) | big_p(c11)), inference(lemma,lemma(discharge,[]))).
% 22.55/22.78  tff(382,plain,
% 22.55/22.78      (~big_p(f1(c3))),
% 22.55/22.78      inference(unit_resolution,[status(thm)],[381, 363, 3, 5])).
% 22.55/22.78  tff(383,plain,
% 22.55/22.78      (big_p(f3(elem!0))),
% 22.55/22.78      inference(unit_resolution,[status(thm)],[187, 306, 5, 146, 307, 3])).
% 22.55/22.78  tff(384,plain,
% 22.55/22.78      (((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))) | (big_q(c14) | (~big_q(c16)) | big_p(c11) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_p(f3(elem!0))))) <=> ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))) | big_q(c14) | (~big_q(c16)) | big_p(c11) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_p(f3(elem!0))))),
% 22.55/22.78      inference(rewrite,[status(thm)],[])).
% 22.55/22.78  tff(385,plain,
% 22.55/22.78      (((~big_q(c16)) | big_p(elem!0) | big_q(c14) | big_q(elem!0) | (~big_p(f3(elem!0))) | big_p(c11) | big_p(c19) | big_q(f4(elem!0))) <=> (big_q(c14) | (~big_q(c16)) | big_p(c11) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_p(f3(elem!0))))),
% 22.55/22.78      inference(rewrite,[status(thm)],[])).
% 22.55/22.78  tff(386,plain,
% 22.55/22.78      (((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))) | ((~big_q(c16)) | big_p(elem!0) | big_q(c14) | big_q(elem!0) | (~big_p(f3(elem!0))) | big_p(c11) | big_p(c19) | big_q(f4(elem!0)))) <=> ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))) | (big_q(c14) | (~big_q(c16)) | big_p(c11) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_p(f3(elem!0)))))),
% 22.55/22.78      inference(monotonicity,[status(thm)],[385])).
% 22.55/22.78  tff(387,plain,
% 22.55/22.78      (((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))) | ((~big_q(c16)) | big_p(elem!0) | big_q(c14) | big_q(elem!0) | (~big_p(f3(elem!0))) | big_p(c11) | big_p(c19) | big_q(f4(elem!0)))) <=> ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))) | big_q(c14) | (~big_q(c16)) | big_p(c11) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_p(f3(elem!0))))),
% 22.55/22.78      inference(transitivity,[status(thm)],[386, 384])).
% 22.55/22.78  tff(388,plain,
% 22.55/22.78      ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))) | ((~big_q(c16)) | big_p(elem!0) | big_q(c14) | big_q(elem!0) | (~big_p(f3(elem!0))) | big_p(c11) | big_p(c19) | big_q(f4(elem!0)))),
% 22.55/22.78      inference(quant_inst,[status(thm)],[])).
% 22.55/22.78  tff(389,plain,
% 22.55/22.78      ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | (~big_p(X7)) | big_p(c11) | big_p(c19) | big_q(f4(X16)))) | big_q(c14) | (~big_q(c16)) | big_p(c11) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_p(f3(elem!0)))),
% 22.55/22.78      inference(modus_ponens,[status(thm)],[388, 387])).
% 22.55/22.78  tff(390,plain,
% 22.55/22.78      ($false),
% 22.55/22.78      inference(unit_resolution,[status(thm)],[389, 205, 146, 307, 5, 306, 383, 3, 344, 1])).
% 22.55/22.78  tff(391,plain,(big_q(f4(elem!0)) | big_q(c14) | big_p(c19) | big_q(elem!0) | big_p(elem!0) | big_p(c11)), inference(lemma,lemma(discharge,[]))).
% 22.55/22.78  tff(392,plain,
% 22.55/22.78      (big_p(c19)),
% 22.55/22.78      inference(unit_resolution,[status(thm)],[391, 146, 306, 5, 3, 1])).
% 22.55/22.78  tff(393,plain,
% 22.55/22.78      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c14) | (~big_q(c16)) | big_p(c11) | big_p(elem!0) | (~big_p(c19)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c14) | (~big_q(c16)) | big_p(c11) | big_p(elem!0) | (~big_p(c19)))),
% 22.55/22.78      inference(rewrite,[status(thm)],[])).
% 22.55/22.78  tff(394,plain,
% 22.55/22.78      (((~big_q(c16)) | big_q(c14) | big_q(c14) | (~big_p(c19)) | (~big_q(c16)) | big_p(c11) | (~big_p(c19)) | big_p(elem!0)) <=> (big_q(c14) | (~big_q(c16)) | big_p(c11) | big_p(elem!0) | (~big_p(c19)))),
% 22.55/22.78      inference(rewrite,[status(thm)],[])).
% 22.55/22.78  tff(395,plain,
% 22.55/22.78      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_q(c14) | big_q(c14) | (~big_p(c19)) | (~big_q(c16)) | big_p(c11) | (~big_p(c19)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c14) | (~big_q(c16)) | big_p(c11) | big_p(elem!0) | (~big_p(c19))))),
% 22.55/22.78      inference(monotonicity,[status(thm)],[394])).
% 22.55/22.78  tff(396,plain,
% 22.55/22.78      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_q(c14) | big_q(c14) | (~big_p(c19)) | (~big_q(c16)) | big_p(c11) | (~big_p(c19)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c14) | (~big_q(c16)) | big_p(c11) | big_p(elem!0) | (~big_p(c19)))),
% 22.55/22.78      inference(transitivity,[status(thm)],[395, 393])).
% 22.55/22.78  tff(397,plain,
% 22.55/22.78      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_q(c14) | big_q(c14) | (~big_p(c19)) | (~big_q(c16)) | big_p(c11) | (~big_p(c19)) | big_p(elem!0))),
% 22.55/22.78      inference(quant_inst,[status(thm)],[])).
% 22.55/22.78  tff(398,plain,
% 22.55/22.78      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c14) | (~big_q(c16)) | big_p(c11) | big_p(elem!0) | (~big_p(c19))),
% 22.55/22.78      inference(modus_ponens,[status(thm)],[397, 396])).
% 22.55/22.78  tff(399,plain,
% 22.55/22.78      ($false),
% 22.55/22.78      inference(unit_resolution,[status(thm)],[398, 373, 146, 392, 3, 344, 1])).
% 22.55/22.78  tff(400,plain,(big_q(c14) | big_p(elem!0) | big_p(c11) | big_q(f4(elem!0)) | big_q(elem!0)), inference(lemma,lemma(discharge,[]))).
% 22.55/22.78  tff(401,plain,
% 22.55/22.78      (big_q(c14)),
% 22.55/22.78      inference(unit_resolution,[status(thm)],[400, 306, 1, 3, 5])).
% 22.55/22.78  tff(402,assumption,(big_q(c14)), introduced(assumption)).
% 22.55/22.78  tff(403,plain,
% 22.55/22.78      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_p(c3) | (~big_q(c8)) | big_p(c9) | (~big_q(c16)) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(f1(c3)))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | big_p(c3) | (~big_q(c8)) | big_p(c9) | (~big_q(c16)) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(f1(c3)))),
% 22.55/22.78      inference(rewrite,[status(thm)],[])).
% 22.55/22.78  tff(404,plain,
% 22.55/22.78      (((~big_q(c8)) | big_p(c3) | big_q(elem!0) | big_p(c9) | big_q(f4(elem!0)) | (~big_q(c16)) | big_p(f1(c3)) | big_p(c3)) <=> (big_p(c3) | (~big_q(c8)) | big_p(c9) | (~big_q(c16)) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(f1(c3)))),
% 22.55/22.78      inference(rewrite,[status(thm)],[])).
% 22.55/22.78  tff(405,plain,
% 22.55/22.78      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | ((~big_q(c8)) | big_p(c3) | big_q(elem!0) | big_p(c9) | big_q(f4(elem!0)) | (~big_q(c16)) | big_p(f1(c3)) | big_p(c3))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_p(c3) | (~big_q(c8)) | big_p(c9) | (~big_q(c16)) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(f1(c3))))),
% 22.55/22.78      inference(monotonicity,[status(thm)],[404])).
% 22.55/22.78  tff(406,plain,
% 22.55/22.78      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | ((~big_q(c8)) | big_p(c3) | big_q(elem!0) | big_p(c9) | big_q(f4(elem!0)) | (~big_q(c16)) | big_p(f1(c3)) | big_p(c3))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | big_p(c3) | (~big_q(c8)) | big_p(c9) | (~big_q(c16)) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(f1(c3)))),
% 22.55/22.78      inference(transitivity,[status(thm)],[405, 403])).
% 22.55/22.78  tff(407,plain,
% 22.55/22.78      ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | ((~big_q(c8)) | big_p(c3) | big_q(elem!0) | big_p(c9) | big_q(f4(elem!0)) | (~big_q(c16)) | big_p(f1(c3)) | big_p(c3))),
% 22.55/22.78      inference(quant_inst,[status(thm)],[])).
% 22.55/22.78  tff(408,plain,
% 22.55/22.78      ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | big_p(c3) | (~big_q(c8)) | big_p(c9) | (~big_q(c16)) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(f1(c3))),
% 22.55/22.78      inference(modus_ponens,[status(thm)],[407, 406])).
% 22.55/22.78  tff(409,plain,
% 22.55/22.78      (big_p(c3) | (~big_q(c8)) | big_p(c9) | (~big_q(c16)) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(f1(c3))),
% 22.55/22.79      inference(unit_resolution,[status(thm)],[408, 117])).
% 22.55/22.79  tff(410,plain,
% 22.55/22.79      (~big_q(c8)),
% 22.55/22.79      inference(unit_resolution,[status(thm)],[409, 107, 344, 5, 306, 126, 106])).
% 22.55/22.79  tff(411,plain,
% 22.55/22.79      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_p(c3) | big_q(c8) | big_p(c9) | big_q(f4(elem!0)) | big_p(elem!0) | big_p(f1(c3)) | (~big_q(c14)))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | big_p(c3) | big_q(c8) | big_p(c9) | big_q(f4(elem!0)) | big_p(elem!0) | big_p(f1(c3)) | (~big_q(c14)))),
% 22.55/22.79      inference(rewrite,[status(thm)],[])).
% 22.55/22.79  tff(412,plain,
% 22.55/22.79      ((big_q(c8) | big_p(elem!0) | (~big_q(c14)) | big_p(c9) | big_q(f4(elem!0)) | (~big_q(c14)) | big_p(f1(c3)) | big_p(c3)) <=> (big_p(c3) | big_q(c8) | big_p(c9) | big_q(f4(elem!0)) | big_p(elem!0) | big_p(f1(c3)) | (~big_q(c14)))),
% 22.55/22.79      inference(rewrite,[status(thm)],[])).
% 22.55/22.79  tff(413,plain,
% 22.55/22.79      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_q(c8) | big_p(elem!0) | (~big_q(c14)) | big_p(c9) | big_q(f4(elem!0)) | (~big_q(c14)) | big_p(f1(c3)) | big_p(c3))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_p(c3) | big_q(c8) | big_p(c9) | big_q(f4(elem!0)) | big_p(elem!0) | big_p(f1(c3)) | (~big_q(c14))))),
% 22.55/22.79      inference(monotonicity,[status(thm)],[412])).
% 22.55/22.79  tff(414,plain,
% 22.55/22.79      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_q(c8) | big_p(elem!0) | (~big_q(c14)) | big_p(c9) | big_q(f4(elem!0)) | (~big_q(c14)) | big_p(f1(c3)) | big_p(c3))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | big_p(c3) | big_q(c8) | big_p(c9) | big_q(f4(elem!0)) | big_p(elem!0) | big_p(f1(c3)) | (~big_q(c14)))),
% 22.55/22.79      inference(transitivity,[status(thm)],[413, 411])).
% 22.55/22.79  tff(415,plain,
% 22.55/22.79      ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_q(c8) | big_p(elem!0) | (~big_q(c14)) | big_p(c9) | big_q(f4(elem!0)) | (~big_q(c14)) | big_p(f1(c3)) | big_p(c3))),
% 22.55/22.79      inference(quant_inst,[status(thm)],[])).
% 22.55/22.79  tff(416,plain,
% 22.55/22.79      ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | big_p(c3) | big_q(c8) | big_p(c9) | big_q(f4(elem!0)) | big_p(elem!0) | big_p(f1(c3)) | (~big_q(c14))),
% 22.55/22.79      inference(modus_ponens,[status(thm)],[415, 414])).
% 22.55/22.79  tff(417,plain,
% 22.55/22.79      (big_p(c3) | big_q(c8) | big_p(c9) | big_q(f4(elem!0)) | big_p(elem!0) | big_p(f1(c3)) | (~big_q(c14))),
% 22.55/22.79      inference(unit_resolution,[status(thm)],[416, 137])).
% 22.55/22.79  tff(418,plain,
% 22.55/22.79      ($false),
% 22.55/22.79      inference(unit_resolution,[status(thm)],[417, 410, 107, 3, 402, 306, 126, 106])).
% 22.55/22.79  tff(419,plain,(big_p(c9) | big_p(elem!0) | (~big_q(c14)) | big_q(f4(elem!0)) | big_p(c3) | big_p(f1(c3)) | big_q(elem!0)), inference(lemma,lemma(discharge,[]))).
% 22.55/22.79  tff(420,plain,
% 22.55/22.79      (big_p(c9)),
% 22.55/22.79      inference(unit_resolution,[status(thm)],[419, 401, 3, 306, 126, 106, 5])).
% 22.55/22.79  tff(421,plain,
% 22.55/22.79      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(c9)) | (~big_q(c14)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(c9)) | (~big_q(c14)))),
% 22.55/22.79      inference(rewrite,[status(thm)],[])).
% 22.55/22.79  tff(422,plain,
% 22.55/22.79      (((~big_q(c14)) | big_q(elem!0) | big_q(elem!0) | (~big_p(c9)) | (~big_q(c16)) | big_p(c11) | (~big_p(c9)) | big_p(elem!0)) <=> ((~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(c9)) | (~big_q(c14)))),
% 22.55/22.79      inference(rewrite,[status(thm)],[])).
% 22.55/22.79  tff(423,plain,
% 22.55/22.79      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c14)) | big_q(elem!0) | big_q(elem!0) | (~big_p(c9)) | (~big_q(c16)) | big_p(c11) | (~big_p(c9)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(c9)) | (~big_q(c14))))),
% 22.55/22.79      inference(monotonicity,[status(thm)],[422])).
% 22.55/22.79  tff(424,plain,
% 22.55/22.79      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c14)) | big_q(elem!0) | big_q(elem!0) | (~big_p(c9)) | (~big_q(c16)) | big_p(c11) | (~big_p(c9)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(c9)) | (~big_q(c14)))),
% 22.55/22.79      inference(transitivity,[status(thm)],[423, 421])).
% 22.55/22.79  tff(425,plain,
% 22.55/22.79      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c14)) | big_q(elem!0) | big_q(elem!0) | (~big_p(c9)) | (~big_q(c16)) | big_p(c11) | (~big_p(c9)) | big_p(elem!0))),
% 22.55/22.79      inference(quant_inst,[status(thm)],[])).
% 22.55/22.79  tff(426,plain,
% 22.55/22.79      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(c9)) | (~big_q(c14))),
% 22.55/22.79      inference(modus_ponens,[status(thm)],[425, 424])).
% 22.55/22.79  tff(427,plain,
% 22.55/22.79      ($false),
% 22.55/22.79      inference(unit_resolution,[status(thm)],[426, 373, 401, 5, 3, 344, 420, 1])).
% 22.55/22.79  tff(428,plain,(big_q(f4(elem!0)) | big_q(elem!0) | big_p(elem!0) | big_p(c11) | big_p(c3) | big_p(f1(c3))), inference(lemma,lemma(discharge,[]))).
% 22.55/22.79  tff(429,plain,
% 22.55/22.79      (big_q(f4(elem!0))),
% 22.55/22.79      inference(unit_resolution,[status(thm)],[428, 126, 3, 363, 382, 5])).
% 22.55/22.79  tff(430,assumption,(big_q(f4(elem!0))), introduced(assumption)).
% 22.55/22.79  tff(431,plain,
% 22.55/22.79      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(f4(elem!0))) | (~big_p(c9)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(f4(elem!0))) | (~big_p(c9)))),
% 22.55/22.79      inference(rewrite,[status(thm)],[])).
% 22.55/22.79  tff(432,plain,
% 22.55/22.79      (((~big_q(f4(elem!0))) | big_q(elem!0) | big_q(elem!0) | (~big_p(c9)) | (~big_q(c16)) | big_p(c11) | (~big_p(c9)) | big_p(elem!0)) <=> ((~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(f4(elem!0))) | (~big_p(c9)))),
% 22.55/22.79      inference(rewrite,[status(thm)],[])).
% 22.55/22.79  tff(433,plain,
% 22.55/22.79      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f4(elem!0))) | big_q(elem!0) | big_q(elem!0) | (~big_p(c9)) | (~big_q(c16)) | big_p(c11) | (~big_p(c9)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(f4(elem!0))) | (~big_p(c9))))),
% 22.63/22.79      inference(monotonicity,[status(thm)],[432])).
% 22.63/22.79  tff(434,plain,
% 22.63/22.79      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f4(elem!0))) | big_q(elem!0) | big_q(elem!0) | (~big_p(c9)) | (~big_q(c16)) | big_p(c11) | (~big_p(c9)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(f4(elem!0))) | (~big_p(c9)))),
% 22.63/22.79      inference(transitivity,[status(thm)],[433, 431])).
% 22.63/22.79  tff(435,plain,
% 22.63/22.79      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f4(elem!0))) | big_q(elem!0) | big_q(elem!0) | (~big_p(c9)) | (~big_q(c16)) | big_p(c11) | (~big_p(c9)) | big_p(elem!0))),
% 22.63/22.79      inference(quant_inst,[status(thm)],[])).
% 22.63/22.79  tff(436,plain,
% 22.63/22.79      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(f4(elem!0))) | (~big_p(c9))),
% 22.63/22.79      inference(modus_ponens,[status(thm)],[435, 434])).
% 22.63/22.79  tff(437,plain,
% 22.63/22.79      ($false),
% 22.63/22.79      inference(unit_resolution,[status(thm)],[436, 373, 5, 430, 3, 344, 89, 363])).
% 22.63/22.79  tff(438,plain,((~big_p(c9)) | big_q(elem!0) | (~big_q(f4(elem!0))) | big_p(elem!0)), inference(lemma,lemma(discharge,[]))).
% 22.63/22.79  tff(439,plain,
% 22.63/22.79      (~big_p(c9)),
% 22.63/22.79      inference(unit_resolution,[status(thm)],[438, 429, 5, 3])).
% 22.63/22.79  tff(440,plain,
% 22.63/22.79      (big_q(c8)),
% 22.63/22.79      inference(unit_resolution,[status(thm)],[144, 107, 3, 5, 88, 429])).
% 22.63/22.79  tff(441,plain,
% 22.63/22.79      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_p(c3) | (~big_q(c8)) | big_p(c9) | big_q(elem!0) | big_p(f1(c3)))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | big_p(c3) | (~big_q(c8)) | big_p(c9) | big_q(elem!0) | big_p(f1(c3)))),
% 22.63/22.79      inference(rewrite,[status(thm)],[])).
% 22.63/22.79  tff(442,plain,
% 22.63/22.79      (((~big_q(c8)) | big_p(c3) | big_q(elem!0) | big_p(c9) | big_q(elem!0) | (~big_q(c8)) | big_p(f1(c3)) | big_p(c3)) <=> (big_p(c3) | (~big_q(c8)) | big_p(c9) | big_q(elem!0) | big_p(f1(c3)))),
% 22.63/22.79      inference(rewrite,[status(thm)],[])).
% 22.63/22.79  tff(443,plain,
% 22.63/22.79      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | ((~big_q(c8)) | big_p(c3) | big_q(elem!0) | big_p(c9) | big_q(elem!0) | (~big_q(c8)) | big_p(f1(c3)) | big_p(c3))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_p(c3) | (~big_q(c8)) | big_p(c9) | big_q(elem!0) | big_p(f1(c3))))),
% 22.63/22.79      inference(monotonicity,[status(thm)],[442])).
% 22.63/22.79  tff(444,plain,
% 22.63/22.79      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | ((~big_q(c8)) | big_p(c3) | big_q(elem!0) | big_p(c9) | big_q(elem!0) | (~big_q(c8)) | big_p(f1(c3)) | big_p(c3))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | big_p(c3) | (~big_q(c8)) | big_p(c9) | big_q(elem!0) | big_p(f1(c3)))),
% 22.63/22.79      inference(transitivity,[status(thm)],[443, 441])).
% 22.63/22.79  tff(445,plain,
% 22.63/22.79      ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | ((~big_q(c8)) | big_p(c3) | big_q(elem!0) | big_p(c9) | big_q(elem!0) | (~big_q(c8)) | big_p(f1(c3)) | big_p(c3))),
% 22.63/22.79      inference(quant_inst,[status(thm)],[])).
% 22.63/22.79  tff(446,plain,
% 22.63/22.79      ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | big_p(c3) | (~big_q(c8)) | big_p(c9) | big_q(elem!0) | big_p(f1(c3))),
% 22.63/22.79      inference(modus_ponens,[status(thm)],[445, 444])).
% 22.63/22.79  tff(447,plain,
% 22.63/22.79      (big_p(c3) | (~big_q(c8)) | big_p(c9) | big_q(elem!0) | big_p(f1(c3))),
% 22.63/22.79      inference(unit_resolution,[status(thm)],[446, 117])).
% 22.63/22.79  tff(448,plain,
% 22.63/22.79      ($false),
% 22.63/22.79      inference(unit_resolution,[status(thm)],[447, 440, 107, 5, 126, 382])).
% 22.63/22.79  tff(449,plain,(big_p(c9) | big_q(elem!0) | big_p(c3) | big_p(elem!0) | big_p(f1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 22.63/22.79  tff(450,plain,
% 22.63/22.79      (big_p(f1(elem!0))),
% 22.63/22.79      inference(unit_resolution,[status(thm)],[449, 439, 126, 3, 5])).
% 22.63/22.79  tff(451,plain,
% 22.63/22.79      (~big_q(c8)),
% 22.63/22.79      inference(unit_resolution,[status(thm)],[447, 439, 5, 126, 382])).
% 22.63/22.79  tff(452,plain,
% 22.63/22.79      (~big_q(c14)),
% 22.63/22.79      inference(unit_resolution,[status(thm)],[238, 451, 3, 5, 439, 126, 382])).
% 22.63/22.79  tff(453,plain,
% 22.63/22.79      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c14) | big_p(c9) | (~big_q(c16)) | big_p(c11) | (~big_p(f1(elem!0))) | (~big_q(f4(elem!0))))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c14) | big_p(c9) | (~big_q(c16)) | big_p(c11) | (~big_p(f1(elem!0))) | (~big_q(f4(elem!0))))),
% 22.63/22.79      inference(rewrite,[status(thm)],[])).
% 22.63/22.79  tff(454,plain,
% 22.63/22.79      (((~big_q(f4(elem!0))) | big_q(c14) | big_q(c14) | (~big_p(f1(elem!0))) | (~big_q(c16)) | big_p(c11) | (~big_p(f1(elem!0))) | big_p(c9)) <=> (big_q(c14) | big_p(c9) | (~big_q(c16)) | big_p(c11) | (~big_p(f1(elem!0))) | (~big_q(f4(elem!0))))),
% 22.63/22.79      inference(rewrite,[status(thm)],[])).
% 22.63/22.79  tff(455,plain,
% 22.63/22.79      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f4(elem!0))) | big_q(c14) | big_q(c14) | (~big_p(f1(elem!0))) | (~big_q(c16)) | big_p(c11) | (~big_p(f1(elem!0))) | big_p(c9))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c14) | big_p(c9) | (~big_q(c16)) | big_p(c11) | (~big_p(f1(elem!0))) | (~big_q(f4(elem!0)))))),
% 22.63/22.79      inference(monotonicity,[status(thm)],[454])).
% 22.63/22.79  tff(456,plain,
% 22.63/22.79      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f4(elem!0))) | big_q(c14) | big_q(c14) | (~big_p(f1(elem!0))) | (~big_q(c16)) | big_p(c11) | (~big_p(f1(elem!0))) | big_p(c9))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c14) | big_p(c9) | (~big_q(c16)) | big_p(c11) | (~big_p(f1(elem!0))) | (~big_q(f4(elem!0))))),
% 22.63/22.79      inference(transitivity,[status(thm)],[455, 453])).
% 22.63/22.79  tff(457,plain,
% 22.63/22.79      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f4(elem!0))) | big_q(c14) | big_q(c14) | (~big_p(f1(elem!0))) | (~big_q(c16)) | big_p(c11) | (~big_p(f1(elem!0))) | big_p(c9))),
% 22.63/22.79      inference(quant_inst,[status(thm)],[])).
% 22.63/22.79  tff(458,plain,
% 22.63/22.79      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c14) | big_p(c9) | (~big_q(c16)) | big_p(c11) | (~big_p(f1(elem!0))) | (~big_q(f4(elem!0)))),
% 22.63/22.79      inference(modus_ponens,[status(thm)],[457, 456])).
% 22.63/22.79  tff(459,plain,
% 22.63/22.79      ($false),
% 22.63/22.79      inference(unit_resolution,[status(thm)],[458, 373, 452, 429, 450, 344, 439, 363])).
% 22.63/22.79  tff(460,plain,(big_p(c3) | big_p(elem!0) | big_q(elem!0)), inference(lemma,lemma(discharge,[]))).
% 22.63/22.79  tff(461,plain,
% 22.63/22.79      (big_p(c3)),
% 22.63/22.79      inference(unit_resolution,[status(thm)],[460, 5, 3])).
% 22.63/22.79  tff(462,plain,
% 22.63/22.79      (~big_p(f1(c3))),
% 22.63/22.79      inference(unit_resolution,[status(thm)],[381, 1, 3, 5])).
% 22.63/22.79  tff(463,plain,
% 22.63/22.79      (big_q(f4(elem!0))),
% 22.63/22.79      inference(unit_resolution,[status(thm)],[428, 106, 3, 1, 126, 5])).
% 22.63/22.79  tff(464,plain,
% 22.63/22.79      (big_q(c8)),
% 22.63/22.79      inference(unit_resolution,[status(thm)],[144, 430, 3, 5, 88, 107])).
% 22.63/22.79  tff(465,plain,
% 22.63/22.79      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_p(c3) | (~big_q(c8)) | big_p(c9) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_q(f4(elem!0))) | big_p(f1(c3)))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | big_p(c3) | (~big_q(c8)) | big_p(c9) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_q(f4(elem!0))) | big_p(f1(c3)))),
% 22.63/22.79      inference(rewrite,[status(thm)],[])).
% 22.63/22.79  tff(466,plain,
% 22.63/22.79      (((~big_q(c8)) | big_p(elem!0) | big_q(f2(elem!0)) | big_p(c9) | big_q(f2(elem!0)) | (~big_q(f4(elem!0))) | big_p(f1(c3)) | big_p(c3)) <=> (big_p(c3) | (~big_q(c8)) | big_p(c9) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_q(f4(elem!0))) | big_p(f1(c3)))),
% 22.63/22.79      inference(rewrite,[status(thm)],[])).
% 22.63/22.79  tff(467,plain,
% 22.63/22.79      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | ((~big_q(c8)) | big_p(elem!0) | big_q(f2(elem!0)) | big_p(c9) | big_q(f2(elem!0)) | (~big_q(f4(elem!0))) | big_p(f1(c3)) | big_p(c3))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_p(c3) | (~big_q(c8)) | big_p(c9) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_q(f4(elem!0))) | big_p(f1(c3))))),
% 22.63/22.79      inference(monotonicity,[status(thm)],[466])).
% 22.63/22.79  tff(468,plain,
% 22.63/22.79      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | ((~big_q(c8)) | big_p(elem!0) | big_q(f2(elem!0)) | big_p(c9) | big_q(f2(elem!0)) | (~big_q(f4(elem!0))) | big_p(f1(c3)) | big_p(c3))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | big_p(c3) | (~big_q(c8)) | big_p(c9) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_q(f4(elem!0))) | big_p(f1(c3)))),
% 22.63/22.79      inference(transitivity,[status(thm)],[467, 465])).
% 22.63/22.79  tff(469,plain,
% 22.63/22.79      ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | ((~big_q(c8)) | big_p(elem!0) | big_q(f2(elem!0)) | big_p(c9) | big_q(f2(elem!0)) | (~big_q(f4(elem!0))) | big_p(f1(c3)) | big_p(c3))),
% 22.63/22.79      inference(quant_inst,[status(thm)],[])).
% 22.63/22.79  tff(470,plain,
% 22.63/22.79      ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | big_p(c3) | (~big_q(c8)) | big_p(c9) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_q(f4(elem!0))) | big_p(f1(c3))),
% 22.63/22.79      inference(modus_ponens,[status(thm)],[469, 468])).
% 22.63/22.79  tff(471,plain,
% 22.63/22.79      (big_p(c3) | (~big_q(c8)) | big_p(c9) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_q(f4(elem!0))) | big_p(f1(c3))),
% 22.63/22.79      inference(unit_resolution,[status(thm)],[470, 117])).
% 22.63/22.79  tff(472,plain,
% 22.63/22.79      ($false),
% 22.63/22.79      inference(unit_resolution,[status(thm)],[471, 464, 430, 3, 8, 107, 126, 106])).
% 22.63/22.79  tff(473,plain,((~big_q(f4(elem!0))) | big_p(elem!0) | big_q(f2(elem!0)) | big_p(c9) | big_p(c3) | big_p(f1(c3)) | big_q(elem!0) | big_p(f1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 22.63/22.79  tff(474,plain,
% 22.63/22.79      (big_p(c9)),
% 22.63/22.79      inference(unit_resolution,[status(thm)],[473, 463, 8, 3, 126, 106, 5, 88])).
% 22.63/22.79  tff(475,plain,
% 22.63/22.79      ($false),
% 22.63/22.79      inference(unit_resolution,[status(thm)],[436, 373, 5, 463, 3, 344, 474, 1])).
% 22.63/22.79  tff(476,plain,(big_p(f1(c3)) | big_q(elem!0) | big_p(elem!0) | big_p(c11) | big_q(f2(elem!0)) | big_p(c3) | big_p(f1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 22.63/22.79  tff(477,plain,
% 22.63/22.79      (big_p(f1(elem!0))),
% 22.63/22.79      inference(unit_resolution,[status(thm)],[476, 126, 3, 1, 8, 462, 5])).
% 22.63/22.79  tff(478,plain,
% 22.63/22.79      (big_q(f4(elem!0))),
% 22.63/22.79      inference(unit_resolution,[status(thm)],[428, 126, 3, 1, 462, 5])).
% 22.63/22.79  tff(479,plain,
% 22.63/22.79      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(f1(elem!0))) | (~big_q(f4(elem!0))))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(f1(elem!0))) | (~big_q(f4(elem!0))))),
% 22.63/22.79      inference(rewrite,[status(thm)],[])).
% 22.63/22.79  tff(480,plain,
% 22.63/22.79      (((~big_q(f4(elem!0))) | big_q(elem!0) | big_q(elem!0) | (~big_p(f1(elem!0))) | (~big_q(c16)) | big_p(c11) | (~big_p(f1(elem!0))) | big_p(elem!0)) <=> ((~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(f1(elem!0))) | (~big_q(f4(elem!0))))),
% 22.63/22.79      inference(rewrite,[status(thm)],[])).
% 22.63/22.79  tff(481,plain,
% 22.63/22.79      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f4(elem!0))) | big_q(elem!0) | big_q(elem!0) | (~big_p(f1(elem!0))) | (~big_q(c16)) | big_p(c11) | (~big_p(f1(elem!0))) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(f1(elem!0))) | (~big_q(f4(elem!0)))))),
% 22.63/22.79      inference(monotonicity,[status(thm)],[480])).
% 22.63/22.79  tff(482,plain,
% 22.63/22.79      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f4(elem!0))) | big_q(elem!0) | big_q(elem!0) | (~big_p(f1(elem!0))) | (~big_q(c16)) | big_p(c11) | (~big_p(f1(elem!0))) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(f1(elem!0))) | (~big_q(f4(elem!0))))),
% 22.63/22.79      inference(transitivity,[status(thm)],[481, 479])).
% 22.63/22.79  tff(483,plain,
% 22.63/22.79      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f4(elem!0))) | big_q(elem!0) | big_q(elem!0) | (~big_p(f1(elem!0))) | (~big_q(c16)) | big_p(c11) | (~big_p(f1(elem!0))) | big_p(elem!0))),
% 22.63/22.79      inference(quant_inst,[status(thm)],[])).
% 22.63/22.79  tff(484,plain,
% 22.63/22.79      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_p(f1(elem!0))) | (~big_q(f4(elem!0)))),
% 22.63/22.79      inference(modus_ponens,[status(thm)],[483, 482])).
% 22.63/22.79  tff(485,plain,
% 22.63/22.79      ($false),
% 22.63/22.79      inference(unit_resolution,[status(thm)],[484, 373, 5, 478, 3, 477, 344, 1])).
% 22.63/22.79  tff(486,plain,(big_p(c3) | big_q(elem!0) | big_p(elem!0) | big_p(c11) | big_q(f2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 22.63/22.79  tff(487,plain,
% 22.63/22.79      (big_p(c3)),
% 22.63/22.79      inference(unit_resolution,[status(thm)],[486, 1, 3, 5, 8])).
% 22.63/22.79  tff(488,plain,
% 22.63/22.79      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c3)) | (~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_p(c3)) | (~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0))),
% 22.63/22.80      inference(rewrite,[status(thm)],[])).
% 22.63/22.80  tff(489,plain,
% 22.63/22.80      (((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | (~big_p(c3)) | (~big_q(c16)) | big_p(c11) | (~big_p(c3)) | big_p(elem!0)) <=> ((~big_p(c3)) | (~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0))),
% 22.63/22.80      inference(rewrite,[status(thm)],[])).
% 22.63/22.80  tff(490,plain,
% 22.63/22.80      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | (~big_p(c3)) | (~big_q(c16)) | big_p(c11) | (~big_p(c3)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c3)) | (~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0)))),
% 22.63/22.80      inference(monotonicity,[status(thm)],[489])).
% 22.63/22.80  tff(491,plain,
% 22.63/22.80      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | (~big_p(c3)) | (~big_q(c16)) | big_p(c11) | (~big_p(c3)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_p(c3)) | (~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0))),
% 22.63/22.80      inference(transitivity,[status(thm)],[490, 488])).
% 22.63/22.80  tff(492,plain,
% 22.63/22.80      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | (~big_p(c3)) | (~big_q(c16)) | big_p(c11) | (~big_p(c3)) | big_p(elem!0))),
% 22.63/22.80      inference(quant_inst,[status(thm)],[])).
% 22.63/22.80  tff(493,plain,
% 22.63/22.80      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_p(c3)) | (~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0)),
% 22.63/22.80      inference(modus_ponens,[status(thm)],[492, 491])).
% 22.63/22.80  tff(494,plain,
% 22.63/22.80      ($false),
% 22.63/22.80      inference(unit_resolution,[status(thm)],[493, 373, 5, 3, 344, 1, 487])).
% 22.63/22.80  tff(495,plain,(big_p(c11) | big_q(elem!0) | big_p(elem!0) | big_q(f2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 22.63/22.80  tff(496,plain,
% 22.63/22.80      (big_q(f2(elem!0))),
% 22.63/22.80      inference(unit_resolution,[status(thm)],[495, 363, 3, 5])).
% 22.63/22.80  tff(497,plain,
% 22.63/22.80      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c3)) | (~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(f2(elem!0))))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_p(c3)) | (~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(f2(elem!0))))),
% 22.63/22.80      inference(rewrite,[status(thm)],[])).
% 22.63/22.80  tff(498,plain,
% 22.63/22.80      (((~big_q(f2(elem!0))) | big_q(elem!0) | big_q(elem!0) | (~big_p(c3)) | (~big_q(c16)) | big_p(c11) | (~big_p(c3)) | big_p(elem!0)) <=> ((~big_p(c3)) | (~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(f2(elem!0))))),
% 22.63/22.80      inference(rewrite,[status(thm)],[])).
% 22.63/22.80  tff(499,plain,
% 22.63/22.80      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(elem!0))) | big_q(elem!0) | big_q(elem!0) | (~big_p(c3)) | (~big_q(c16)) | big_p(c11) | (~big_p(c3)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c3)) | (~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(f2(elem!0)))))),
% 22.63/22.80      inference(monotonicity,[status(thm)],[498])).
% 22.63/22.80  tff(500,plain,
% 22.63/22.80      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(elem!0))) | big_q(elem!0) | big_q(elem!0) | (~big_p(c3)) | (~big_q(c16)) | big_p(c11) | (~big_p(c3)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_p(c3)) | (~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(f2(elem!0))))),
% 22.63/22.80      inference(transitivity,[status(thm)],[499, 497])).
% 22.63/22.80  tff(501,plain,
% 22.63/22.80      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(elem!0))) | big_q(elem!0) | big_q(elem!0) | (~big_p(c3)) | (~big_q(c16)) | big_p(c11) | (~big_p(c3)) | big_p(elem!0))),
% 22.63/22.80      inference(quant_inst,[status(thm)],[])).
% 22.63/22.80  tff(502,plain,
% 22.63/22.80      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_p(c3)) | (~big_q(c16)) | big_p(c11) | big_q(elem!0) | big_p(elem!0) | (~big_q(f2(elem!0)))),
% 22.63/22.80      inference(modus_ponens,[status(thm)],[501, 500])).
% 22.63/22.80  tff(503,plain,
% 22.63/22.80      ($false),
% 22.63/22.80      inference(unit_resolution,[status(thm)],[502, 373, 5, 3, 496, 344, 363, 461])).
% 22.63/22.80  tff(504,plain,(big_q(elem!0) | big_p(elem!0)), inference(lemma,lemma(discharge,[]))).
% 22.63/22.80  tff(505,plain,
% 22.63/22.80      (big_q(elem!0)),
% 22.63/22.80      inference(unit_resolution,[status(thm)],[504, 3])).
% 22.63/22.80  tff(506,assumption,(big_q(elem!0)), introduced(assumption)).
% 22.63/22.80  tff(507,plain,
% 22.63/22.80      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | big_p(c11) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9)))),
% 22.63/22.80      inference(rewrite,[status(thm)],[])).
% 22.63/22.80  tff(508,plain,
% 22.63/22.80      (((~big_q(elem!0)) | big_q(f2(elem!0)) | (~big_q(elem!0)) | (~big_p(c9)) | big_q(c16) | big_p(c11) | (~big_p(c9)) | big_p(elem!0)) <=> (big_q(c16) | big_p(c11) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9)))),
% 22.63/22.80      inference(rewrite,[status(thm)],[])).
% 22.63/22.80  tff(509,plain,
% 22.63/22.80      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f2(elem!0)) | (~big_q(elem!0)) | (~big_p(c9)) | big_q(c16) | big_p(c11) | (~big_p(c9)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | big_p(c11) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9))))),
% 22.63/22.80      inference(monotonicity,[status(thm)],[508])).
% 22.63/22.80  tff(510,plain,
% 22.63/22.80      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f2(elem!0)) | (~big_q(elem!0)) | (~big_p(c9)) | big_q(c16) | big_p(c11) | (~big_p(c9)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9)))),
% 22.63/22.80      inference(transitivity,[status(thm)],[509, 507])).
% 22.63/22.80  tff(511,plain,
% 22.63/22.80      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f2(elem!0)) | (~big_q(elem!0)) | (~big_p(c9)) | big_q(c16) | big_p(c11) | (~big_p(c9)) | big_p(elem!0))),
% 22.63/22.80      inference(quant_inst,[status(thm)],[])).
% 22.63/22.80  tff(512,plain,
% 22.63/22.80      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9))),
% 22.63/22.80      inference(modus_ponens,[status(thm)],[511, 510])).
% 22.63/22.80  tff(513,plain,
% 22.63/22.80      ($false),
% 22.63/22.80      inference(unit_resolution,[status(thm)],[512, 35, 506, 3, 8, 2, 1, 89])).
% 22.63/22.80  tff(514,plain,((~big_p(c9)) | (~big_q(elem!0)) | big_p(elem!0) | big_q(f2(elem!0)) | big_q(c16) | big_p(c11)), inference(lemma,lemma(discharge,[]))).
% 22.63/22.80  tff(515,plain,
% 22.63/22.80      (~big_p(c9)),
% 22.63/22.80      inference(unit_resolution,[status(thm)],[514, 8, 3, 506, 2, 1])).
% 22.63/22.80  tff(516,plain,
% 22.63/22.80      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | ((~big_q(c8)) | big_p(c9) | big_q(f2(elem!0)) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0)))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (~big_q(c8)) | big_p(c9) | big_q(f2(elem!0)) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0)))),
% 22.63/22.80      inference(rewrite,[status(thm)],[])).
% 22.63/22.80  tff(517,plain,
% 22.63/22.80      (((~big_q(c8)) | big_p(elem!0) | big_q(f2(elem!0)) | big_p(c9) | big_q(f2(elem!0)) | (~big_q(elem!0)) | big_p(f1(elem!0)) | big_p(elem!0)) <=> ((~big_q(c8)) | big_p(c9) | big_q(f2(elem!0)) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0)))),
% 22.63/22.80      inference(rewrite,[status(thm)],[])).
% 22.63/22.80  tff(518,plain,
% 22.63/22.80      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | ((~big_q(c8)) | big_p(elem!0) | big_q(f2(elem!0)) | big_p(c9) | big_q(f2(elem!0)) | (~big_q(elem!0)) | big_p(f1(elem!0)) | big_p(elem!0))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | ((~big_q(c8)) | big_p(c9) | big_q(f2(elem!0)) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0))))),
% 22.63/22.80      inference(monotonicity,[status(thm)],[517])).
% 22.63/22.80  tff(519,plain,
% 22.63/22.80      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | ((~big_q(c8)) | big_p(elem!0) | big_q(f2(elem!0)) | big_p(c9) | big_q(f2(elem!0)) | (~big_q(elem!0)) | big_p(f1(elem!0)) | big_p(elem!0))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (~big_q(c8)) | big_p(c9) | big_q(f2(elem!0)) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0)))),
% 22.63/22.80      inference(transitivity,[status(thm)],[518, 516])).
% 22.63/22.80  tff(520,plain,
% 22.63/22.80      ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | ((~big_q(c8)) | big_p(elem!0) | big_q(f2(elem!0)) | big_p(c9) | big_q(f2(elem!0)) | (~big_q(elem!0)) | big_p(f1(elem!0)) | big_p(elem!0))),
% 22.63/22.80      inference(quant_inst,[status(thm)],[])).
% 22.63/22.80  tff(521,plain,
% 22.63/22.80      ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (~big_q(c8)) | big_p(c9) | big_q(f2(elem!0)) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0))),
% 22.63/22.80      inference(modus_ponens,[status(thm)],[520, 519])).
% 22.63/22.80  tff(522,plain,
% 22.63/22.80      ((~big_q(c8)) | big_p(c9)),
% 22.63/22.80      inference(unit_resolution,[status(thm)],[521, 117, 506, 3, 88, 8])).
% 22.63/22.80  tff(523,plain,
% 22.63/22.80      (~big_q(c8)),
% 22.63/22.80      inference(unit_resolution,[status(thm)],[522, 515])).
% 22.63/22.80  tff(524,plain,
% 22.63/22.80      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_q(c8) | big_p(c9) | big_q(f2(elem!0)) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0)))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | big_q(c8) | big_p(c9) | big_q(f2(elem!0)) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0)))),
% 22.63/22.80      inference(rewrite,[status(thm)],[])).
% 22.63/22.80  tff(525,plain,
% 22.63/22.80      ((big_q(c8) | big_p(elem!0) | (~big_q(elem!0)) | big_p(c9) | big_q(f2(elem!0)) | (~big_q(elem!0)) | big_p(f1(elem!0)) | big_p(elem!0)) <=> (big_q(c8) | big_p(c9) | big_q(f2(elem!0)) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0)))),
% 22.63/22.80      inference(rewrite,[status(thm)],[])).
% 22.63/22.80  tff(526,plain,
% 22.63/22.80      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_q(c8) | big_p(elem!0) | (~big_q(elem!0)) | big_p(c9) | big_q(f2(elem!0)) | (~big_q(elem!0)) | big_p(f1(elem!0)) | big_p(elem!0))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_q(c8) | big_p(c9) | big_q(f2(elem!0)) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0))))),
% 22.63/22.80      inference(monotonicity,[status(thm)],[525])).
% 22.63/22.80  tff(527,plain,
% 22.63/22.80      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_q(c8) | big_p(elem!0) | (~big_q(elem!0)) | big_p(c9) | big_q(f2(elem!0)) | (~big_q(elem!0)) | big_p(f1(elem!0)) | big_p(elem!0))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | big_q(c8) | big_p(c9) | big_q(f2(elem!0)) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0)))),
% 22.63/22.80      inference(transitivity,[status(thm)],[526, 524])).
% 22.63/22.80  tff(528,plain,
% 22.63/22.80      ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_q(c8) | big_p(elem!0) | (~big_q(elem!0)) | big_p(c9) | big_q(f2(elem!0)) | (~big_q(elem!0)) | big_p(f1(elem!0)) | big_p(elem!0))),
% 22.63/22.80      inference(quant_inst,[status(thm)],[])).
% 22.63/22.80  tff(529,plain,
% 22.63/22.80      ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | big_q(c8) | big_p(c9) | big_q(f2(elem!0)) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0))),
% 22.63/22.80      inference(modus_ponens,[status(thm)],[528, 527])).
% 22.63/22.80  tff(530,plain,
% 22.63/22.80      (big_q(c8) | big_p(c9)),
% 22.63/22.80      inference(unit_resolution,[status(thm)],[529, 137, 506, 3, 88, 8])).
% 22.63/22.80  tff(531,plain,
% 22.63/22.80      ($false),
% 22.63/22.80      inference(unit_resolution,[status(thm)],[530, 523, 515])).
% 22.63/22.80  tff(532,plain,(big_q(f2(elem!0)) | (~big_q(elem!0)) | big_p(elem!0) | big_p(f1(elem!0)) | big_q(c16) | big_p(c11)), inference(lemma,lemma(discharge,[]))).
% 22.63/22.80  tff(533,plain,
% 22.63/22.80      (big_q(f2(elem!0))),
% 22.63/22.80      inference(unit_resolution,[status(thm)],[532, 1, 3, 88, 2, 506])).
% 22.63/22.80  tff(534,assumption,(~big_q(c7)), introduced(assumption)).
% 22.63/22.80  tff(535,plain,
% 22.63/22.80      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | ((~big_q(c8)) | big_q(c7) | big_p(c9) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0)))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (~big_q(c8)) | big_q(c7) | big_p(c9) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0)))),
% 22.63/22.80      inference(rewrite,[status(thm)],[])).
% 22.63/22.80  tff(536,plain,
% 22.63/22.80      (((~big_q(c8)) | big_p(elem!0) | big_q(c7) | big_p(c9) | big_q(c7) | (~big_q(elem!0)) | big_p(f1(elem!0)) | big_p(elem!0)) <=> ((~big_q(c8)) | big_q(c7) | big_p(c9) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0)))),
% 22.63/22.80      inference(rewrite,[status(thm)],[])).
% 22.63/22.80  tff(537,plain,
% 22.63/22.80      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | ((~big_q(c8)) | big_p(elem!0) | big_q(c7) | big_p(c9) | big_q(c7) | (~big_q(elem!0)) | big_p(f1(elem!0)) | big_p(elem!0))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | ((~big_q(c8)) | big_q(c7) | big_p(c9) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0))))),
% 22.63/22.80      inference(monotonicity,[status(thm)],[536])).
% 22.63/22.80  tff(538,plain,
% 22.63/22.80      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | ((~big_q(c8)) | big_p(elem!0) | big_q(c7) | big_p(c9) | big_q(c7) | (~big_q(elem!0)) | big_p(f1(elem!0)) | big_p(elem!0))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (~big_q(c8)) | big_q(c7) | big_p(c9) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0)))),
% 22.63/22.80      inference(transitivity,[status(thm)],[537, 535])).
% 22.63/22.80  tff(539,plain,
% 22.63/22.80      ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | ((~big_q(c8)) | big_p(elem!0) | big_q(c7) | big_p(c9) | big_q(c7) | (~big_q(elem!0)) | big_p(f1(elem!0)) | big_p(elem!0))),
% 22.63/22.80      inference(quant_inst,[status(thm)],[])).
% 22.63/22.80  tff(540,plain,
% 22.63/22.80      ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : ((~big_q(c8)) | big_p(V) | big_q(Z) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (~big_q(c8)) | big_q(c7) | big_p(c9) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0))),
% 22.63/22.80      inference(modus_ponens,[status(thm)],[539, 538])).
% 22.63/22.80  tff(541,plain,
% 22.63/22.80      ((~big_q(c8)) | big_p(c9)),
% 22.63/22.80      inference(unit_resolution,[status(thm)],[540, 117, 506, 3, 534, 88])).
% 22.63/22.80  tff(542,plain,
% 22.63/22.80      (~big_q(c8)),
% 22.63/22.80      inference(unit_resolution,[status(thm)],[541, 107])).
% 22.63/22.80  tff(543,plain,
% 22.63/22.80      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_q(c7) | big_q(c8) | big_p(c9) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0)))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | big_q(c7) | big_q(c8) | big_p(c9) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0)))),
% 22.63/22.80      inference(rewrite,[status(thm)],[])).
% 22.63/22.80  tff(544,plain,
% 22.63/22.80      ((big_q(c8) | big_p(elem!0) | (~big_q(elem!0)) | big_p(c9) | big_q(c7) | (~big_q(elem!0)) | big_p(f1(elem!0)) | big_p(elem!0)) <=> (big_q(c7) | big_q(c8) | big_p(c9) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0)))),
% 22.63/22.80      inference(rewrite,[status(thm)],[])).
% 22.63/22.80  tff(545,plain,
% 22.63/22.80      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_q(c8) | big_p(elem!0) | (~big_q(elem!0)) | big_p(c9) | big_q(c7) | (~big_q(elem!0)) | big_p(f1(elem!0)) | big_p(elem!0))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_q(c7) | big_q(c8) | big_p(c9) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0))))),
% 22.63/22.80      inference(monotonicity,[status(thm)],[544])).
% 22.63/22.80  tff(546,plain,
% 22.63/22.80      (((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_q(c8) | big_p(elem!0) | (~big_q(elem!0)) | big_p(c9) | big_q(c7) | (~big_q(elem!0)) | big_p(f1(elem!0)) | big_p(elem!0))) <=> ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | big_q(c7) | big_q(c8) | big_p(c9) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0)))),
% 22.63/22.80      inference(transitivity,[status(thm)],[545, 543])).
% 22.63/22.80  tff(547,plain,
% 22.63/22.80      ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | (big_q(c8) | big_p(elem!0) | (~big_q(elem!0)) | big_p(c9) | big_q(c7) | (~big_q(elem!0)) | big_p(f1(elem!0)) | big_p(elem!0))),
% 22.63/22.80      inference(quant_inst,[status(thm)],[])).
% 22.63/22.80  tff(548,plain,
% 22.63/22.80      ((~![V: $i, Z: $i, U: $i, X: $i, X5: $i] : (big_q(c8) | big_p(V) | (~big_q(Z)) | big_p(c9) | big_q(X5) | (~big_q(U)) | big_p(f1(X)) | big_p(X))) | big_q(c7) | big_q(c8) | big_p(c9) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0))),
% 22.63/22.80      inference(modus_ponens,[status(thm)],[547, 546])).
% 22.63/22.80  tff(549,plain,
% 22.63/22.80      (big_q(c8) | big_p(c9)),
% 22.63/22.80      inference(unit_resolution,[status(thm)],[548, 137, 506, 3, 534, 88])).
% 22.63/22.80  tff(550,plain,
% 22.63/22.80      ($false),
% 22.63/22.80      inference(unit_resolution,[status(thm)],[549, 542, 107])).
% 22.63/22.80  tff(551,plain,(big_p(c9) | (~big_q(elem!0)) | big_p(elem!0) | big_q(c7) | big_p(f1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 22.63/22.80  tff(552,plain,
% 22.63/22.80      (big_p(c9)),
% 22.63/22.80      inference(unit_resolution,[status(thm)],[551, 534, 3, 506, 88])).
% 22.63/22.80  tff(553,plain,
% 22.63/22.80      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c7) | big_q(c16) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c7) | big_q(c16) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9)))),
% 22.63/22.80      inference(rewrite,[status(thm)],[])).
% 22.63/22.80  tff(554,plain,
% 22.63/22.80      (((~big_q(elem!0)) | big_q(c7) | (~big_q(elem!0)) | (~big_p(c9)) | big_q(c16) | big_p(c11) | (~big_p(c9)) | big_p(elem!0)) <=> (big_q(c7) | big_q(c16) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9)))),
% 22.63/22.80      inference(rewrite,[status(thm)],[])).
% 22.63/22.80  tff(555,plain,
% 22.63/22.80      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c7) | (~big_q(elem!0)) | (~big_p(c9)) | big_q(c16) | big_p(c11) | (~big_p(c9)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c7) | big_q(c16) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9))))),
% 22.63/22.80      inference(monotonicity,[status(thm)],[554])).
% 22.63/22.80  tff(556,plain,
% 22.63/22.80      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c7) | (~big_q(elem!0)) | (~big_p(c9)) | big_q(c16) | big_p(c11) | (~big_p(c9)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c7) | big_q(c16) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9)))),
% 22.63/22.80      inference(transitivity,[status(thm)],[555, 553])).
% 22.63/22.80  tff(557,plain,
% 22.63/22.80      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c7) | (~big_q(elem!0)) | (~big_p(c9)) | big_q(c16) | big_p(c11) | (~big_p(c9)) | big_p(elem!0))),
% 22.63/22.80      inference(quant_inst,[status(thm)],[])).
% 22.63/22.80  tff(558,plain,
% 22.63/22.80      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c7) | big_q(c16) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9))),
% 22.63/22.80      inference(modus_ponens,[status(thm)],[557, 556])).
% 22.63/22.80  tff(559,plain,
% 22.63/22.80      (big_q(c16) | big_p(c11)),
% 22.63/22.80      inference(unit_resolution,[status(thm)],[558, 35, 506, 3, 534, 89])).
% 22.63/22.81  tff(560,plain,
% 22.63/22.81      (big_p(c11)),
% 22.63/22.81      inference(unit_resolution,[status(thm)],[559, 2])).
% 22.63/22.81  tff(561,plain,
% 22.63/22.81      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c7) | big_q(c16) | (~big_p(c11)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c7) | big_q(c16) | (~big_p(c11)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9)))),
% 22.63/22.81      inference(rewrite,[status(thm)],[])).
% 22.63/22.81  tff(562,plain,
% 22.63/22.81      (((~big_q(elem!0)) | big_q(c7) | (~big_q(elem!0)) | big_p(elem!0) | big_q(c16) | (~big_p(c11)) | (~big_p(c9)) | big_p(elem!0)) <=> (big_q(c7) | big_q(c16) | (~big_p(c11)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9)))),
% 22.63/22.81      inference(rewrite,[status(thm)],[])).
% 22.63/22.81  tff(563,plain,
% 22.63/22.81      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c7) | (~big_q(elem!0)) | big_p(elem!0) | big_q(c16) | (~big_p(c11)) | (~big_p(c9)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c7) | big_q(c16) | (~big_p(c11)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9))))),
% 22.63/22.81      inference(monotonicity,[status(thm)],[562])).
% 22.63/22.81  tff(564,plain,
% 22.63/22.81      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c7) | (~big_q(elem!0)) | big_p(elem!0) | big_q(c16) | (~big_p(c11)) | (~big_p(c9)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c7) | big_q(c16) | (~big_p(c11)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9)))),
% 22.63/22.81      inference(transitivity,[status(thm)],[563, 561])).
% 22.63/22.81  tff(565,plain,
% 22.63/22.81      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c7) | (~big_q(elem!0)) | big_p(elem!0) | big_q(c16) | (~big_p(c11)) | (~big_p(c9)) | big_p(elem!0))),
% 22.63/22.81      inference(quant_inst,[status(thm)],[])).
% 22.63/22.81  tff(566,plain,
% 22.63/22.81      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c7) | big_q(c16) | (~big_p(c11)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9))),
% 22.63/22.81      inference(modus_ponens,[status(thm)],[565, 564])).
% 22.63/22.81  tff(567,plain,
% 22.63/22.81      (big_q(c16) | (~big_p(c11))),
% 22.63/22.81      inference(unit_resolution,[status(thm)],[566, 52, 506, 3, 534, 89])).
% 22.63/22.81  tff(568,plain,
% 22.63/22.81      ($false),
% 22.63/22.81      inference(unit_resolution,[status(thm)],[567, 560, 2])).
% 22.63/22.81  tff(569,plain,(big_q(c16) | (~big_q(elem!0)) | big_p(elem!0) | big_q(c7) | (~big_p(c9))), inference(lemma,lemma(discharge,[]))).
% 22.63/22.81  tff(570,plain,
% 22.63/22.81      (big_q(c16)),
% 22.63/22.81      inference(unit_resolution,[status(thm)],[569, 534, 3, 506, 552])).
% 22.63/22.81  tff(571,plain,
% 22.63/22.81      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c7) | (~big_q(c16)) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c7) | (~big_q(c16)) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9)))),
% 22.63/22.81      inference(rewrite,[status(thm)],[])).
% 22.63/22.81  tff(572,plain,
% 22.63/22.81      (((~big_q(elem!0)) | big_q(c7) | big_q(c7) | (~big_p(c9)) | (~big_q(c16)) | big_p(c11) | (~big_p(c9)) | big_p(elem!0)) <=> (big_q(c7) | (~big_q(c16)) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9)))),
% 22.63/22.81      inference(rewrite,[status(thm)],[])).
% 22.63/22.81  tff(573,plain,
% 22.63/22.81      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c7) | big_q(c7) | (~big_p(c9)) | (~big_q(c16)) | big_p(c11) | (~big_p(c9)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c7) | (~big_q(c16)) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9))))),
% 22.63/22.81      inference(monotonicity,[status(thm)],[572])).
% 22.63/22.81  tff(574,plain,
% 22.63/22.81      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c7) | big_q(c7) | (~big_p(c9)) | (~big_q(c16)) | big_p(c11) | (~big_p(c9)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c7) | (~big_q(c16)) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9)))),
% 22.63/22.81      inference(transitivity,[status(thm)],[573, 571])).
% 22.63/22.81  tff(575,plain,
% 22.63/22.81      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c7) | big_q(c7) | (~big_p(c9)) | (~big_q(c16)) | big_p(c11) | (~big_p(c9)) | big_p(elem!0))),
% 22.63/22.81      inference(quant_inst,[status(thm)],[])).
% 22.63/22.81  tff(576,plain,
% 22.63/22.81      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c7) | (~big_q(c16)) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9))),
% 22.63/22.81      inference(modus_ponens,[status(thm)],[575, 574])).
% 22.63/22.81  tff(577,plain,
% 22.63/22.81      ((~big_q(c16)) | big_p(c11)),
% 22.63/22.81      inference(unit_resolution,[status(thm)],[576, 373, 506, 3, 534, 552])).
% 22.63/22.81  tff(578,plain,
% 22.63/22.81      (big_p(c11)),
% 22.63/22.81      inference(unit_resolution,[status(thm)],[577, 570])).
% 22.63/22.81  tff(579,plain,
% 22.63/22.81      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (big_q(c7) | (~big_p(c11)) | (~big_q(c16)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | big_q(c7) | (~big_p(c11)) | (~big_q(c16)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9)))),
% 22.63/22.81      inference(rewrite,[status(thm)],[])).
% 22.63/22.81  tff(580,plain,
% 22.63/22.81      (((~big_q(elem!0)) | big_q(c7) | big_q(c7) | big_p(elem!0) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c9)) | big_p(elem!0)) <=> (big_q(c7) | (~big_p(c11)) | (~big_q(c16)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9)))),
% 22.63/22.81      inference(rewrite,[status(thm)],[])).
% 22.63/22.81  tff(581,plain,
% 22.63/22.81      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c7) | big_q(c7) | big_p(elem!0) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c9)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (big_q(c7) | (~big_p(c11)) | (~big_q(c16)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9))))),
% 22.63/22.81      inference(monotonicity,[status(thm)],[580])).
% 22.63/22.81  tff(582,plain,
% 22.63/22.81      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c7) | big_q(c7) | big_p(elem!0) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c9)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | big_q(c7) | (~big_p(c11)) | (~big_q(c16)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9)))),
% 22.63/22.81      inference(transitivity,[status(thm)],[581, 579])).
% 22.63/22.81  tff(583,plain,
% 22.63/22.81      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c7) | big_q(c7) | big_p(elem!0) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c9)) | big_p(elem!0))),
% 22.63/22.81      inference(quant_inst,[status(thm)],[])).
% 22.63/22.81  tff(584,plain,
% 22.63/22.81      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | big_q(c7) | (~big_p(c11)) | (~big_q(c16)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9))),
% 22.63/22.81      inference(modus_ponens,[status(thm)],[583, 582])).
% 22.63/22.81  tff(585,plain,
% 22.63/22.81      ((~big_p(c11)) | (~big_q(c16))),
% 22.63/22.81      inference(unit_resolution,[status(thm)],[584, 354, 506, 3, 534, 552])).
% 22.63/22.81  tff(586,plain,
% 22.63/22.81      ($false),
% 22.63/22.81      inference(unit_resolution,[status(thm)],[585, 578, 570])).
% 22.63/22.81  tff(587,plain,(big_q(c7) | (~big_q(elem!0)) | big_p(elem!0) | big_p(f1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 22.63/22.81  tff(588,plain,
% 22.63/22.81      (big_q(c7)),
% 22.63/22.81      inference(unit_resolution,[status(thm)],[587, 506, 3, 88])).
% 22.63/22.81  tff(589,plain,
% 22.63/22.81      (^[W: $i, V: $i, U: $i, X: $i] : refl((big_p(c6) | (~big_q(c7)) | (~big_q(f2(W))) | big_p(X) | (~big_q(W)) | big_p(V) | (~big_q(U)) | big_p(f1(X))) <=> (big_p(c6) | (~big_q(c7)) | (~big_q(f2(W))) | big_p(X) | (~big_q(W)) | big_p(V) | (~big_q(U)) | big_p(f1(X))))),
% 22.63/22.81      inference(bind,[status(th)],[])).
% 22.63/22.81  tff(590,plain,
% 22.63/22.81      (![W: $i, V: $i, U: $i, X: $i] : (big_p(c6) | (~big_q(c7)) | (~big_q(f2(W))) | big_p(X) | (~big_q(W)) | big_p(V) | (~big_q(U)) | big_p(f1(X))) <=> ![W: $i, V: $i, U: $i, X: $i] : (big_p(c6) | (~big_q(c7)) | (~big_q(f2(W))) | big_p(X) | (~big_q(W)) | big_p(V) | (~big_q(U)) | big_p(f1(X)))),
% 22.63/22.81      inference(quant_intro,[status(thm)],[589])).
% 22.63/22.81  tff(591,plain,
% 22.63/22.81      (![W: $i, V: $i, U: $i, X: $i] : (big_p(c6) | (~big_q(c7)) | (~big_q(f2(W))) | big_p(X) | (~big_q(W)) | big_p(V) | (~big_q(U)) | big_p(f1(X))) <=> ![W: $i, V: $i, U: $i, X: $i] : (big_p(c6) | (~big_q(c7)) | (~big_q(f2(W))) | big_p(X) | (~big_q(W)) | big_p(V) | (~big_q(U)) | big_p(f1(X)))),
% 22.63/22.81      inference(rewrite,[status(thm)],[])).
% 22.63/22.81  tff(592,plain,
% 22.63/22.81      (^[W: $i, V: $i, U: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(X) | big_p(f1(X))) | (~big_q(U))) <=> (big_p(X) | (~big_q(U)) | big_p(f1(X)))), ((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) <=> ((big_p(X) | (~big_q(U)) | big_p(f1(X))) | big_p(V)))), rewrite(((big_p(X) | (~big_q(U)) | big_p(f1(X))) | big_p(V)) <=> (big_p(X) | big_p(V) | (~big_q(U)) | big_p(f1(X)))), ((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) <=> (big_p(X) | big_p(V) | (~big_q(U)) | big_p(f1(X))))), (((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) | (~big_q(f2(W)))) <=> ((big_p(X) | big_p(V) | (~big_q(U)) | big_p(f1(X))) | (~big_q(f2(W)))))), rewrite(((big_p(X) | big_p(V) | (~big_q(U)) | big_p(f1(X))) | (~big_q(f2(W)))) <=> ((~big_q(f2(W))) | big_p(X) | big_p(V) | (~big_q(U)) | big_p(f1(X)))), (((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) | (~big_q(f2(W)))) <=> ((~big_q(f2(W))) | big_p(X) | big_p(V) | (~big_q(U)) | big_p(f1(X))))), ((((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) | (~big_q(f2(W)))) | (~big_q(W))) <=> (((~big_q(f2(W))) | big_p(X) | big_p(V) | (~big_q(U)) | big_p(f1(X))) | (~big_q(W))))), rewrite((((~big_q(f2(W))) | big_p(X) | big_p(V) | (~big_q(U)) | big_p(f1(X))) | (~big_q(W))) <=> ((~big_q(f2(W))) | big_p(X) | (~big_q(W)) | big_p(V) | (~big_q(U)) | big_p(f1(X)))), ((((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) | (~big_q(f2(W)))) | (~big_q(W))) <=> ((~big_q(f2(W))) | big_p(X) | (~big_q(W)) | big_p(V) | (~big_q(U)) | big_p(f1(X))))), (((((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) | (~big_q(f2(W)))) | (~big_q(W))) | big_p(c6)) <=> (((~big_q(f2(W))) | big_p(X) | (~big_q(W)) | big_p(V) | (~big_q(U)) | big_p(f1(X))) | big_p(c6)))), rewrite((((~big_q(f2(W))) | big_p(X) | (~big_q(W)) | big_p(V) | (~big_q(U)) | big_p(f1(X))) | big_p(c6)) <=> (big_p(c6) | (~big_q(f2(W))) | big_p(X) | (~big_q(W)) | big_p(V) | (~big_q(U)) | big_p(f1(X)))), (((((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) | (~big_q(f2(W)))) | (~big_q(W))) | big_p(c6)) <=> (big_p(c6) | (~big_q(f2(W))) | big_p(X) | (~big_q(W)) | big_p(V) | (~big_q(U)) | big_p(f1(X))))), ((((((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) | (~big_q(f2(W)))) | (~big_q(W))) | big_p(c6)) | (~big_q(c7))) <=> ((big_p(c6) | (~big_q(f2(W))) | big_p(X) | (~big_q(W)) | big_p(V) | (~big_q(U)) | big_p(f1(X))) | (~big_q(c7))))), rewrite(((big_p(c6) | (~big_q(f2(W))) | big_p(X) | (~big_q(W)) | big_p(V) | (~big_q(U)) | big_p(f1(X))) | (~big_q(c7))) <=> (big_p(c6) | (~big_q(c7)) | (~big_q(f2(W))) | big_p(X) | (~big_q(W)) | big_p(V) | (~big_q(U)) | big_p(f1(X)))), ((((((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) | (~big_q(f2(W)))) | (~big_q(W))) | big_p(c6)) | (~big_q(c7))) <=> (big_p(c6) | (~big_q(c7)) | (~big_q(f2(W))) | big_p(X) | (~big_q(W)) | big_p(V) | (~big_q(U)) | big_p(f1(X)))))),
% 22.63/22.81      inference(bind,[status(th)],[])).
% 22.63/22.81  tff(593,plain,
% 22.63/22.81      (![W: $i, V: $i, U: $i, X: $i] : (((((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) | (~big_q(f2(W)))) | (~big_q(W))) | big_p(c6)) | (~big_q(c7))) <=> ![W: $i, V: $i, U: $i, X: $i] : (big_p(c6) | (~big_q(c7)) | (~big_q(f2(W))) | big_p(X) | (~big_q(W)) | big_p(V) | (~big_q(U)) | big_p(f1(X)))),
% 22.63/22.81      inference(quant_intro,[status(thm)],[592])).
% 22.63/22.81  tff(594,axiom,(![W: $i, V: $i, U: $i, X: $i] : (((((((big_p(X) | big_p(f1(X))) | (~big_q(U))) | big_p(V)) | (~big_q(f2(W)))) | (~big_q(W))) | big_p(c6)) | (~big_q(c7)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_4')).
% 22.63/22.81  tff(595,plain,
% 22.63/22.81      (![W: $i, V: $i, U: $i, X: $i] : (big_p(c6) | (~big_q(c7)) | (~big_q(f2(W))) | big_p(X) | (~big_q(W)) | big_p(V) | (~big_q(U)) | big_p(f1(X)))),
% 22.63/22.81      inference(modus_ponens,[status(thm)],[594, 593])).
% 22.63/22.81  tff(596,plain,
% 22.63/22.81      (![W: $i, V: $i, U: $i, X: $i] : (big_p(c6) | (~big_q(c7)) | (~big_q(f2(W))) | big_p(X) | (~big_q(W)) | big_p(V) | (~big_q(U)) | big_p(f1(X)))),
% 22.63/22.81      inference(modus_ponens,[status(thm)],[595, 591])).
% 22.63/22.81  tff(597,plain,(
% 22.63/22.81      ![W: $i, V: $i, U: $i, X: $i] : (big_p(c6) | (~big_q(c7)) | (~big_q(f2(W))) | big_p(X) | (~big_q(W)) | big_p(V) | (~big_q(U)) | big_p(f1(X)))),
% 22.63/22.81      inference(skolemize,[status(sab)],[596])).
% 22.63/22.81  tff(598,plain,
% 22.63/22.81      (![W: $i, V: $i, U: $i, X: $i] : (big_p(c6) | (~big_q(c7)) | (~big_q(f2(W))) | big_p(X) | (~big_q(W)) | big_p(V) | (~big_q(U)) | big_p(f1(X)))),
% 22.63/22.81      inference(modus_ponens,[status(thm)],[597, 590])).
% 22.63/22.81  tff(599,plain,
% 22.63/22.81      (((~![W: $i, V: $i, U: $i, X: $i] : (big_p(c6) | (~big_q(c7)) | (~big_q(f2(W))) | big_p(X) | (~big_q(W)) | big_p(V) | (~big_q(U)) | big_p(f1(X)))) | (big_p(c6) | (~big_q(c7)) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_q(f2(elem!0))))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (big_p(c6) | (~big_q(c7)) | (~big_q(f2(W))) | big_p(X) | (~big_q(W)) | big_p(V) | (~big_q(U)) | big_p(f1(X)))) | big_p(c6) | (~big_q(c7)) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_q(f2(elem!0))))),
% 22.63/22.81      inference(rewrite,[status(thm)],[])).
% 22.63/22.81  tff(600,plain,
% 22.63/22.81      ((big_p(c6) | (~big_q(c7)) | (~big_q(f2(elem!0))) | big_p(elem!0) | (~big_q(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | big_p(f1(elem!0))) <=> (big_p(c6) | (~big_q(c7)) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_q(f2(elem!0))))),
% 22.63/22.81      inference(rewrite,[status(thm)],[])).
% 22.63/22.81  tff(601,plain,
% 22.63/22.81      (((~![W: $i, V: $i, U: $i, X: $i] : (big_p(c6) | (~big_q(c7)) | (~big_q(f2(W))) | big_p(X) | (~big_q(W)) | big_p(V) | (~big_q(U)) | big_p(f1(X)))) | (big_p(c6) | (~big_q(c7)) | (~big_q(f2(elem!0))) | big_p(elem!0) | (~big_q(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | big_p(f1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (big_p(c6) | (~big_q(c7)) | (~big_q(f2(W))) | big_p(X) | (~big_q(W)) | big_p(V) | (~big_q(U)) | big_p(f1(X)))) | (big_p(c6) | (~big_q(c7)) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_q(f2(elem!0)))))),
% 22.63/22.81      inference(monotonicity,[status(thm)],[600])).
% 22.63/22.81  tff(602,plain,
% 22.63/22.81      (((~![W: $i, V: $i, U: $i, X: $i] : (big_p(c6) | (~big_q(c7)) | (~big_q(f2(W))) | big_p(X) | (~big_q(W)) | big_p(V) | (~big_q(U)) | big_p(f1(X)))) | (big_p(c6) | (~big_q(c7)) | (~big_q(f2(elem!0))) | big_p(elem!0) | (~big_q(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | big_p(f1(elem!0)))) <=> ((~![W: $i, V: $i, U: $i, X: $i] : (big_p(c6) | (~big_q(c7)) | (~big_q(f2(W))) | big_p(X) | (~big_q(W)) | big_p(V) | (~big_q(U)) | big_p(f1(X)))) | big_p(c6) | (~big_q(c7)) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_q(f2(elem!0))))),
% 22.63/22.81      inference(transitivity,[status(thm)],[601, 599])).
% 22.63/22.81  tff(603,plain,
% 22.63/22.81      ((~![W: $i, V: $i, U: $i, X: $i] : (big_p(c6) | (~big_q(c7)) | (~big_q(f2(W))) | big_p(X) | (~big_q(W)) | big_p(V) | (~big_q(U)) | big_p(f1(X)))) | (big_p(c6) | (~big_q(c7)) | (~big_q(f2(elem!0))) | big_p(elem!0) | (~big_q(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | big_p(f1(elem!0)))),
% 22.63/22.81      inference(quant_inst,[status(thm)],[])).
% 22.63/22.81  tff(604,plain,
% 22.63/22.81      ((~![W: $i, V: $i, U: $i, X: $i] : (big_p(c6) | (~big_q(c7)) | (~big_q(f2(W))) | big_p(X) | (~big_q(W)) | big_p(V) | (~big_q(U)) | big_p(f1(X)))) | big_p(c6) | (~big_q(c7)) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_q(f2(elem!0)))),
% 22.63/22.81      inference(modus_ponens,[status(thm)],[603, 602])).
% 22.63/22.81  tff(605,plain,
% 22.63/22.81      (big_p(c6) | (~big_q(c7)) | big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_q(f2(elem!0)))),
% 22.63/22.81      inference(unit_resolution,[status(thm)],[604, 598])).
% 22.63/22.81  tff(606,plain,
% 22.63/22.81      (big_p(c6)),
% 22.63/22.81      inference(unit_resolution,[status(thm)],[605, 533, 3, 506, 88, 588])).
% 22.63/22.81  tff(607,plain,
% 22.63/22.81      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_q(f2(elem!0))) | (~big_p(c6)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_q(f2(elem!0))) | (~big_p(c6)))),
% 22.63/22.81      inference(rewrite,[status(thm)],[])).
% 22.63/22.81  tff(608,plain,
% 22.63/22.81      (((~big_q(elem!0)) | big_q(c16) | (~big_q(f2(elem!0))) | (~big_p(c6)) | big_q(c16) | big_p(c11) | (~big_p(c6)) | big_p(elem!0)) <=> (big_q(c16) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_q(f2(elem!0))) | (~big_p(c6)))),
% 22.63/22.81      inference(rewrite,[status(thm)],[])).
% 22.63/22.81  tff(609,plain,
% 22.63/22.81      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c16) | (~big_q(f2(elem!0))) | (~big_p(c6)) | big_q(c16) | big_p(c11) | (~big_p(c6)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_q(f2(elem!0))) | (~big_p(c6))))),
% 22.63/22.81      inference(monotonicity,[status(thm)],[608])).
% 22.63/22.81  tff(610,plain,
% 22.63/22.81      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c16) | (~big_q(f2(elem!0))) | (~big_p(c6)) | big_q(c16) | big_p(c11) | (~big_p(c6)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_q(f2(elem!0))) | (~big_p(c6)))),
% 22.63/22.81      inference(transitivity,[status(thm)],[609, 607])).
% 22.63/22.81  tff(611,plain,
% 22.63/22.81      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c16) | (~big_q(f2(elem!0))) | (~big_p(c6)) | big_q(c16) | big_p(c11) | (~big_p(c6)) | big_p(elem!0))),
% 22.63/22.81      inference(quant_inst,[status(thm)],[])).
% 22.63/22.81  tff(612,plain,
% 22.63/22.81      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_q(f2(elem!0))) | (~big_p(c6))),
% 22.63/22.81      inference(modus_ponens,[status(thm)],[611, 610])).
% 22.63/22.81  tff(613,plain,
% 22.63/22.81      ($false),
% 22.63/22.81      inference(unit_resolution,[status(thm)],[612, 35, 506, 3, 606, 533, 2, 1])).
% 22.63/22.81  tff(614,plain,(big_p(c11) | (~big_q(elem!0)) | big_p(elem!0) | big_q(c16) | big_p(f1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 22.63/22.81  tff(615,plain,
% 22.63/22.81      (big_p(c11)),
% 22.63/22.81      inference(unit_resolution,[status(thm)],[614, 2, 3, 506, 88])).
% 22.63/22.81  tff(616,plain,
% 22.63/22.81      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | (~big_p(c11)) | big_p(elem!0) | (~big_q(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_p(elem!0) | (~big_q(elem!0)))),
% 22.63/22.81      inference(rewrite,[status(thm)],[])).
% 22.63/22.81  tff(617,plain,
% 22.63/22.81      (((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | big_p(elem!0) | big_q(c16) | (~big_p(c11)) | (~big_p(c11)) | big_p(elem!0)) <=> (big_q(c16) | (~big_p(c11)) | big_p(elem!0) | (~big_q(elem!0)))),
% 22.63/22.81      inference(rewrite,[status(thm)],[])).
% 22.63/22.81  tff(618,plain,
% 22.63/22.81      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | big_p(elem!0) | big_q(c16) | (~big_p(c11)) | (~big_p(c11)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | (~big_p(c11)) | big_p(elem!0) | (~big_q(elem!0))))),
% 22.63/22.81      inference(monotonicity,[status(thm)],[617])).
% 22.63/22.81  tff(619,plain,
% 22.63/22.81      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | big_p(elem!0) | big_q(c16) | (~big_p(c11)) | (~big_p(c11)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_p(elem!0) | (~big_q(elem!0)))),
% 22.63/22.81      inference(transitivity,[status(thm)],[618, 616])).
% 22.63/22.81  tff(620,plain,
% 22.63/22.81      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | big_p(elem!0) | big_q(c16) | (~big_p(c11)) | (~big_p(c11)) | big_p(elem!0))),
% 22.63/22.81      inference(quant_inst,[status(thm)],[])).
% 22.63/22.81  tff(621,plain,
% 22.63/22.81      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_p(elem!0) | (~big_q(elem!0))),
% 22.63/22.81      inference(modus_ponens,[status(thm)],[620, 619])).
% 22.63/22.81  tff(622,plain,
% 22.63/22.81      ($false),
% 22.63/22.81      inference(unit_resolution,[status(thm)],[621, 52, 506, 3, 2, 615])).
% 22.63/22.81  tff(623,plain,(big_q(c16) | (~big_q(elem!0)) | big_p(elem!0) | big_p(f1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 22.63/22.81  tff(624,plain,
% 22.63/22.81      (big_p(f1(elem!0))),
% 22.63/22.81      inference(unit_resolution,[status(thm)],[623, 2, 3, 505])).
% 22.63/22.81  tff(625,plain,
% 22.63/22.81      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0))))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0))))),
% 22.63/22.81      inference(rewrite,[status(thm)],[])).
% 22.63/22.81  tff(626,plain,
% 22.63/22.81      (((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | (~big_p(f1(elem!0))) | big_q(c16) | big_p(c11) | (~big_p(f1(elem!0))) | big_p(elem!0)) <=> (big_q(c16) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0))))),
% 22.63/22.81      inference(rewrite,[status(thm)],[])).
% 22.63/22.81  tff(627,plain,
% 22.63/22.81      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | (~big_p(f1(elem!0))) | big_q(c16) | big_p(c11) | (~big_p(f1(elem!0))) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0)))))),
% 22.63/22.81      inference(monotonicity,[status(thm)],[626])).
% 22.63/22.81  tff(628,plain,
% 22.63/22.81      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | (~big_p(f1(elem!0))) | big_q(c16) | big_p(c11) | (~big_p(f1(elem!0))) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0))))),
% 22.63/22.81      inference(transitivity,[status(thm)],[627, 625])).
% 22.63/22.81  tff(629,plain,
% 22.63/22.81      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | (~big_p(f1(elem!0))) | big_q(c16) | big_p(c11) | (~big_p(f1(elem!0))) | big_p(elem!0))),
% 22.63/22.81      inference(quant_inst,[status(thm)],[])).
% 22.63/22.81  tff(630,plain,
% 22.63/22.81      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0)))),
% 22.63/22.81      inference(modus_ponens,[status(thm)],[629, 628])).
% 22.63/22.81  tff(631,plain,
% 22.63/22.81      (big_p(c11)),
% 22.63/22.81      inference(unit_resolution,[status(thm)],[630, 35, 505, 3, 624, 2])).
% 22.63/22.81  tff(632,plain,
% 22.63/22.81      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | (~big_p(c11)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0))))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0))))),
% 22.63/22.81      inference(rewrite,[status(thm)],[])).
% 22.63/22.81  tff(633,plain,
% 22.63/22.81      (((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | big_p(elem!0) | big_q(c16) | (~big_p(c11)) | (~big_p(f1(elem!0))) | big_p(elem!0)) <=> (big_q(c16) | (~big_p(c11)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0))))),
% 22.63/22.81      inference(rewrite,[status(thm)],[])).
% 22.63/22.81  tff(634,plain,
% 22.63/22.81      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | big_p(elem!0) | big_q(c16) | (~big_p(c11)) | (~big_p(f1(elem!0))) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | (~big_p(c11)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0)))))),
% 22.63/22.82      inference(monotonicity,[status(thm)],[633])).
% 22.63/22.82  tff(635,plain,
% 22.63/22.82      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | big_p(elem!0) | big_q(c16) | (~big_p(c11)) | (~big_p(f1(elem!0))) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0))))),
% 22.63/22.82      inference(transitivity,[status(thm)],[634, 632])).
% 22.63/22.82  tff(636,plain,
% 22.63/22.82      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | big_p(elem!0) | big_q(c16) | (~big_p(c11)) | (~big_p(f1(elem!0))) | big_p(elem!0))),
% 22.63/22.82      inference(quant_inst,[status(thm)],[])).
% 22.63/22.82  tff(637,plain,
% 22.63/22.82      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0)))),
% 22.63/22.82      inference(modus_ponens,[status(thm)],[636, 635])).
% 22.63/22.82  tff(638,plain,
% 22.63/22.82      ($false),
% 22.63/22.82      inference(unit_resolution,[status(thm)],[637, 52, 505, 3, 624, 2, 631])).
% 22.63/22.82  tff(639,plain,(big_q(c16) | big_p(elem!0)), inference(lemma,lemma(discharge,[]))).
% 22.63/22.82  tff(640,plain,
% 22.63/22.82      (big_q(c16)),
% 22.63/22.82      inference(unit_resolution,[status(thm)],[639, 3])).
% 22.63/22.82  tff(641,plain,
% 22.63/22.82      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_p(c11) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c6)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c6)))),
% 22.63/22.82      inference(rewrite,[status(thm)],[])).
% 22.63/22.82  tff(642,plain,
% 22.63/22.82      (((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | (~big_p(c6)) | (~big_q(c16)) | big_p(c11) | (~big_p(c6)) | big_p(elem!0)) <=> ((~big_q(c16)) | big_p(c11) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c6)))),
% 22.63/22.82      inference(rewrite,[status(thm)],[])).
% 22.63/22.82  tff(643,plain,
% 22.63/22.82      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | (~big_p(c6)) | (~big_q(c16)) | big_p(c11) | (~big_p(c6)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_p(c11) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c6))))),
% 22.63/22.82      inference(monotonicity,[status(thm)],[642])).
% 22.63/22.82  tff(644,plain,
% 22.63/22.82      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | (~big_p(c6)) | (~big_q(c16)) | big_p(c11) | (~big_p(c6)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c6)))),
% 22.63/22.82      inference(transitivity,[status(thm)],[643, 641])).
% 22.63/22.82  tff(645,plain,
% 22.63/22.82      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | (~big_p(c6)) | (~big_q(c16)) | big_p(c11) | (~big_p(c6)) | big_p(elem!0))),
% 22.63/22.82      inference(quant_inst,[status(thm)],[])).
% 22.63/22.82  tff(646,plain,
% 22.63/22.82      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c6))),
% 22.63/22.82      inference(modus_ponens,[status(thm)],[645, 644])).
% 22.63/22.82  tff(647,plain,
% 22.63/22.82      ($false),
% 22.63/22.82      inference(unit_resolution,[status(thm)],[646, 373, 505, 306, 3, 4, 640, 1])).
% 22.63/22.82  tff(648,plain,(big_q(f4(elem!0)) | big_p(elem!0) | (~big_p(c6)) | big_p(c11)), inference(lemma,lemma(discharge,[]))).
% 22.63/22.82  tff(649,plain,
% 22.63/22.82      (big_q(f4(elem!0))),
% 22.63/22.82      inference(unit_resolution,[status(thm)],[648, 4, 3, 1])).
% 22.63/22.82  tff(650,plain,
% 22.63/22.82      (^[X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : refl(((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16)))) <=> ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16)))))),
% 22.63/22.82      inference(bind,[status(th)],[])).
% 22.63/22.82  tff(651,plain,
% 22.63/22.82      (![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16)))) <=> ![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))),
% 22.63/22.82      inference(quant_intro,[status(thm)],[650])).
% 22.63/22.82  tff(652,plain,
% 22.63/22.82      (![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16)))) <=> ![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))),
% 22.63/22.82      inference(rewrite,[status(thm)],[])).
% 22.63/22.82  tff(653,plain,
% 22.63/22.82      (^[X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) <=> ((~big_q(X8)) | (~big_p(X7)) | big_p(c11))), ((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) <=> (((~big_q(X8)) | (~big_p(X7)) | big_p(c11)) | big_p(X9)))), rewrite((((~big_q(X8)) | (~big_p(X7)) | big_p(c11)) | big_p(X9)) <=> ((~big_q(X8)) | big_p(X9) | (~big_p(X7)) | big_p(c11))), ((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) <=> ((~big_q(X8)) | big_p(X9) | (~big_p(X7)) | big_p(c11)))), (((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) <=> (((~big_q(X8)) | big_p(X9) | (~big_p(X7)) | big_p(c11)) | (~big_q(f4(X16)))))), rewrite((((~big_q(X8)) | big_p(X9) | (~big_p(X7)) | big_p(c11)) | (~big_q(f4(X16)))) <=> ((~big_q(X8)) | big_p(X9) | (~big_p(X7)) | big_p(c11) | (~big_q(f4(X16))))), (((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) <=> ((~big_q(X8)) | big_p(X9) | (~big_p(X7)) | big_p(c11) | (~big_q(f4(X16)))))), ((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) <=> (((~big_q(X8)) | big_p(X9) | (~big_p(X7)) | big_p(c11) | (~big_q(f4(X16)))) | (~big_q(X16))))), rewrite((((~big_q(X8)) | big_p(X9) | (~big_p(X7)) | big_p(c11) | (~big_q(f4(X16)))) | (~big_q(X16))) <=> ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | (~big_q(f4(X16))))), ((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) <=> ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | (~big_q(f4(X16)))))), (((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) | (~big_p(X18))) <=> (((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | (~big_q(f4(X16)))) | (~big_p(X18))))), rewrite((((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | (~big_q(f4(X16)))) | (~big_p(X18))) <=> ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(f4(X16))))), (((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) | (~big_p(X18))) <=> ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(f4(X16)))))), ((((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) | (~big_p(X18))) | (~big_q(c20))) <=> (((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(f4(X16)))) | (~big_q(c20))))), rewrite((((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(f4(X16)))) | (~big_q(c20))) <=> ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))), ((((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) | (~big_p(X18))) | (~big_q(c20))) <=> ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))))),
% 22.63/22.82      inference(bind,[status(th)],[])).
% 22.63/22.82  tff(654,plain,
% 22.63/22.82      (![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : (((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) | (~big_p(X18))) | (~big_q(c20))) <=> ![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))),
% 22.63/22.82      inference(quant_intro,[status(thm)],[653])).
% 22.63/22.82  tff(655,axiom,(![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : (((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) | (~big_p(X18))) | (~big_q(c20)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_88')).
% 22.63/22.82  tff(656,plain,
% 22.63/22.82      (![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))),
% 22.63/22.82      inference(modus_ponens,[status(thm)],[655, 654])).
% 22.63/22.82  tff(657,plain,
% 22.63/22.82      (![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))),
% 22.63/22.82      inference(modus_ponens,[status(thm)],[656, 652])).
% 22.63/22.82  tff(658,plain,(
% 22.63/22.82      ![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))),
% 22.63/22.82      inference(skolemize,[status(sab)],[657])).
% 22.63/22.82  tff(659,plain,
% 22.63/22.82      (![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))),
% 22.63/22.82      inference(modus_ponens,[status(thm)],[658, 651])).
% 22.63/22.82  tff(660,plain,
% 22.63/22.82      (((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | (big_p(c11) | (~big_q(c20)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(c6)))) <=> ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | big_p(c11) | (~big_q(c20)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(c6)))),
% 22.63/22.82      inference(rewrite,[status(thm)],[])).
% 22.63/22.82  tff(661,plain,
% 22.63/22.82      (((~big_q(f4(elem!0))) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c6)) | (~big_p(c6)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(elem!0)))) <=> (big_p(c11) | (~big_q(c20)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(c6)))),
% 22.63/22.82      inference(rewrite,[status(thm)],[])).
% 22.63/22.82  tff(662,plain,
% 22.63/22.82      (((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_q(f4(elem!0))) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c6)) | (~big_p(c6)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(elem!0))))) <=> ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | (big_p(c11) | (~big_q(c20)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(c6))))),
% 22.63/22.82      inference(monotonicity,[status(thm)],[661])).
% 22.63/22.82  tff(663,plain,
% 22.63/22.82      (((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_q(f4(elem!0))) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c6)) | (~big_p(c6)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(elem!0))))) <=> ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | big_p(c11) | (~big_q(c20)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(c6)))),
% 22.63/22.82      inference(transitivity,[status(thm)],[662, 660])).
% 22.63/22.82  tff(664,plain,
% 22.63/22.82      ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_q(f4(elem!0))) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c6)) | (~big_p(c6)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(elem!0))))),
% 22.63/22.82      inference(quant_inst,[status(thm)],[])).
% 22.63/22.82  tff(665,plain,
% 22.63/22.82      ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | big_p(c11) | (~big_q(c20)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(c6))),
% 22.63/22.82      inference(modus_ponens,[status(thm)],[664, 663])).
% 22.63/22.82  tff(666,plain,
% 22.63/22.82      (~big_q(c20)),
% 22.63/22.82      inference(unit_resolution,[status(thm)],[665, 659, 505, 649, 3, 4, 1])).
% 22.63/22.82  tff(667,plain,
% 22.63/22.82      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c20) | (~big_q(c16)) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c6)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c20) | (~big_q(c16)) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c6)))),
% 22.63/22.82      inference(rewrite,[status(thm)],[])).
% 22.63/22.82  tff(668,plain,
% 22.63/22.82      (((~big_q(elem!0)) | big_q(c20) | big_q(c20) | (~big_p(c6)) | (~big_q(c16)) | big_p(c11) | (~big_p(c6)) | big_p(elem!0)) <=> (big_q(c20) | (~big_q(c16)) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c6)))),
% 22.63/22.82      inference(rewrite,[status(thm)],[])).
% 22.63/22.82  tff(669,plain,
% 22.63/22.82      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c20) | big_q(c20) | (~big_p(c6)) | (~big_q(c16)) | big_p(c11) | (~big_p(c6)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c20) | (~big_q(c16)) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c6))))),
% 22.63/22.82      inference(monotonicity,[status(thm)],[668])).
% 22.63/22.82  tff(670,plain,
% 22.63/22.82      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c20) | big_q(c20) | (~big_p(c6)) | (~big_q(c16)) | big_p(c11) | (~big_p(c6)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c20) | (~big_q(c16)) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c6)))),
% 22.63/22.82      inference(transitivity,[status(thm)],[669, 667])).
% 22.63/22.82  tff(671,plain,
% 22.63/22.82      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c20) | big_q(c20) | (~big_p(c6)) | (~big_q(c16)) | big_p(c11) | (~big_p(c6)) | big_p(elem!0))),
% 22.63/22.82      inference(quant_inst,[status(thm)],[])).
% 22.63/22.82  tff(672,plain,
% 22.63/22.82      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c20) | (~big_q(c16)) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c6))),
% 22.63/22.82      inference(modus_ponens,[status(thm)],[671, 670])).
% 22.63/22.82  tff(673,plain,
% 22.63/22.82      ($false),
% 22.63/22.82      inference(unit_resolution,[status(thm)],[672, 373, 505, 3, 4, 640, 666, 1])).
% 22.63/22.82  tff(674,plain,((~big_p(c6)) | big_p(elem!0) | big_p(c11)), inference(lemma,lemma(discharge,[]))).
% 22.63/22.82  tff(675,plain,
% 22.63/22.82      (~big_p(c6)),
% 22.63/22.82      inference(unit_resolution,[status(thm)],[674, 1, 3])).
% 22.63/22.82  tff(676,plain,
% 22.63/22.82      (~big_q(c8)),
% 22.63/22.82      inference(unit_resolution,[status(thm)],[522, 107])).
% 22.63/22.82  tff(677,plain,
% 22.63/22.82      ($false),
% 22.63/22.82      inference(unit_resolution,[status(thm)],[530, 676, 107])).
% 22.63/22.82  tff(678,plain,(big_p(c9) | (~big_q(elem!0)) | big_p(elem!0) | big_p(f1(elem!0)) | big_q(f2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 22.63/22.82  tff(679,plain,
% 22.63/22.82      (big_p(c9)),
% 22.63/22.82      inference(unit_resolution,[status(thm)],[678, 8, 3, 88, 506])).
% 22.63/22.82  tff(680,plain,
% 22.63/22.82      (big_q(c16)),
% 22.63/22.82      inference(unit_resolution,[status(thm)],[623, 506, 3, 88])).
% 22.63/22.82  tff(681,plain,
% 22.63/22.82      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_p(c11) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9)))),
% 22.63/22.82      inference(rewrite,[status(thm)],[])).
% 22.63/22.82  tff(682,plain,
% 22.63/22.82      (((~big_q(elem!0)) | big_q(f2(elem!0)) | big_q(f2(elem!0)) | (~big_p(c9)) | (~big_q(c16)) | big_p(c11) | (~big_p(c9)) | big_p(elem!0)) <=> ((~big_q(c16)) | big_p(c11) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9)))),
% 22.63/22.82      inference(rewrite,[status(thm)],[])).
% 22.63/22.82  tff(683,plain,
% 22.63/22.82      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f2(elem!0)) | big_q(f2(elem!0)) | (~big_p(c9)) | (~big_q(c16)) | big_p(c11) | (~big_p(c9)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_p(c11) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9))))),
% 22.63/22.82      inference(monotonicity,[status(thm)],[682])).
% 22.63/22.82  tff(684,plain,
% 22.63/22.82      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f2(elem!0)) | big_q(f2(elem!0)) | (~big_p(c9)) | (~big_q(c16)) | big_p(c11) | (~big_p(c9)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9)))),
% 22.63/22.82      inference(transitivity,[status(thm)],[683, 681])).
% 22.63/22.82  tff(685,plain,
% 22.63/22.82      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f2(elem!0)) | big_q(f2(elem!0)) | (~big_p(c9)) | (~big_q(c16)) | big_p(c11) | (~big_p(c9)) | big_p(elem!0))),
% 22.63/22.82      inference(quant_inst,[status(thm)],[])).
% 22.63/22.82  tff(686,plain,
% 22.63/22.82      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(c9))),
% 22.63/22.82      inference(modus_ponens,[status(thm)],[685, 684])).
% 22.63/22.82  tff(687,plain,
% 22.63/22.82      ($false),
% 22.63/22.82      inference(unit_resolution,[status(thm)],[686, 373, 506, 3, 8, 680, 1, 679])).
% 22.63/22.82  tff(688,plain,(big_q(f2(elem!0)) | (~big_q(elem!0)) | big_p(elem!0) | big_p(c11) | big_p(f1(elem!0))), inference(lemma,lemma(discharge,[]))).
% 22.63/22.82  tff(689,plain,
% 22.63/22.82      (big_p(f1(elem!0))),
% 22.63/22.82      inference(unit_resolution,[status(thm)],[688, 8, 3, 505, 1])).
% 22.63/22.82  tff(690,plain,
% 22.63/22.82      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_p(c11) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0))))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0))))),
% 22.63/22.82      inference(rewrite,[status(thm)],[])).
% 22.63/22.82  tff(691,plain,
% 22.63/22.82      (((~big_q(elem!0)) | big_q(f2(elem!0)) | big_q(f2(elem!0)) | (~big_p(f1(elem!0))) | (~big_q(c16)) | big_p(c11) | (~big_p(f1(elem!0))) | big_p(elem!0)) <=> ((~big_q(c16)) | big_p(c11) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0))))),
% 22.63/22.82      inference(rewrite,[status(thm)],[])).
% 22.63/22.82  tff(692,plain,
% 22.63/22.82      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f2(elem!0)) | big_q(f2(elem!0)) | (~big_p(f1(elem!0))) | (~big_q(c16)) | big_p(c11) | (~big_p(f1(elem!0))) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_p(c11) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0)))))),
% 22.63/22.82      inference(monotonicity,[status(thm)],[691])).
% 22.63/22.82  tff(693,plain,
% 22.63/22.82      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f2(elem!0)) | big_q(f2(elem!0)) | (~big_p(f1(elem!0))) | (~big_q(c16)) | big_p(c11) | (~big_p(f1(elem!0))) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0))))),
% 22.63/22.82      inference(transitivity,[status(thm)],[692, 690])).
% 22.63/22.82  tff(694,plain,
% 22.63/22.82      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f2(elem!0)) | big_q(f2(elem!0)) | (~big_p(f1(elem!0))) | (~big_q(c16)) | big_p(c11) | (~big_p(f1(elem!0))) | big_p(elem!0))),
% 22.63/22.82      inference(quant_inst,[status(thm)],[])).
% 22.63/22.82  tff(695,plain,
% 22.63/22.82      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_q(f2(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0)))),
% 22.63/22.82      inference(modus_ponens,[status(thm)],[694, 693])).
% 22.63/22.82  tff(696,plain,
% 22.63/22.82      ($false),
% 22.63/22.82      inference(unit_resolution,[status(thm)],[695, 373, 505, 3, 689, 8, 640, 1])).
% 22.63/22.82  tff(697,plain,(big_q(f2(elem!0)) | big_p(elem!0) | big_p(c11)), inference(lemma,lemma(discharge,[]))).
% 22.63/22.82  tff(698,plain,
% 22.63/22.82      (big_q(f2(elem!0))),
% 22.63/22.82      inference(unit_resolution,[status(thm)],[697, 1, 3])).
% 22.63/22.82  tff(699,assumption,(~big_p(c6)), introduced(assumption)).
% 22.63/22.82  tff(700,plain,
% 22.63/22.82      (big_q(c7)),
% 22.63/22.82      inference(unit_resolution,[status(thm)],[587, 88, 3, 505])).
% 22.63/22.82  tff(701,plain,
% 22.63/22.82      ($false),
% 22.63/22.82      inference(unit_resolution,[status(thm)],[605, 700, 88, 3, 505, 305, 699])).
% 22.63/22.82  tff(702,plain,(big_p(f1(elem!0)) | big_p(elem!0) | (~big_q(f2(elem!0))) | big_p(c6)), inference(lemma,lemma(discharge,[]))).
% 22.63/22.82  tff(703,plain,
% 22.63/22.82      (big_p(f1(elem!0))),
% 22.63/22.82      inference(unit_resolution,[status(thm)],[702, 698, 3, 675])).
% 22.63/22.82  tff(704,plain,
% 22.63/22.82      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_p(c11) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0))))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0))))),
% 22.63/22.82      inference(rewrite,[status(thm)],[])).
% 22.63/22.82  tff(705,plain,
% 22.63/22.82      (((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | (~big_p(f1(elem!0))) | (~big_q(c16)) | big_p(c11) | (~big_p(f1(elem!0))) | big_p(elem!0)) <=> ((~big_q(c16)) | big_p(c11) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0))))),
% 22.63/22.82      inference(rewrite,[status(thm)],[])).
% 22.63/22.82  tff(706,plain,
% 22.63/22.82      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | (~big_p(f1(elem!0))) | (~big_q(c16)) | big_p(c11) | (~big_p(f1(elem!0))) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_p(c11) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0)))))),
% 22.63/22.82      inference(monotonicity,[status(thm)],[705])).
% 22.63/22.82  tff(707,plain,
% 22.63/22.82      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | (~big_p(f1(elem!0))) | (~big_q(c16)) | big_p(c11) | (~big_p(f1(elem!0))) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0))))),
% 22.63/22.82      inference(transitivity,[status(thm)],[706, 704])).
% 22.63/22.82  tff(708,plain,
% 22.63/22.82      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | (~big_p(f1(elem!0))) | (~big_q(c16)) | big_p(c11) | (~big_p(f1(elem!0))) | big_p(elem!0))),
% 22.63/22.82      inference(quant_inst,[status(thm)],[])).
% 22.63/22.82  tff(709,plain,
% 22.63/22.82      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0)))),
% 22.63/22.83      inference(modus_ponens,[status(thm)],[708, 707])).
% 22.63/22.83  tff(710,plain,
% 22.63/22.83      ($false),
% 22.63/22.83      inference(unit_resolution,[status(thm)],[709, 373, 505, 306, 3, 703, 640, 1])).
% 22.63/22.83  tff(711,plain,(big_q(f4(elem!0)) | big_p(elem!0) | big_p(c11)), inference(lemma,lemma(discharge,[]))).
% 22.63/22.83  tff(712,plain,
% 22.63/22.83      (big_q(f4(elem!0))),
% 22.63/22.83      inference(unit_resolution,[status(thm)],[711, 1, 3])).
% 22.63/22.83  tff(713,plain,
% 22.63/22.83      (((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | (big_p(c11) | (~big_q(c20)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0))) | (~big_q(f4(elem!0))))) <=> ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | big_p(c11) | (~big_q(c20)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0))) | (~big_q(f4(elem!0))))),
% 22.63/22.83      inference(rewrite,[status(thm)],[])).
% 22.63/22.83  tff(714,plain,
% 22.63/22.83      (((~big_q(f4(elem!0))) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0))) | (~big_p(f1(elem!0))) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(elem!0)))) <=> (big_p(c11) | (~big_q(c20)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0))) | (~big_q(f4(elem!0))))),
% 22.63/22.83      inference(rewrite,[status(thm)],[])).
% 22.63/22.83  tff(715,plain,
% 22.63/22.83      (((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_q(f4(elem!0))) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0))) | (~big_p(f1(elem!0))) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(elem!0))))) <=> ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | (big_p(c11) | (~big_q(c20)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0))) | (~big_q(f4(elem!0)))))),
% 22.63/22.83      inference(monotonicity,[status(thm)],[714])).
% 22.63/22.83  tff(716,plain,
% 22.63/22.83      (((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_q(f4(elem!0))) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0))) | (~big_p(f1(elem!0))) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(elem!0))))) <=> ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | big_p(c11) | (~big_q(c20)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0))) | (~big_q(f4(elem!0))))),
% 22.63/22.83      inference(transitivity,[status(thm)],[715, 713])).
% 22.63/22.83  tff(717,plain,
% 22.63/22.83      ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_q(f4(elem!0))) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0))) | (~big_p(f1(elem!0))) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(elem!0))))),
% 22.63/22.83      inference(quant_inst,[status(thm)],[])).
% 22.63/22.83  tff(718,plain,
% 22.63/22.83      ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | big_p(c11) | (~big_q(c20)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0))) | (~big_q(f4(elem!0)))),
% 22.63/22.83      inference(modus_ponens,[status(thm)],[717, 716])).
% 22.63/22.83  tff(719,plain,
% 22.63/22.83      (~big_q(c20)),
% 22.63/22.83      inference(unit_resolution,[status(thm)],[718, 659, 505, 712, 3, 703, 1])).
% 22.63/22.83  tff(720,plain,
% 22.63/22.83      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c20) | (~big_q(c16)) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0))))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c20) | (~big_q(c16)) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0))))),
% 22.63/22.83      inference(rewrite,[status(thm)],[])).
% 22.63/22.83  tff(721,plain,
% 22.63/22.83      (((~big_q(elem!0)) | big_q(c20) | big_q(c20) | (~big_p(f1(elem!0))) | (~big_q(c16)) | big_p(c11) | (~big_p(f1(elem!0))) | big_p(elem!0)) <=> (big_q(c20) | (~big_q(c16)) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0))))),
% 22.63/22.83      inference(rewrite,[status(thm)],[])).
% 22.63/22.83  tff(722,plain,
% 22.63/22.83      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c20) | big_q(c20) | (~big_p(f1(elem!0))) | (~big_q(c16)) | big_p(c11) | (~big_p(f1(elem!0))) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c20) | (~big_q(c16)) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0)))))),
% 22.63/22.83      inference(monotonicity,[status(thm)],[721])).
% 22.63/22.83  tff(723,plain,
% 22.63/22.83      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c20) | big_q(c20) | (~big_p(f1(elem!0))) | (~big_q(c16)) | big_p(c11) | (~big_p(f1(elem!0))) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c20) | (~big_q(c16)) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0))))),
% 22.63/22.83      inference(transitivity,[status(thm)],[722, 720])).
% 22.63/22.83  tff(724,plain,
% 22.63/22.83      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c20) | big_q(c20) | (~big_p(f1(elem!0))) | (~big_q(c16)) | big_p(c11) | (~big_p(f1(elem!0))) | big_p(elem!0))),
% 22.63/22.83      inference(quant_inst,[status(thm)],[])).
% 22.63/22.83  tff(725,plain,
% 22.63/22.83      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c20) | (~big_q(c16)) | big_p(c11) | big_p(elem!0) | (~big_q(elem!0)) | (~big_p(f1(elem!0)))),
% 22.63/22.83      inference(modus_ponens,[status(thm)],[724, 723])).
% 22.63/22.83  tff(726,plain,
% 22.63/22.83      ($false),
% 22.63/22.83      inference(unit_resolution,[status(thm)],[725, 373, 505, 3, 703, 640, 719, 1])).
% 22.63/22.83  tff(727,plain,(big_p(c11) | big_p(elem!0)), inference(lemma,lemma(discharge,[]))).
% 22.63/22.83  tff(728,plain,
% 22.63/22.83      (big_p(c11)),
% 22.63/22.83      inference(unit_resolution,[status(thm)],[727, 3])).
% 22.63/22.83  tff(729,plain,
% 22.63/22.83      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | (~big_q(c16)) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_q(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_q(elem!0)))),
% 22.63/22.83      inference(rewrite,[status(thm)],[])).
% 22.63/22.83  tff(730,plain,
% 22.63/22.83      (((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c11)) | big_p(elem!0)) <=> ((~big_p(c11)) | (~big_q(c16)) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_q(elem!0)))),
% 22.63/22.83      inference(rewrite,[status(thm)],[])).
% 22.63/22.83  tff(731,plain,
% 22.63/22.83      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c11)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | (~big_q(c16)) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_q(elem!0))))),
% 22.63/22.83      inference(monotonicity,[status(thm)],[730])).
% 22.63/22.83  tff(732,plain,
% 22.63/22.83      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c11)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_q(elem!0)))),
% 22.63/22.83      inference(transitivity,[status(thm)],[731, 729])).
% 22.63/22.83  tff(733,plain,
% 22.63/22.83      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c11)) | big_p(elem!0))),
% 22.63/22.83      inference(quant_inst,[status(thm)],[])).
% 22.63/22.83  tff(734,plain,
% 22.63/22.83      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_q(f4(elem!0)) | big_p(elem!0) | (~big_q(elem!0))),
% 22.63/22.83      inference(modus_ponens,[status(thm)],[733, 732])).
% 22.63/22.83  tff(735,plain,
% 22.63/22.83      ($false),
% 22.63/22.83      inference(unit_resolution,[status(thm)],[734, 354, 505, 306, 3, 640, 728])).
% 22.63/22.83  tff(736,plain,(big_q(f4(elem!0)) | big_p(elem!0)), inference(lemma,lemma(discharge,[]))).
% 22.63/22.83  tff(737,plain,
% 22.63/22.83      (big_q(f4(elem!0))),
% 22.63/22.83      inference(unit_resolution,[status(thm)],[736, 3])).
% 22.63/22.83  tff(738,plain,
% 22.63/22.83      (^[X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : refl(((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16)))) <=> ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16)))))),
% 22.63/22.83      inference(bind,[status(th)],[])).
% 22.63/22.83  tff(739,plain,
% 22.63/22.83      (![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16)))) <=> ![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))),
% 22.63/22.83      inference(quant_intro,[status(thm)],[738])).
% 22.63/22.83  tff(740,plain,
% 22.63/22.83      (![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16)))) <=> ![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))),
% 22.63/22.83      inference(rewrite,[status(thm)],[])).
% 22.63/22.83  tff(741,plain,
% 22.63/22.83      (^[X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(c11)) | big_p(X7)) <=> (big_p(X7) | (~big_p(c11)))), ((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) <=> ((big_p(X7) | (~big_p(c11))) | (~big_q(X8))))), rewrite(((big_p(X7) | (~big_p(c11))) | (~big_q(X8))) <=> ((~big_q(X8)) | big_p(X7) | (~big_p(c11)))), ((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) <=> ((~big_q(X8)) | big_p(X7) | (~big_p(c11))))), (((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) <=> (((~big_q(X8)) | big_p(X7) | (~big_p(c11))) | big_p(X9)))), rewrite((((~big_q(X8)) | big_p(X7) | (~big_p(c11))) | big_p(X9)) <=> ((~big_q(X8)) | big_p(X9) | big_p(X7) | (~big_p(c11)))), (((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) <=> ((~big_q(X8)) | big_p(X9) | big_p(X7) | (~big_p(c11))))), ((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) <=> (((~big_q(X8)) | big_p(X9) | big_p(X7) | (~big_p(c11))) | (~big_q(f4(X16)))))), rewrite((((~big_q(X8)) | big_p(X9) | big_p(X7) | (~big_p(c11))) | (~big_q(f4(X16)))) <=> ((~big_q(X8)) | big_p(X9) | big_p(X7) | (~big_p(c11)) | (~big_q(f4(X16))))), ((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) <=> ((~big_q(X8)) | big_p(X9) | big_p(X7) | (~big_p(c11)) | (~big_q(f4(X16)))))), (((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) <=> (((~big_q(X8)) | big_p(X9) | big_p(X7) | (~big_p(c11)) | (~big_q(f4(X16)))) | (~big_q(X16))))), rewrite((((~big_q(X8)) | big_p(X9) | big_p(X7) | (~big_p(c11)) | (~big_q(f4(X16)))) | (~big_q(X16))) <=> ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | (~big_q(f4(X16))))), (((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) <=> ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | (~big_q(f4(X16)))))), ((((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) | (~big_p(X18))) <=> (((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | (~big_q(f4(X16)))) | (~big_p(X18))))), rewrite((((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | (~big_q(f4(X16)))) | (~big_p(X18))) <=> ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(f4(X16))))), ((((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) | (~big_p(X18))) <=> ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(f4(X16)))))), (((((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) | (~big_p(X18))) | (~big_q(c20))) <=> (((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(f4(X16)))) | (~big_q(c20))))), rewrite((((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(f4(X16)))) | (~big_q(c20))) <=> ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))), (((((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) | (~big_p(X18))) | (~big_q(c20))) <=> ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))))),
% 22.63/22.83      inference(bind,[status(th)],[])).
% 22.63/22.83  tff(742,plain,
% 22.63/22.83      (![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) | (~big_p(X18))) | (~big_q(c20))) <=> ![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))),
% 22.63/22.83      inference(quant_intro,[status(thm)],[741])).
% 22.63/22.83  tff(743,axiom,(![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) | (~big_p(X18))) | (~big_q(c20)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_72')).
% 22.63/22.83  tff(744,plain,
% 22.63/22.83      (![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))),
% 22.63/22.83      inference(modus_ponens,[status(thm)],[743, 742])).
% 22.63/22.83  tff(745,plain,
% 22.63/22.83      (![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))),
% 22.63/22.83      inference(modus_ponens,[status(thm)],[744, 740])).
% 22.63/22.83  tff(746,plain,(
% 22.63/22.83      ![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))),
% 22.63/22.83      inference(skolemize,[status(sab)],[745])).
% 22.63/22.83  tff(747,plain,
% 22.63/22.83      (![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))),
% 22.63/22.83      inference(modus_ponens,[status(thm)],[746, 739])).
% 22.63/22.83  tff(748,plain,
% 22.63/22.83      (((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_p(c11)) | (~big_q(c20)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_q(f4(elem!0))))) <=> ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | (~big_p(c11)) | (~big_q(c20)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_q(f4(elem!0))))),
% 22.63/22.83      inference(rewrite,[status(thm)],[])).
% 22.63/22.83  tff(749,plain,
% 22.63/22.83      (((~big_q(f4(elem!0))) | big_p(elem!0) | (~big_q(elem!0)) | big_p(elem!0) | (~big_p(c11)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(elem!0)))) <=> ((~big_p(c11)) | (~big_q(c20)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_q(f4(elem!0))))),
% 22.63/22.83      inference(rewrite,[status(thm)],[])).
% 22.63/22.83  tff(750,plain,
% 22.63/22.83      (((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_q(f4(elem!0))) | big_p(elem!0) | (~big_q(elem!0)) | big_p(elem!0) | (~big_p(c11)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(elem!0))))) <=> ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_p(c11)) | (~big_q(c20)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_q(f4(elem!0)))))),
% 22.63/22.83      inference(monotonicity,[status(thm)],[749])).
% 22.63/22.83  tff(751,plain,
% 22.63/22.83      (((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_q(f4(elem!0))) | big_p(elem!0) | (~big_q(elem!0)) | big_p(elem!0) | (~big_p(c11)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(elem!0))))) <=> ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | (~big_p(c11)) | (~big_q(c20)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_q(f4(elem!0))))),
% 22.63/22.83      inference(transitivity,[status(thm)],[750, 748])).
% 22.63/22.83  tff(752,plain,
% 22.63/22.83      ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_q(f4(elem!0))) | big_p(elem!0) | (~big_q(elem!0)) | big_p(elem!0) | (~big_p(c11)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(elem!0))))),
% 22.63/22.83      inference(quant_inst,[status(thm)],[])).
% 22.63/22.83  tff(753,plain,
% 22.63/22.83      ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | (~big_p(c11)) | (~big_q(c20)) | big_p(elem!0) | (~big_q(elem!0)) | (~big_q(f4(elem!0)))),
% 22.63/22.83      inference(modus_ponens,[status(thm)],[752, 751])).
% 22.63/22.83  tff(754,plain,
% 22.63/22.83      (~big_q(c20)),
% 22.63/22.83      inference(unit_resolution,[status(thm)],[753, 747, 505, 737, 3, 728])).
% 22.63/22.83  tff(755,plain,
% 22.63/22.83      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | big_q(c20) | (~big_q(c16)) | big_p(elem!0) | (~big_q(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | big_q(c20) | (~big_q(c16)) | big_p(elem!0) | (~big_q(elem!0)))),
% 22.63/22.83      inference(rewrite,[status(thm)],[])).
% 22.63/22.83  tff(756,plain,
% 22.63/22.83      (((~big_q(elem!0)) | big_q(c20) | big_q(c20) | big_p(elem!0) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c11)) | big_p(elem!0)) <=> ((~big_p(c11)) | big_q(c20) | (~big_q(c16)) | big_p(elem!0) | (~big_q(elem!0)))),
% 22.63/22.83      inference(rewrite,[status(thm)],[])).
% 22.63/22.83  tff(757,plain,
% 22.63/22.83      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c20) | big_q(c20) | big_p(elem!0) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c11)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | big_q(c20) | (~big_q(c16)) | big_p(elem!0) | (~big_q(elem!0))))),
% 22.63/22.83      inference(monotonicity,[status(thm)],[756])).
% 22.63/22.83  tff(758,plain,
% 22.63/22.83      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c20) | big_q(c20) | big_p(elem!0) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c11)) | big_p(elem!0))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | big_q(c20) | (~big_q(c16)) | big_p(elem!0) | (~big_q(elem!0)))),
% 22.63/22.83      inference(transitivity,[status(thm)],[757, 755])).
% 22.63/22.83  tff(759,plain,
% 22.63/22.83      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c20) | big_q(c20) | big_p(elem!0) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c11)) | big_p(elem!0))),
% 22.63/22.83      inference(quant_inst,[status(thm)],[])).
% 22.63/22.83  tff(760,plain,
% 22.63/22.83      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | big_q(c20) | (~big_q(c16)) | big_p(elem!0) | (~big_q(elem!0))),
% 22.63/22.83      inference(modus_ponens,[status(thm)],[759, 758])).
% 22.63/22.83  tff(761,plain,
% 22.63/22.83      ($false),
% 22.63/22.83      inference(unit_resolution,[status(thm)],[760, 354, 505, 3, 640, 754, 728])).
% 22.63/22.83  tff(762,plain,(big_p(elem!0)), inference(lemma,lemma(discharge,[]))).
% 22.63/22.83  tff(763,assumption,(~big_p(f3(c2))), introduced(assumption)).
% 22.63/22.83  tff(764,assumption,(big_q(c4)), introduced(assumption)).
% 22.63/22.83  tff(765,plain,
% 22.63/22.83      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c14) | big_q(c16) | big_p(c11) | (~big_p(elem!0)) | (~big_q(c4)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c14) | big_q(c16) | big_p(c11) | (~big_p(elem!0)) | (~big_q(c4)))),
% 22.63/22.83      inference(rewrite,[status(thm)],[])).
% 22.63/22.83  tff(766,plain,
% 22.63/22.83      (((~big_q(c4)) | big_q(c14) | (~big_q(c4)) | (~big_p(elem!0)) | big_q(c16) | big_p(c11) | (~big_p(elem!0)) | big_p(c11)) <=> (big_q(c14) | big_q(c16) | big_p(c11) | (~big_p(elem!0)) | (~big_q(c4)))),
% 22.63/22.83      inference(rewrite,[status(thm)],[])).
% 22.63/22.83  tff(767,plain,
% 22.63/22.83      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(c14) | (~big_q(c4)) | (~big_p(elem!0)) | big_q(c16) | big_p(c11) | (~big_p(elem!0)) | big_p(c11))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c14) | big_q(c16) | big_p(c11) | (~big_p(elem!0)) | (~big_q(c4))))),
% 22.63/22.83      inference(monotonicity,[status(thm)],[766])).
% 22.63/22.83  tff(768,plain,
% 22.63/22.83      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(c14) | (~big_q(c4)) | (~big_p(elem!0)) | big_q(c16) | big_p(c11) | (~big_p(elem!0)) | big_p(c11))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c14) | big_q(c16) | big_p(c11) | (~big_p(elem!0)) | (~big_q(c4)))),
% 22.63/22.83      inference(transitivity,[status(thm)],[767, 765])).
% 22.63/22.83  tff(769,plain,
% 22.63/22.83      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(c14) | (~big_q(c4)) | (~big_p(elem!0)) | big_q(c16) | big_p(c11) | (~big_p(elem!0)) | big_p(c11))),
% 22.63/22.83      inference(quant_inst,[status(thm)],[])).
% 22.63/22.83  tff(770,plain,
% 22.63/22.83      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c14) | big_q(c16) | big_p(c11) | (~big_p(elem!0)) | (~big_q(c4))),
% 22.63/22.83      inference(modus_ponens,[status(thm)],[769, 768])).
% 22.63/22.83  tff(771,plain,
% 22.63/22.83      ($false),
% 22.63/22.83      inference(unit_resolution,[status(thm)],[770, 35, 146, 762, 2, 1, 764])).
% 22.63/22.83  tff(772,plain,((~big_q(c4)) | big_q(c14) | big_q(c16) | big_p(c11)), inference(lemma,lemma(discharge,[]))).
% 22.63/22.83  tff(773,plain,
% 22.63/22.83      (big_q(c14)),
% 22.63/22.83      inference(unit_resolution,[status(thm)],[772, 764, 2, 1])).
% 22.63/22.83  tff(774,plain,
% 22.63/22.83      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | big_p(c11) | big_q(elem!0) | (~big_p(elem!0)) | (~big_q(c4)) | (~big_q(c14)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | big_q(elem!0) | (~big_p(elem!0)) | (~big_q(c4)) | (~big_q(c14)))),
% 22.63/22.83      inference(rewrite,[status(thm)],[])).
% 22.63/22.83  tff(775,plain,
% 22.63/22.83      (((~big_q(c14)) | big_q(elem!0) | (~big_q(c4)) | (~big_p(elem!0)) | big_q(c16) | big_p(c11) | (~big_p(elem!0)) | big_p(c11)) <=> (big_q(c16) | big_p(c11) | big_q(elem!0) | (~big_p(elem!0)) | (~big_q(c4)) | (~big_q(c14)))),
% 22.63/22.83      inference(rewrite,[status(thm)],[])).
% 22.63/22.83  tff(776,plain,
% 22.63/22.83      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c14)) | big_q(elem!0) | (~big_q(c4)) | (~big_p(elem!0)) | big_q(c16) | big_p(c11) | (~big_p(elem!0)) | big_p(c11))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | big_p(c11) | big_q(elem!0) | (~big_p(elem!0)) | (~big_q(c4)) | (~big_q(c14))))),
% 22.63/22.83      inference(monotonicity,[status(thm)],[775])).
% 22.63/22.83  tff(777,plain,
% 22.63/22.83      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c14)) | big_q(elem!0) | (~big_q(c4)) | (~big_p(elem!0)) | big_q(c16) | big_p(c11) | (~big_p(elem!0)) | big_p(c11))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | big_q(elem!0) | (~big_p(elem!0)) | (~big_q(c4)) | (~big_q(c14)))),
% 22.63/22.83      inference(transitivity,[status(thm)],[776, 774])).
% 22.63/22.83  tff(778,plain,
% 22.63/22.83      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c14)) | big_q(elem!0) | (~big_q(c4)) | (~big_p(elem!0)) | big_q(c16) | big_p(c11) | (~big_p(elem!0)) | big_p(c11))),
% 22.63/22.83      inference(quant_inst,[status(thm)],[])).
% 22.63/22.83  tff(779,plain,
% 22.63/22.83      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | big_q(elem!0) | (~big_p(elem!0)) | (~big_q(c4)) | (~big_q(c14))),
% 22.63/22.83      inference(modus_ponens,[status(thm)],[778, 777])).
% 22.63/22.83  tff(780,plain,
% 22.63/22.83      ($false),
% 22.63/22.83      inference(unit_resolution,[status(thm)],[779, 35, 773, 5, 762, 2, 1, 764])).
% 22.63/22.83  tff(781,plain,((~big_q(c4)) | big_q(elem!0) | big_q(c16) | big_p(c11)), inference(lemma,lemma(discharge,[]))).
% 22.63/22.84  tff(782,plain,
% 22.63/22.84      (~big_q(c4)),
% 22.63/22.84      inference(unit_resolution,[status(thm)],[781, 1, 2, 5])).
% 22.63/22.84  tff(783,assumption,(~big_q(c4)), introduced(assumption)).
% 22.63/22.84  tff(784,plain,
% 22.63/22.84      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(c4) | big_p(c11) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0)))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | big_p(c3) | big_q(c4) | big_p(c11) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0)))),
% 22.63/22.84      inference(rewrite,[status(thm)],[])).
% 22.63/22.84  tff(785,plain,
% 22.63/22.84      ((big_p(c3) | big_q(c4) | (~big_p(elem!0)) | big_p(c11) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0))) <=> (big_p(c3) | big_q(c4) | big_p(c11) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0)))),
% 22.63/22.84      inference(rewrite,[status(thm)],[])).
% 22.63/22.84  tff(786,plain,
% 22.63/22.84      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(c4) | (~big_p(elem!0)) | big_p(c11) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0)))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(c4) | big_p(c11) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0))))),
% 22.63/22.84      inference(monotonicity,[status(thm)],[785])).
% 22.63/22.84  tff(787,plain,
% 22.63/22.84      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(c4) | (~big_p(elem!0)) | big_p(c11) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0)))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | big_p(c3) | big_q(c4) | big_p(c11) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0)))),
% 22.63/22.84      inference(transitivity,[status(thm)],[786, 784])).
% 22.63/22.84  tff(788,plain,
% 22.63/22.84      ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(c4) | (~big_p(elem!0)) | big_p(c11) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0)))),
% 22.63/22.84      inference(quant_inst,[status(thm)],[])).
% 22.63/22.84  tff(789,plain,
% 22.63/22.84      ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | big_p(c3) | big_q(c4) | big_p(c11) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0))),
% 22.63/22.84      inference(modus_ponens,[status(thm)],[788, 787])).
% 22.63/22.84  tff(790,plain,
% 22.63/22.84      ($false),
% 22.63/22.84      inference(unit_resolution,[status(thm)],[789, 71, 5, 762, 8, 1, 126, 783])).
% 22.63/22.84  tff(791,plain,(big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(c11) | big_p(c3)), inference(lemma,lemma(discharge,[]))).
% 22.63/22.84  tff(792,plain,
% 22.63/22.84      (big_p(c3)),
% 22.63/22.84      inference(unit_resolution,[status(thm)],[791, 8, 783, 1, 5])).
% 22.63/22.84  tff(793,plain,
% 22.63/22.84      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | ((~big_p(c3)) | big_q(c4) | big_p(c11) | big_q(elem!0) | big_q(f2(elem!0)))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | (~big_p(c3)) | big_q(c4) | big_p(c11) | big_q(elem!0) | big_q(f2(elem!0)))),
% 22.63/22.84      inference(rewrite,[status(thm)],[])).
% 22.63/22.84  tff(794,plain,
% 22.63/22.84      (((~big_p(c3)) | big_q(elem!0) | (~big_p(c3)) | big_p(c11) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(c11)) <=> ((~big_p(c3)) | big_q(c4) | big_p(c11) | big_q(elem!0) | big_q(f2(elem!0)))),
% 22.63/22.84      inference(rewrite,[status(thm)],[])).
% 22.63/22.84  tff(795,plain,
% 22.63/22.84      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | ((~big_p(c3)) | big_q(elem!0) | (~big_p(c3)) | big_p(c11) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(c11))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | ((~big_p(c3)) | big_q(c4) | big_p(c11) | big_q(elem!0) | big_q(f2(elem!0))))),
% 22.63/22.84      inference(monotonicity,[status(thm)],[794])).
% 22.63/22.84  tff(796,plain,
% 22.63/22.84      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | ((~big_p(c3)) | big_q(elem!0) | (~big_p(c3)) | big_p(c11) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(c11))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | (~big_p(c3)) | big_q(c4) | big_p(c11) | big_q(elem!0) | big_q(f2(elem!0)))),
% 22.63/22.84      inference(transitivity,[status(thm)],[795, 793])).
% 22.63/22.84  tff(797,plain,
% 22.63/22.84      ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | ((~big_p(c3)) | big_q(elem!0) | (~big_p(c3)) | big_p(c11) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(c11))),
% 22.63/22.84      inference(quant_inst,[status(thm)],[])).
% 22.63/22.84  tff(798,plain,
% 22.63/22.84      ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | (~big_p(c3)) | big_q(c4) | big_p(c11) | big_q(elem!0) | big_q(f2(elem!0))),
% 22.63/22.84      inference(modus_ponens,[status(thm)],[797, 796])).
% 22.63/22.84  tff(799,plain,
% 22.63/22.84      ($false),
% 22.63/22.84      inference(unit_resolution,[status(thm)],[798, 18, 5, 8, 1, 792, 783])).
% 22.63/22.84  tff(800,plain,(big_q(f2(elem!0)) | big_q(elem!0) | big_p(c11) | big_q(c4)), inference(lemma,lemma(discharge,[]))).
% 22.63/22.84  tff(801,plain,
% 22.63/22.84      (big_q(f2(elem!0))),
% 22.63/22.84      inference(unit_resolution,[status(thm)],[800, 1, 5, 782])).
% 22.63/22.84  tff(802,plain,
% 22.63/22.84      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | big_p(c11) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(elem!0)))),
% 22.63/22.84      inference(rewrite,[status(thm)],[])).
% 22.63/22.84  tff(803,plain,
% 22.63/22.84      (((~big_q(f2(elem!0))) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(elem!0)) | big_q(c16) | big_p(c11) | (~big_p(elem!0)) | big_p(c11)) <=> (big_q(c16) | big_p(c11) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(elem!0)))),
% 22.63/22.84      inference(rewrite,[status(thm)],[])).
% 22.63/22.84  tff(804,plain,
% 22.63/22.84      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(elem!0))) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(elem!0)) | big_q(c16) | big_p(c11) | (~big_p(elem!0)) | big_p(c11))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | big_p(c11) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(elem!0))))),
% 22.63/22.84      inference(monotonicity,[status(thm)],[803])).
% 22.63/22.84  tff(805,plain,
% 22.63/22.84      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(elem!0))) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(elem!0)) | big_q(c16) | big_p(c11) | (~big_p(elem!0)) | big_p(c11))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(elem!0)))),
% 22.63/22.84      inference(transitivity,[status(thm)],[804, 802])).
% 22.63/22.84  tff(806,plain,
% 22.63/22.84      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(elem!0))) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(elem!0)) | big_q(c16) | big_p(c11) | (~big_p(elem!0)) | big_p(c11))),
% 22.63/22.84      inference(quant_inst,[status(thm)],[])).
% 22.63/22.84  tff(807,plain,
% 22.63/22.84      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(elem!0))),
% 22.63/22.84      inference(modus_ponens,[status(thm)],[806, 805])).
% 22.63/22.84  tff(808,plain,
% 22.63/22.84      ($false),
% 22.63/22.84      inference(unit_resolution,[status(thm)],[807, 35, 5, 762, 801, 2, 1])).
% 22.63/22.84  tff(809,plain,(big_p(c11) | big_q(elem!0) | big_q(c16)), inference(lemma,lemma(discharge,[]))).
% 22.63/22.84  tff(810,plain,
% 22.63/22.84      (big_q(c16)),
% 22.63/22.84      inference(unit_resolution,[status(thm)],[809, 1, 5])).
% 22.63/22.84  tff(811,plain,
% 22.63/22.84      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_p(c11) | big_q(elem!0) | (~big_p(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_q(elem!0) | (~big_p(elem!0)))),
% 22.63/22.84      inference(rewrite,[status(thm)],[])).
% 22.63/22.84  tff(812,plain,
% 22.63/22.84      (((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | (~big_p(elem!0)) | (~big_q(c16)) | big_p(c11) | (~big_p(elem!0)) | big_p(c11)) <=> ((~big_q(c16)) | big_p(c11) | big_q(elem!0) | (~big_p(elem!0)))),
% 22.63/22.84      inference(rewrite,[status(thm)],[])).
% 22.63/22.84  tff(813,plain,
% 22.63/22.84      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | (~big_p(elem!0)) | (~big_q(c16)) | big_p(c11) | (~big_p(elem!0)) | big_p(c11))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_p(c11) | big_q(elem!0) | (~big_p(elem!0))))),
% 22.63/22.84      inference(monotonicity,[status(thm)],[812])).
% 22.63/22.84  tff(814,plain,
% 22.63/22.84      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | (~big_p(elem!0)) | (~big_q(c16)) | big_p(c11) | (~big_p(elem!0)) | big_p(c11))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_q(elem!0) | (~big_p(elem!0)))),
% 22.63/22.84      inference(transitivity,[status(thm)],[813, 811])).
% 22.63/22.84  tff(815,plain,
% 22.63/22.84      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | (~big_p(elem!0)) | (~big_q(c16)) | big_p(c11) | (~big_p(elem!0)) | big_p(c11))),
% 22.63/22.84      inference(quant_inst,[status(thm)],[])).
% 22.63/22.84  tff(816,plain,
% 22.63/22.84      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_q(elem!0) | (~big_p(elem!0))),
% 22.63/22.84      inference(modus_ponens,[status(thm)],[815, 814])).
% 22.63/22.84  tff(817,plain,
% 22.63/22.84      ($false),
% 22.63/22.84      inference(unit_resolution,[status(thm)],[816, 373, 5, 762, 810, 1])).
% 22.63/22.84  tff(818,plain,(big_p(c11) | big_q(elem!0)), inference(lemma,lemma(discharge,[]))).
% 22.63/22.84  tff(819,plain,
% 22.63/22.84      (big_p(c11)),
% 22.63/22.84      inference(unit_resolution,[status(thm)],[818, 5])).
% 22.63/22.84  tff(820,assumption,(~big_p(f3(elem!0))), introduced(assumption)).
% 22.63/22.84  tff(821,assumption,(big_q(c8)), introduced(assumption)).
% 22.63/22.84  tff(822,plain,
% 22.63/22.84      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c8)) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_p(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (~big_q(c8)) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_p(elem!0)))),
% 22.63/22.84      inference(rewrite,[status(thm)],[])).
% 22.63/22.84  tff(823,plain,
% 22.63/22.84      (((~big_q(c8)) | big_q(elem!0) | (~big_q(c8)) | big_p(f3(elem!0)) | big_q(c16) | (~big_p(c11)) | (~big_p(elem!0)) | big_p(f3(elem!0))) <=> ((~big_q(c8)) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_p(elem!0)))),
% 22.63/22.84      inference(rewrite,[status(thm)],[])).
% 22.63/22.84  tff(824,plain,
% 22.63/22.84      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c8)) | big_q(elem!0) | (~big_q(c8)) | big_p(f3(elem!0)) | big_q(c16) | (~big_p(c11)) | (~big_p(elem!0)) | big_p(f3(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c8)) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_p(elem!0))))),
% 22.63/22.84      inference(monotonicity,[status(thm)],[823])).
% 22.63/22.84  tff(825,plain,
% 22.63/22.84      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c8)) | big_q(elem!0) | (~big_q(c8)) | big_p(f3(elem!0)) | big_q(c16) | (~big_p(c11)) | (~big_p(elem!0)) | big_p(f3(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (~big_q(c8)) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_p(elem!0)))),
% 22.63/22.84      inference(transitivity,[status(thm)],[824, 822])).
% 22.63/22.84  tff(826,plain,
% 22.63/22.84      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c8)) | big_q(elem!0) | (~big_q(c8)) | big_p(f3(elem!0)) | big_q(c16) | (~big_p(c11)) | (~big_p(elem!0)) | big_p(f3(elem!0)))),
% 22.63/22.84      inference(quant_inst,[status(thm)],[])).
% 22.63/22.84  tff(827,plain,
% 22.63/22.84      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (~big_q(c8)) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_p(elem!0))),
% 22.63/22.84      inference(modus_ponens,[status(thm)],[826, 825])).
% 22.63/22.84  tff(828,plain,
% 22.63/22.84      ($false),
% 22.63/22.84      inference(unit_resolution,[status(thm)],[827, 52, 5, 820, 762, 2, 819, 821])).
% 22.63/22.84  tff(829,plain,(big_p(f3(elem!0)) | big_q(elem!0) | big_q(c16) | (~big_q(c8))), inference(lemma,lemma(discharge,[]))).
% 22.63/22.84  tff(830,plain,
% 22.63/22.84      (~big_q(c8)),
% 22.63/22.84      inference(unit_resolution,[status(thm)],[829, 820, 2, 5])).
% 22.63/22.84  tff(831,assumption,(~big_p(f1(c11))), introduced(assumption)).
% 22.63/22.84  tff(832,plain,
% 22.63/22.84      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0)) | big_p(f1(c11)))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | big_p(c3) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0)) | big_p(f1(c11)))),
% 22.63/22.84      inference(rewrite,[status(thm)],[])).
% 22.63/22.84  tff(833,plain,
% 22.63/22.84      ((big_p(c3) | big_q(elem!0) | (~big_p(elem!0)) | big_p(f1(c11)) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0))) <=> (big_p(c3) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0)) | big_p(f1(c11)))),
% 22.63/22.84      inference(rewrite,[status(thm)],[])).
% 22.63/22.84  tff(834,plain,
% 22.63/22.84      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(elem!0) | (~big_p(elem!0)) | big_p(f1(c11)) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0)))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0)) | big_p(f1(c11))))),
% 22.63/22.84      inference(monotonicity,[status(thm)],[833])).
% 22.63/22.84  tff(835,plain,
% 22.63/22.84      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(elem!0) | (~big_p(elem!0)) | big_p(f1(c11)) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0)))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | big_p(c3) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0)) | big_p(f1(c11)))),
% 22.63/22.84      inference(transitivity,[status(thm)],[834, 832])).
% 22.63/22.84  tff(836,plain,
% 22.63/22.84      ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(elem!0) | (~big_p(elem!0)) | big_p(f1(c11)) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0)))),
% 22.63/22.84      inference(quant_inst,[status(thm)],[])).
% 22.63/22.84  tff(837,plain,
% 22.63/22.84      ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | big_p(c3) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0)) | big_p(f1(c11))),
% 22.63/22.84      inference(modus_ponens,[status(thm)],[836, 835])).
% 22.63/22.84  tff(838,plain,
% 22.63/22.84      ($false),
% 22.63/22.84      inference(unit_resolution,[status(thm)],[837, 71, 5, 762, 8, 126, 831, 783])).
% 22.63/22.84  tff(839,plain,(big_p(f1(c11)) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(c3) | big_q(c4)), inference(lemma,lemma(discharge,[]))).
% 22.63/22.84  tff(840,plain,
% 22.63/22.84      (big_p(f1(c11))),
% 22.63/22.84      inference(unit_resolution,[status(thm)],[839, 783, 8, 126, 5])).
% 22.63/22.84  tff(841,plain,
% 22.63/22.84      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0)) | (~big_p(f1(c11))))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | big_p(c3) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0)) | (~big_p(f1(c11))))),
% 22.63/22.84      inference(rewrite,[status(thm)],[])).
% 22.63/22.84  tff(842,plain,
% 22.63/22.84      ((big_p(c3) | big_q(elem!0) | (~big_p(elem!0)) | big_p(c3) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f1(c11)))) <=> (big_p(c3) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0)) | (~big_p(f1(c11))))),
% 22.63/22.84      inference(rewrite,[status(thm)],[])).
% 22.63/22.84  tff(843,plain,
% 22.63/22.84      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(elem!0) | (~big_p(elem!0)) | big_p(c3) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f1(c11))))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0)) | (~big_p(f1(c11)))))),
% 22.63/22.84      inference(monotonicity,[status(thm)],[842])).
% 22.63/22.84  tff(844,plain,
% 22.63/22.84      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(elem!0) | (~big_p(elem!0)) | big_p(c3) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f1(c11))))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | big_p(c3) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0)) | (~big_p(f1(c11))))),
% 22.63/22.84      inference(transitivity,[status(thm)],[843, 841])).
% 22.63/22.84  tff(845,plain,
% 22.63/22.84      ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | (big_p(c3) | big_q(elem!0) | (~big_p(elem!0)) | big_p(c3) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f1(c11))))),
% 22.63/22.84      inference(quant_inst,[status(thm)],[])).
% 22.63/22.84  tff(846,plain,
% 22.63/22.84      ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : (big_p(c3) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | (~big_p(Y)))) | big_p(c3) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0)) | (~big_p(f1(c11)))),
% 22.63/22.84      inference(modus_ponens,[status(thm)],[845, 844])).
% 22.63/22.84  tff(847,plain,
% 22.63/22.84      ($false),
% 22.63/22.84      inference(unit_resolution,[status(thm)],[846, 71, 5, 762, 8, 126, 840, 783])).
% 22.63/22.84  tff(848,plain,(big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(c3)), inference(lemma,lemma(discharge,[]))).
% 22.63/22.84  tff(849,plain,
% 22.63/22.84      (big_q(c4)),
% 22.63/22.84      inference(unit_resolution,[status(thm)],[848, 126, 8, 5])).
% 22.63/22.84  tff(850,plain,
% 22.63/22.84      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_p(c3) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | (~big_p(elem!0)) | (~big_q(c4)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_p(c3) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | (~big_p(elem!0)) | (~big_q(c4)))),
% 22.63/22.84      inference(rewrite,[status(thm)],[])).
% 22.63/22.84  tff(851,plain,
% 22.63/22.84      (((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | big_p(c3) | big_q(c16) | (~big_p(c11)) | (~big_p(elem!0)) | big_p(c3)) <=> (big_p(c3) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | (~big_p(elem!0)) | (~big_q(c4)))),
% 22.63/22.84      inference(rewrite,[status(thm)],[])).
% 22.63/22.84  tff(852,plain,
% 22.63/22.84      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | big_p(c3) | big_q(c16) | (~big_p(c11)) | (~big_p(elem!0)) | big_p(c3))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_p(c3) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | (~big_p(elem!0)) | (~big_q(c4))))),
% 22.63/22.84      inference(monotonicity,[status(thm)],[851])).
% 22.63/22.84  tff(853,plain,
% 22.63/22.84      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | big_p(c3) | big_q(c16) | (~big_p(c11)) | (~big_p(elem!0)) | big_p(c3))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_p(c3) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | (~big_p(elem!0)) | (~big_q(c4)))),
% 22.63/22.84      inference(transitivity,[status(thm)],[852, 850])).
% 22.63/22.84  tff(854,plain,
% 22.63/22.84      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | big_p(c3) | big_q(c16) | (~big_p(c11)) | (~big_p(elem!0)) | big_p(c3))),
% 22.63/22.84      inference(quant_inst,[status(thm)],[])).
% 22.63/22.84  tff(855,plain,
% 22.63/22.84      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_p(c3) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | (~big_p(elem!0)) | (~big_q(c4))),
% 22.63/22.85      inference(modus_ponens,[status(thm)],[854, 853])).
% 22.63/22.85  tff(856,plain,
% 22.63/22.85      ($false),
% 22.63/22.85      inference(unit_resolution,[status(thm)],[855, 52, 5, 762, 2, 819, 126, 849])).
% 22.63/22.85  tff(857,plain,(big_p(c3) | big_q(elem!0) | big_q(c16) | big_q(f2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 22.63/22.85  tff(858,plain,
% 22.63/22.85      (big_p(c3)),
% 22.63/22.85      inference(unit_resolution,[status(thm)],[857, 8, 2, 5])).
% 22.63/22.85  tff(859,plain,
% 22.63/22.85      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | ((~big_p(c3)) | big_q(c8) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(f3(elem!0)) | (~big_p(elem!0)))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | (~big_p(c3)) | big_q(c8) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(f3(elem!0)) | (~big_p(elem!0)))),
% 22.63/22.85      inference(rewrite,[status(thm)],[])).
% 22.63/22.85  tff(860,plain,
% 22.63/22.85      (((~big_p(c3)) | big_q(c8) | (~big_p(elem!0)) | big_p(f3(elem!0)) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(f3(elem!0))) <=> ((~big_p(c3)) | big_q(c8) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(f3(elem!0)) | (~big_p(elem!0)))),
% 22.63/22.85      inference(rewrite,[status(thm)],[])).
% 22.63/22.85  tff(861,plain,
% 22.63/22.85      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | ((~big_p(c3)) | big_q(c8) | (~big_p(elem!0)) | big_p(f3(elem!0)) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(f3(elem!0)))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | ((~big_p(c3)) | big_q(c8) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(f3(elem!0)) | (~big_p(elem!0))))),
% 22.63/22.85      inference(monotonicity,[status(thm)],[860])).
% 22.63/22.85  tff(862,plain,
% 22.63/22.85      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | ((~big_p(c3)) | big_q(c8) | (~big_p(elem!0)) | big_p(f3(elem!0)) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(f3(elem!0)))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | (~big_p(c3)) | big_q(c8) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(f3(elem!0)) | (~big_p(elem!0)))),
% 22.63/22.85      inference(transitivity,[status(thm)],[861, 859])).
% 22.63/22.85  tff(863,plain,
% 22.63/22.85      ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | ((~big_p(c3)) | big_q(c8) | (~big_p(elem!0)) | big_p(f3(elem!0)) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(f3(elem!0)))),
% 22.63/22.85      inference(quant_inst,[status(thm)],[])).
% 22.63/22.85  tff(864,plain,
% 22.63/22.85      ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | (~big_p(c3)) | big_q(c8) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(f3(elem!0)) | (~big_p(elem!0))),
% 22.63/22.85      inference(modus_ponens,[status(thm)],[863, 862])).
% 22.63/22.85  tff(865,plain,
% 22.63/22.85      ((~big_p(c3)) | big_q(c8) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(f3(elem!0))),
% 22.63/22.85      inference(unit_resolution,[status(thm)],[864, 18, 762])).
% 22.63/22.85  tff(866,plain,
% 22.63/22.85      (big_q(c4)),
% 22.63/22.85      inference(unit_resolution,[status(thm)],[865, 858, 5, 830, 820, 8])).
% 22.63/22.85  tff(867,plain,
% 22.63/22.85      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c3)) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_q(c4)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c3)) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_q(c4)))),
% 22.63/22.85      inference(rewrite,[status(thm)],[])).
% 22.63/22.85  tff(868,plain,
% 22.63/22.85      (((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | big_p(f3(elem!0)) | big_q(c16) | (~big_p(c11)) | (~big_p(c3)) | big_p(f3(elem!0))) <=> ((~big_p(c3)) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_q(c4)))),
% 22.63/22.85      inference(rewrite,[status(thm)],[])).
% 22.63/22.85  tff(869,plain,
% 22.63/22.85      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | big_p(f3(elem!0)) | big_q(c16) | (~big_p(c11)) | (~big_p(c3)) | big_p(f3(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c3)) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_q(c4))))),
% 22.63/22.85      inference(monotonicity,[status(thm)],[868])).
% 22.63/22.85  tff(870,plain,
% 22.63/22.85      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | big_p(f3(elem!0)) | big_q(c16) | (~big_p(c11)) | (~big_p(c3)) | big_p(f3(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c3)) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_q(c4)))),
% 22.63/22.85      inference(transitivity,[status(thm)],[869, 867])).
% 22.63/22.85  tff(871,plain,
% 22.63/22.85      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | big_p(f3(elem!0)) | big_q(c16) | (~big_p(c11)) | (~big_p(c3)) | big_p(f3(elem!0)))),
% 22.63/22.85      inference(quant_inst,[status(thm)],[])).
% 22.63/22.85  tff(872,plain,
% 22.63/22.85      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c3)) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_q(c4))),
% 22.63/22.85      inference(modus_ponens,[status(thm)],[871, 870])).
% 22.63/22.85  tff(873,plain,
% 22.63/22.85      ($false),
% 22.63/22.85      inference(unit_resolution,[status(thm)],[872, 52, 5, 820, 2, 819, 858, 866])).
% 22.63/22.85  tff(874,plain,(big_q(f2(elem!0)) | big_q(elem!0) | big_p(f3(elem!0)) | big_q(c16)), inference(lemma,lemma(discharge,[]))).
% 22.63/22.85  tff(875,plain,
% 22.63/22.85      (big_q(f2(elem!0))),
% 22.63/22.85      inference(unit_resolution,[status(thm)],[874, 820, 5, 2])).
% 22.63/22.85  tff(876,plain,
% 22.63/22.85      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_q(f2(elem!0))) | (~big_p(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_q(f2(elem!0))) | (~big_p(elem!0)))),
% 22.63/22.85      inference(rewrite,[status(thm)],[])).
% 22.63/22.85  tff(877,plain,
% 22.63/22.85      (((~big_q(f2(elem!0))) | big_q(elem!0) | (~big_q(f2(elem!0))) | big_p(f3(elem!0)) | big_q(c16) | (~big_p(c11)) | (~big_p(elem!0)) | big_p(f3(elem!0))) <=> (big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_q(f2(elem!0))) | (~big_p(elem!0)))),
% 22.63/22.85      inference(rewrite,[status(thm)],[])).
% 22.63/22.85  tff(878,plain,
% 22.63/22.85      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(elem!0))) | big_q(elem!0) | (~big_q(f2(elem!0))) | big_p(f3(elem!0)) | big_q(c16) | (~big_p(c11)) | (~big_p(elem!0)) | big_p(f3(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_q(f2(elem!0))) | (~big_p(elem!0))))),
% 22.63/22.85      inference(monotonicity,[status(thm)],[877])).
% 22.63/22.85  tff(879,plain,
% 22.63/22.85      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(elem!0))) | big_q(elem!0) | (~big_q(f2(elem!0))) | big_p(f3(elem!0)) | big_q(c16) | (~big_p(c11)) | (~big_p(elem!0)) | big_p(f3(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_q(f2(elem!0))) | (~big_p(elem!0)))),
% 22.63/22.85      inference(transitivity,[status(thm)],[878, 876])).
% 22.63/22.85  tff(880,plain,
% 22.63/22.85      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(elem!0))) | big_q(elem!0) | (~big_q(f2(elem!0))) | big_p(f3(elem!0)) | big_q(c16) | (~big_p(c11)) | (~big_p(elem!0)) | big_p(f3(elem!0)))),
% 22.63/22.85      inference(quant_inst,[status(thm)],[])).
% 22.63/22.85  tff(881,plain,
% 22.63/22.85      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_q(f2(elem!0))) | (~big_p(elem!0))),
% 22.63/22.85      inference(modus_ponens,[status(thm)],[880, 879])).
% 22.63/22.85  tff(882,plain,
% 22.63/22.85      ($false),
% 22.63/22.85      inference(unit_resolution,[status(thm)],[881, 52, 5, 820, 762, 875, 2, 819])).
% 22.63/22.85  tff(883,plain,(big_p(f3(elem!0)) | big_q(elem!0) | big_q(c16)), inference(lemma,lemma(discharge,[]))).
% 22.63/22.85  tff(884,plain,
% 22.63/22.85      (big_p(f3(elem!0))),
% 22.63/22.85      inference(unit_resolution,[status(thm)],[883, 2, 5])).
% 22.63/22.85  tff(885,plain,
% 22.63/22.85      (^[X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : refl(((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10)))) <=> ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10)))))),
% 22.63/22.85      inference(bind,[status(th)],[])).
% 22.63/22.85  tff(886,plain,
% 22.63/22.85      (![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10)))) <=> ![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))),
% 22.63/22.85      inference(quant_intro,[status(thm)],[885])).
% 22.63/22.85  tff(887,plain,
% 22.63/22.85      (![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10)))) <=> ![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))),
% 22.63/22.85      inference(rewrite,[status(thm)],[])).
% 22.63/22.85  tff(888,plain,
% 22.63/22.85      (^[X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) <=> ((~big_q(X12)) | (~big_p(X10)) | (~big_p(f3(X10))))), (((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) <=> (((~big_q(X12)) | (~big_p(X10)) | (~big_p(f3(X10)))) | (~big_p(c15))))), rewrite((((~big_q(X12)) | (~big_p(X10)) | (~big_p(f3(X10)))) | (~big_p(c15))) <=> ((~big_q(X12)) | (~big_p(X10)) | (~big_p(c15)) | (~big_p(f3(X10))))), (((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) <=> ((~big_q(X12)) | (~big_p(X10)) | (~big_p(c15)) | (~big_p(f3(X10)))))), ((((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) | (~big_q(X13))) <=> (((~big_q(X12)) | (~big_p(X10)) | (~big_p(c15)) | (~big_p(f3(X10)))) | (~big_q(X13))))), rewrite((((~big_q(X12)) | (~big_p(X10)) | (~big_p(c15)) | (~big_p(f3(X10)))) | (~big_q(X13))) <=> ((~big_q(X12)) | (~big_q(X13)) | (~big_p(X10)) | (~big_p(c15)) | (~big_p(f3(X10))))), ((((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) | (~big_q(X13))) <=> ((~big_q(X12)) | (~big_q(X13)) | (~big_p(X10)) | (~big_p(c15)) | (~big_p(f3(X10)))))), (((((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) | (~big_q(X13))) | big_q(c16)) <=> (((~big_q(X12)) | (~big_q(X13)) | (~big_p(X10)) | (~big_p(c15)) | (~big_p(f3(X10)))) | big_q(c16)))), rewrite((((~big_q(X12)) | (~big_q(X13)) | (~big_p(X10)) | (~big_p(c15)) | (~big_p(f3(X10)))) | big_q(c16)) <=> ((~big_q(X12)) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(c15)) | (~big_p(f3(X10))))), (((((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) | (~big_q(X13))) | big_q(c16)) <=> ((~big_q(X12)) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(c15)) | (~big_p(f3(X10)))))), ((((((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) | (~big_q(X13))) | big_q(c16)) | (~big_p(X14))) <=> (((~big_q(X12)) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(c15)) | (~big_p(f3(X10)))) | (~big_p(X14))))), rewrite((((~big_q(X12)) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(c15)) | (~big_p(f3(X10)))) | (~big_p(X14))) <=> ((~big_q(X12)) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))), ((((((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) | (~big_q(X13))) | big_q(c16)) | (~big_p(X14))) <=> ((~big_q(X12)) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10)))))), (((((((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) | (~big_q(X13))) | big_q(c16)) | (~big_p(X14))) | big_q(X15)) <=> (((~big_q(X12)) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10)))) | big_q(X15)))), rewrite((((~big_q(X12)) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10)))) | big_q(X15)) <=> ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))), (((((((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) | (~big_q(X13))) | big_q(c16)) | (~big_p(X14))) | big_q(X15)) <=> ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))))),
% 22.63/22.85      inference(bind,[status(th)],[])).
% 22.63/22.85  tff(889,plain,
% 22.63/22.85      (![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((((((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) | (~big_q(X13))) | big_q(c16)) | (~big_p(X14))) | big_q(X15)) <=> ![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))),
% 22.63/22.85      inference(quant_intro,[status(thm)],[888])).
% 22.63/22.85  tff(890,axiom,(![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((((((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) | (~big_q(X13))) | big_q(c16)) | (~big_p(X14))) | big_q(X15))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_121')).
% 22.63/22.85  tff(891,plain,
% 22.63/22.85      (![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))),
% 22.63/22.85      inference(modus_ponens,[status(thm)],[890, 889])).
% 22.63/22.85  tff(892,plain,
% 22.63/22.85      (![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))),
% 22.63/22.85      inference(modus_ponens,[status(thm)],[891, 887])).
% 22.63/22.85  tff(893,plain,(
% 22.63/22.85      ![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))),
% 22.63/22.85      inference(skolemize,[status(sab)],[892])).
% 22.63/22.85  tff(894,plain,
% 22.63/22.85      (![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))),
% 22.63/22.85      inference(modus_ponens,[status(thm)],[893, 886])).
% 22.63/22.85  tff(895,plain,
% 22.63/22.85      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (big_q(c16) | (~big_p(c15)) | big_q(elem!0) | (~big_q(f4(elem!0))) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | big_q(c16) | (~big_p(c15)) | big_q(elem!0) | (~big_q(f4(elem!0))) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))),
% 22.63/22.85      inference(rewrite,[status(thm)],[])).
% 22.63/22.85  tff(896,plain,
% 22.63/22.85      (((~big_q(f4(elem!0))) | big_q(elem!0) | (~big_q(f4(elem!0))) | (~big_p(elem!0)) | big_q(c16) | (~big_p(f3(elem!0))) | (~big_p(c15)) | (~big_p(f3(elem!0)))) <=> (big_q(c16) | (~big_p(c15)) | big_q(elem!0) | (~big_q(f4(elem!0))) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))),
% 22.63/22.85      inference(rewrite,[status(thm)],[])).
% 22.63/22.85  tff(897,plain,
% 22.63/22.85      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(f4(elem!0))) | big_q(elem!0) | (~big_q(f4(elem!0))) | (~big_p(elem!0)) | big_q(c16) | (~big_p(f3(elem!0))) | (~big_p(c15)) | (~big_p(f3(elem!0))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (big_q(c16) | (~big_p(c15)) | big_q(elem!0) | (~big_q(f4(elem!0))) | (~big_p(f3(elem!0))) | (~big_p(elem!0))))),
% 22.63/22.85      inference(monotonicity,[status(thm)],[896])).
% 22.63/22.85  tff(898,plain,
% 22.63/22.85      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(f4(elem!0))) | big_q(elem!0) | (~big_q(f4(elem!0))) | (~big_p(elem!0)) | big_q(c16) | (~big_p(f3(elem!0))) | (~big_p(c15)) | (~big_p(f3(elem!0))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | big_q(c16) | (~big_p(c15)) | big_q(elem!0) | (~big_q(f4(elem!0))) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))),
% 22.63/22.85      inference(transitivity,[status(thm)],[897, 895])).
% 22.63/22.85  tff(899,plain,
% 22.63/22.85      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(f4(elem!0))) | big_q(elem!0) | (~big_q(f4(elem!0))) | (~big_p(elem!0)) | big_q(c16) | (~big_p(f3(elem!0))) | (~big_p(c15)) | (~big_p(f3(elem!0))))),
% 22.63/22.85      inference(quant_inst,[status(thm)],[])).
% 22.63/22.85  tff(900,plain,
% 22.63/22.85      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | big_q(c16) | (~big_p(c15)) | big_q(elem!0) | (~big_q(f4(elem!0))) | (~big_p(f3(elem!0))) | (~big_p(elem!0))),
% 22.63/22.85      inference(modus_ponens,[status(thm)],[899, 898])).
% 22.63/22.85  tff(901,plain,
% 22.63/22.85      (~big_p(c15)),
% 22.63/22.85      inference(unit_resolution,[status(thm)],[900, 894, 5, 430, 884, 762, 2])).
% 22.63/22.85  tff(902,plain,
% 22.63/22.85      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | (~big_p(c11)) | big_p(c15) | big_q(elem!0) | (~big_q(f4(elem!0))) | (~big_p(f3(elem!0))))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_p(c15) | big_q(elem!0) | (~big_q(f4(elem!0))) | (~big_p(f3(elem!0))))),
% 22.63/22.85      inference(rewrite,[status(thm)],[])).
% 22.63/22.85  tff(903,plain,
% 22.63/22.85      (((~big_q(f4(elem!0))) | big_q(elem!0) | (~big_q(f4(elem!0))) | big_p(c15) | big_q(c16) | (~big_p(c11)) | (~big_p(f3(elem!0))) | big_p(c15)) <=> (big_q(c16) | (~big_p(c11)) | big_p(c15) | big_q(elem!0) | (~big_q(f4(elem!0))) | (~big_p(f3(elem!0))))),
% 22.63/22.85      inference(rewrite,[status(thm)],[])).
% 22.63/22.85  tff(904,plain,
% 22.63/22.85      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f4(elem!0))) | big_q(elem!0) | (~big_q(f4(elem!0))) | big_p(c15) | big_q(c16) | (~big_p(c11)) | (~big_p(f3(elem!0))) | big_p(c15))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | (~big_p(c11)) | big_p(c15) | big_q(elem!0) | (~big_q(f4(elem!0))) | (~big_p(f3(elem!0)))))),
% 22.63/22.85      inference(monotonicity,[status(thm)],[903])).
% 22.63/22.85  tff(905,plain,
% 22.63/22.85      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f4(elem!0))) | big_q(elem!0) | (~big_q(f4(elem!0))) | big_p(c15) | big_q(c16) | (~big_p(c11)) | (~big_p(f3(elem!0))) | big_p(c15))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_p(c15) | big_q(elem!0) | (~big_q(f4(elem!0))) | (~big_p(f3(elem!0))))),
% 22.63/22.85      inference(transitivity,[status(thm)],[904, 902])).
% 22.63/22.85  tff(906,plain,
% 22.63/22.85      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f4(elem!0))) | big_q(elem!0) | (~big_q(f4(elem!0))) | big_p(c15) | big_q(c16) | (~big_p(c11)) | (~big_p(f3(elem!0))) | big_p(c15))),
% 22.63/22.85      inference(quant_inst,[status(thm)],[])).
% 22.63/22.85  tff(907,plain,
% 22.63/22.85      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_p(c15) | big_q(elem!0) | (~big_q(f4(elem!0))) | (~big_p(f3(elem!0)))),
% 22.63/22.85      inference(modus_ponens,[status(thm)],[906, 905])).
% 22.63/22.85  tff(908,plain,
% 22.63/22.85      ($false),
% 22.63/22.85      inference(unit_resolution,[status(thm)],[907, 52, 5, 430, 884, 2, 901, 819])).
% 22.63/22.85  tff(909,plain,((~big_q(f4(elem!0))) | big_q(elem!0) | big_q(c16)), inference(lemma,lemma(discharge,[]))).
% 22.63/22.85  tff(910,plain,
% 22.63/22.85      (~big_q(f4(elem!0))),
% 22.63/22.85      inference(unit_resolution,[status(thm)],[909, 2, 5])).
% 22.63/22.85  tff(911,assumption,(~big_p(c2)), introduced(assumption)).
% 22.63/22.85  tff(912,plain,
% 22.63/22.85      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | ((~big_p(c3)) | big_p(c2) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0)))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | (~big_p(c3)) | big_p(c2) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0)))),
% 22.63/22.85      inference(rewrite,[status(thm)],[])).
% 22.63/22.85  tff(913,plain,
% 22.63/22.85      (((~big_p(c3)) | big_q(elem!0) | (~big_p(elem!0)) | big_p(c2) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(c2)) <=> ((~big_p(c3)) | big_p(c2) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0)))),
% 22.63/22.85      inference(rewrite,[status(thm)],[])).
% 22.63/22.85  tff(914,plain,
% 22.63/22.85      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | ((~big_p(c3)) | big_q(elem!0) | (~big_p(elem!0)) | big_p(c2) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(c2))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | ((~big_p(c3)) | big_p(c2) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0))))),
% 22.63/22.85      inference(monotonicity,[status(thm)],[913])).
% 22.63/22.85  tff(915,plain,
% 22.63/22.85      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | ((~big_p(c3)) | big_q(elem!0) | (~big_p(elem!0)) | big_p(c2) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(c2))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | (~big_p(c3)) | big_p(c2) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0)))),
% 22.63/22.85      inference(transitivity,[status(thm)],[914, 912])).
% 22.63/22.85  tff(916,plain,
% 22.63/22.85      ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | ((~big_p(c3)) | big_q(elem!0) | (~big_p(elem!0)) | big_p(c2) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(c2))),
% 22.63/22.85      inference(quant_inst,[status(thm)],[])).
% 22.63/22.85  tff(917,plain,
% 22.63/22.85      ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | (~big_p(c3)) | big_p(c2) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(elem!0))),
% 22.63/22.85      inference(modus_ponens,[status(thm)],[916, 915])).
% 22.63/22.85  tff(918,plain,
% 22.63/22.85      ($false),
% 22.63/22.85      inference(unit_resolution,[status(thm)],[917, 18, 5, 762, 8, 911, 7, 783])).
% 22.63/22.85  tff(919,plain,(big_p(c2) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(c3)) | big_q(c4)), inference(lemma,lemma(discharge,[]))).
% 22.63/22.85  tff(920,plain,
% 22.63/22.85      (big_q(c4)),
% 22.63/22.85      inference(unit_resolution,[status(thm)],[919, 911, 8, 7, 5])).
% 22.63/22.85  tff(921,plain,
% 22.63/22.85      (((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | (big_p(c2) | (~big_p(c11)) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_q(c4)))) <=> ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | big_p(c2) | (~big_p(c11)) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_q(c4)))),
% 22.63/22.85      inference(rewrite,[status(thm)],[])).
% 22.63/22.85  tff(922,plain,
% 22.63/22.85      (((~big_q(c4)) | big_p(c2) | big_q(elem!0) | big_q(elem!0) | big_p(c2) | (~big_p(c11)) | big_p(c19) | big_q(f4(elem!0))) <=> (big_p(c2) | (~big_p(c11)) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_q(c4)))),
% 22.63/22.85      inference(rewrite,[status(thm)],[])).
% 22.63/22.85  tff(923,plain,
% 22.63/22.85      (((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | ((~big_q(c4)) | big_p(c2) | big_q(elem!0) | big_q(elem!0) | big_p(c2) | (~big_p(c11)) | big_p(c19) | big_q(f4(elem!0)))) <=> ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | (big_p(c2) | (~big_p(c11)) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_q(c4))))),
% 22.63/22.85      inference(monotonicity,[status(thm)],[922])).
% 22.63/22.85  tff(924,plain,
% 22.63/22.85      (((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | ((~big_q(c4)) | big_p(c2) | big_q(elem!0) | big_q(elem!0) | big_p(c2) | (~big_p(c11)) | big_p(c19) | big_q(f4(elem!0)))) <=> ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | big_p(c2) | (~big_p(c11)) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_q(c4)))),
% 22.63/22.85      inference(transitivity,[status(thm)],[923, 921])).
% 22.63/22.85  tff(925,plain,
% 22.63/22.85      ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | ((~big_q(c4)) | big_p(c2) | big_q(elem!0) | big_q(elem!0) | big_p(c2) | (~big_p(c11)) | big_p(c19) | big_q(f4(elem!0)))),
% 22.63/22.86      inference(quant_inst,[status(thm)],[])).
% 22.63/22.86  tff(926,plain,
% 22.63/22.86      ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | big_p(c2) | (~big_p(c11)) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_q(c4))),
% 22.63/22.86      inference(modus_ponens,[status(thm)],[925, 924])).
% 22.63/22.86  tff(927,plain,
% 22.63/22.86      ($false),
% 22.63/22.86      inference(unit_resolution,[status(thm)],[926, 222, 307, 5, 306, 911, 819, 920])).
% 22.63/22.86  tff(928,plain,(big_p(c2) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_q(f2(elem!0)) | (~big_p(c3))), inference(lemma,lemma(discharge,[]))).
% 22.63/22.86  tff(929,plain,
% 22.63/22.86      (big_p(c2)),
% 22.63/22.86      inference(unit_resolution,[status(thm)],[928, 307, 5, 306, 8, 858])).
% 22.63/22.86  tff(930,assumption,(big_p(c2)), introduced(assumption)).
% 22.63/22.86  tff(931,assumption,(~big_q(c8)), introduced(assumption)).
% 22.63/22.86  tff(932,plain,
% 22.63/22.86      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | ((~big_p(c3)) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(f1(elem!0)) | (~big_p(elem!0)))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | (~big_p(c3)) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(f1(elem!0)) | (~big_p(elem!0)))),
% 22.63/22.86      inference(rewrite,[status(thm)],[])).
% 22.63/22.86  tff(933,plain,
% 22.63/22.86      (((~big_p(c3)) | big_q(elem!0) | (~big_p(elem!0)) | big_p(f1(elem!0)) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(f1(elem!0))) <=> ((~big_p(c3)) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(f1(elem!0)) | (~big_p(elem!0)))),
% 22.63/22.86      inference(rewrite,[status(thm)],[])).
% 22.63/22.86  tff(934,plain,
% 22.63/22.86      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | ((~big_p(c3)) | big_q(elem!0) | (~big_p(elem!0)) | big_p(f1(elem!0)) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(f1(elem!0)))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | ((~big_p(c3)) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(f1(elem!0)) | (~big_p(elem!0))))),
% 22.63/22.86      inference(monotonicity,[status(thm)],[933])).
% 22.63/22.86  tff(935,plain,
% 22.63/22.86      (((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | ((~big_p(c3)) | big_q(elem!0) | (~big_p(elem!0)) | big_p(f1(elem!0)) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(f1(elem!0)))) <=> ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | (~big_p(c3)) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(f1(elem!0)) | (~big_p(elem!0)))),
% 22.63/22.86      inference(transitivity,[status(thm)],[934, 932])).
% 22.63/22.86  tff(936,plain,
% 22.63/22.86      ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | ((~big_p(c3)) | big_q(elem!0) | (~big_p(elem!0)) | big_p(f1(elem!0)) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(f1(elem!0)))),
% 22.63/22.86      inference(quant_inst,[status(thm)],[])).
% 22.63/22.86  tff(937,plain,
% 22.63/22.86      ((~![W: $i, Y: $i, X3: $i, X2: $i, X1: $i] : ((~big_p(c3)) | big_q(X2) | (~big_p(X1)) | big_p(X3) | big_q(c4) | big_q(W) | big_q(f2(W)) | big_p(Y))) | (~big_p(c3)) | big_q(c4) | big_q(elem!0) | big_q(f2(elem!0)) | big_p(f1(elem!0)) | (~big_p(elem!0))),
% 22.63/22.86      inference(modus_ponens,[status(thm)],[936, 935])).
% 22.63/22.86  tff(938,plain,
% 22.63/22.86      (big_q(c4)),
% 22.63/22.86      inference(unit_resolution,[status(thm)],[937, 18, 5, 762, 88, 8, 858])).
% 22.63/22.86  tff(939,plain,
% 22.63/22.86      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(f1(elem!0)) | (~big_p(elem!0)) | (~big_q(c4)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(f1(elem!0)) | (~big_p(elem!0)) | (~big_q(c4)))),
% 22.63/22.86      inference(rewrite,[status(thm)],[])).
% 22.63/22.86  tff(940,plain,
% 22.63/22.86      (((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | big_p(f1(elem!0)) | big_q(c16) | (~big_p(c11)) | (~big_p(elem!0)) | big_p(f1(elem!0))) <=> (big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(f1(elem!0)) | (~big_p(elem!0)) | (~big_q(c4)))),
% 22.63/22.86      inference(rewrite,[status(thm)],[])).
% 22.63/22.86  tff(941,plain,
% 22.63/22.86      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | big_p(f1(elem!0)) | big_q(c16) | (~big_p(c11)) | (~big_p(elem!0)) | big_p(f1(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(f1(elem!0)) | (~big_p(elem!0)) | (~big_q(c4))))),
% 22.63/22.86      inference(monotonicity,[status(thm)],[940])).
% 22.63/22.86  tff(942,plain,
% 22.63/22.86      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | big_p(f1(elem!0)) | big_q(c16) | (~big_p(c11)) | (~big_p(elem!0)) | big_p(f1(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(f1(elem!0)) | (~big_p(elem!0)) | (~big_q(c4)))),
% 22.63/22.86      inference(transitivity,[status(thm)],[941, 939])).
% 22.63/22.86  tff(943,plain,
% 22.63/22.86      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | big_p(f1(elem!0)) | big_q(c16) | (~big_p(c11)) | (~big_p(elem!0)) | big_p(f1(elem!0)))),
% 22.63/22.86      inference(quant_inst,[status(thm)],[])).
% 22.63/22.86  tff(944,plain,
% 22.63/22.86      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(f1(elem!0)) | (~big_p(elem!0)) | (~big_q(c4))),
% 22.63/22.86      inference(modus_ponens,[status(thm)],[943, 942])).
% 22.63/22.86  tff(945,plain,
% 22.63/22.86      ($false),
% 22.63/22.86      inference(unit_resolution,[status(thm)],[944, 52, 5, 762, 88, 2, 819, 938])).
% 22.63/22.86  tff(946,plain,(big_p(f1(elem!0)) | big_q(elem!0) | big_q(c16) | big_q(f2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 22.63/22.86  tff(947,plain,
% 22.63/22.86      (big_p(f1(elem!0))),
% 22.63/22.86      inference(unit_resolution,[status(thm)],[946, 8, 2, 5])).
% 22.63/22.86  tff(948,assumption,(big_p(f1(elem!0))), introduced(assumption)).
% 22.63/22.86  tff(949,assumption,(big_q(c1)), introduced(assumption)).
% 22.63/22.86  tff(950,plain,
% 22.63/22.86      (((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | ((~big_p(c11)) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(f3(elem!0)) | (~big_q(c1)))) <=> ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | (~big_p(c11)) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(f3(elem!0)) | (~big_q(c1)))),
% 22.63/22.86      inference(rewrite,[status(thm)],[])).
% 22.63/22.86  tff(951,plain,
% 22.63/22.86      (((~big_q(c1)) | big_p(f3(elem!0)) | big_q(elem!0) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_p(c11)) | big_p(c19) | big_q(f4(elem!0))) <=> ((~big_p(c11)) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(f3(elem!0)) | (~big_q(c1)))),
% 22.63/22.86      inference(rewrite,[status(thm)],[])).
% 22.63/22.86  tff(952,plain,
% 22.63/22.86      (((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | ((~big_q(c1)) | big_p(f3(elem!0)) | big_q(elem!0) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_p(c11)) | big_p(c19) | big_q(f4(elem!0)))) <=> ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | ((~big_p(c11)) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(f3(elem!0)) | (~big_q(c1))))),
% 22.63/22.86      inference(monotonicity,[status(thm)],[951])).
% 22.63/22.86  tff(953,plain,
% 22.63/22.86      (((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | ((~big_q(c1)) | big_p(f3(elem!0)) | big_q(elem!0) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_p(c11)) | big_p(c19) | big_q(f4(elem!0)))) <=> ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | (~big_p(c11)) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(f3(elem!0)) | (~big_q(c1)))),
% 22.63/22.86      inference(transitivity,[status(thm)],[952, 950])).
% 22.63/22.86  tff(954,plain,
% 22.63/22.86      ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | ((~big_q(c1)) | big_p(f3(elem!0)) | big_q(elem!0) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_p(c11)) | big_p(c19) | big_q(f4(elem!0)))),
% 22.63/22.86      inference(quant_inst,[status(thm)],[])).
% 22.63/22.86  tff(955,plain,
% 22.63/22.86      ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | (~big_p(c11)) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(f3(elem!0)) | (~big_q(c1))),
% 22.63/22.86      inference(modus_ponens,[status(thm)],[954, 953])).
% 22.63/22.86  tff(956,plain,
% 22.63/22.86      ($false),
% 22.63/22.86      inference(unit_resolution,[status(thm)],[955, 222, 307, 5, 306, 820, 949, 819])).
% 22.63/22.86  tff(957,plain,((~big_q(c1)) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(f3(elem!0))), inference(lemma,lemma(discharge,[]))).
% 22.63/22.86  tff(958,plain,
% 22.63/22.86      (~big_q(c1)),
% 22.63/22.86      inference(unit_resolution,[status(thm)],[957, 820, 5, 306, 307])).
% 22.63/22.86  tff(959,plain,
% 22.63/22.86      (^[W: $i, X: $i, X2: $i, X1: $i] : refl((big_q(c1) | big_q(X2) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X)))) <=> (big_q(c1) | big_q(X2) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X)))))),
% 22.63/22.86      inference(bind,[status(th)],[])).
% 22.63/22.86  tff(960,plain,
% 22.63/22.86      (![W: $i, X: $i, X2: $i, X1: $i] : (big_q(c1) | big_q(X2) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X)))) <=> ![W: $i, X: $i, X2: $i, X1: $i] : (big_q(c1) | big_q(X2) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X))))),
% 22.63/22.86      inference(quant_intro,[status(thm)],[959])).
% 22.63/22.86  tff(961,plain,
% 22.63/22.86      (![W: $i, X: $i, X2: $i, X1: $i] : (big_q(c1) | big_q(X2) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X)))) <=> ![W: $i, X: $i, X2: $i, X1: $i] : (big_q(c1) | big_q(X2) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X))))),
% 22.63/22.86      inference(rewrite,[status(thm)],[])).
% 22.63/22.86  tff(962,plain,
% 22.63/22.86      (^[W: $i, X: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(X)) | (~big_p(f1(X)))) | big_q(c1)) <=> (big_q(c1) | (~big_p(X)) | (~big_p(f1(X))))), (((((~big_p(X)) | (~big_p(f1(X)))) | big_q(c1)) | (~big_p(c2))) <=> ((big_q(c1) | (~big_p(X)) | (~big_p(f1(X)))) | (~big_p(c2))))), rewrite(((big_q(c1) | (~big_p(X)) | (~big_p(f1(X)))) | (~big_p(c2))) <=> (big_q(c1) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X))))), (((((~big_p(X)) | (~big_p(f1(X)))) | big_q(c1)) | (~big_p(c2))) <=> (big_q(c1) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X)))))), ((((((~big_p(X)) | (~big_p(f1(X)))) | big_q(c1)) | (~big_p(c2))) | big_q(f2(W))) <=> ((big_q(c1) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X)))) | big_q(f2(W))))), rewrite(((big_q(c1) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X)))) | big_q(f2(W))) <=> (big_q(c1) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X))))), ((((((~big_p(X)) | (~big_p(f1(X)))) | big_q(c1)) | (~big_p(c2))) | big_q(f2(W))) <=> (big_q(c1) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X)))))), (((((((~big_p(X)) | (~big_p(f1(X)))) | big_q(c1)) | (~big_p(c2))) | big_q(f2(W))) | big_q(W)) <=> ((big_q(c1) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X)))) | big_q(W)))), rewrite(((big_q(c1) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X)))) | big_q(W)) <=> (big_q(c1) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X))))), (((((((~big_p(X)) | (~big_p(f1(X)))) | big_q(c1)) | (~big_p(c2))) | big_q(f2(W))) | big_q(W)) <=> (big_q(c1) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X)))))), ((((((((~big_p(X)) | (~big_p(f1(X)))) | big_q(c1)) | (~big_p(c2))) | big_q(f2(W))) | big_q(W)) | (~big_p(X1))) <=> ((big_q(c1) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X)))) | (~big_p(X1))))), rewrite(((big_q(c1) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X)))) | (~big_p(X1))) <=> (big_q(c1) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X))))), ((((((((~big_p(X)) | (~big_p(f1(X)))) | big_q(c1)) | (~big_p(c2))) | big_q(f2(W))) | big_q(W)) | (~big_p(X1))) <=> (big_q(c1) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X)))))), (((((((((~big_p(X)) | (~big_p(f1(X)))) | big_q(c1)) | (~big_p(c2))) | big_q(f2(W))) | big_q(W)) | (~big_p(X1))) | big_q(X2)) <=> ((big_q(c1) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X)))) | big_q(X2)))), rewrite(((big_q(c1) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X)))) | big_q(X2)) <=> (big_q(c1) | big_q(X2) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X))))), (((((((((~big_p(X)) | (~big_p(f1(X)))) | big_q(c1)) | (~big_p(c2))) | big_q(f2(W))) | big_q(W)) | (~big_p(X1))) | big_q(X2)) <=> (big_q(c1) | big_q(X2) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X))))))),
% 22.63/22.86      inference(bind,[status(th)],[])).
% 22.63/22.86  tff(963,plain,
% 22.63/22.86      (![W: $i, X: $i, X2: $i, X1: $i] : ((((((((~big_p(X)) | (~big_p(f1(X)))) | big_q(c1)) | (~big_p(c2))) | big_q(f2(W))) | big_q(W)) | (~big_p(X1))) | big_q(X2)) <=> ![W: $i, X: $i, X2: $i, X1: $i] : (big_q(c1) | big_q(X2) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X))))),
% 22.63/22.86      inference(quant_intro,[status(thm)],[962])).
% 22.63/22.86  tff(964,axiom,(![W: $i, X: $i, X2: $i, X1: $i] : ((((((((~big_p(X)) | (~big_p(f1(X)))) | big_q(c1)) | (~big_p(c2))) | big_q(f2(W))) | big_q(W)) | (~big_p(X1))) | big_q(X2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_25')).
% 22.63/22.86  tff(965,plain,
% 22.63/22.86      (![W: $i, X: $i, X2: $i, X1: $i] : (big_q(c1) | big_q(X2) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X))))),
% 22.63/22.86      inference(modus_ponens,[status(thm)],[964, 963])).
% 22.63/22.86  tff(966,plain,
% 22.63/22.86      (![W: $i, X: $i, X2: $i, X1: $i] : (big_q(c1) | big_q(X2) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X))))),
% 22.63/22.86      inference(modus_ponens,[status(thm)],[965, 961])).
% 22.63/22.86  tff(967,plain,(
% 22.63/22.86      ![W: $i, X: $i, X2: $i, X1: $i] : (big_q(c1) | big_q(X2) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X))))),
% 22.63/22.86      inference(skolemize,[status(sab)],[966])).
% 22.63/22.86  tff(968,plain,
% 22.63/22.86      (![W: $i, X: $i, X2: $i, X1: $i] : (big_q(c1) | big_q(X2) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X))))),
% 22.63/22.86      inference(modus_ponens,[status(thm)],[967, 960])).
% 22.63/22.86  tff(969,plain,
% 22.63/22.86      (((~![W: $i, X: $i, X2: $i, X1: $i] : (big_q(c1) | big_q(X2) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X))))) | (big_q(c1) | big_q(c8) | (~big_p(c2)) | (~big_p(c11)) | big_q(elem!0) | (~big_p(f1(elem!0))) | (~big_p(elem!0)) | big_q(f2(c8)))) <=> ((~![W: $i, X: $i, X2: $i, X1: $i] : (big_q(c1) | big_q(X2) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X))))) | big_q(c1) | big_q(c8) | (~big_p(c2)) | (~big_p(c11)) | big_q(elem!0) | (~big_p(f1(elem!0))) | (~big_p(elem!0)) | big_q(f2(c8)))),
% 22.63/22.86      inference(rewrite,[status(thm)],[])).
% 22.63/22.86  tff(970,plain,
% 22.63/22.86      ((big_q(c1) | big_q(elem!0) | (~big_p(c11)) | big_q(c8) | big_q(f2(c8)) | (~big_p(c2)) | (~big_p(elem!0)) | (~big_p(f1(elem!0)))) <=> (big_q(c1) | big_q(c8) | (~big_p(c2)) | (~big_p(c11)) | big_q(elem!0) | (~big_p(f1(elem!0))) | (~big_p(elem!0)) | big_q(f2(c8)))),
% 22.63/22.86      inference(rewrite,[status(thm)],[])).
% 22.63/22.86  tff(971,plain,
% 22.63/22.86      (((~![W: $i, X: $i, X2: $i, X1: $i] : (big_q(c1) | big_q(X2) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X))))) | (big_q(c1) | big_q(elem!0) | (~big_p(c11)) | big_q(c8) | big_q(f2(c8)) | (~big_p(c2)) | (~big_p(elem!0)) | (~big_p(f1(elem!0))))) <=> ((~![W: $i, X: $i, X2: $i, X1: $i] : (big_q(c1) | big_q(X2) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X))))) | (big_q(c1) | big_q(c8) | (~big_p(c2)) | (~big_p(c11)) | big_q(elem!0) | (~big_p(f1(elem!0))) | (~big_p(elem!0)) | big_q(f2(c8))))),
% 22.63/22.86      inference(monotonicity,[status(thm)],[970])).
% 22.63/22.86  tff(972,plain,
% 22.63/22.86      (((~![W: $i, X: $i, X2: $i, X1: $i] : (big_q(c1) | big_q(X2) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X))))) | (big_q(c1) | big_q(elem!0) | (~big_p(c11)) | big_q(c8) | big_q(f2(c8)) | (~big_p(c2)) | (~big_p(elem!0)) | (~big_p(f1(elem!0))))) <=> ((~![W: $i, X: $i, X2: $i, X1: $i] : (big_q(c1) | big_q(X2) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X))))) | big_q(c1) | big_q(c8) | (~big_p(c2)) | (~big_p(c11)) | big_q(elem!0) | (~big_p(f1(elem!0))) | (~big_p(elem!0)) | big_q(f2(c8)))),
% 22.63/22.86      inference(transitivity,[status(thm)],[971, 969])).
% 22.63/22.86  tff(973,plain,
% 22.63/22.86      ((~![W: $i, X: $i, X2: $i, X1: $i] : (big_q(c1) | big_q(X2) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X))))) | (big_q(c1) | big_q(elem!0) | (~big_p(c11)) | big_q(c8) | big_q(f2(c8)) | (~big_p(c2)) | (~big_p(elem!0)) | (~big_p(f1(elem!0))))),
% 22.63/22.86      inference(quant_inst,[status(thm)],[])).
% 22.63/22.86  tff(974,plain,
% 22.63/22.86      ((~![W: $i, X: $i, X2: $i, X1: $i] : (big_q(c1) | big_q(X2) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X))))) | big_q(c1) | big_q(c8) | (~big_p(c2)) | (~big_p(c11)) | big_q(elem!0) | (~big_p(f1(elem!0))) | (~big_p(elem!0)) | big_q(f2(c8))),
% 22.63/22.86      inference(modus_ponens,[status(thm)],[973, 972])).
% 22.63/22.86  tff(975,plain,
% 22.63/22.86      (big_q(c1) | big_q(c8) | (~big_p(c2)) | (~big_p(c11)) | big_q(elem!0) | (~big_p(f1(elem!0))) | big_q(f2(c8))),
% 22.63/22.86      inference(unit_resolution,[status(thm)],[974, 968, 762])).
% 22.63/22.86  tff(976,plain,
% 22.63/22.86      (big_q(f2(c8))),
% 22.63/22.86      inference(unit_resolution,[status(thm)],[975, 958, 5, 948, 819, 930, 931])).
% 22.63/22.86  tff(977,plain,
% 22.63/22.86      (((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | (big_q(c1) | (~big_p(c11)) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(f3(elem!0)) | (~big_q(f2(c8))))) <=> ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | big_q(c1) | (~big_p(c11)) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(f3(elem!0)) | (~big_q(f2(c8))))),
% 22.63/22.86      inference(rewrite,[status(thm)],[])).
% 22.63/22.86  tff(978,plain,
% 22.63/22.86      (((~big_q(f2(c8))) | big_p(f3(elem!0)) | big_q(c1) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_p(c11)) | big_p(c19) | big_q(f4(elem!0))) <=> (big_q(c1) | (~big_p(c11)) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(f3(elem!0)) | (~big_q(f2(c8))))),
% 22.63/22.86      inference(rewrite,[status(thm)],[])).
% 22.63/22.86  tff(979,plain,
% 22.63/22.86      (((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | ((~big_q(f2(c8))) | big_p(f3(elem!0)) | big_q(c1) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_p(c11)) | big_p(c19) | big_q(f4(elem!0)))) <=> ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | (big_q(c1) | (~big_p(c11)) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(f3(elem!0)) | (~big_q(f2(c8)))))),
% 22.63/22.86      inference(monotonicity,[status(thm)],[978])).
% 22.63/22.86  tff(980,plain,
% 22.63/22.86      (((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | ((~big_q(f2(c8))) | big_p(f3(elem!0)) | big_q(c1) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_p(c11)) | big_p(c19) | big_q(f4(elem!0)))) <=> ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | big_q(c1) | (~big_p(c11)) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(f3(elem!0)) | (~big_q(f2(c8))))),
% 22.63/22.86      inference(transitivity,[status(thm)],[979, 977])).
% 22.63/22.86  tff(981,plain,
% 22.63/22.86      ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | ((~big_q(f2(c8))) | big_p(f3(elem!0)) | big_q(c1) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_p(c11)) | big_p(c19) | big_q(f4(elem!0)))),
% 22.63/22.86      inference(quant_inst,[status(thm)],[])).
% 22.63/22.86  tff(982,plain,
% 22.63/22.86      ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | big_q(c1) | (~big_p(c11)) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_p(f3(elem!0)) | (~big_q(f2(c8)))),
% 22.63/22.86      inference(modus_ponens,[status(thm)],[981, 980])).
% 22.63/22.86  tff(983,plain,
% 22.63/22.86      ($false),
% 22.63/22.86      inference(unit_resolution,[status(thm)],[982, 222, 307, 5, 306, 820, 958, 819, 976])).
% 22.63/22.86  tff(984,plain,(big_p(f3(elem!0)) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_p(f1(elem!0))) | (~big_p(c2)) | big_q(c8)), inference(lemma,lemma(discharge,[]))).
% 22.63/22.86  tff(985,plain,
% 22.63/22.86      (big_p(f3(elem!0))),
% 22.63/22.86      inference(unit_resolution,[status(thm)],[984, 307, 5, 306, 947, 930, 931])).
% 22.63/22.86  tff(986,assumption,(~big_p(c15)), introduced(assumption)).
% 22.63/22.86  tff(987,assumption,(big_p(f3(elem!0))), introduced(assumption)).
% 22.63/22.86  tff(988,plain,
% 22.63/22.86      (^[X11: $i, X17: $i, X10: $i, X16: $i] : refl((big_q(c14) | big_q(X16) | big_q(X17) | (~big_p(X10)) | big_p(X11) | big_p(c19) | big_q(f4(X16)) | (~big_p(f3(X10)))) <=> (big_q(c14) | big_q(X16) | big_q(X17) | (~big_p(X10)) | big_p(X11) | big_p(c19) | big_q(f4(X16)) | (~big_p(f3(X10)))))),
% 22.63/22.86      inference(bind,[status(th)],[])).
% 22.63/22.86  tff(989,plain,
% 22.63/22.86      (![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | (~big_p(X10)) | big_p(X11) | big_p(c19) | big_q(f4(X16)) | (~big_p(f3(X10)))) <=> ![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | (~big_p(X10)) | big_p(X11) | big_p(c19) | big_q(f4(X16)) | (~big_p(f3(X10))))),
% 22.63/22.86      inference(quant_intro,[status(thm)],[988])).
% 22.63/22.86  tff(990,plain,
% 22.63/22.86      (![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | (~big_p(X10)) | big_p(X11) | big_p(c19) | big_q(f4(X16)) | (~big_p(f3(X10)))) <=> ![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | (~big_p(X10)) | big_p(X11) | big_p(c19) | big_q(f4(X16)) | (~big_p(f3(X10))))),
% 22.63/22.86      inference(rewrite,[status(thm)],[])).
% 22.63/22.86  tff(991,plain,
% 22.63/22.86      (^[X11: $i, X17: $i, X10: $i, X16: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(X10)) | (~big_p(f3(X10)))) | big_q(c14)) <=> (big_q(c14) | (~big_p(X10)) | (~big_p(f3(X10))))), (((((~big_p(X10)) | (~big_p(f3(X10)))) | big_q(c14)) | big_p(X11)) <=> ((big_q(c14) | (~big_p(X10)) | (~big_p(f3(X10)))) | big_p(X11)))), rewrite(((big_q(c14) | (~big_p(X10)) | (~big_p(f3(X10)))) | big_p(X11)) <=> (big_q(c14) | (~big_p(X10)) | big_p(X11) | (~big_p(f3(X10))))), (((((~big_p(X10)) | (~big_p(f3(X10)))) | big_q(c14)) | big_p(X11)) <=> (big_q(c14) | (~big_p(X10)) | big_p(X11) | (~big_p(f3(X10)))))), ((((((~big_p(X10)) | (~big_p(f3(X10)))) | big_q(c14)) | big_p(X11)) | big_q(f4(X16))) <=> ((big_q(c14) | (~big_p(X10)) | big_p(X11) | (~big_p(f3(X10)))) | big_q(f4(X16))))), rewrite(((big_q(c14) | (~big_p(X10)) | big_p(X11) | (~big_p(f3(X10)))) | big_q(f4(X16))) <=> (big_q(c14) | (~big_p(X10)) | big_p(X11) | big_q(f4(X16)) | (~big_p(f3(X10))))), ((((((~big_p(X10)) | (~big_p(f3(X10)))) | big_q(c14)) | big_p(X11)) | big_q(f4(X16))) <=> (big_q(c14) | (~big_p(X10)) | big_p(X11) | big_q(f4(X16)) | (~big_p(f3(X10)))))), (((((((~big_p(X10)) | (~big_p(f3(X10)))) | big_q(c14)) | big_p(X11)) | big_q(f4(X16))) | big_q(X16)) <=> ((big_q(c14) | (~big_p(X10)) | big_p(X11) | big_q(f4(X16)) | (~big_p(f3(X10)))) | big_q(X16)))), rewrite(((big_q(c14) | (~big_p(X10)) | big_p(X11) | big_q(f4(X16)) | (~big_p(f3(X10)))) | big_q(X16)) <=> (big_q(c14) | big_q(X16) | (~big_p(X10)) | big_p(X11) | big_q(f4(X16)) | (~big_p(f3(X10))))), (((((((~big_p(X10)) | (~big_p(f3(X10)))) | big_q(c14)) | big_p(X11)) | big_q(f4(X16))) | big_q(X16)) <=> (big_q(c14) | big_q(X16) | (~big_p(X10)) | big_p(X11) | big_q(f4(X16)) | (~big_p(f3(X10)))))), ((((((((~big_p(X10)) | (~big_p(f3(X10)))) | big_q(c14)) | big_p(X11)) | big_q(f4(X16))) | big_q(X16)) | big_p(c19)) <=> ((big_q(c14) | big_q(X16) | (~big_p(X10)) | big_p(X11) | big_q(f4(X16)) | (~big_p(f3(X10)))) | big_p(c19)))), rewrite(((big_q(c14) | big_q(X16) | (~big_p(X10)) | big_p(X11) | big_q(f4(X16)) | (~big_p(f3(X10)))) | big_p(c19)) <=> (big_q(c14) | big_q(X16) | (~big_p(X10)) | big_p(X11) | big_p(c19) | big_q(f4(X16)) | (~big_p(f3(X10))))), ((((((((~big_p(X10)) | (~big_p(f3(X10)))) | big_q(c14)) | big_p(X11)) | big_q(f4(X16))) | big_q(X16)) | big_p(c19)) <=> (big_q(c14) | big_q(X16) | (~big_p(X10)) | big_p(X11) | big_p(c19) | big_q(f4(X16)) | (~big_p(f3(X10)))))), (((((((((~big_p(X10)) | (~big_p(f3(X10)))) | big_q(c14)) | big_p(X11)) | big_q(f4(X16))) | big_q(X16)) | big_p(c19)) | big_q(X17)) <=> ((big_q(c14) | big_q(X16) | (~big_p(X10)) | big_p(X11) | big_p(c19) | big_q(f4(X16)) | (~big_p(f3(X10)))) | big_q(X17)))), rewrite(((big_q(c14) | big_q(X16) | (~big_p(X10)) | big_p(X11) | big_p(c19) | big_q(f4(X16)) | (~big_p(f3(X10)))) | big_q(X17)) <=> (big_q(c14) | big_q(X16) | big_q(X17) | (~big_p(X10)) | big_p(X11) | big_p(c19) | big_q(f4(X16)) | (~big_p(f3(X10))))), (((((((((~big_p(X10)) | (~big_p(f3(X10)))) | big_q(c14)) | big_p(X11)) | big_q(f4(X16))) | big_q(X16)) | big_p(c19)) | big_q(X17)) <=> (big_q(c14) | big_q(X16) | big_q(X17) | (~big_p(X10)) | big_p(X11) | big_p(c19) | big_q(f4(X16)) | (~big_p(f3(X10))))))),
% 22.63/22.87      inference(bind,[status(th)],[])).
% 22.63/22.87  tff(992,plain,
% 22.63/22.87      (![X11: $i, X17: $i, X10: $i, X16: $i] : ((((((((~big_p(X10)) | (~big_p(f3(X10)))) | big_q(c14)) | big_p(X11)) | big_q(f4(X16))) | big_q(X16)) | big_p(c19)) | big_q(X17)) <=> ![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | (~big_p(X10)) | big_p(X11) | big_p(c19) | big_q(f4(X16)) | (~big_p(f3(X10))))),
% 22.63/22.87      inference(quant_intro,[status(thm)],[991])).
% 22.63/22.87  tff(993,axiom,(![X11: $i, X17: $i, X10: $i, X16: $i] : ((((((((~big_p(X10)) | (~big_p(f3(X10)))) | big_q(c14)) | big_p(X11)) | big_q(f4(X16))) | big_q(X16)) | big_p(c19)) | big_q(X17))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_117')).
% 22.63/22.87  tff(994,plain,
% 22.63/22.87      (![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | (~big_p(X10)) | big_p(X11) | big_p(c19) | big_q(f4(X16)) | (~big_p(f3(X10))))),
% 22.63/22.87      inference(modus_ponens,[status(thm)],[993, 992])).
% 22.63/22.87  tff(995,plain,
% 22.63/22.87      (![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | (~big_p(X10)) | big_p(X11) | big_p(c19) | big_q(f4(X16)) | (~big_p(f3(X10))))),
% 22.63/22.87      inference(modus_ponens,[status(thm)],[994, 990])).
% 22.63/22.87  tff(996,plain,(
% 22.63/22.87      ![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | (~big_p(X10)) | big_p(X11) | big_p(c19) | big_q(f4(X16)) | (~big_p(f3(X10))))),
% 22.63/22.87      inference(skolemize,[status(sab)],[995])).
% 22.63/22.87  tff(997,plain,
% 22.63/22.87      (![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | (~big_p(X10)) | big_p(X11) | big_p(c19) | big_q(f4(X16)) | (~big_p(f3(X10))))),
% 22.63/22.87      inference(modus_ponens,[status(thm)],[996, 989])).
% 22.63/22.87  tff(998,plain,
% 22.63/22.87      (((~![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | (~big_p(X10)) | big_p(X11) | big_p(c19) | big_q(f4(X16)) | (~big_p(f3(X10))))) | (big_q(c14) | big_p(c19) | big_p(c15) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))) <=> ((~![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | (~big_p(X10)) | big_p(X11) | big_p(c19) | big_q(f4(X16)) | (~big_p(f3(X10))))) | big_q(c14) | big_p(c19) | big_p(c15) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))),
% 22.63/22.87      inference(rewrite,[status(thm)],[])).
% 22.63/22.87  tff(999,plain,
% 22.63/22.87      ((big_q(c14) | big_q(elem!0) | big_q(elem!0) | (~big_p(elem!0)) | big_p(c15) | big_p(c19) | big_q(f4(elem!0)) | (~big_p(f3(elem!0)))) <=> (big_q(c14) | big_p(c19) | big_p(c15) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))),
% 22.63/22.87      inference(rewrite,[status(thm)],[])).
% 22.63/22.87  tff(1000,plain,
% 22.63/22.87      (((~![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | (~big_p(X10)) | big_p(X11) | big_p(c19) | big_q(f4(X16)) | (~big_p(f3(X10))))) | (big_q(c14) | big_q(elem!0) | big_q(elem!0) | (~big_p(elem!0)) | big_p(c15) | big_p(c19) | big_q(f4(elem!0)) | (~big_p(f3(elem!0))))) <=> ((~![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | (~big_p(X10)) | big_p(X11) | big_p(c19) | big_q(f4(X16)) | (~big_p(f3(X10))))) | (big_q(c14) | big_p(c19) | big_p(c15) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_p(f3(elem!0))) | (~big_p(elem!0))))),
% 22.63/22.87      inference(monotonicity,[status(thm)],[999])).
% 22.63/22.87  tff(1001,plain,
% 22.63/22.87      (((~![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | (~big_p(X10)) | big_p(X11) | big_p(c19) | big_q(f4(X16)) | (~big_p(f3(X10))))) | (big_q(c14) | big_q(elem!0) | big_q(elem!0) | (~big_p(elem!0)) | big_p(c15) | big_p(c19) | big_q(f4(elem!0)) | (~big_p(f3(elem!0))))) <=> ((~![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | (~big_p(X10)) | big_p(X11) | big_p(c19) | big_q(f4(X16)) | (~big_p(f3(X10))))) | big_q(c14) | big_p(c19) | big_p(c15) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))),
% 22.63/22.87      inference(transitivity,[status(thm)],[1000, 998])).
% 22.63/22.87  tff(1002,plain,
% 22.63/22.87      ((~![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | (~big_p(X10)) | big_p(X11) | big_p(c19) | big_q(f4(X16)) | (~big_p(f3(X10))))) | (big_q(c14) | big_q(elem!0) | big_q(elem!0) | (~big_p(elem!0)) | big_p(c15) | big_p(c19) | big_q(f4(elem!0)) | (~big_p(f3(elem!0))))),
% 22.63/22.87      inference(quant_inst,[status(thm)],[])).
% 22.63/22.87  tff(1003,plain,
% 22.63/22.87      ((~![X11: $i, X17: $i, X10: $i, X16: $i] : (big_q(c14) | big_q(X16) | big_q(X17) | (~big_p(X10)) | big_p(X11) | big_p(c19) | big_q(f4(X16)) | (~big_p(f3(X10))))) | big_q(c14) | big_p(c19) | big_p(c15) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_p(f3(elem!0))) | (~big_p(elem!0))),
% 22.63/22.87      inference(modus_ponens,[status(thm)],[1002, 1001])).
% 22.63/22.87  tff(1004,plain,
% 22.63/22.87      ($false),
% 22.63/22.87      inference(unit_resolution,[status(thm)],[1003, 997, 146, 307, 5, 306, 987, 762, 986])).
% 22.63/22.87  tff(1005,plain,(big_p(c15) | big_q(c14) | big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_p(f3(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 22.63/22.87  tff(1006,plain,
% 22.63/22.87      (big_p(c15)),
% 22.63/22.87      inference(unit_resolution,[status(thm)],[1005, 307, 146, 5, 306, 985])).
% 22.63/22.87  tff(1007,plain,
% 22.63/22.87      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_p(c2)) | big_q(c16) | (~big_p(c15)) | big_q(f2(elem!0)) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_q(c1)))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (~big_p(c2)) | big_q(c16) | (~big_p(c15)) | big_q(f2(elem!0)) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_q(c1)))),
% 22.63/22.87      inference(rewrite,[status(thm)],[])).
% 22.63/22.87  tff(1008,plain,
% 22.63/22.87      (((~big_q(c1)) | big_q(f2(elem!0)) | (~big_q(c1)) | (~big_p(elem!0)) | big_q(c16) | (~big_p(c2)) | (~big_p(c15)) | (~big_p(f3(elem!0)))) <=> ((~big_p(c2)) | big_q(c16) | (~big_p(c15)) | big_q(f2(elem!0)) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_q(c1)))),
% 22.63/22.87      inference(rewrite,[status(thm)],[])).
% 22.63/22.87  tff(1009,plain,
% 22.63/22.87      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(c1)) | big_q(f2(elem!0)) | (~big_q(c1)) | (~big_p(elem!0)) | big_q(c16) | (~big_p(c2)) | (~big_p(c15)) | (~big_p(f3(elem!0))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_p(c2)) | big_q(c16) | (~big_p(c15)) | big_q(f2(elem!0)) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_q(c1))))),
% 22.63/22.87      inference(monotonicity,[status(thm)],[1008])).
% 22.63/22.87  tff(1010,plain,
% 22.63/22.87      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(c1)) | big_q(f2(elem!0)) | (~big_q(c1)) | (~big_p(elem!0)) | big_q(c16) | (~big_p(c2)) | (~big_p(c15)) | (~big_p(f3(elem!0))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (~big_p(c2)) | big_q(c16) | (~big_p(c15)) | big_q(f2(elem!0)) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_q(c1)))),
% 22.63/22.87      inference(transitivity,[status(thm)],[1009, 1007])).
% 22.63/22.87  tff(1011,plain,
% 22.63/22.87      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(c1)) | big_q(f2(elem!0)) | (~big_q(c1)) | (~big_p(elem!0)) | big_q(c16) | (~big_p(c2)) | (~big_p(c15)) | (~big_p(f3(elem!0))))),
% 22.63/22.87      inference(quant_inst,[status(thm)],[])).
% 22.63/22.87  tff(1012,plain,
% 22.63/22.87      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (~big_p(c2)) | big_q(c16) | (~big_p(c15)) | big_q(f2(elem!0)) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_q(c1))),
% 22.63/22.87      inference(modus_ponens,[status(thm)],[1011, 1010])).
% 22.63/22.87  tff(1013,plain,
% 22.63/22.87      ((~big_p(c2)) | big_q(c16) | (~big_p(c15)) | big_q(f2(elem!0)) | (~big_p(f3(elem!0))) | (~big_q(c1))),
% 22.63/22.87      inference(unit_resolution,[status(thm)],[1012, 894, 762])).
% 22.63/22.87  tff(1014,plain,
% 22.63/22.87      (~big_q(c1)),
% 22.63/22.87      inference(unit_resolution,[status(thm)],[1013, 1006, 8, 930, 2, 985])).
% 22.63/22.87  tff(1015,plain,
% 22.63/22.87      (big_q(f2(c8))),
% 22.63/22.87      inference(unit_resolution,[status(thm)],[975, 1014, 5, 947, 819, 930, 931])).
% 22.63/22.87  tff(1016,plain,
% 22.63/22.87      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (big_q(c16) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_q(f2(c8))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | big_q(c16) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_q(f2(c8))))),
% 22.63/22.87      inference(rewrite,[status(thm)],[])).
% 22.63/22.87  tff(1017,plain,
% 22.63/22.87      (((~big_q(f2(c8))) | big_q(elem!0) | (~big_q(f2(c8))) | (~big_p(elem!0)) | big_q(c16) | (~big_p(c15)) | (~big_p(c15)) | (~big_p(f3(elem!0)))) <=> (big_q(c16) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_q(f2(c8))))),
% 22.63/22.87      inference(rewrite,[status(thm)],[])).
% 22.63/22.87  tff(1018,plain,
% 22.63/22.87      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(f2(c8))) | big_q(elem!0) | (~big_q(f2(c8))) | (~big_p(elem!0)) | big_q(c16) | (~big_p(c15)) | (~big_p(c15)) | (~big_p(f3(elem!0))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (big_q(c16) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_q(f2(c8)))))),
% 22.63/22.87      inference(monotonicity,[status(thm)],[1017])).
% 22.63/22.87  tff(1019,plain,
% 22.63/22.87      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(f2(c8))) | big_q(elem!0) | (~big_q(f2(c8))) | (~big_p(elem!0)) | big_q(c16) | (~big_p(c15)) | (~big_p(c15)) | (~big_p(f3(elem!0))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | big_q(c16) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_q(f2(c8))))),
% 22.63/22.87      inference(transitivity,[status(thm)],[1018, 1016])).
% 22.63/22.87  tff(1020,plain,
% 22.63/22.87      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(f2(c8))) | big_q(elem!0) | (~big_q(f2(c8))) | (~big_p(elem!0)) | big_q(c16) | (~big_p(c15)) | (~big_p(c15)) | (~big_p(f3(elem!0))))),
% 22.63/22.87      inference(quant_inst,[status(thm)],[])).
% 22.63/22.87  tff(1021,plain,
% 22.63/22.87      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | big_q(c16) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_q(f2(c8)))),
% 22.63/22.87      inference(modus_ponens,[status(thm)],[1020, 1019])).
% 22.63/22.87  tff(1022,plain,
% 22.63/22.87      ($false),
% 22.63/22.87      inference(unit_resolution,[status(thm)],[1021, 894, 5, 985, 762, 2, 1006, 1015])).
% 22.63/22.87  tff(1023,plain,(big_p(c19) | big_q(elem!0) | big_q(c16) | (~big_p(c2)) | big_q(c8) | big_q(f2(elem!0)) | big_q(c14) | big_q(f4(elem!0))), inference(lemma,lemma(discharge,[]))).
% 22.63/22.87  tff(1024,plain,
% 22.63/22.87      (big_p(c19)),
% 22.63/22.87      inference(unit_resolution,[status(thm)],[1023, 931, 2, 930, 5, 8, 146, 306])).
% 22.63/22.87  tff(1025,assumption,(big_q(f2(c8))), introduced(assumption)).
% 22.63/22.87  tff(1026,plain,
% 22.63/22.87      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_p(c19)) | (~big_q(f2(c8))))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_p(c19)) | (~big_q(f2(c8))))),
% 22.63/22.87      inference(rewrite,[status(thm)],[])).
% 22.63/22.87  tff(1027,plain,
% 22.63/22.87      (((~big_q(f2(c8))) | big_q(elem!0) | (~big_q(f2(c8))) | big_p(f3(elem!0)) | big_q(c16) | (~big_p(c11)) | (~big_p(c19)) | big_p(f3(elem!0))) <=> (big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_p(c19)) | (~big_q(f2(c8))))),
% 22.63/22.87      inference(rewrite,[status(thm)],[])).
% 22.63/22.87  tff(1028,plain,
% 22.63/22.87      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(c8))) | big_q(elem!0) | (~big_q(f2(c8))) | big_p(f3(elem!0)) | big_q(c16) | (~big_p(c11)) | (~big_p(c19)) | big_p(f3(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_p(c19)) | (~big_q(f2(c8)))))),
% 22.63/22.87      inference(monotonicity,[status(thm)],[1027])).
% 22.63/22.87  tff(1029,plain,
% 22.63/22.87      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(c8))) | big_q(elem!0) | (~big_q(f2(c8))) | big_p(f3(elem!0)) | big_q(c16) | (~big_p(c11)) | (~big_p(c19)) | big_p(f3(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_p(c19)) | (~big_q(f2(c8))))),
% 22.63/22.87      inference(transitivity,[status(thm)],[1028, 1026])).
% 22.63/22.87  tff(1030,plain,
% 22.63/22.87      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(c8))) | big_q(elem!0) | (~big_q(f2(c8))) | big_p(f3(elem!0)) | big_q(c16) | (~big_p(c11)) | (~big_p(c19)) | big_p(f3(elem!0)))),
% 22.63/22.87      inference(quant_inst,[status(thm)],[])).
% 22.63/22.87  tff(1031,plain,
% 22.63/22.87      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | big_p(f3(elem!0)) | (~big_p(c19)) | (~big_q(f2(c8)))),
% 22.63/22.87      inference(modus_ponens,[status(thm)],[1030, 1029])).
% 22.63/22.87  tff(1032,plain,
% 22.63/22.87      ($false),
% 22.63/22.87      inference(unit_resolution,[status(thm)],[1031, 52, 147, 5, 820, 2, 819, 1025])).
% 22.63/22.87  tff(1033,plain,((~big_q(f2(c8))) | (~big_p(c19)) | big_q(elem!0) | big_p(f3(elem!0)) | big_q(c16)), inference(lemma,lemma(discharge,[]))).
% 22.63/22.87  tff(1034,plain,
% 22.63/22.87      (~big_q(f2(c8))),
% 22.63/22.87      inference(unit_resolution,[status(thm)],[1033, 820, 5, 147, 2])).
% 22.63/22.87  tff(1035,plain,
% 22.63/22.87      (big_q(c1)),
% 22.63/22.87      inference(unit_resolution,[status(thm)],[975, 1034, 5, 948, 819, 930, 931])).
% 22.63/22.87  tff(1036,plain,
% 22.63/22.87      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | (~big_p(c11)) | big_p(f3(elem!0)) | (~big_p(c19)) | big_q(f2(c8)) | (~big_q(c1)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_p(f3(elem!0)) | (~big_p(c19)) | big_q(f2(c8)) | (~big_q(c1)))),
% 22.63/22.87      inference(rewrite,[status(thm)],[])).
% 22.63/22.87  tff(1037,plain,
% 22.63/22.87      (((~big_q(c1)) | big_q(f2(c8)) | (~big_q(c1)) | big_p(f3(elem!0)) | big_q(c16) | (~big_p(c11)) | (~big_p(c19)) | big_p(f3(elem!0))) <=> (big_q(c16) | (~big_p(c11)) | big_p(f3(elem!0)) | (~big_p(c19)) | big_q(f2(c8)) | (~big_q(c1)))),
% 22.63/22.87      inference(rewrite,[status(thm)],[])).
% 22.63/22.87  tff(1038,plain,
% 22.63/22.87      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c1)) | big_q(f2(c8)) | (~big_q(c1)) | big_p(f3(elem!0)) | big_q(c16) | (~big_p(c11)) | (~big_p(c19)) | big_p(f3(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | (~big_p(c11)) | big_p(f3(elem!0)) | (~big_p(c19)) | big_q(f2(c8)) | (~big_q(c1))))),
% 22.63/22.87      inference(monotonicity,[status(thm)],[1037])).
% 22.63/22.87  tff(1039,plain,
% 22.63/22.87      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c1)) | big_q(f2(c8)) | (~big_q(c1)) | big_p(f3(elem!0)) | big_q(c16) | (~big_p(c11)) | (~big_p(c19)) | big_p(f3(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_p(f3(elem!0)) | (~big_p(c19)) | big_q(f2(c8)) | (~big_q(c1)))),
% 22.63/22.87      inference(transitivity,[status(thm)],[1038, 1036])).
% 22.63/22.87  tff(1040,plain,
% 22.63/22.87      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c1)) | big_q(f2(c8)) | (~big_q(c1)) | big_p(f3(elem!0)) | big_q(c16) | (~big_p(c11)) | (~big_p(c19)) | big_p(f3(elem!0)))),
% 22.63/22.87      inference(quant_inst,[status(thm)],[])).
% 22.63/22.87  tff(1041,plain,
% 22.63/22.87      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_p(f3(elem!0)) | (~big_p(c19)) | big_q(f2(c8)) | (~big_q(c1))),
% 22.63/22.87      inference(modus_ponens,[status(thm)],[1040, 1039])).
% 22.63/22.87  tff(1042,plain,
% 22.63/22.87      ($false),
% 22.63/22.87      inference(unit_resolution,[status(thm)],[1041, 52, 147, 820, 1035, 2, 819, 1034])).
% 22.63/22.87  tff(1043,plain,(big_p(f3(elem!0)) | (~big_p(c19)) | big_q(c16) | big_q(elem!0) | (~big_p(f1(elem!0))) | (~big_p(c2)) | big_q(c8)), inference(lemma,lemma(discharge,[]))).
% 22.63/22.87  tff(1044,plain,
% 22.63/22.87      (big_p(f3(elem!0))),
% 22.63/22.87      inference(unit_resolution,[status(thm)],[1043, 1024, 2, 5, 947, 930, 931])).
% 22.63/22.87  tff(1045,plain,
% 22.63/22.87      (~big_p(c15)),
% 22.63/22.87      inference(unit_resolution,[status(thm)],[1013, 949, 8, 930, 2, 987])).
% 22.63/22.87  tff(1046,plain,
% 22.63/22.87      (^[X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : refl((big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10)))) <=> (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10)))))),
% 22.63/22.87      inference(bind,[status(th)],[])).
% 22.63/22.87  tff(1047,plain,
% 22.63/22.87      (![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10)))) <=> ![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))),
% 22.63/22.87      inference(quant_intro,[status(thm)],[1046])).
% 22.63/22.87  tff(1048,plain,
% 22.63/22.87      (![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10)))) <=> ![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))),
% 22.63/22.87      inference(rewrite,[status(thm)],[])).
% 22.63/22.87  tff(1049,plain,
% 22.63/22.87      (^[X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(X10)) | (~big_p(f3(X10)))) | big_q(c14)) <=> (big_q(c14) | (~big_p(X10)) | (~big_p(f3(X10))))), (((((~big_p(X10)) | (~big_p(f3(X10)))) | big_q(c14)) | big_p(X11)) <=> ((big_q(c14) | (~big_p(X10)) | (~big_p(f3(X10)))) | big_p(X11)))), rewrite(((big_q(c14) | (~big_p(X10)) | (~big_p(f3(X10)))) | big_p(X11)) <=> (big_q(c14) | (~big_p(X10)) | big_p(X11) | (~big_p(f3(X10))))), (((((~big_p(X10)) | (~big_p(f3(X10)))) | big_q(c14)) | big_p(X11)) <=> (big_q(c14) | (~big_p(X10)) | big_p(X11) | (~big_p(f3(X10)))))), ((((((~big_p(X10)) | (~big_p(f3(X10)))) | big_q(c14)) | big_p(X11)) | (~big_q(X13))) <=> ((big_q(c14) | (~big_p(X10)) | big_p(X11) | (~big_p(f3(X10)))) | (~big_q(X13))))), rewrite(((big_q(c14) | (~big_p(X10)) | big_p(X11) | (~big_p(f3(X10)))) | (~big_q(X13))) <=> (big_q(c14) | (~big_q(X13)) | (~big_p(X10)) | big_p(X11) | (~big_p(f3(X10))))), ((((((~big_p(X10)) | (~big_p(f3(X10)))) | big_q(c14)) | big_p(X11)) | (~big_q(X13))) <=> (big_q(c14) | (~big_q(X13)) | (~big_p(X10)) | big_p(X11) | (~big_p(f3(X10)))))), (((((((~big_p(X10)) | (~big_p(f3(X10)))) | big_q(c14)) | big_p(X11)) | (~big_q(X13))) | big_q(c16)) <=> ((big_q(c14) | (~big_q(X13)) | (~big_p(X10)) | big_p(X11) | (~big_p(f3(X10)))) | big_q(c16)))), rewrite(((big_q(c14) | (~big_q(X13)) | (~big_p(X10)) | big_p(X11) | (~big_p(f3(X10)))) | big_q(c16)) <=> (big_q(c14) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(f3(X10))))), (((((((~big_p(X10)) | (~big_p(f3(X10)))) | big_q(c14)) | big_p(X11)) | (~big_q(X13))) | big_q(c16)) <=> (big_q(c14) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(f3(X10)))))), ((((((((~big_p(X10)) | (~big_p(f3(X10)))) | big_q(c14)) | big_p(X11)) | (~big_q(X13))) | big_q(c16)) | (~big_p(X14))) <=> ((big_q(c14) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(f3(X10)))) | (~big_p(X14))))), rewrite(((big_q(c14) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(f3(X10)))) | (~big_p(X14))) <=> (big_q(c14) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))), ((((((((~big_p(X10)) | (~big_p(f3(X10)))) | big_q(c14)) | big_p(X11)) | (~big_q(X13))) | big_q(c16)) | (~big_p(X14))) <=> (big_q(c14) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10)))))), (((((((((~big_p(X10)) | (~big_p(f3(X10)))) | big_q(c14)) | big_p(X11)) | (~big_q(X13))) | big_q(c16)) | (~big_p(X14))) | big_q(X15)) <=> ((big_q(c14) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10)))) | big_q(X15)))), rewrite(((big_q(c14) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10)))) | big_q(X15)) <=> (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))), (((((((((~big_p(X10)) | (~big_p(f3(X10)))) | big_q(c14)) | big_p(X11)) | (~big_q(X13))) | big_q(c16)) | (~big_p(X14))) | big_q(X15)) <=> (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))))),
% 22.63/22.87      inference(bind,[status(th)],[])).
% 22.63/22.87  tff(1050,plain,
% 22.63/22.87      (![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : ((((((((~big_p(X10)) | (~big_p(f3(X10)))) | big_q(c14)) | big_p(X11)) | (~big_q(X13))) | big_q(c16)) | (~big_p(X14))) | big_q(X15)) <=> ![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))),
% 22.63/22.87      inference(quant_intro,[status(thm)],[1049])).
% 22.63/22.87  tff(1051,axiom,(![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : ((((((((~big_p(X10)) | (~big_p(f3(X10)))) | big_q(c14)) | big_p(X11)) | (~big_q(X13))) | big_q(c16)) | (~big_p(X14))) | big_q(X15))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_113')).
% 22.63/22.87  tff(1052,plain,
% 22.63/22.87      (![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))),
% 22.63/22.87      inference(modus_ponens,[status(thm)],[1051, 1050])).
% 22.63/22.87  tff(1053,plain,
% 22.63/22.87      (![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))),
% 22.63/22.87      inference(modus_ponens,[status(thm)],[1052, 1048])).
% 22.63/22.87  tff(1054,plain,(
% 22.63/22.87      ![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))),
% 22.63/22.87      inference(skolemize,[status(sab)],[1053])).
% 22.63/22.87  tff(1055,plain,
% 22.63/22.87      (![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))),
% 22.63/22.87      inference(modus_ponens,[status(thm)],[1054, 1047])).
% 22.63/22.87  tff(1056,plain,
% 22.63/22.87      (((~![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))) | (big_q(c14) | big_q(c16) | big_p(c15) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_p(c19)) | (~big_q(c1)))) <=> ((~![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))) | big_q(c14) | big_q(c16) | big_p(c15) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_p(c19)) | (~big_q(c1)))),
% 22.63/22.88      inference(rewrite,[status(thm)],[])).
% 22.63/22.88  tff(1057,plain,
% 22.63/22.88      ((big_q(c14) | big_q(elem!0) | (~big_q(c1)) | (~big_p(elem!0)) | big_q(c16) | big_p(c15) | (~big_p(c19)) | (~big_p(f3(elem!0)))) <=> (big_q(c14) | big_q(c16) | big_p(c15) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_p(c19)) | (~big_q(c1)))),
% 22.63/22.88      inference(rewrite,[status(thm)],[])).
% 22.63/22.88  tff(1058,plain,
% 22.63/22.88      (((~![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))) | (big_q(c14) | big_q(elem!0) | (~big_q(c1)) | (~big_p(elem!0)) | big_q(c16) | big_p(c15) | (~big_p(c19)) | (~big_p(f3(elem!0))))) <=> ((~![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))) | (big_q(c14) | big_q(c16) | big_p(c15) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_p(c19)) | (~big_q(c1))))),
% 22.63/22.88      inference(monotonicity,[status(thm)],[1057])).
% 22.63/22.88  tff(1059,plain,
% 22.63/22.88      (((~![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))) | (big_q(c14) | big_q(elem!0) | (~big_q(c1)) | (~big_p(elem!0)) | big_q(c16) | big_p(c15) | (~big_p(c19)) | (~big_p(f3(elem!0))))) <=> ((~![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))) | big_q(c14) | big_q(c16) | big_p(c15) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_p(c19)) | (~big_q(c1)))),
% 22.63/22.88      inference(transitivity,[status(thm)],[1058, 1056])).
% 22.63/22.88  tff(1060,plain,
% 22.63/22.88      ((~![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))) | (big_q(c14) | big_q(elem!0) | (~big_q(c1)) | (~big_p(elem!0)) | big_q(c16) | big_p(c15) | (~big_p(c19)) | (~big_p(f3(elem!0))))),
% 22.63/22.88      inference(quant_inst,[status(thm)],[])).
% 22.63/22.88  tff(1061,plain,
% 22.63/22.88      ((~![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))) | big_q(c14) | big_q(c16) | big_p(c15) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_p(c19)) | (~big_q(c1))),
% 22.63/22.88      inference(modus_ponens,[status(thm)],[1060, 1059])).
% 22.63/22.88  tff(1062,plain,
% 22.63/22.88      ($false),
% 22.63/22.88      inference(unit_resolution,[status(thm)],[1061, 1055, 146, 147, 5, 987, 762, 949, 2, 1045])).
% 22.63/22.88  tff(1063,plain,((~big_q(c1)) | big_q(c14) | (~big_p(c19)) | big_q(elem!0) | (~big_p(f3(elem!0))) | big_q(c16) | big_q(f2(elem!0)) | (~big_p(c2))), inference(lemma,lemma(discharge,[]))).
% 22.63/22.88  tff(1064,plain,
% 22.63/22.88      (~big_q(c1)),
% 22.63/22.88      inference(unit_resolution,[status(thm)],[1063, 1024, 146, 5, 1044, 2, 8, 930])).
% 22.63/22.88  tff(1065,plain,
% 22.63/22.88      (big_q(f2(c8))),
% 22.63/22.88      inference(unit_resolution,[status(thm)],[975, 1064, 5, 947, 819, 930, 931])).
% 22.63/22.88  tff(1066,plain,
% 22.63/22.88      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (big_q(c1) | big_q(c16) | (~big_p(c15)) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_p(c19)) | (~big_q(f2(c8))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | big_q(c1) | big_q(c16) | (~big_p(c15)) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_p(c19)) | (~big_q(f2(c8))))),
% 22.63/22.88      inference(rewrite,[status(thm)],[])).
% 22.63/22.88  tff(1067,plain,
% 22.63/22.88      (((~big_q(f2(c8))) | big_q(c1) | (~big_q(f2(c8))) | (~big_p(elem!0)) | big_q(c16) | (~big_p(c19)) | (~big_p(c15)) | (~big_p(f3(elem!0)))) <=> (big_q(c1) | big_q(c16) | (~big_p(c15)) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_p(c19)) | (~big_q(f2(c8))))),
% 22.63/22.88      inference(rewrite,[status(thm)],[])).
% 22.63/22.88  tff(1068,plain,
% 22.63/22.88      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(f2(c8))) | big_q(c1) | (~big_q(f2(c8))) | (~big_p(elem!0)) | big_q(c16) | (~big_p(c19)) | (~big_p(c15)) | (~big_p(f3(elem!0))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (big_q(c1) | big_q(c16) | (~big_p(c15)) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_p(c19)) | (~big_q(f2(c8)))))),
% 22.63/22.88      inference(monotonicity,[status(thm)],[1067])).
% 22.63/22.88  tff(1069,plain,
% 22.63/22.88      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(f2(c8))) | big_q(c1) | (~big_q(f2(c8))) | (~big_p(elem!0)) | big_q(c16) | (~big_p(c19)) | (~big_p(c15)) | (~big_p(f3(elem!0))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | big_q(c1) | big_q(c16) | (~big_p(c15)) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_p(c19)) | (~big_q(f2(c8))))),
% 22.63/22.88      inference(transitivity,[status(thm)],[1068, 1066])).
% 22.63/22.88  tff(1070,plain,
% 22.63/22.88      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(f2(c8))) | big_q(c1) | (~big_q(f2(c8))) | (~big_p(elem!0)) | big_q(c16) | (~big_p(c19)) | (~big_p(c15)) | (~big_p(f3(elem!0))))),
% 22.63/22.88      inference(quant_inst,[status(thm)],[])).
% 22.63/22.88  tff(1071,plain,
% 22.63/22.88      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | big_q(c1) | big_q(c16) | (~big_p(c15)) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_p(c19)) | (~big_q(f2(c8)))),
% 22.63/22.88      inference(modus_ponens,[status(thm)],[1070, 1069])).
% 22.63/22.88  tff(1072,plain,
% 22.63/22.88      (~big_p(c15)),
% 22.63/22.88      inference(unit_resolution,[status(thm)],[1071, 894, 1024, 1044, 762, 1064, 2, 1065])).
% 22.63/22.88  tff(1073,plain,
% 22.63/22.88      (((~![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))) | (big_q(c14) | big_q(c16) | big_p(c15) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_p(c19)) | (~big_q(f2(c8))))) <=> ((~![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))) | big_q(c14) | big_q(c16) | big_p(c15) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_p(c19)) | (~big_q(f2(c8))))),
% 22.63/22.88      inference(rewrite,[status(thm)],[])).
% 22.63/22.88  tff(1074,plain,
% 22.63/22.88      ((big_q(c14) | big_q(elem!0) | (~big_q(f2(c8))) | (~big_p(elem!0)) | big_q(c16) | big_p(c15) | (~big_p(c19)) | (~big_p(f3(elem!0)))) <=> (big_q(c14) | big_q(c16) | big_p(c15) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_p(c19)) | (~big_q(f2(c8))))),
% 22.63/22.88      inference(rewrite,[status(thm)],[])).
% 22.63/22.88  tff(1075,plain,
% 22.63/22.88      (((~![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))) | (big_q(c14) | big_q(elem!0) | (~big_q(f2(c8))) | (~big_p(elem!0)) | big_q(c16) | big_p(c15) | (~big_p(c19)) | (~big_p(f3(elem!0))))) <=> ((~![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))) | (big_q(c14) | big_q(c16) | big_p(c15) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_p(c19)) | (~big_q(f2(c8)))))),
% 22.63/22.88      inference(monotonicity,[status(thm)],[1074])).
% 22.63/22.88  tff(1076,plain,
% 22.63/22.88      (((~![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))) | (big_q(c14) | big_q(elem!0) | (~big_q(f2(c8))) | (~big_p(elem!0)) | big_q(c16) | big_p(c15) | (~big_p(c19)) | (~big_p(f3(elem!0))))) <=> ((~![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))) | big_q(c14) | big_q(c16) | big_p(c15) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_p(c19)) | (~big_q(f2(c8))))),
% 22.63/22.88      inference(transitivity,[status(thm)],[1075, 1073])).
% 22.63/22.88  tff(1077,plain,
% 22.63/22.88      ((~![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))) | (big_q(c14) | big_q(elem!0) | (~big_q(f2(c8))) | (~big_p(elem!0)) | big_q(c16) | big_p(c15) | (~big_p(c19)) | (~big_p(f3(elem!0))))),
% 22.63/22.88      inference(quant_inst,[status(thm)],[])).
% 22.63/22.88  tff(1078,plain,
% 22.63/22.88      ((~![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))) | big_q(c14) | big_q(c16) | big_p(c15) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_p(c19)) | (~big_q(f2(c8)))),
% 22.63/22.88      inference(modus_ponens,[status(thm)],[1077, 1076])).
% 22.63/22.88  tff(1079,plain,
% 22.63/22.88      ($false),
% 22.63/22.88      inference(unit_resolution,[status(thm)],[1078, 1055, 146, 1024, 5, 1044, 762, 2, 1072, 1065])).
% 22.63/22.88  tff(1080,plain,(big_q(c8) | big_q(c14) | big_q(elem!0) | big_q(c16) | (~big_p(c2)) | big_q(f2(elem!0)) | big_q(f4(elem!0))), inference(lemma,lemma(discharge,[]))).
% 22.63/22.88  tff(1081,plain,
% 22.63/22.88      (big_q(c8)),
% 22.63/22.88      inference(unit_resolution,[status(thm)],[1080, 146, 5, 2, 930, 8, 306])).
% 22.63/22.88  tff(1082,plain,
% 22.63/22.88      (big_p(f3(elem!0))),
% 22.63/22.88      inference(unit_resolution,[status(thm)],[829, 1081, 2, 5])).
% 22.63/22.88  tff(1083,plain,
% 22.63/22.88      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(c8)) | big_q(c16) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (~big_q(c8)) | big_q(c16) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))),
% 22.63/22.88      inference(rewrite,[status(thm)],[])).
% 22.63/22.88  tff(1084,plain,
% 22.63/22.88      (((~big_q(c8)) | big_q(elem!0) | (~big_q(c8)) | (~big_p(elem!0)) | big_q(c16) | (~big_p(f3(elem!0))) | (~big_p(c15)) | (~big_p(f3(elem!0)))) <=> ((~big_q(c8)) | big_q(c16) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))),
% 22.63/22.88      inference(rewrite,[status(thm)],[])).
% 22.63/22.88  tff(1085,plain,
% 22.63/22.88      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(c8)) | big_q(elem!0) | (~big_q(c8)) | (~big_p(elem!0)) | big_q(c16) | (~big_p(f3(elem!0))) | (~big_p(c15)) | (~big_p(f3(elem!0))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(c8)) | big_q(c16) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0))))),
% 22.63/22.88      inference(monotonicity,[status(thm)],[1084])).
% 22.63/22.88  tff(1086,plain,
% 22.63/22.88      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(c8)) | big_q(elem!0) | (~big_q(c8)) | (~big_p(elem!0)) | big_q(c16) | (~big_p(f3(elem!0))) | (~big_p(c15)) | (~big_p(f3(elem!0))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (~big_q(c8)) | big_q(c16) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))),
% 22.72/22.88      inference(transitivity,[status(thm)],[1085, 1083])).
% 22.72/22.88  tff(1087,plain,
% 22.72/22.88      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(c8)) | big_q(elem!0) | (~big_q(c8)) | (~big_p(elem!0)) | big_q(c16) | (~big_p(f3(elem!0))) | (~big_p(c15)) | (~big_p(f3(elem!0))))),
% 22.72/22.88      inference(quant_inst,[status(thm)],[])).
% 22.72/22.88  tff(1088,plain,
% 22.72/22.88      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (~big_q(c8)) | big_q(c16) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0))),
% 22.72/22.88      inference(modus_ponens,[status(thm)],[1087, 1086])).
% 22.72/22.88  tff(1089,plain,
% 22.72/22.88      (~big_p(c15)),
% 22.72/22.88      inference(unit_resolution,[status(thm)],[1088, 894, 5, 1082, 762, 2, 1081])).
% 22.72/22.88  tff(1090,plain,
% 22.72/22.88      (((~![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))) | (big_q(c14) | (~big_q(c8)) | big_q(c16) | big_p(c15) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))) <=> ((~![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))) | big_q(c14) | (~big_q(c8)) | big_q(c16) | big_p(c15) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))),
% 22.72/22.88      inference(rewrite,[status(thm)],[])).
% 22.72/22.88  tff(1091,plain,
% 22.72/22.88      ((big_q(c14) | big_q(elem!0) | (~big_q(c8)) | (~big_p(elem!0)) | big_q(c16) | big_p(c15) | (~big_p(f3(elem!0))) | (~big_p(f3(elem!0)))) <=> (big_q(c14) | (~big_q(c8)) | big_q(c16) | big_p(c15) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))),
% 22.72/22.88      inference(rewrite,[status(thm)],[])).
% 22.72/22.88  tff(1092,plain,
% 22.72/22.88      (((~![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))) | (big_q(c14) | big_q(elem!0) | (~big_q(c8)) | (~big_p(elem!0)) | big_q(c16) | big_p(c15) | (~big_p(f3(elem!0))) | (~big_p(f3(elem!0))))) <=> ((~![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))) | (big_q(c14) | (~big_q(c8)) | big_q(c16) | big_p(c15) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0))))),
% 22.72/22.88      inference(monotonicity,[status(thm)],[1091])).
% 22.72/22.88  tff(1093,plain,
% 22.72/22.88      (((~![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))) | (big_q(c14) | big_q(elem!0) | (~big_q(c8)) | (~big_p(elem!0)) | big_q(c16) | big_p(c15) | (~big_p(f3(elem!0))) | (~big_p(f3(elem!0))))) <=> ((~![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))) | big_q(c14) | (~big_q(c8)) | big_q(c16) | big_p(c15) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))),
% 22.72/22.88      inference(transitivity,[status(thm)],[1092, 1090])).
% 22.72/22.88  tff(1094,plain,
% 22.72/22.88      ((~![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))) | (big_q(c14) | big_q(elem!0) | (~big_q(c8)) | (~big_p(elem!0)) | big_q(c16) | big_p(c15) | (~big_p(f3(elem!0))) | (~big_p(f3(elem!0))))),
% 22.72/22.88      inference(quant_inst,[status(thm)],[])).
% 22.72/22.88  tff(1095,plain,
% 22.72/22.88      ((~![X14: $i, X11: $i, X13: $i, X10: $i, X15: $i] : (big_q(c14) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | big_p(X11) | (~big_p(X14)) | (~big_p(f3(X10))))) | big_q(c14) | (~big_q(c8)) | big_q(c16) | big_p(c15) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0))),
% 22.72/22.88      inference(modus_ponens,[status(thm)],[1094, 1093])).
% 22.72/22.88  tff(1096,plain,
% 22.72/22.88      ($false),
% 22.72/22.88      inference(unit_resolution,[status(thm)],[1095, 1055, 146, 5, 1082, 762, 2, 1089, 1081])).
% 22.72/22.88  tff(1097,plain,(big_q(c14) | big_q(elem!0) | big_q(c16) | (~big_p(c2)) | big_q(f2(elem!0)) | big_q(f4(elem!0))), inference(lemma,lemma(discharge,[]))).
% 22.72/22.88  tff(1098,plain,
% 22.72/22.88      (big_q(c14)),
% 22.72/22.88      inference(unit_resolution,[status(thm)],[1097, 929, 2, 306, 8, 5])).
% 22.72/22.88  tff(1099,plain,
% 22.72/22.88      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_p(c2)) | big_q(c16) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_q(c14)))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (~big_p(c2)) | big_q(c16) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_q(c14)))),
% 22.72/22.88      inference(rewrite,[status(thm)],[])).
% 22.72/22.88  tff(1100,plain,
% 22.72/22.88      (((~big_q(c14)) | big_q(elem!0) | (~big_q(c14)) | (~big_p(elem!0)) | big_q(c16) | (~big_p(c2)) | (~big_p(c15)) | (~big_p(f3(elem!0)))) <=> ((~big_p(c2)) | big_q(c16) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_q(c14)))),
% 22.72/22.88      inference(rewrite,[status(thm)],[])).
% 22.72/22.88  tff(1101,plain,
% 22.72/22.88      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(c14)) | big_q(elem!0) | (~big_q(c14)) | (~big_p(elem!0)) | big_q(c16) | (~big_p(c2)) | (~big_p(c15)) | (~big_p(f3(elem!0))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_p(c2)) | big_q(c16) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_q(c14))))),
% 22.72/22.88      inference(monotonicity,[status(thm)],[1100])).
% 22.72/22.88  tff(1102,plain,
% 22.72/22.88      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(c14)) | big_q(elem!0) | (~big_q(c14)) | (~big_p(elem!0)) | big_q(c16) | (~big_p(c2)) | (~big_p(c15)) | (~big_p(f3(elem!0))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (~big_p(c2)) | big_q(c16) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_q(c14)))),
% 22.72/22.88      inference(transitivity,[status(thm)],[1101, 1099])).
% 22.72/22.88  tff(1103,plain,
% 22.72/22.88      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(c14)) | big_q(elem!0) | (~big_q(c14)) | (~big_p(elem!0)) | big_q(c16) | (~big_p(c2)) | (~big_p(c15)) | (~big_p(f3(elem!0))))),
% 22.72/22.88      inference(quant_inst,[status(thm)],[])).
% 22.72/22.88  tff(1104,plain,
% 22.72/22.88      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (~big_p(c2)) | big_q(c16) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_q(c14))),
% 22.72/22.88      inference(modus_ponens,[status(thm)],[1103, 1102])).
% 22.72/22.88  tff(1105,plain,
% 22.72/22.88      (~big_p(c15)),
% 22.72/22.88      inference(unit_resolution,[status(thm)],[1104, 894, 1098, 5, 884, 762, 929, 2])).
% 22.72/22.88  tff(1106,plain,
% 22.72/22.88      (((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | ((~big_p(c11)) | big_p(c19) | big_p(c15) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_q(c14)))) <=> ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | (~big_p(c11)) | big_p(c19) | big_p(c15) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_q(c14)))),
% 22.72/22.88      inference(rewrite,[status(thm)],[])).
% 22.72/22.88  tff(1107,plain,
% 22.72/22.88      (((~big_q(c14)) | big_p(c15) | big_q(elem!0) | big_q(elem!0) | big_p(c15) | (~big_p(c11)) | big_p(c19) | big_q(f4(elem!0))) <=> ((~big_p(c11)) | big_p(c19) | big_p(c15) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_q(c14)))),
% 22.72/22.88      inference(rewrite,[status(thm)],[])).
% 22.72/22.88  tff(1108,plain,
% 22.72/22.88      (((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | ((~big_q(c14)) | big_p(c15) | big_q(elem!0) | big_q(elem!0) | big_p(c15) | (~big_p(c11)) | big_p(c19) | big_q(f4(elem!0)))) <=> ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | ((~big_p(c11)) | big_p(c19) | big_p(c15) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_q(c14))))),
% 22.72/22.88      inference(monotonicity,[status(thm)],[1107])).
% 22.72/22.88  tff(1109,plain,
% 22.72/22.88      (((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | ((~big_q(c14)) | big_p(c15) | big_q(elem!0) | big_q(elem!0) | big_p(c15) | (~big_p(c11)) | big_p(c19) | big_q(f4(elem!0)))) <=> ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | (~big_p(c11)) | big_p(c19) | big_p(c15) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_q(c14)))),
% 22.72/22.88      inference(transitivity,[status(thm)],[1108, 1106])).
% 22.72/22.88  tff(1110,plain,
% 22.72/22.88      ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | ((~big_q(c14)) | big_p(c15) | big_q(elem!0) | big_q(elem!0) | big_p(c15) | (~big_p(c11)) | big_p(c19) | big_q(f4(elem!0)))),
% 22.72/22.88      inference(quant_inst,[status(thm)],[])).
% 22.72/22.88  tff(1111,plain,
% 22.72/22.88      ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | big_q(X16) | big_p(X7) | (~big_p(c11)) | big_p(c19) | big_q(f4(X16)))) | (~big_p(c11)) | big_p(c19) | big_p(c15) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_q(c14))),
% 22.72/22.88      inference(modus_ponens,[status(thm)],[1110, 1109])).
% 22.72/22.88  tff(1112,plain,
% 22.72/22.88      ($false),
% 22.72/22.88      inference(unit_resolution,[status(thm)],[1111, 222, 1098, 307, 5, 306, 1105, 819])).
% 22.72/22.88  tff(1113,plain,(big_p(c19) | big_q(elem!0) | big_q(f4(elem!0)) | big_q(c16) | big_q(f2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 22.72/22.88  tff(1114,plain,
% 22.72/22.88      (big_p(c19)),
% 22.72/22.88      inference(unit_resolution,[status(thm)],[1113, 306, 5, 2, 8])).
% 22.72/22.88  tff(1115,plain,
% 22.72/22.88      (big_q(c4)),
% 22.72/22.88      inference(unit_resolution,[status(thm)],[919, 911, 8, 858, 5])).
% 22.72/22.88  tff(1116,plain,
% 22.72/22.88      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_p(c2) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | (~big_p(c19)) | (~big_q(c4)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_p(c2) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | (~big_p(c19)) | (~big_q(c4)))),
% 22.72/22.88      inference(rewrite,[status(thm)],[])).
% 22.72/22.88  tff(1117,plain,
% 22.72/22.88      (((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | big_p(c2) | big_q(c16) | (~big_p(c11)) | (~big_p(c19)) | big_p(c2)) <=> (big_p(c2) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | (~big_p(c19)) | (~big_q(c4)))),
% 22.72/22.88      inference(rewrite,[status(thm)],[])).
% 22.72/22.88  tff(1118,plain,
% 22.72/22.88      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | big_p(c2) | big_q(c16) | (~big_p(c11)) | (~big_p(c19)) | big_p(c2))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_p(c2) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | (~big_p(c19)) | (~big_q(c4))))),
% 22.72/22.88      inference(monotonicity,[status(thm)],[1117])).
% 22.72/22.88  tff(1119,plain,
% 22.72/22.88      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | big_p(c2) | big_q(c16) | (~big_p(c11)) | (~big_p(c19)) | big_p(c2))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_p(c2) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | (~big_p(c19)) | (~big_q(c4)))),
% 22.72/22.88      inference(transitivity,[status(thm)],[1118, 1116])).
% 22.72/22.88  tff(1120,plain,
% 22.72/22.88      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c4)) | big_q(elem!0) | (~big_q(c4)) | big_p(c2) | big_q(c16) | (~big_p(c11)) | (~big_p(c19)) | big_p(c2))),
% 22.72/22.88      inference(quant_inst,[status(thm)],[])).
% 22.72/22.88  tff(1121,plain,
% 22.72/22.88      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_p(c2) | big_q(c16) | (~big_p(c11)) | big_q(elem!0) | (~big_p(c19)) | (~big_q(c4))),
% 22.72/22.88      inference(modus_ponens,[status(thm)],[1120, 1119])).
% 22.72/22.88  tff(1122,plain,
% 22.72/22.88      ($false),
% 22.72/22.88      inference(unit_resolution,[status(thm)],[1121, 52, 147, 5, 911, 2, 819, 1115])).
% 22.72/22.88  tff(1123,plain,(big_p(c2) | (~big_p(c19)) | big_q(elem!0) | big_q(c16) | big_q(f2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 22.72/22.88  tff(1124,plain,
% 22.72/22.88      (big_p(c2)),
% 22.72/22.88      inference(unit_resolution,[status(thm)],[1123, 1114, 5, 2, 8])).
% 22.72/22.88  tff(1125,plain,
% 22.72/22.88      (big_q(c14)),
% 22.72/22.88      inference(unit_resolution,[status(thm)],[1097, 1124, 2, 306, 8, 5])).
% 22.72/22.88  tff(1126,plain,
% 22.72/22.88      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | (~big_p(c11)) | big_p(c15) | big_q(elem!0) | (~big_p(c19)) | (~big_q(c14)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_p(c15) | big_q(elem!0) | (~big_p(c19)) | (~big_q(c14)))),
% 22.72/22.89      inference(rewrite,[status(thm)],[])).
% 22.72/22.89  tff(1127,plain,
% 22.72/22.89      (((~big_q(c14)) | big_q(elem!0) | (~big_q(c14)) | big_p(c15) | big_q(c16) | (~big_p(c11)) | (~big_p(c19)) | big_p(c15)) <=> (big_q(c16) | (~big_p(c11)) | big_p(c15) | big_q(elem!0) | (~big_p(c19)) | (~big_q(c14)))),
% 22.72/22.89      inference(rewrite,[status(thm)],[])).
% 22.72/22.89  tff(1128,plain,
% 22.72/22.89      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c14)) | big_q(elem!0) | (~big_q(c14)) | big_p(c15) | big_q(c16) | (~big_p(c11)) | (~big_p(c19)) | big_p(c15))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | (~big_p(c11)) | big_p(c15) | big_q(elem!0) | (~big_p(c19)) | (~big_q(c14))))),
% 22.72/22.89      inference(monotonicity,[status(thm)],[1127])).
% 22.72/22.89  tff(1129,plain,
% 22.72/22.89      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c14)) | big_q(elem!0) | (~big_q(c14)) | big_p(c15) | big_q(c16) | (~big_p(c11)) | (~big_p(c19)) | big_p(c15))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_p(c15) | big_q(elem!0) | (~big_p(c19)) | (~big_q(c14)))),
% 22.72/22.89      inference(transitivity,[status(thm)],[1128, 1126])).
% 22.73/22.89  tff(1130,plain,
% 22.73/22.89      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c14)) | big_q(elem!0) | (~big_q(c14)) | big_p(c15) | big_q(c16) | (~big_p(c11)) | (~big_p(c19)) | big_p(c15))),
% 22.73/22.89      inference(quant_inst,[status(thm)],[])).
% 22.73/22.89  tff(1131,plain,
% 22.73/22.89      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_p(c15) | big_q(elem!0) | (~big_p(c19)) | (~big_q(c14))),
% 22.73/22.89      inference(modus_ponens,[status(thm)],[1130, 1129])).
% 22.73/22.89  tff(1132,plain,
% 22.73/22.89      ($false),
% 22.73/22.89      inference(unit_resolution,[status(thm)],[1131, 52, 402, 147, 5, 2, 986, 819])).
% 22.73/22.89  tff(1133,plain,(big_p(c15) | (~big_q(c14)) | (~big_p(c19)) | big_q(elem!0) | big_q(c16)), inference(lemma,lemma(discharge,[]))).
% 22.73/22.89  tff(1134,plain,
% 22.73/22.89      (big_p(c15)),
% 22.73/22.89      inference(unit_resolution,[status(thm)],[1133, 1125, 1114, 5, 2])).
% 22.73/22.89  tff(1135,plain,
% 22.73/22.89      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (big_q(c16) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_q(c14)))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | big_q(c16) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_q(c14)))),
% 22.73/22.89      inference(rewrite,[status(thm)],[])).
% 22.73/22.89  tff(1136,plain,
% 22.73/22.89      (((~big_q(c14)) | big_q(elem!0) | (~big_q(c14)) | (~big_p(elem!0)) | big_q(c16) | (~big_p(c15)) | (~big_p(c15)) | (~big_p(f3(elem!0)))) <=> (big_q(c16) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_q(c14)))),
% 22.73/22.89      inference(rewrite,[status(thm)],[])).
% 22.73/22.89  tff(1137,plain,
% 22.73/22.89      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(c14)) | big_q(elem!0) | (~big_q(c14)) | (~big_p(elem!0)) | big_q(c16) | (~big_p(c15)) | (~big_p(c15)) | (~big_p(f3(elem!0))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (big_q(c16) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_q(c14))))),
% 22.73/22.89      inference(monotonicity,[status(thm)],[1136])).
% 22.73/22.89  tff(1138,plain,
% 22.73/22.89      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(c14)) | big_q(elem!0) | (~big_q(c14)) | (~big_p(elem!0)) | big_q(c16) | (~big_p(c15)) | (~big_p(c15)) | (~big_p(f3(elem!0))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | big_q(c16) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_q(c14)))),
% 22.73/22.89      inference(transitivity,[status(thm)],[1137, 1135])).
% 22.73/22.89  tff(1139,plain,
% 22.73/22.89      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(c14)) | big_q(elem!0) | (~big_q(c14)) | (~big_p(elem!0)) | big_q(c16) | (~big_p(c15)) | (~big_p(c15)) | (~big_p(f3(elem!0))))),
% 22.73/22.89      inference(quant_inst,[status(thm)],[])).
% 22.73/22.89  tff(1140,plain,
% 22.73/22.89      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | big_q(c16) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(elem!0))) | (~big_p(elem!0)) | (~big_q(c14))),
% 22.73/22.89      inference(modus_ponens,[status(thm)],[1139, 1138])).
% 22.73/22.89  tff(1141,plain,
% 22.73/22.89      ($false),
% 22.73/22.89      inference(unit_resolution,[status(thm)],[1140, 894, 1125, 5, 884, 762, 2, 1134])).
% 22.73/22.89  tff(1142,plain,(big_q(f4(elem!0)) | big_q(elem!0) | big_q(c16) | big_q(f2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 22.73/22.89  tff(1143,plain,
% 22.73/22.89      (big_q(f2(elem!0))),
% 22.73/22.89      inference(unit_resolution,[status(thm)],[1142, 910, 2, 5])).
% 22.73/22.89  tff(1144,plain,
% 22.73/22.89      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (big_q(c16) | (~big_p(c15)) | big_q(f4(elem!0)) | (~big_q(f2(elem!0))) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | big_q(c16) | (~big_p(c15)) | big_q(f4(elem!0)) | (~big_q(f2(elem!0))) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))),
% 22.73/22.89      inference(rewrite,[status(thm)],[])).
% 22.73/22.89  tff(1145,plain,
% 22.73/22.89      (((~big_q(f2(elem!0))) | big_q(f4(elem!0)) | (~big_q(f2(elem!0))) | (~big_p(elem!0)) | big_q(c16) | (~big_p(f3(elem!0))) | (~big_p(c15)) | (~big_p(f3(elem!0)))) <=> (big_q(c16) | (~big_p(c15)) | big_q(f4(elem!0)) | (~big_q(f2(elem!0))) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))),
% 22.73/22.89      inference(rewrite,[status(thm)],[])).
% 22.73/22.89  tff(1146,plain,
% 22.73/22.89      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(f2(elem!0))) | big_q(f4(elem!0)) | (~big_q(f2(elem!0))) | (~big_p(elem!0)) | big_q(c16) | (~big_p(f3(elem!0))) | (~big_p(c15)) | (~big_p(f3(elem!0))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (big_q(c16) | (~big_p(c15)) | big_q(f4(elem!0)) | (~big_q(f2(elem!0))) | (~big_p(f3(elem!0))) | (~big_p(elem!0))))),
% 22.73/22.89      inference(monotonicity,[status(thm)],[1145])).
% 22.73/22.89  tff(1147,plain,
% 22.73/22.89      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(f2(elem!0))) | big_q(f4(elem!0)) | (~big_q(f2(elem!0))) | (~big_p(elem!0)) | big_q(c16) | (~big_p(f3(elem!0))) | (~big_p(c15)) | (~big_p(f3(elem!0))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | big_q(c16) | (~big_p(c15)) | big_q(f4(elem!0)) | (~big_q(f2(elem!0))) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))),
% 22.73/22.89      inference(transitivity,[status(thm)],[1146, 1144])).
% 22.73/22.89  tff(1148,plain,
% 22.73/22.89      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(f2(elem!0))) | big_q(f4(elem!0)) | (~big_q(f2(elem!0))) | (~big_p(elem!0)) | big_q(c16) | (~big_p(f3(elem!0))) | (~big_p(c15)) | (~big_p(f3(elem!0))))),
% 22.73/22.89      inference(quant_inst,[status(thm)],[])).
% 22.73/22.89  tff(1149,plain,
% 22.73/22.89      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | big_q(c16) | (~big_p(c15)) | big_q(f4(elem!0)) | (~big_q(f2(elem!0))) | (~big_p(f3(elem!0))) | (~big_p(elem!0))),
% 22.73/22.89      inference(modus_ponens,[status(thm)],[1148, 1147])).
% 22.73/22.89  tff(1150,plain,
% 22.73/22.89      (~big_p(c15)),
% 22.73/22.89      inference(unit_resolution,[status(thm)],[1149, 894, 910, 884, 762, 1143, 2])).
% 22.73/22.89  tff(1151,plain,
% 22.73/22.89      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | (~big_p(c11)) | big_p(c15) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(f3(elem!0))))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_p(c15) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(f3(elem!0))))),
% 22.73/22.89      inference(rewrite,[status(thm)],[])).
% 22.73/22.89  tff(1152,plain,
% 22.73/22.89      (((~big_q(f2(elem!0))) | big_q(elem!0) | (~big_q(f2(elem!0))) | big_p(c15) | big_q(c16) | (~big_p(c11)) | (~big_p(f3(elem!0))) | big_p(c15)) <=> (big_q(c16) | (~big_p(c11)) | big_p(c15) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(f3(elem!0))))),
% 22.73/22.89      inference(rewrite,[status(thm)],[])).
% 22.73/22.89  tff(1153,plain,
% 22.73/22.89      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(elem!0))) | big_q(elem!0) | (~big_q(f2(elem!0))) | big_p(c15) | big_q(c16) | (~big_p(c11)) | (~big_p(f3(elem!0))) | big_p(c15))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | (~big_p(c11)) | big_p(c15) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(f3(elem!0)))))),
% 22.73/22.89      inference(monotonicity,[status(thm)],[1152])).
% 22.73/22.89  tff(1154,plain,
% 22.73/22.89      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(elem!0))) | big_q(elem!0) | (~big_q(f2(elem!0))) | big_p(c15) | big_q(c16) | (~big_p(c11)) | (~big_p(f3(elem!0))) | big_p(c15))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_p(c15) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(f3(elem!0))))),
% 22.73/22.89      inference(transitivity,[status(thm)],[1153, 1151])).
% 22.73/22.89  tff(1155,plain,
% 22.73/22.89      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(elem!0))) | big_q(elem!0) | (~big_q(f2(elem!0))) | big_p(c15) | big_q(c16) | (~big_p(c11)) | (~big_p(f3(elem!0))) | big_p(c15))),
% 22.73/22.89      inference(quant_inst,[status(thm)],[])).
% 22.73/22.89  tff(1156,plain,
% 22.73/22.89      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_p(c15) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(f3(elem!0)))),
% 22.73/22.89      inference(modus_ponens,[status(thm)],[1155, 1154])).
% 22.73/22.89  tff(1157,plain,
% 22.73/22.89      ($false),
% 22.73/22.89      inference(unit_resolution,[status(thm)],[1156, 52, 5, 884, 1143, 2, 1150, 819])).
% 22.73/22.89  tff(1158,plain,(big_q(c16) | big_q(elem!0)), inference(lemma,lemma(discharge,[]))).
% 22.73/22.89  tff(1159,plain,
% 22.73/22.89      (big_q(c16)),
% 22.73/22.89      inference(unit_resolution,[status(thm)],[1158, 5])).
% 22.73/22.89  tff(1160,plain,
% 22.73/22.89      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | (~big_q(c16)) | big_p(c19) | big_q(elem!0) | (~big_p(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_p(c19) | big_q(elem!0) | (~big_p(elem!0)))),
% 22.73/22.89      inference(rewrite,[status(thm)],[])).
% 22.73/22.89  tff(1161,plain,
% 22.73/22.89      (((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | big_p(c19) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(elem!0)) | big_p(c19)) <=> ((~big_p(c11)) | (~big_q(c16)) | big_p(c19) | big_q(elem!0) | (~big_p(elem!0)))),
% 22.73/22.89      inference(rewrite,[status(thm)],[])).
% 22.73/22.89  tff(1162,plain,
% 22.73/22.89      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | big_p(c19) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(elem!0)) | big_p(c19))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | (~big_q(c16)) | big_p(c19) | big_q(elem!0) | (~big_p(elem!0))))),
% 22.73/22.89      inference(monotonicity,[status(thm)],[1161])).
% 22.73/22.89  tff(1163,plain,
% 22.73/22.89      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | big_p(c19) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(elem!0)) | big_p(c19))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_p(c19) | big_q(elem!0) | (~big_p(elem!0)))),
% 22.73/22.89      inference(transitivity,[status(thm)],[1162, 1160])).
% 22.73/22.89  tff(1164,plain,
% 22.73/22.89      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | big_p(c19) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(elem!0)) | big_p(c19))),
% 22.73/22.89      inference(quant_inst,[status(thm)],[])).
% 22.73/22.89  tff(1165,plain,
% 22.73/22.89      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_p(c19) | big_q(elem!0) | (~big_p(elem!0))),
% 22.73/22.89      inference(modus_ponens,[status(thm)],[1164, 1163])).
% 22.73/22.89  tff(1166,plain,
% 22.73/22.89      ($false),
% 22.73/22.89      inference(unit_resolution,[status(thm)],[1165, 354, 307, 5, 762, 1159, 819])).
% 22.73/22.89  tff(1167,plain,(big_p(c19) | big_q(elem!0)), inference(lemma,lemma(discharge,[]))).
% 22.73/22.89  tff(1168,plain,
% 22.73/22.89      (big_p(c19)),
% 22.73/22.89      inference(unit_resolution,[status(thm)],[1167, 5])).
% 22.73/22.89  tff(1169,plain,
% 22.73/22.89      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (big_p(c2) | (~big_p(c11)) | (~big_q(c16)) | big_q(elem!0) | (~big_p(c19)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | big_p(c2) | (~big_p(c11)) | (~big_q(c16)) | big_q(elem!0) | (~big_p(c19)))),
% 22.73/22.89      inference(rewrite,[status(thm)],[])).
% 22.73/22.89  tff(1170,plain,
% 22.73/22.89      (((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | big_p(c2) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(c2)) <=> (big_p(c2) | (~big_p(c11)) | (~big_q(c16)) | big_q(elem!0) | (~big_p(c19)))),
% 22.73/22.89      inference(rewrite,[status(thm)],[])).
% 22.73/22.89  tff(1171,plain,
% 22.73/22.89      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | big_p(c2) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(c2))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (big_p(c2) | (~big_p(c11)) | (~big_q(c16)) | big_q(elem!0) | (~big_p(c19))))),
% 22.73/22.89      inference(monotonicity,[status(thm)],[1170])).
% 22.73/22.89  tff(1172,plain,
% 22.73/22.89      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | big_p(c2) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(c2))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | big_p(c2) | (~big_p(c11)) | (~big_q(c16)) | big_q(elem!0) | (~big_p(c19)))),
% 22.73/22.89      inference(transitivity,[status(thm)],[1171, 1169])).
% 22.73/22.89  tff(1173,plain,
% 22.73/22.89      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | big_p(c2) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(c2))),
% 22.73/22.89      inference(quant_inst,[status(thm)],[])).
% 22.73/22.89  tff(1174,plain,
% 22.73/22.89      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | big_p(c2) | (~big_p(c11)) | (~big_q(c16)) | big_q(elem!0) | (~big_p(c19))),
% 22.73/22.89      inference(modus_ponens,[status(thm)],[1173, 1172])).
% 22.73/22.89  tff(1175,plain,
% 22.73/22.89      ($false),
% 22.73/22.89      inference(unit_resolution,[status(thm)],[1174, 354, 147, 5, 911, 1159, 819])).
% 22.73/22.89  tff(1176,plain,(big_p(c2) | (~big_p(c19)) | big_q(elem!0)), inference(lemma,lemma(discharge,[]))).
% 22.73/22.89  tff(1177,plain,
% 22.73/22.89      (big_p(c2)),
% 22.73/22.89      inference(unit_resolution,[status(thm)],[1176, 1168, 5])).
% 22.73/22.89  tff(1178,plain,
% 22.73/22.89      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | (~big_q(c16)) | big_q(elem!0) | big_p(f1(elem!0)) | (~big_p(c19)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_q(elem!0) | big_p(f1(elem!0)) | (~big_p(c19)))),
% 22.73/22.89      inference(rewrite,[status(thm)],[])).
% 22.73/22.89  tff(1179,plain,
% 22.73/22.89      (((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | big_p(f1(elem!0)) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(f1(elem!0))) <=> ((~big_p(c11)) | (~big_q(c16)) | big_q(elem!0) | big_p(f1(elem!0)) | (~big_p(c19)))),
% 22.73/22.89      inference(rewrite,[status(thm)],[])).
% 22.73/22.89  tff(1180,plain,
% 22.73/22.89      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | big_p(f1(elem!0)) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(f1(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | (~big_q(c16)) | big_q(elem!0) | big_p(f1(elem!0)) | (~big_p(c19))))),
% 22.73/22.89      inference(monotonicity,[status(thm)],[1179])).
% 22.73/22.89  tff(1181,plain,
% 22.73/22.89      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | big_p(f1(elem!0)) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(f1(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_q(elem!0) | big_p(f1(elem!0)) | (~big_p(c19)))),
% 22.73/22.89      inference(transitivity,[status(thm)],[1180, 1178])).
% 22.73/22.89  tff(1182,plain,
% 22.73/22.89      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | big_p(f1(elem!0)) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(f1(elem!0)))),
% 22.73/22.89      inference(quant_inst,[status(thm)],[])).
% 22.73/22.89  tff(1183,plain,
% 22.73/22.89      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_q(elem!0) | big_p(f1(elem!0)) | (~big_p(c19))),
% 22.73/22.89      inference(modus_ponens,[status(thm)],[1182, 1181])).
% 22.73/22.89  tff(1184,plain,
% 22.73/22.89      ($false),
% 22.73/22.89      inference(unit_resolution,[status(thm)],[1183, 354, 147, 5, 88, 1159, 819])).
% 22.73/22.89  tff(1185,plain,(big_p(f1(elem!0)) | (~big_p(c19)) | big_q(elem!0)), inference(lemma,lemma(discharge,[]))).
% 22.73/22.89  tff(1186,plain,
% 22.73/22.89      (big_p(f1(elem!0))),
% 22.73/22.89      inference(unit_resolution,[status(thm)],[1185, 1168, 5])).
% 22.73/22.89  tff(1187,plain,
% 22.73/22.89      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | (~big_q(c16)) | big_p(c15) | big_q(elem!0) | (~big_p(c19)) | (~big_q(c1)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_p(c15) | big_q(elem!0) | (~big_p(c19)) | (~big_q(c1)))),
% 22.73/22.89      inference(rewrite,[status(thm)],[])).
% 22.73/22.89  tff(1188,plain,
% 22.73/22.89      (((~big_q(c1)) | big_q(elem!0) | big_q(elem!0) | big_p(c15) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(c15)) <=> ((~big_p(c11)) | (~big_q(c16)) | big_p(c15) | big_q(elem!0) | (~big_p(c19)) | (~big_q(c1)))),
% 22.73/22.89      inference(rewrite,[status(thm)],[])).
% 22.73/22.89  tff(1189,plain,
% 22.73/22.89      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c1)) | big_q(elem!0) | big_q(elem!0) | big_p(c15) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(c15))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | (~big_q(c16)) | big_p(c15) | big_q(elem!0) | (~big_p(c19)) | (~big_q(c1))))),
% 22.73/22.89      inference(monotonicity,[status(thm)],[1188])).
% 22.73/22.89  tff(1190,plain,
% 22.73/22.89      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c1)) | big_q(elem!0) | big_q(elem!0) | big_p(c15) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(c15))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_p(c15) | big_q(elem!0) | (~big_p(c19)) | (~big_q(c1)))),
% 22.73/22.89      inference(transitivity,[status(thm)],[1189, 1187])).
% 22.73/22.89  tff(1191,plain,
% 22.73/22.89      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c1)) | big_q(elem!0) | big_q(elem!0) | big_p(c15) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(c15))),
% 22.73/22.89      inference(quant_inst,[status(thm)],[])).
% 22.73/22.89  tff(1192,plain,
% 22.73/22.89      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_p(c15) | big_q(elem!0) | (~big_p(c19)) | (~big_q(c1))),
% 22.73/22.89      inference(modus_ponens,[status(thm)],[1191, 1190])).
% 22.73/22.89  tff(1193,plain,
% 22.73/22.89      ($false),
% 22.73/22.89      inference(unit_resolution,[status(thm)],[1192, 354, 147, 5, 949, 1159, 986, 819])).
% 22.73/22.89  tff(1194,plain,(big_p(c15) | (~big_p(c19)) | big_q(elem!0) | (~big_q(c1))), inference(lemma,lemma(discharge,[]))).
% 22.73/22.89  tff(1195,plain,
% 22.73/22.89      (~big_q(c1)),
% 22.73/22.89      inference(unit_resolution,[status(thm)],[1194, 986, 5, 1168])).
% 22.73/22.89  tff(1196,plain,
% 22.73/22.89      (((~![W: $i, X: $i, X2: $i, X1: $i] : (big_q(c1) | big_q(X2) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X))))) | (big_q(c1) | (~big_p(c2)) | (~big_p(c11)) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f1(elem!0))) | (~big_p(elem!0)) | big_q(f2(f2(elem!0))))) <=> ((~![W: $i, X: $i, X2: $i, X1: $i] : (big_q(c1) | big_q(X2) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X))))) | big_q(c1) | (~big_p(c2)) | (~big_p(c11)) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f1(elem!0))) | (~big_p(elem!0)) | big_q(f2(f2(elem!0))))),
% 22.73/22.89      inference(rewrite,[status(thm)],[])).
% 22.73/22.89  tff(1197,plain,
% 22.73/22.89      ((big_q(c1) | big_q(elem!0) | (~big_p(c11)) | big_q(f2(elem!0)) | big_q(f2(f2(elem!0))) | (~big_p(c2)) | (~big_p(elem!0)) | (~big_p(f1(elem!0)))) <=> (big_q(c1) | (~big_p(c2)) | (~big_p(c11)) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f1(elem!0))) | (~big_p(elem!0)) | big_q(f2(f2(elem!0))))),
% 22.73/22.90      inference(rewrite,[status(thm)],[])).
% 22.73/22.90  tff(1198,plain,
% 22.73/22.90      (((~![W: $i, X: $i, X2: $i, X1: $i] : (big_q(c1) | big_q(X2) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X))))) | (big_q(c1) | big_q(elem!0) | (~big_p(c11)) | big_q(f2(elem!0)) | big_q(f2(f2(elem!0))) | (~big_p(c2)) | (~big_p(elem!0)) | (~big_p(f1(elem!0))))) <=> ((~![W: $i, X: $i, X2: $i, X1: $i] : (big_q(c1) | big_q(X2) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X))))) | (big_q(c1) | (~big_p(c2)) | (~big_p(c11)) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f1(elem!0))) | (~big_p(elem!0)) | big_q(f2(f2(elem!0)))))),
% 22.73/22.90      inference(monotonicity,[status(thm)],[1197])).
% 22.73/22.90  tff(1199,plain,
% 22.73/22.90      (((~![W: $i, X: $i, X2: $i, X1: $i] : (big_q(c1) | big_q(X2) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X))))) | (big_q(c1) | big_q(elem!0) | (~big_p(c11)) | big_q(f2(elem!0)) | big_q(f2(f2(elem!0))) | (~big_p(c2)) | (~big_p(elem!0)) | (~big_p(f1(elem!0))))) <=> ((~![W: $i, X: $i, X2: $i, X1: $i] : (big_q(c1) | big_q(X2) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X))))) | big_q(c1) | (~big_p(c2)) | (~big_p(c11)) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f1(elem!0))) | (~big_p(elem!0)) | big_q(f2(f2(elem!0))))),
% 22.73/22.90      inference(transitivity,[status(thm)],[1198, 1196])).
% 22.73/22.90  tff(1200,plain,
% 22.73/22.90      ((~![W: $i, X: $i, X2: $i, X1: $i] : (big_q(c1) | big_q(X2) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X))))) | (big_q(c1) | big_q(elem!0) | (~big_p(c11)) | big_q(f2(elem!0)) | big_q(f2(f2(elem!0))) | (~big_p(c2)) | (~big_p(elem!0)) | (~big_p(f1(elem!0))))),
% 22.73/22.90      inference(quant_inst,[status(thm)],[])).
% 22.73/22.90  tff(1201,plain,
% 22.73/22.90      ((~![W: $i, X: $i, X2: $i, X1: $i] : (big_q(c1) | big_q(X2) | (~big_p(X1)) | big_q(W) | big_q(f2(W)) | (~big_p(c2)) | (~big_p(X)) | (~big_p(f1(X))))) | big_q(c1) | (~big_p(c2)) | (~big_p(c11)) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f1(elem!0))) | (~big_p(elem!0)) | big_q(f2(f2(elem!0)))),
% 22.73/22.90      inference(modus_ponens,[status(thm)],[1200, 1199])).
% 22.73/22.90  tff(1202,plain,
% 22.73/22.90      (big_q(c1) | (~big_p(c2)) | (~big_p(c11)) | big_q(elem!0) | big_q(f2(elem!0)) | (~big_p(f1(elem!0))) | big_q(f2(f2(elem!0)))),
% 22.73/22.90      inference(unit_resolution,[status(thm)],[1201, 968, 762])).
% 22.73/22.90  tff(1203,plain,
% 22.73/22.90      (big_q(f2(f2(elem!0)))),
% 22.73/22.90      inference(unit_resolution,[status(thm)],[1202, 1195, 5, 8, 1186, 819, 1177])).
% 22.73/22.90  tff(1204,plain,
% 22.73/22.90      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | (~big_q(c16)) | big_p(c15) | big_q(elem!0) | (~big_p(c19)) | (~big_q(f2(f2(elem!0)))))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_p(c15) | big_q(elem!0) | (~big_p(c19)) | (~big_q(f2(f2(elem!0)))))),
% 22.73/22.90      inference(rewrite,[status(thm)],[])).
% 22.73/22.90  tff(1205,plain,
% 22.73/22.90      (((~big_q(f2(f2(elem!0)))) | big_q(elem!0) | big_q(elem!0) | big_p(c15) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(c15)) <=> ((~big_p(c11)) | (~big_q(c16)) | big_p(c15) | big_q(elem!0) | (~big_p(c19)) | (~big_q(f2(f2(elem!0)))))),
% 22.73/22.90      inference(rewrite,[status(thm)],[])).
% 22.73/22.90  tff(1206,plain,
% 22.73/22.90      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(f2(elem!0)))) | big_q(elem!0) | big_q(elem!0) | big_p(c15) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(c15))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | (~big_q(c16)) | big_p(c15) | big_q(elem!0) | (~big_p(c19)) | (~big_q(f2(f2(elem!0))))))),
% 22.73/22.90      inference(monotonicity,[status(thm)],[1205])).
% 22.73/22.90  tff(1207,plain,
% 22.73/22.90      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(f2(elem!0)))) | big_q(elem!0) | big_q(elem!0) | big_p(c15) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(c15))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_p(c15) | big_q(elem!0) | (~big_p(c19)) | (~big_q(f2(f2(elem!0)))))),
% 22.73/22.90      inference(transitivity,[status(thm)],[1206, 1204])).
% 22.73/22.90  tff(1208,plain,
% 22.73/22.90      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(f2(elem!0)))) | big_q(elem!0) | big_q(elem!0) | big_p(c15) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(c15))),
% 22.73/22.90      inference(quant_inst,[status(thm)],[])).
% 22.73/22.90  tff(1209,plain,
% 22.73/22.90      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_p(c15) | big_q(elem!0) | (~big_p(c19)) | (~big_q(f2(f2(elem!0))))),
% 22.73/22.90      inference(modus_ponens,[status(thm)],[1208, 1207])).
% 22.73/22.90  tff(1210,plain,
% 22.73/22.90      ($false),
% 22.73/22.90      inference(unit_resolution,[status(thm)],[1209, 354, 1168, 5, 1159, 986, 819, 1203])).
% 22.73/22.90  tff(1211,plain,(big_p(c15) | big_q(elem!0) | big_q(f2(elem!0))), inference(lemma,lemma(discharge,[]))).
% 22.73/22.90  tff(1212,plain,
% 22.73/22.90      (big_p(c15)),
% 22.73/22.90      inference(unit_resolution,[status(thm)],[1211, 8, 5])).
% 22.73/22.90  tff(1213,plain,
% 22.73/22.90      (^[X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : refl(((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10)))) <=> ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10)))))),
% 22.73/22.90      inference(bind,[status(th)],[])).
% 22.73/22.90  tff(1214,plain,
% 22.73/22.90      (![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10)))) <=> ![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))),
% 22.73/22.90      inference(quant_intro,[status(thm)],[1213])).
% 22.73/22.90  tff(1215,plain,
% 22.73/22.90      (![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10)))) <=> ![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))),
% 22.73/22.90      inference(rewrite,[status(thm)],[])).
% 22.73/22.90  tff(1216,plain,
% 22.73/22.90      (^[X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) <=> ((~big_q(X12)) | (~big_p(X10)) | (~big_p(f3(X10))))), (((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) <=> (((~big_q(X12)) | (~big_p(X10)) | (~big_p(f3(X10)))) | (~big_p(c15))))), rewrite((((~big_q(X12)) | (~big_p(X10)) | (~big_p(f3(X10)))) | (~big_p(c15))) <=> ((~big_q(X12)) | (~big_p(X10)) | (~big_p(c15)) | (~big_p(f3(X10))))), (((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) <=> ((~big_q(X12)) | (~big_p(X10)) | (~big_p(c15)) | (~big_p(f3(X10)))))), ((((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) | big_q(X13)) <=> (((~big_q(X12)) | (~big_p(X10)) | (~big_p(c15)) | (~big_p(f3(X10)))) | big_q(X13)))), rewrite((((~big_q(X12)) | (~big_p(X10)) | (~big_p(c15)) | (~big_p(f3(X10)))) | big_q(X13)) <=> ((~big_q(X12)) | big_q(X13) | (~big_p(X10)) | (~big_p(c15)) | (~big_p(f3(X10))))), ((((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) | big_q(X13)) <=> ((~big_q(X12)) | big_q(X13) | (~big_p(X10)) | (~big_p(c15)) | (~big_p(f3(X10)))))), (((((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) | big_q(X13)) | (~big_q(c16))) <=> (((~big_q(X12)) | big_q(X13) | (~big_p(X10)) | (~big_p(c15)) | (~big_p(f3(X10)))) | (~big_q(c16))))), rewrite((((~big_q(X12)) | big_q(X13) | (~big_p(X10)) | (~big_p(c15)) | (~big_p(f3(X10)))) | (~big_q(c16))) <=> ((~big_q(X12)) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(c15)) | (~big_p(f3(X10))))), (((((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) | big_q(X13)) | (~big_q(c16))) <=> ((~big_q(X12)) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(c15)) | (~big_p(f3(X10)))))), ((((((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) | big_q(X13)) | (~big_q(c16))) | (~big_p(X14))) <=> (((~big_q(X12)) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(c15)) | (~big_p(f3(X10)))) | (~big_p(X14))))), rewrite((((~big_q(X12)) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(c15)) | (~big_p(f3(X10)))) | (~big_p(X14))) <=> ((~big_q(X12)) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))), ((((((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) | big_q(X13)) | (~big_q(c16))) | (~big_p(X14))) <=> ((~big_q(X12)) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10)))))), (((((((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) | big_q(X13)) | (~big_q(c16))) | (~big_p(X14))) | big_q(X15)) <=> (((~big_q(X12)) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10)))) | big_q(X15)))), rewrite((((~big_q(X12)) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10)))) | big_q(X15)) <=> ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))), (((((((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) | big_q(X13)) | (~big_q(c16))) | (~big_p(X14))) | big_q(X15)) <=> ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))))),
% 22.73/22.90      inference(bind,[status(th)],[])).
% 22.73/22.90  tff(1217,plain,
% 22.73/22.90      (![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((((((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) | big_q(X13)) | (~big_q(c16))) | (~big_p(X14))) | big_q(X15)) <=> ![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))),
% 22.73/22.90      inference(quant_intro,[status(thm)],[1216])).
% 22.73/22.90  tff(1218,axiom,(![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((((((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) | big_q(X13)) | (~big_q(c16))) | (~big_p(X14))) | big_q(X15))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_123')).
% 22.73/22.90  tff(1219,plain,
% 22.73/22.90      (![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))),
% 22.73/22.90      inference(modus_ponens,[status(thm)],[1218, 1217])).
% 22.73/22.90  tff(1220,plain,
% 22.73/22.90      (![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))),
% 22.73/22.90      inference(modus_ponens,[status(thm)],[1219, 1215])).
% 22.73/22.90  tff(1221,plain,(
% 22.73/22.90      ![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))),
% 22.73/22.90      inference(skolemize,[status(sab)],[1220])).
% 22.73/22.90  tff(1222,plain,
% 22.73/22.90      (![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))),
% 22.73/22.90      inference(modus_ponens,[status(thm)],[1221, 1214])).
% 22.73/22.90  tff(1223,plain,
% 22.73/22.90      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_p(c11)) | (~big_q(c16)) | (~big_p(c15)) | big_q(f2(elem!0)) | (~big_p(c19)) | (~big_p(f3(c11))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c15)) | big_q(f2(elem!0)) | (~big_p(c19)) | (~big_p(f3(c11))))),
% 22.73/22.90      inference(rewrite,[status(thm)],[])).
% 22.73/22.90  tff(1224,plain,
% 22.73/22.90      (((~big_q(c16)) | big_q(f2(elem!0)) | big_q(f2(elem!0)) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | (~big_p(c15)) | (~big_p(f3(c11)))) <=> ((~big_p(c11)) | (~big_q(c16)) | (~big_p(c15)) | big_q(f2(elem!0)) | (~big_p(c19)) | (~big_p(f3(c11))))),
% 22.73/22.90      inference(rewrite,[status(thm)],[])).
% 22.73/22.90  tff(1225,plain,
% 22.73/22.90      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(c16)) | big_q(f2(elem!0)) | big_q(f2(elem!0)) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | (~big_p(c15)) | (~big_p(f3(c11))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_p(c11)) | (~big_q(c16)) | (~big_p(c15)) | big_q(f2(elem!0)) | (~big_p(c19)) | (~big_p(f3(c11)))))),
% 22.73/22.90      inference(monotonicity,[status(thm)],[1224])).
% 22.73/22.90  tff(1226,plain,
% 22.73/22.90      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(c16)) | big_q(f2(elem!0)) | big_q(f2(elem!0)) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | (~big_p(c15)) | (~big_p(f3(c11))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c15)) | big_q(f2(elem!0)) | (~big_p(c19)) | (~big_p(f3(c11))))),
% 22.73/22.90      inference(transitivity,[status(thm)],[1225, 1223])).
% 22.73/22.90  tff(1227,plain,
% 22.73/22.90      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(c16)) | big_q(f2(elem!0)) | big_q(f2(elem!0)) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | (~big_p(c15)) | (~big_p(f3(c11))))),
% 22.73/22.90      inference(quant_inst,[status(thm)],[])).
% 22.73/22.90  tff(1228,plain,
% 22.73/22.90      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c15)) | big_q(f2(elem!0)) | (~big_p(c19)) | (~big_p(f3(c11)))),
% 22.73/22.90      inference(modus_ponens,[status(thm)],[1227, 1226])).
% 22.73/22.90  tff(1229,plain,
% 22.73/22.90      ((~big_p(c11)) | (~big_q(c16)) | (~big_p(c15)) | big_q(f2(elem!0)) | (~big_p(c19)) | (~big_p(f3(c11)))),
% 22.73/22.90      inference(unit_resolution,[status(thm)],[1228, 1222])).
% 22.73/22.90  tff(1230,plain,
% 22.73/22.90      (~big_p(f3(c11))),
% 22.73/22.90      inference(unit_resolution,[status(thm)],[1229, 1212, 1159, 1168, 819, 8])).
% 22.73/22.90  tff(1231,plain,
% 22.73/22.90      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | (~big_q(c16)) | (~big_p(c15)) | big_q(elem!0) | big_p(f3(c11)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c15)) | big_q(elem!0) | big_p(f3(c11)))),
% 22.73/22.90      inference(rewrite,[status(thm)],[])).
% 22.73/22.90  tff(1232,plain,
% 22.73/22.90      (((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | big_p(f3(c11)) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c15)) | big_p(f3(c11))) <=> ((~big_p(c11)) | (~big_q(c16)) | (~big_p(c15)) | big_q(elem!0) | big_p(f3(c11)))),
% 22.73/22.90      inference(rewrite,[status(thm)],[])).
% 22.73/22.90  tff(1233,plain,
% 22.73/22.90      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | big_p(f3(c11)) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c15)) | big_p(f3(c11)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | (~big_q(c16)) | (~big_p(c15)) | big_q(elem!0) | big_p(f3(c11))))),
% 22.73/22.90      inference(monotonicity,[status(thm)],[1232])).
% 22.73/22.90  tff(1234,plain,
% 22.73/22.90      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | big_p(f3(c11)) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c15)) | big_p(f3(c11)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c15)) | big_q(elem!0) | big_p(f3(c11)))),
% 22.73/22.90      inference(transitivity,[status(thm)],[1233, 1231])).
% 22.73/22.90  tff(1235,plain,
% 22.73/22.90      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_q(elem!0) | big_q(elem!0) | big_p(f3(c11)) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c15)) | big_p(f3(c11)))),
% 22.73/22.90      inference(quant_inst,[status(thm)],[])).
% 22.73/22.90  tff(1236,plain,
% 22.73/22.90      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c15)) | big_q(elem!0) | big_p(f3(c11))),
% 22.73/22.90      inference(modus_ponens,[status(thm)],[1235, 1234])).
% 22.73/22.90  tff(1237,plain,
% 22.73/22.90      ($false),
% 22.73/22.90      inference(unit_resolution,[status(thm)],[1236, 354, 5, 1159, 1212, 819, 1230])).
% 22.73/22.90  tff(1238,plain,(big_q(f2(elem!0)) | big_q(elem!0)), inference(lemma,lemma(discharge,[]))).
% 22.73/22.90  tff(1239,plain,
% 22.73/22.90      (big_q(f2(elem!0))),
% 22.73/22.90      inference(unit_resolution,[status(thm)],[1238, 5])).
% 22.73/22.90  tff(1240,plain,
% 22.73/22.90      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | (~big_q(c16)) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(c19)) | big_p(f3(c2)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(c19)) | big_p(f3(c2)))),
% 22.73/22.90      inference(rewrite,[status(thm)],[])).
% 22.73/22.90  tff(1241,plain,
% 22.73/22.90      (((~big_q(f2(elem!0))) | big_q(elem!0) | big_q(elem!0) | big_p(f3(c2)) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(f3(c2))) <=> ((~big_p(c11)) | (~big_q(c16)) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(c19)) | big_p(f3(c2)))),
% 22.73/22.90      inference(rewrite,[status(thm)],[])).
% 22.73/22.90  tff(1242,plain,
% 22.73/22.90      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(elem!0))) | big_q(elem!0) | big_q(elem!0) | big_p(f3(c2)) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(f3(c2)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | (~big_q(c16)) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(c19)) | big_p(f3(c2))))),
% 22.73/22.90      inference(monotonicity,[status(thm)],[1241])).
% 22.73/22.90  tff(1243,plain,
% 22.73/22.90      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(elem!0))) | big_q(elem!0) | big_q(elem!0) | big_p(f3(c2)) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(f3(c2)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(c19)) | big_p(f3(c2)))),
% 22.73/22.90      inference(transitivity,[status(thm)],[1242, 1240])).
% 22.73/22.90  tff(1244,plain,
% 22.73/22.90      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(elem!0))) | big_q(elem!0) | big_q(elem!0) | big_p(f3(c2)) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(f3(c2)))),
% 22.73/22.90      inference(quant_inst,[status(thm)],[])).
% 22.73/22.90  tff(1245,plain,
% 22.73/22.90      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(c19)) | big_p(f3(c2))),
% 22.73/22.90      inference(modus_ponens,[status(thm)],[1244, 1243])).
% 22.73/22.90  tff(1246,plain,
% 22.73/22.90      ($false),
% 22.73/22.90      inference(unit_resolution,[status(thm)],[1245, 354, 1168, 5, 1239, 1159, 819, 763])).
% 22.73/22.90  tff(1247,plain,(big_p(f3(c2)) | big_q(elem!0)), inference(lemma,lemma(discharge,[]))).
% 22.73/22.90  tff(1248,plain,
% 22.73/22.90      (big_p(f3(c2))),
% 22.73/22.90      inference(unit_resolution,[status(thm)],[1247, 5])).
% 22.73/22.90  tff(1249,plain,
% 22.73/22.90      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | (~big_q(c16)) | big_p(c15) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(c19)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_p(c15) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(c19)))),
% 22.73/22.90      inference(rewrite,[status(thm)],[])).
% 22.73/22.90  tff(1250,plain,
% 22.73/22.90      (((~big_q(f2(elem!0))) | big_q(elem!0) | big_q(elem!0) | big_p(c15) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(c15)) <=> ((~big_p(c11)) | (~big_q(c16)) | big_p(c15) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(c19)))),
% 22.73/22.90      inference(rewrite,[status(thm)],[])).
% 22.73/22.90  tff(1251,plain,
% 22.73/22.90      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(elem!0))) | big_q(elem!0) | big_q(elem!0) | big_p(c15) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(c15))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | (~big_q(c16)) | big_p(c15) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(c19))))),
% 22.73/22.90      inference(monotonicity,[status(thm)],[1250])).
% 22.73/22.90  tff(1252,plain,
% 22.73/22.90      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(elem!0))) | big_q(elem!0) | big_q(elem!0) | big_p(c15) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(c15))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_p(c15) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(c19)))),
% 22.73/22.90      inference(transitivity,[status(thm)],[1251, 1249])).
% 22.73/22.90  tff(1253,plain,
% 22.73/22.90      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(elem!0))) | big_q(elem!0) | big_q(elem!0) | big_p(c15) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(c15))),
% 22.73/22.91      inference(quant_inst,[status(thm)],[])).
% 22.73/22.91  tff(1254,plain,
% 22.73/22.91      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_p(c15) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(c19))),
% 22.73/22.91      inference(modus_ponens,[status(thm)],[1253, 1252])).
% 22.73/22.91  tff(1255,plain,
% 22.73/22.91      ($false),
% 22.73/22.91      inference(unit_resolution,[status(thm)],[1254, 354, 1168, 5, 1239, 1159, 986, 819])).
% 22.73/22.91  tff(1256,plain,(big_p(c15) | big_q(elem!0)), inference(lemma,lemma(discharge,[]))).
% 22.73/22.91  tff(1257,plain,
% 22.73/22.91      (big_p(c15)),
% 22.73/22.91      inference(unit_resolution,[status(thm)],[1256, 5])).
% 22.73/22.91  tff(1258,assumption,(~big_q(c20)), introduced(assumption)).
% 22.73/22.91  tff(1259,plain,
% 22.73/22.91      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_p(c11)) | big_q(c20) | (~big_q(c16)) | (~big_p(c15)) | (~big_p(c19)) | (~big_p(f3(c19))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (~big_p(c11)) | big_q(c20) | (~big_q(c16)) | (~big_p(c15)) | (~big_p(c19)) | (~big_p(f3(c19))))),
% 22.73/22.91      inference(rewrite,[status(thm)],[])).
% 22.73/22.91  tff(1260,plain,
% 22.73/22.91      (((~big_q(c16)) | big_q(c20) | big_q(c20) | (~big_p(c19)) | (~big_q(c16)) | (~big_p(c11)) | (~big_p(c15)) | (~big_p(f3(c19)))) <=> ((~big_p(c11)) | big_q(c20) | (~big_q(c16)) | (~big_p(c15)) | (~big_p(c19)) | (~big_p(f3(c19))))),
% 22.73/22.91      inference(rewrite,[status(thm)],[])).
% 22.73/22.91  tff(1261,plain,
% 22.73/22.91      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(c16)) | big_q(c20) | big_q(c20) | (~big_p(c19)) | (~big_q(c16)) | (~big_p(c11)) | (~big_p(c15)) | (~big_p(f3(c19))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_p(c11)) | big_q(c20) | (~big_q(c16)) | (~big_p(c15)) | (~big_p(c19)) | (~big_p(f3(c19)))))),
% 22.73/22.91      inference(monotonicity,[status(thm)],[1260])).
% 22.73/22.91  tff(1262,plain,
% 22.73/22.91      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(c16)) | big_q(c20) | big_q(c20) | (~big_p(c19)) | (~big_q(c16)) | (~big_p(c11)) | (~big_p(c15)) | (~big_p(f3(c19))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (~big_p(c11)) | big_q(c20) | (~big_q(c16)) | (~big_p(c15)) | (~big_p(c19)) | (~big_p(f3(c19))))),
% 22.73/22.91      inference(transitivity,[status(thm)],[1261, 1259])).
% 22.73/22.91  tff(1263,plain,
% 22.73/22.91      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(c16)) | big_q(c20) | big_q(c20) | (~big_p(c19)) | (~big_q(c16)) | (~big_p(c11)) | (~big_p(c15)) | (~big_p(f3(c19))))),
% 22.73/22.91      inference(quant_inst,[status(thm)],[])).
% 22.73/22.91  tff(1264,plain,
% 22.73/22.91      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (~big_p(c11)) | big_q(c20) | (~big_q(c16)) | (~big_p(c15)) | (~big_p(c19)) | (~big_p(f3(c19)))),
% 22.73/22.91      inference(modus_ponens,[status(thm)],[1263, 1262])).
% 22.73/22.91  tff(1265,plain,
% 22.73/22.91      ((~big_p(c11)) | big_q(c20) | (~big_q(c16)) | (~big_p(c15)) | (~big_p(c19)) | (~big_p(f3(c19)))),
% 22.73/22.91      inference(unit_resolution,[status(thm)],[1264, 1222])).
% 22.73/22.91  tff(1266,plain,
% 22.73/22.91      (~big_p(f3(c19))),
% 22.73/22.91      inference(unit_resolution,[status(thm)],[1265, 1258, 1159, 1168, 819, 1257])).
% 22.73/22.91  tff(1267,plain,
% 22.73/22.91      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_p(c2)) | big_q(c20) | (~big_q(c16)) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(c2))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (~big_p(c2)) | big_q(c20) | (~big_q(c16)) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(c2))))),
% 22.73/22.91      inference(rewrite,[status(thm)],[])).
% 22.73/22.91  tff(1268,plain,
% 22.73/22.91      (((~big_q(c16)) | big_q(elem!0) | big_q(c20) | (~big_p(c2)) | (~big_q(c16)) | (~big_p(c2)) | (~big_p(c15)) | (~big_p(f3(c2)))) <=> ((~big_p(c2)) | big_q(c20) | (~big_q(c16)) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(c2))))),
% 22.73/22.91      inference(rewrite,[status(thm)],[])).
% 22.73/22.91  tff(1269,plain,
% 22.73/22.91      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(c16)) | big_q(elem!0) | big_q(c20) | (~big_p(c2)) | (~big_q(c16)) | (~big_p(c2)) | (~big_p(c15)) | (~big_p(f3(c2))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_p(c2)) | big_q(c20) | (~big_q(c16)) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(c2)))))),
% 22.73/22.91      inference(monotonicity,[status(thm)],[1268])).
% 22.73/22.91  tff(1270,plain,
% 22.73/22.91      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(c16)) | big_q(elem!0) | big_q(c20) | (~big_p(c2)) | (~big_q(c16)) | (~big_p(c2)) | (~big_p(c15)) | (~big_p(f3(c2))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (~big_p(c2)) | big_q(c20) | (~big_q(c16)) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(c2))))),
% 22.73/22.91      inference(transitivity,[status(thm)],[1269, 1267])).
% 22.73/22.91  tff(1271,plain,
% 22.73/22.91      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(c16)) | big_q(elem!0) | big_q(c20) | (~big_p(c2)) | (~big_q(c16)) | (~big_p(c2)) | (~big_p(c15)) | (~big_p(f3(c2))))),
% 22.73/22.91      inference(quant_inst,[status(thm)],[])).
% 22.73/22.91  tff(1272,plain,
% 22.73/22.91      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (~big_p(c2)) | big_q(c20) | (~big_q(c16)) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(c2)))),
% 22.73/22.91      inference(modus_ponens,[status(thm)],[1271, 1270])).
% 22.73/22.91  tff(1273,plain,
% 22.73/22.91      ((~big_p(c2)) | big_q(c20) | (~big_q(c16)) | (~big_p(c15)) | big_q(elem!0) | (~big_p(f3(c2)))),
% 22.73/22.91      inference(unit_resolution,[status(thm)],[1272, 1222])).
% 22.73/22.91  tff(1274,plain,
% 22.73/22.91      (~big_p(f3(c2))),
% 22.73/22.91      inference(unit_resolution,[status(thm)],[1273, 1258, 1159, 5, 1177, 1257])).
% 22.73/22.91  tff(1275,plain,
% 22.73/22.91      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | (~big_q(c16)) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(c19)) | big_p(f3(c2)) | big_p(f3(c19)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(c19)) | big_p(f3(c2)) | big_p(f3(c19)))),
% 22.73/22.91      inference(rewrite,[status(thm)],[])).
% 22.73/22.91  tff(1276,plain,
% 22.73/22.91      (((~big_q(f2(elem!0))) | big_q(elem!0) | big_q(elem!0) | big_p(f3(c2)) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(f3(c19))) <=> ((~big_p(c11)) | (~big_q(c16)) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(c19)) | big_p(f3(c2)) | big_p(f3(c19)))),
% 22.73/22.91      inference(rewrite,[status(thm)],[])).
% 22.73/22.91  tff(1277,plain,
% 22.73/22.91      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(elem!0))) | big_q(elem!0) | big_q(elem!0) | big_p(f3(c2)) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(f3(c19)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | (~big_q(c16)) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(c19)) | big_p(f3(c2)) | big_p(f3(c19))))),
% 22.73/22.91      inference(monotonicity,[status(thm)],[1276])).
% 22.73/22.91  tff(1278,plain,
% 22.73/22.91      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(elem!0))) | big_q(elem!0) | big_q(elem!0) | big_p(f3(c2)) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(f3(c19)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(c19)) | big_p(f3(c2)) | big_p(f3(c19)))),
% 22.73/22.91      inference(transitivity,[status(thm)],[1277, 1275])).
% 22.73/22.91  tff(1279,plain,
% 22.73/22.91      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(f2(elem!0))) | big_q(elem!0) | big_q(elem!0) | big_p(f3(c2)) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(f3(c19)))),
% 22.73/22.91      inference(quant_inst,[status(thm)],[])).
% 22.73/22.91  tff(1280,plain,
% 22.73/22.91      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_q(elem!0) | (~big_q(f2(elem!0))) | (~big_p(c19)) | big_p(f3(c2)) | big_p(f3(c19))),
% 22.73/22.91      inference(modus_ponens,[status(thm)],[1279, 1278])).
% 22.73/22.91  tff(1281,plain,
% 22.73/22.91      ($false),
% 22.73/22.91      inference(unit_resolution,[status(thm)],[1280, 354, 1168, 5, 1239, 1159, 819, 1274, 1266])).
% 22.73/22.91  tff(1282,plain,(big_q(c20) | big_q(elem!0)), inference(lemma,lemma(discharge,[]))).
% 22.73/22.91  tff(1283,plain,
% 22.73/22.91      (big_q(c20)),
% 22.73/22.91      inference(unit_resolution,[status(thm)],[1282, 5])).
% 22.73/22.91  tff(1284,plain,
% 22.73/22.91      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_p(c2)) | (~big_p(c11)) | (~big_q(c16)) | (~big_q(c20)) | (~big_p(c15)) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_p(f3(c2))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (~big_p(c2)) | (~big_p(c11)) | (~big_q(c16)) | (~big_q(c20)) | (~big_p(c15)) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_p(f3(c2))))),
% 22.73/22.91      inference(rewrite,[status(thm)],[])).
% 22.73/22.91  tff(1285,plain,
% 22.73/22.91      (((~big_q(c20)) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_p(c2)) | (~big_q(c16)) | (~big_p(c11)) | (~big_p(c15)) | (~big_p(f3(c2)))) <=> ((~big_p(c2)) | (~big_p(c11)) | (~big_q(c16)) | (~big_q(c20)) | (~big_p(c15)) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_p(f3(c2))))),
% 22.73/22.91      inference(rewrite,[status(thm)],[])).
% 22.73/22.91  tff(1286,plain,
% 22.73/22.91      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(c20)) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_p(c2)) | (~big_q(c16)) | (~big_p(c11)) | (~big_p(c15)) | (~big_p(f3(c2))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_p(c2)) | (~big_p(c11)) | (~big_q(c16)) | (~big_q(c20)) | (~big_p(c15)) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_p(f3(c2)))))),
% 22.73/22.91      inference(monotonicity,[status(thm)],[1285])).
% 22.73/22.91  tff(1287,plain,
% 22.73/22.91      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(c20)) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_p(c2)) | (~big_q(c16)) | (~big_p(c11)) | (~big_p(c15)) | (~big_p(f3(c2))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (~big_p(c2)) | (~big_p(c11)) | (~big_q(c16)) | (~big_q(c20)) | (~big_p(c15)) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_p(f3(c2))))),
% 22.73/22.91      inference(transitivity,[status(thm)],[1286, 1284])).
% 22.73/22.91  tff(1288,plain,
% 22.73/22.91      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(c20)) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_p(c2)) | (~big_q(c16)) | (~big_p(c11)) | (~big_p(c15)) | (~big_p(f3(c2))))),
% 22.73/22.91      inference(quant_inst,[status(thm)],[])).
% 22.73/22.91  tff(1289,plain,
% 22.73/22.91      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (~big_p(c2)) | (~big_p(c11)) | (~big_q(c16)) | (~big_q(c20)) | (~big_p(c15)) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_p(f3(c2)))),
% 22.73/22.91      inference(modus_ponens,[status(thm)],[1288, 1287])).
% 22.73/22.91  tff(1290,plain,
% 22.73/22.91      ((~big_p(c2)) | (~big_p(c11)) | (~big_q(c16)) | (~big_q(c20)) | (~big_p(c15)) | big_q(elem!0) | big_q(f4(elem!0)) | (~big_p(f3(c2)))),
% 22.73/22.91      inference(unit_resolution,[status(thm)],[1289, 1222])).
% 22.73/22.91  tff(1291,plain,
% 22.73/22.91      (big_q(f4(elem!0))),
% 22.73/22.91      inference(unit_resolution,[status(thm)],[1290, 1248, 5, 1159, 1257, 1283, 819, 1177])).
% 22.73/22.91  tff(1292,plain,
% 22.73/22.91      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_p(c2)) | (~big_q(c16)) | (~big_p(c15)) | big_q(elem!0) | (~big_q(f4(elem!0))) | (~big_p(f3(c2))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (~big_p(c2)) | (~big_q(c16)) | (~big_p(c15)) | big_q(elem!0) | (~big_q(f4(elem!0))) | (~big_p(f3(c2))))),
% 22.73/22.91      inference(rewrite,[status(thm)],[])).
% 22.73/22.91  tff(1293,plain,
% 22.73/22.91      (((~big_q(f4(elem!0))) | big_q(elem!0) | big_q(elem!0) | (~big_p(c2)) | (~big_q(c16)) | (~big_p(f3(c2))) | (~big_p(c15)) | (~big_p(f3(c2)))) <=> ((~big_p(c2)) | (~big_q(c16)) | (~big_p(c15)) | big_q(elem!0) | (~big_q(f4(elem!0))) | (~big_p(f3(c2))))),
% 22.73/22.91      inference(rewrite,[status(thm)],[])).
% 22.73/22.91  tff(1294,plain,
% 22.73/22.91      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(f4(elem!0))) | big_q(elem!0) | big_q(elem!0) | (~big_p(c2)) | (~big_q(c16)) | (~big_p(f3(c2))) | (~big_p(c15)) | (~big_p(f3(c2))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_p(c2)) | (~big_q(c16)) | (~big_p(c15)) | big_q(elem!0) | (~big_q(f4(elem!0))) | (~big_p(f3(c2)))))),
% 22.73/22.91      inference(monotonicity,[status(thm)],[1293])).
% 22.73/22.91  tff(1295,plain,
% 22.73/22.91      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(f4(elem!0))) | big_q(elem!0) | big_q(elem!0) | (~big_p(c2)) | (~big_q(c16)) | (~big_p(f3(c2))) | (~big_p(c15)) | (~big_p(f3(c2))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (~big_p(c2)) | (~big_q(c16)) | (~big_p(c15)) | big_q(elem!0) | (~big_q(f4(elem!0))) | (~big_p(f3(c2))))),
% 22.73/22.91      inference(transitivity,[status(thm)],[1294, 1292])).
% 22.73/22.91  tff(1296,plain,
% 22.73/22.91      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(f4(elem!0))) | big_q(elem!0) | big_q(elem!0) | (~big_p(c2)) | (~big_q(c16)) | (~big_p(f3(c2))) | (~big_p(c15)) | (~big_p(f3(c2))))),
% 22.73/22.91      inference(quant_inst,[status(thm)],[])).
% 22.73/22.91  tff(1297,plain,
% 22.73/22.91      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (~big_p(c2)) | (~big_q(c16)) | (~big_p(c15)) | big_q(elem!0) | (~big_q(f4(elem!0))) | (~big_p(f3(c2)))),
% 22.73/22.91      inference(modus_ponens,[status(thm)],[1296, 1295])).
% 22.73/22.91  tff(1298,plain,
% 22.73/22.91      ($false),
% 22.73/22.91      inference(unit_resolution,[status(thm)],[1297, 1222, 5, 1291, 1177, 1159, 1257, 1248])).
% 22.73/22.91  tff(1299,plain,(big_q(elem!0)), inference(lemma,lemma(discharge,[]))).
% 22.73/22.91  tff(1300,plain,
% 22.73/22.91      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | big_p(c11) | (~big_q(elem!0)) | (~big_p(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | (~big_q(elem!0)) | (~big_p(elem!0)))),
% 22.73/22.91      inference(rewrite,[status(thm)],[])).
% 22.73/22.91  tff(1301,plain,
% 22.73/22.91      (((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | (~big_p(elem!0)) | big_q(c16) | big_p(c11) | (~big_p(elem!0)) | big_p(c11)) <=> (big_q(c16) | big_p(c11) | (~big_q(elem!0)) | (~big_p(elem!0)))),
% 22.73/22.91      inference(rewrite,[status(thm)],[])).
% 22.73/22.91  tff(1302,plain,
% 22.73/22.91      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | (~big_p(elem!0)) | big_q(c16) | big_p(c11) | (~big_p(elem!0)) | big_p(c11))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | big_p(c11) | (~big_q(elem!0)) | (~big_p(elem!0))))),
% 22.73/22.91      inference(monotonicity,[status(thm)],[1301])).
% 22.73/22.91  tff(1303,plain,
% 22.73/22.91      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | (~big_p(elem!0)) | big_q(c16) | big_p(c11) | (~big_p(elem!0)) | big_p(c11))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | (~big_q(elem!0)) | (~big_p(elem!0)))),
% 22.73/22.91      inference(transitivity,[status(thm)],[1302, 1300])).
% 22.73/22.91  tff(1304,plain,
% 22.73/22.91      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | (~big_p(elem!0)) | big_q(c16) | big_p(c11) | (~big_p(elem!0)) | big_p(c11))),
% 22.73/22.91      inference(quant_inst,[status(thm)],[])).
% 22.73/22.91  tff(1305,plain,
% 22.73/22.91      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | (~big_p(X7)) | big_q(c16) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | big_p(c11) | (~big_q(elem!0)) | (~big_p(elem!0))),
% 22.73/22.91      inference(modus_ponens,[status(thm)],[1304, 1303])).
% 22.73/22.91  tff(1306,plain,
% 22.73/22.91      ($false),
% 22.73/22.91      inference(unit_resolution,[status(thm)],[1305, 35, 1299, 762, 2, 1])).
% 22.73/22.91  tff(1307,plain,(big_q(c16) | big_p(c11)), inference(lemma,lemma(discharge,[]))).
% 22.73/22.91  tff(1308,plain,
% 22.73/22.91      (big_q(c16)),
% 22.73/22.91      inference(unit_resolution,[status(thm)],[1307, 1])).
% 22.73/22.91  tff(1309,plain,
% 22.73/22.91      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_p(c11) | big_p(c19) | big_q(f4(elem!0)) | (~big_q(elem!0)) | (~big_p(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_p(c19) | big_q(f4(elem!0)) | (~big_q(elem!0)) | (~big_p(elem!0)))),
% 22.73/22.91      inference(rewrite,[status(thm)],[])).
% 22.73/22.91  tff(1310,plain,
% 22.73/22.91      (((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | (~big_p(elem!0)) | (~big_q(c16)) | big_p(c11) | (~big_p(elem!0)) | big_p(c19)) <=> ((~big_q(c16)) | big_p(c11) | big_p(c19) | big_q(f4(elem!0)) | (~big_q(elem!0)) | (~big_p(elem!0)))),
% 22.73/22.91      inference(rewrite,[status(thm)],[])).
% 22.73/22.91  tff(1311,plain,
% 22.73/22.91      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | (~big_p(elem!0)) | (~big_q(c16)) | big_p(c11) | (~big_p(elem!0)) | big_p(c19))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_p(c11) | big_p(c19) | big_q(f4(elem!0)) | (~big_q(elem!0)) | (~big_p(elem!0))))),
% 22.73/22.91      inference(monotonicity,[status(thm)],[1310])).
% 22.73/22.91  tff(1312,plain,
% 22.73/22.91      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | (~big_p(elem!0)) | (~big_q(c16)) | big_p(c11) | (~big_p(elem!0)) | big_p(c19))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_p(c19) | big_q(f4(elem!0)) | (~big_q(elem!0)) | (~big_p(elem!0)))),
% 22.73/22.91      inference(transitivity,[status(thm)],[1311, 1309])).
% 22.73/22.91  tff(1313,plain,
% 22.73/22.91      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | (~big_p(elem!0)) | (~big_q(c16)) | big_p(c11) | (~big_p(elem!0)) | big_p(c19))),
% 22.73/22.91      inference(quant_inst,[status(thm)],[])).
% 22.73/22.91  tff(1314,plain,
% 22.73/22.91      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_p(c19) | big_q(f4(elem!0)) | (~big_q(elem!0)) | (~big_p(elem!0))),
% 22.73/22.91      inference(modus_ponens,[status(thm)],[1313, 1312])).
% 22.73/22.91  tff(1315,plain,
% 22.73/22.91      ($false),
% 22.73/22.91      inference(unit_resolution,[status(thm)],[1314, 373, 307, 1299, 306, 762, 1308, 1])).
% 22.73/22.91  tff(1316,plain,(big_q(f4(elem!0)) | big_p(c19) | big_p(c11)), inference(lemma,lemma(discharge,[]))).
% 22.73/22.91  tff(1317,plain,
% 22.73/22.91      (big_q(f4(elem!0))),
% 22.73/22.91      inference(unit_resolution,[status(thm)],[1316, 307, 1])).
% 22.73/22.91  tff(1318,plain,
% 22.73/22.91      (((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | (big_p(c11) | big_p(c19) | (~big_q(c20)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(elem!0)))) <=> ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | big_p(c11) | big_p(c19) | (~big_q(c20)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(elem!0)))),
% 22.73/22.92      inference(rewrite,[status(thm)],[])).
% 22.73/22.92  tff(1319,plain,
% 22.73/22.92      (((~big_q(f4(elem!0))) | big_p(c19) | (~big_q(elem!0)) | (~big_p(elem!0)) | (~big_p(elem!0)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(elem!0)))) <=> (big_p(c11) | big_p(c19) | (~big_q(c20)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(elem!0)))),
% 22.73/22.92      inference(rewrite,[status(thm)],[])).
% 22.73/22.92  tff(1320,plain,
% 22.73/22.92      (((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_q(f4(elem!0))) | big_p(c19) | (~big_q(elem!0)) | (~big_p(elem!0)) | (~big_p(elem!0)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(elem!0))))) <=> ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | (big_p(c11) | big_p(c19) | (~big_q(c20)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(elem!0))))),
% 22.73/22.92      inference(monotonicity,[status(thm)],[1319])).
% 22.73/22.92  tff(1321,plain,
% 22.73/22.92      (((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_q(f4(elem!0))) | big_p(c19) | (~big_q(elem!0)) | (~big_p(elem!0)) | (~big_p(elem!0)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(elem!0))))) <=> ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | big_p(c11) | big_p(c19) | (~big_q(c20)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(elem!0)))),
% 22.73/22.92      inference(transitivity,[status(thm)],[1320, 1318])).
% 22.73/22.92  tff(1322,plain,
% 22.73/22.92      ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_q(f4(elem!0))) | big_p(c19) | (~big_q(elem!0)) | (~big_p(elem!0)) | (~big_p(elem!0)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(elem!0))))),
% 22.73/22.92      inference(quant_inst,[status(thm)],[])).
% 22.73/22.92  tff(1323,plain,
% 22.73/22.92      ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | big_p(c11) | big_p(c19) | (~big_q(c20)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(elem!0))),
% 22.73/22.92      inference(modus_ponens,[status(thm)],[1322, 1321])).
% 22.73/22.92  tff(1324,plain,
% 22.73/22.92      (~big_q(c20)),
% 22.73/22.92      inference(unit_resolution,[status(thm)],[1323, 659, 307, 1299, 1317, 762, 1])).
% 22.73/22.92  tff(1325,plain,
% 22.73/22.92      (^[X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : refl(((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | big_p(c19) | (~big_q(f4(X16)))) <=> ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | big_p(c19) | (~big_q(f4(X16)))))),
% 22.73/22.92      inference(bind,[status(th)],[])).
% 22.73/22.92  tff(1326,plain,
% 22.73/22.92      (![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | big_p(c19) | (~big_q(f4(X16)))) <=> ![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | big_p(c19) | (~big_q(f4(X16))))),
% 22.73/22.92      inference(quant_intro,[status(thm)],[1325])).
% 22.73/22.92  tff(1327,plain,
% 22.73/22.92      (![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | big_p(c19) | (~big_q(f4(X16)))) <=> ![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | big_p(c19) | (~big_q(f4(X16))))),
% 22.73/22.92      inference(rewrite,[status(thm)],[])).
% 22.73/22.92  tff(1328,plain,
% 22.73/22.92      (^[X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) <=> ((~big_q(X8)) | (~big_p(X7)) | big_p(c11))), ((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) <=> (((~big_q(X8)) | (~big_p(X7)) | big_p(c11)) | big_p(X9)))), rewrite((((~big_q(X8)) | (~big_p(X7)) | big_p(c11)) | big_p(X9)) <=> ((~big_q(X8)) | big_p(X9) | (~big_p(X7)) | big_p(c11))), ((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) <=> ((~big_q(X8)) | big_p(X9) | (~big_p(X7)) | big_p(c11)))), (((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) <=> (((~big_q(X8)) | big_p(X9) | (~big_p(X7)) | big_p(c11)) | (~big_q(f4(X16)))))), rewrite((((~big_q(X8)) | big_p(X9) | (~big_p(X7)) | big_p(c11)) | (~big_q(f4(X16)))) <=> ((~big_q(X8)) | big_p(X9) | (~big_p(X7)) | big_p(c11) | (~big_q(f4(X16))))), (((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) <=> ((~big_q(X8)) | big_p(X9) | (~big_p(X7)) | big_p(c11) | (~big_q(f4(X16)))))), ((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) <=> (((~big_q(X8)) | big_p(X9) | (~big_p(X7)) | big_p(c11) | (~big_q(f4(X16)))) | (~big_q(X16))))), rewrite((((~big_q(X8)) | big_p(X9) | (~big_p(X7)) | big_p(c11) | (~big_q(f4(X16)))) | (~big_q(X16))) <=> ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | (~big_q(f4(X16))))), ((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) <=> ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | (~big_q(f4(X16)))))), (((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) | big_p(c19)) <=> (((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | (~big_q(f4(X16)))) | big_p(c19)))), rewrite((((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | (~big_q(f4(X16)))) | big_p(c19)) <=> ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | big_p(c19) | (~big_q(f4(X16))))), (((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) | big_p(c19)) <=> ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | big_p(c19) | (~big_q(f4(X16)))))), ((((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) | big_p(c19)) | big_q(X17)) <=> (((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | big_p(c19) | (~big_q(f4(X16)))) | big_q(X17)))), rewrite((((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | big_p(c19) | (~big_q(f4(X16)))) | big_q(X17)) <=> ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | big_p(c19) | (~big_q(f4(X16))))), ((((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) | big_p(c19)) | big_q(X17)) <=> ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | big_p(c19) | (~big_q(f4(X16))))))),
% 22.73/22.92      inference(bind,[status(th)],[])).
% 22.73/22.92  tff(1329,plain,
% 22.73/22.92      (![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : (((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) | big_p(c19)) | big_q(X17)) <=> ![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | big_p(c19) | (~big_q(f4(X16))))),
% 22.73/22.92      inference(quant_intro,[status(thm)],[1328])).
% 22.73/22.92  tff(1330,axiom,(![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : (((((((big_p(c11) | (~big_p(X7))) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) | big_p(c19)) | big_q(X17))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_87')).
% 22.73/22.92  tff(1331,plain,
% 22.73/22.92      (![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | big_p(c19) | (~big_q(f4(X16))))),
% 22.73/22.92      inference(modus_ponens,[status(thm)],[1330, 1329])).
% 22.73/22.92  tff(1332,plain,
% 22.73/22.92      (![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | big_p(c19) | (~big_q(f4(X16))))),
% 22.73/22.92      inference(modus_ponens,[status(thm)],[1331, 1327])).
% 22.73/22.92  tff(1333,plain,(
% 22.73/22.92      ![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | big_p(c19) | (~big_q(f4(X16))))),
% 22.73/22.92      inference(skolemize,[status(sab)],[1332])).
% 22.73/22.92  tff(1334,plain,
% 22.73/22.92      (![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | big_p(c19) | (~big_q(f4(X16))))),
% 22.73/22.92      inference(modus_ponens,[status(thm)],[1333, 1326])).
% 22.73/22.92  tff(1335,plain,
% 22.73/22.92      (((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | big_p(c19) | (~big_q(f4(X16))))) | (big_q(c20) | big_p(c11) | big_p(c19) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(elem!0)))) <=> ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | big_p(c19) | (~big_q(f4(X16))))) | big_q(c20) | big_p(c11) | big_p(c19) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(elem!0)))),
% 22.73/22.92      inference(rewrite,[status(thm)],[])).
% 22.73/22.92  tff(1336,plain,
% 22.73/22.92      (((~big_q(elem!0)) | big_p(c19) | big_q(c20) | (~big_q(elem!0)) | (~big_p(elem!0)) | big_p(c11) | big_p(c19) | (~big_q(f4(elem!0)))) <=> (big_q(c20) | big_p(c11) | big_p(c19) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(elem!0)))),
% 22.73/22.92      inference(rewrite,[status(thm)],[])).
% 22.73/22.92  tff(1337,plain,
% 22.73/22.92      (((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | big_p(c19) | (~big_q(f4(X16))))) | ((~big_q(elem!0)) | big_p(c19) | big_q(c20) | (~big_q(elem!0)) | (~big_p(elem!0)) | big_p(c11) | big_p(c19) | (~big_q(f4(elem!0))))) <=> ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | big_p(c19) | (~big_q(f4(X16))))) | (big_q(c20) | big_p(c11) | big_p(c19) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(elem!0))))),
% 22.73/22.92      inference(monotonicity,[status(thm)],[1336])).
% 22.73/22.92  tff(1338,plain,
% 22.73/22.92      (((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | big_p(c19) | (~big_q(f4(X16))))) | ((~big_q(elem!0)) | big_p(c19) | big_q(c20) | (~big_q(elem!0)) | (~big_p(elem!0)) | big_p(c11) | big_p(c19) | (~big_q(f4(elem!0))))) <=> ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | big_p(c19) | (~big_q(f4(X16))))) | big_q(c20) | big_p(c11) | big_p(c19) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(elem!0)))),
% 22.73/22.92      inference(transitivity,[status(thm)],[1337, 1335])).
% 22.73/22.92  tff(1339,plain,
% 22.73/22.92      ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | big_p(c19) | (~big_q(f4(X16))))) | ((~big_q(elem!0)) | big_p(c19) | big_q(c20) | (~big_q(elem!0)) | (~big_p(elem!0)) | big_p(c11) | big_p(c19) | (~big_q(f4(elem!0))))),
% 22.73/22.92      inference(quant_inst,[status(thm)],[])).
% 22.73/22.92  tff(1340,plain,
% 22.73/22.92      ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | (~big_p(X7)) | big_p(c11) | big_p(c19) | (~big_q(f4(X16))))) | big_q(c20) | big_p(c11) | big_p(c19) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(elem!0))),
% 22.73/22.92      inference(modus_ponens,[status(thm)],[1339, 1338])).
% 22.73/22.92  tff(1341,plain,
% 22.73/22.92      ($false),
% 22.73/22.92      inference(unit_resolution,[status(thm)],[1340, 1334, 307, 1299, 1317, 762, 1324, 1])).
% 22.73/22.92  tff(1342,plain,(big_p(c19) | big_p(c11)), inference(lemma,lemma(discharge,[]))).
% 22.73/22.92  tff(1343,plain,
% 22.73/22.92      (big_p(c19)),
% 22.73/22.92      inference(unit_resolution,[status(thm)],[1342, 1])).
% 22.73/22.92  tff(1344,plain,
% 22.73/22.92      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_p(c11) | big_q(f4(elem!0)) | (~big_q(elem!0)) | (~big_p(c19)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_q(f4(elem!0)) | (~big_q(elem!0)) | (~big_p(c19)))),
% 22.76/22.92      inference(rewrite,[status(thm)],[])).
% 22.76/22.92  tff(1345,plain,
% 22.76/22.92      (((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | (~big_p(c19)) | (~big_q(c16)) | big_p(c11) | (~big_p(c19)) | big_p(c11)) <=> ((~big_q(c16)) | big_p(c11) | big_q(f4(elem!0)) | (~big_q(elem!0)) | (~big_p(c19)))),
% 22.76/22.92      inference(rewrite,[status(thm)],[])).
% 22.76/22.92  tff(1346,plain,
% 22.76/22.92      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | (~big_p(c19)) | (~big_q(c16)) | big_p(c11) | (~big_p(c19)) | big_p(c11))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(c16)) | big_p(c11) | big_q(f4(elem!0)) | (~big_q(elem!0)) | (~big_p(c19))))),
% 22.76/22.92      inference(monotonicity,[status(thm)],[1345])).
% 22.76/22.92  tff(1347,plain,
% 22.76/22.92      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | (~big_p(c19)) | (~big_q(c16)) | big_p(c11) | (~big_p(c19)) | big_p(c11))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_q(f4(elem!0)) | (~big_q(elem!0)) | (~big_p(c19)))),
% 22.76/22.92      inference(transitivity,[status(thm)],[1346, 1344])).
% 22.76/22.92  tff(1348,plain,
% 22.76/22.92      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | (~big_p(c19)) | (~big_q(c16)) | big_p(c11) | (~big_p(c19)) | big_p(c11))),
% 22.76/22.92      inference(quant_inst,[status(thm)],[])).
% 22.76/22.92  tff(1349,plain,
% 22.76/22.92      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (~big_q(c16)) | big_p(c11) | big_q(f4(elem!0)) | (~big_q(elem!0)) | (~big_p(c19))),
% 22.76/22.92      inference(modus_ponens,[status(thm)],[1348, 1347])).
% 22.76/22.92  tff(1350,plain,
% 22.76/22.92      ($false),
% 22.76/22.92      inference(unit_resolution,[status(thm)],[1349, 373, 1343, 1299, 306, 1308, 1])).
% 22.76/22.92  tff(1351,plain,(big_q(f4(elem!0)) | big_p(c11)), inference(lemma,lemma(discharge,[]))).
% 22.76/22.92  tff(1352,plain,
% 22.76/22.92      (big_q(f4(elem!0))),
% 22.76/22.92      inference(unit_resolution,[status(thm)],[1351, 1])).
% 22.76/22.92  tff(1353,plain,
% 22.76/22.92      (((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | (big_p(c11) | (~big_q(c20)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(c19)))) <=> ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | big_p(c11) | (~big_q(c20)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(c19)))),
% 22.76/22.92      inference(rewrite,[status(thm)],[])).
% 22.76/22.92  tff(1354,plain,
% 22.76/22.92      (((~big_q(f4(elem!0))) | big_p(c11) | (~big_q(elem!0)) | (~big_p(c19)) | (~big_p(c19)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(elem!0)))) <=> (big_p(c11) | (~big_q(c20)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(c19)))),
% 22.76/22.92      inference(rewrite,[status(thm)],[])).
% 22.76/22.92  tff(1355,plain,
% 22.76/22.92      (((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_q(f4(elem!0))) | big_p(c11) | (~big_q(elem!0)) | (~big_p(c19)) | (~big_p(c19)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(elem!0))))) <=> ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | (big_p(c11) | (~big_q(c20)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(c19))))),
% 22.76/22.92      inference(monotonicity,[status(thm)],[1354])).
% 22.76/22.92  tff(1356,plain,
% 22.76/22.92      (((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_q(f4(elem!0))) | big_p(c11) | (~big_q(elem!0)) | (~big_p(c19)) | (~big_p(c19)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(elem!0))))) <=> ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | big_p(c11) | (~big_q(c20)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(c19)))),
% 22.76/22.92      inference(transitivity,[status(thm)],[1355, 1353])).
% 22.76/22.92  tff(1357,plain,
% 22.76/22.92      ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_q(f4(elem!0))) | big_p(c11) | (~big_q(elem!0)) | (~big_p(c19)) | (~big_p(c19)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(elem!0))))),
% 22.76/22.92      inference(quant_inst,[status(thm)],[])).
% 22.76/22.92  tff(1358,plain,
% 22.76/22.92      ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | (~big_p(X18)) | (~big_p(X7)) | big_p(c11) | (~big_q(c20)) | (~big_q(f4(X16))))) | big_p(c11) | (~big_q(c20)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(c19))),
% 22.76/22.92      inference(modus_ponens,[status(thm)],[1357, 1356])).
% 22.76/22.92  tff(1359,plain,
% 22.76/22.92      (~big_q(c20)),
% 22.76/22.92      inference(unit_resolution,[status(thm)],[1358, 659, 1343, 1299, 1352, 1])).
% 22.76/22.92  tff(1360,plain,
% 22.76/22.92      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c20) | (~big_q(c16)) | big_p(c11) | (~big_q(elem!0)) | (~big_p(c19)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c20) | (~big_q(c16)) | big_p(c11) | (~big_q(elem!0)) | (~big_p(c19)))),
% 22.76/22.92      inference(rewrite,[status(thm)],[])).
% 22.76/22.92  tff(1361,plain,
% 22.76/22.92      (((~big_q(elem!0)) | big_q(c20) | big_q(c20) | (~big_p(c19)) | (~big_q(c16)) | big_p(c11) | (~big_p(c19)) | big_p(c11)) <=> (big_q(c20) | (~big_q(c16)) | big_p(c11) | (~big_q(elem!0)) | (~big_p(c19)))),
% 22.76/22.92      inference(rewrite,[status(thm)],[])).
% 22.76/22.92  tff(1362,plain,
% 22.76/22.92      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c20) | big_q(c20) | (~big_p(c19)) | (~big_q(c16)) | big_p(c11) | (~big_p(c19)) | big_p(c11))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | (big_q(c20) | (~big_q(c16)) | big_p(c11) | (~big_q(elem!0)) | (~big_p(c19))))),
% 22.76/22.92      inference(monotonicity,[status(thm)],[1361])).
% 22.76/22.92  tff(1363,plain,
% 22.76/22.92      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c20) | big_q(c20) | (~big_p(c19)) | (~big_q(c16)) | big_p(c11) | (~big_p(c19)) | big_p(c11))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c20) | (~big_q(c16)) | big_p(c11) | (~big_q(elem!0)) | (~big_p(c19)))),
% 22.76/22.92      inference(transitivity,[status(thm)],[1362, 1360])).
% 22.76/22.92  tff(1364,plain,
% 22.76/22.92      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c20) | big_q(c20) | (~big_p(c19)) | (~big_q(c16)) | big_p(c11) | (~big_p(c19)) | big_p(c11))),
% 22.76/22.92      inference(quant_inst,[status(thm)],[])).
% 22.76/22.92  tff(1365,plain,
% 22.76/22.92      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | (~big_p(X7)) | (~big_q(c16)) | big_p(c11) | (~big_p(X14)) | big_p(X9))) | big_q(c20) | (~big_q(c16)) | big_p(c11) | (~big_q(elem!0)) | (~big_p(c19))),
% 22.76/22.92      inference(modus_ponens,[status(thm)],[1364, 1363])).
% 22.76/22.92  tff(1366,plain,
% 22.76/22.92      ($false),
% 22.76/22.92      inference(unit_resolution,[status(thm)],[1365, 373, 1343, 1299, 1308, 1359, 1])).
% 22.76/22.92  tff(1367,plain,(big_p(c11)), inference(lemma,lemma(discharge,[]))).
% 22.76/22.92  tff(1368,plain,
% 22.76/22.92      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | (~big_p(c11)) | big_p(c19) | (~big_q(elem!0)) | (~big_p(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_p(c19) | (~big_q(elem!0)) | (~big_p(elem!0)))),
% 22.76/22.92      inference(rewrite,[status(thm)],[])).
% 22.76/22.92  tff(1369,plain,
% 22.76/22.92      (((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | big_p(c19) | big_q(c16) | (~big_p(c11)) | (~big_p(elem!0)) | big_p(c19)) <=> (big_q(c16) | (~big_p(c11)) | big_p(c19) | (~big_q(elem!0)) | (~big_p(elem!0)))),
% 22.76/22.92      inference(rewrite,[status(thm)],[])).
% 22.76/22.92  tff(1370,plain,
% 22.76/22.92      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | big_p(c19) | big_q(c16) | (~big_p(c11)) | (~big_p(elem!0)) | big_p(c19))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | (~big_p(c11)) | big_p(c19) | (~big_q(elem!0)) | (~big_p(elem!0))))),
% 22.76/22.92      inference(monotonicity,[status(thm)],[1369])).
% 22.76/22.92  tff(1371,plain,
% 22.76/22.92      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | big_p(c19) | big_q(c16) | (~big_p(c11)) | (~big_p(elem!0)) | big_p(c19))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_p(c19) | (~big_q(elem!0)) | (~big_p(elem!0)))),
% 22.76/22.92      inference(transitivity,[status(thm)],[1370, 1368])).
% 22.76/22.92  tff(1372,plain,
% 22.76/22.92      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | big_p(c19) | big_q(c16) | (~big_p(c11)) | (~big_p(elem!0)) | big_p(c19))),
% 22.76/22.92      inference(quant_inst,[status(thm)],[])).
% 22.76/22.92  tff(1373,plain,
% 22.76/22.92      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_p(c19) | (~big_q(elem!0)) | (~big_p(elem!0))),
% 22.76/22.92      inference(modus_ponens,[status(thm)],[1372, 1371])).
% 22.76/22.92  tff(1374,plain,
% 22.76/22.92      ($false),
% 22.76/22.92      inference(unit_resolution,[status(thm)],[1373, 52, 307, 1299, 762, 2, 1367])).
% 22.76/22.92  tff(1375,plain,(big_p(c19) | big_q(c16)), inference(lemma,lemma(discharge,[]))).
% 22.76/22.92  tff(1376,plain,
% 22.76/22.92      (big_p(c19)),
% 22.76/22.92      inference(unit_resolution,[status(thm)],[1375, 2])).
% 22.76/22.92  tff(1377,plain,
% 22.76/22.92      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | (~big_p(c11)) | big_p(c15) | (~big_q(elem!0)) | (~big_p(c19)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_p(c15) | (~big_q(elem!0)) | (~big_p(c19)))),
% 22.76/22.92      inference(rewrite,[status(thm)],[])).
% 22.76/22.92  tff(1378,plain,
% 22.76/22.92      (((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | big_p(c15) | big_q(c16) | (~big_p(c11)) | (~big_p(c19)) | big_p(c15)) <=> (big_q(c16) | (~big_p(c11)) | big_p(c15) | (~big_q(elem!0)) | (~big_p(c19)))),
% 22.76/22.92      inference(rewrite,[status(thm)],[])).
% 22.76/22.92  tff(1379,plain,
% 22.76/22.92      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | big_p(c15) | big_q(c16) | (~big_p(c11)) | (~big_p(c19)) | big_p(c15))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | (~big_p(c11)) | big_p(c15) | (~big_q(elem!0)) | (~big_p(c19))))),
% 22.76/22.92      inference(monotonicity,[status(thm)],[1378])).
% 22.76/22.92  tff(1380,plain,
% 22.76/22.92      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | big_p(c15) | big_q(c16) | (~big_p(c11)) | (~big_p(c19)) | big_p(c15))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_p(c15) | (~big_q(elem!0)) | (~big_p(c19)))),
% 22.76/22.92      inference(transitivity,[status(thm)],[1379, 1377])).
% 22.76/22.92  tff(1381,plain,
% 22.76/22.92      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | big_p(c15) | big_q(c16) | (~big_p(c11)) | (~big_p(c19)) | big_p(c15))),
% 22.76/22.92      inference(quant_inst,[status(thm)],[])).
% 22.76/22.92  tff(1382,plain,
% 22.76/22.92      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_p(c15) | (~big_q(elem!0)) | (~big_p(c19))),
% 22.76/22.92      inference(modus_ponens,[status(thm)],[1381, 1380])).
% 22.76/22.92  tff(1383,plain,
% 22.76/22.92      ($false),
% 22.76/22.92      inference(unit_resolution,[status(thm)],[1382, 52, 1376, 1299, 2, 986, 1367])).
% 22.76/22.92  tff(1384,plain,(big_p(c15) | big_q(c16)), inference(lemma,lemma(discharge,[]))).
% 22.76/22.92  tff(1385,plain,
% 22.76/22.92      (big_p(c15)),
% 22.76/22.92      inference(unit_resolution,[status(thm)],[1384, 2])).
% 22.76/22.92  tff(1386,plain,
% 22.76/22.92      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | (~big_p(c11)) | big_p(f3(elem!0)) | (~big_q(elem!0)) | (~big_p(c19)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_p(f3(elem!0)) | (~big_q(elem!0)) | (~big_p(c19)))),
% 22.76/22.92      inference(rewrite,[status(thm)],[])).
% 22.76/22.92  tff(1387,plain,
% 22.76/22.92      (((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | big_p(f3(elem!0)) | big_q(c16) | (~big_p(c11)) | (~big_p(c19)) | big_p(f3(elem!0))) <=> (big_q(c16) | (~big_p(c11)) | big_p(f3(elem!0)) | (~big_q(elem!0)) | (~big_p(c19)))),
% 22.76/22.92      inference(rewrite,[status(thm)],[])).
% 22.76/22.92  tff(1388,plain,
% 22.76/22.92      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | big_p(f3(elem!0)) | big_q(c16) | (~big_p(c11)) | (~big_p(c19)) | big_p(f3(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | (big_q(c16) | (~big_p(c11)) | big_p(f3(elem!0)) | (~big_q(elem!0)) | (~big_p(c19))))),
% 22.76/22.93      inference(monotonicity,[status(thm)],[1387])).
% 22.76/22.93  tff(1389,plain,
% 22.76/22.93      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | big_p(f3(elem!0)) | big_q(c16) | (~big_p(c11)) | (~big_p(c19)) | big_p(f3(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_p(f3(elem!0)) | (~big_q(elem!0)) | (~big_p(c19)))),
% 22.76/22.93      inference(transitivity,[status(thm)],[1388, 1386])).
% 22.76/22.93  tff(1390,plain,
% 22.76/22.93      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | big_p(f3(elem!0)) | big_q(c16) | (~big_p(c11)) | (~big_p(c19)) | big_p(f3(elem!0)))),
% 22.76/22.93      inference(quant_inst,[status(thm)],[])).
% 22.76/22.93  tff(1391,plain,
% 22.76/22.93      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | (~big_q(X13)) | big_p(X7) | big_q(c16) | (~big_p(c11)) | (~big_p(X14)) | big_p(X9))) | big_q(c16) | (~big_p(c11)) | big_p(f3(elem!0)) | (~big_q(elem!0)) | (~big_p(c19))),
% 22.76/22.93      inference(modus_ponens,[status(thm)],[1390, 1389])).
% 22.76/22.93  tff(1392,plain,
% 22.76/22.93      ($false),
% 22.76/22.93      inference(unit_resolution,[status(thm)],[1391, 52, 1376, 1299, 820, 2, 1367])).
% 22.76/22.93  tff(1393,plain,(big_p(f3(elem!0)) | big_q(c16)), inference(lemma,lemma(discharge,[]))).
% 22.76/22.93  tff(1394,plain,
% 22.76/22.93      (big_p(f3(elem!0))),
% 22.76/22.93      inference(unit_resolution,[status(thm)],[1393, 2])).
% 22.76/22.93  tff(1395,plain,
% 22.76/22.93      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (big_q(c16) | (~big_p(c15)) | (~big_q(elem!0)) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | big_q(c16) | (~big_p(c15)) | (~big_q(elem!0)) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))),
% 22.76/22.93      inference(rewrite,[status(thm)],[])).
% 22.76/22.93  tff(1396,plain,
% 22.76/22.93      (((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | (~big_p(elem!0)) | big_q(c16) | (~big_p(f3(elem!0))) | (~big_p(c15)) | (~big_p(f3(elem!0)))) <=> (big_q(c16) | (~big_p(c15)) | (~big_q(elem!0)) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))),
% 22.76/22.93      inference(rewrite,[status(thm)],[])).
% 22.76/22.93  tff(1397,plain,
% 22.76/22.93      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | (~big_p(elem!0)) | big_q(c16) | (~big_p(f3(elem!0))) | (~big_p(c15)) | (~big_p(f3(elem!0))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (big_q(c16) | (~big_p(c15)) | (~big_q(elem!0)) | (~big_p(f3(elem!0))) | (~big_p(elem!0))))),
% 22.76/22.93      inference(monotonicity,[status(thm)],[1396])).
% 22.76/22.93  tff(1398,plain,
% 22.76/22.93      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | (~big_p(elem!0)) | big_q(c16) | (~big_p(f3(elem!0))) | (~big_p(c15)) | (~big_p(f3(elem!0))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | big_q(c16) | (~big_p(c15)) | (~big_q(elem!0)) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))),
% 22.76/22.93      inference(transitivity,[status(thm)],[1397, 1395])).
% 22.76/22.93  tff(1399,plain,
% 22.76/22.93      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(elem!0)) | big_q(c16) | (~big_q(elem!0)) | (~big_p(elem!0)) | big_q(c16) | (~big_p(f3(elem!0))) | (~big_p(c15)) | (~big_p(f3(elem!0))))),
% 22.76/22.93      inference(quant_inst,[status(thm)],[])).
% 22.76/22.93  tff(1400,plain,
% 22.76/22.93      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | (~big_q(X13)) | (~big_p(X10)) | big_q(c16) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | big_q(c16) | (~big_p(c15)) | (~big_q(elem!0)) | (~big_p(f3(elem!0))) | (~big_p(elem!0))),
% 22.76/22.93      inference(modus_ponens,[status(thm)],[1399, 1398])).
% 22.76/22.93  tff(1401,plain,
% 22.76/22.93      ($false),
% 22.76/22.93      inference(unit_resolution,[status(thm)],[1400, 894, 1299, 1394, 762, 2, 1385])).
% 22.76/22.93  tff(1402,plain,(big_q(c16)), inference(lemma,lemma(discharge,[]))).
% 22.76/22.93  tff(1403,plain,
% 22.76/22.93      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | (~big_q(c16)) | big_p(c19) | big_q(f4(elem!0)) | (~big_q(elem!0)) | (~big_p(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_p(c19) | big_q(f4(elem!0)) | (~big_q(elem!0)) | (~big_p(elem!0)))),
% 22.76/22.93      inference(rewrite,[status(thm)],[])).
% 22.76/22.93  tff(1404,plain,
% 22.76/22.93      (((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | big_p(c19) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(elem!0)) | big_p(c19)) <=> ((~big_p(c11)) | (~big_q(c16)) | big_p(c19) | big_q(f4(elem!0)) | (~big_q(elem!0)) | (~big_p(elem!0)))),
% 22.76/22.93      inference(rewrite,[status(thm)],[])).
% 22.76/22.93  tff(1405,plain,
% 22.76/22.93      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | big_p(c19) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(elem!0)) | big_p(c19))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | (~big_q(c16)) | big_p(c19) | big_q(f4(elem!0)) | (~big_q(elem!0)) | (~big_p(elem!0))))),
% 22.76/22.93      inference(monotonicity,[status(thm)],[1404])).
% 22.76/22.93  tff(1406,plain,
% 22.76/22.93      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | big_p(c19) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(elem!0)) | big_p(c19))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_p(c19) | big_q(f4(elem!0)) | (~big_q(elem!0)) | (~big_p(elem!0)))),
% 22.76/22.93      inference(transitivity,[status(thm)],[1405, 1403])).
% 22.76/22.93  tff(1407,plain,
% 22.76/22.93      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | big_p(c19) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(elem!0)) | big_p(c19))),
% 22.76/22.93      inference(quant_inst,[status(thm)],[])).
% 22.76/22.93  tff(1408,plain,
% 22.76/22.93      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_p(c19) | big_q(f4(elem!0)) | (~big_q(elem!0)) | (~big_p(elem!0))),
% 22.76/22.93      inference(modus_ponens,[status(thm)],[1407, 1406])).
% 22.76/22.93  tff(1409,plain,
% 22.76/22.93      ($false),
% 22.76/22.93      inference(unit_resolution,[status(thm)],[1408, 354, 307, 1299, 306, 762, 1402, 1367])).
% 22.76/22.93  tff(1410,plain,(big_q(f4(elem!0)) | big_p(c19)), inference(lemma,lemma(discharge,[]))).
% 22.76/22.93  tff(1411,plain,
% 22.76/22.93      (big_q(f4(elem!0))),
% 22.76/22.93      inference(unit_resolution,[status(thm)],[1410, 307])).
% 22.77/22.93  tff(1412,plain,
% 22.77/22.93      (((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_p(c11)) | big_p(c19) | (~big_q(c20)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(elem!0)))) <=> ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | (~big_p(c11)) | big_p(c19) | (~big_q(c20)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(elem!0)))),
% 22.77/22.93      inference(rewrite,[status(thm)],[])).
% 22.77/22.93  tff(1413,plain,
% 22.77/22.93      (((~big_q(f4(elem!0))) | big_p(c19) | (~big_q(elem!0)) | big_p(c19) | (~big_p(elem!0)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(elem!0)))) <=> ((~big_p(c11)) | big_p(c19) | (~big_q(c20)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(elem!0)))),
% 22.77/22.93      inference(rewrite,[status(thm)],[])).
% 22.77/22.93  tff(1414,plain,
% 22.77/22.93      (((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_q(f4(elem!0))) | big_p(c19) | (~big_q(elem!0)) | big_p(c19) | (~big_p(elem!0)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(elem!0))))) <=> ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_p(c11)) | big_p(c19) | (~big_q(c20)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(elem!0))))),
% 22.77/22.93      inference(monotonicity,[status(thm)],[1413])).
% 22.77/22.93  tff(1415,plain,
% 22.77/22.93      (((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_q(f4(elem!0))) | big_p(c19) | (~big_q(elem!0)) | big_p(c19) | (~big_p(elem!0)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(elem!0))))) <=> ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | (~big_p(c11)) | big_p(c19) | (~big_q(c20)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(elem!0)))),
% 22.77/22.93      inference(transitivity,[status(thm)],[1414, 1412])).
% 22.77/22.93  tff(1416,plain,
% 22.77/22.93      ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_q(f4(elem!0))) | big_p(c19) | (~big_q(elem!0)) | big_p(c19) | (~big_p(elem!0)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(elem!0))))),
% 22.77/22.93      inference(quant_inst,[status(thm)],[])).
% 22.77/22.93  tff(1417,plain,
% 22.77/22.93      ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | (~big_p(c11)) | big_p(c19) | (~big_q(c20)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(elem!0))),
% 22.77/22.93      inference(modus_ponens,[status(thm)],[1416, 1415])).
% 22.77/22.93  tff(1418,plain,
% 22.77/22.93      (~big_q(c20)),
% 22.77/22.93      inference(unit_resolution,[status(thm)],[1417, 747, 307, 1299, 1411, 762, 1367])).
% 22.77/22.93  tff(1419,plain,
% 22.77/22.93      (^[X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : refl(((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | big_p(c19) | (~big_q(f4(X16)))) <=> ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | big_p(c19) | (~big_q(f4(X16)))))),
% 22.77/22.93      inference(bind,[status(th)],[])).
% 22.77/22.93  tff(1420,plain,
% 22.77/22.93      (![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | big_p(c19) | (~big_q(f4(X16)))) <=> ![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | big_p(c19) | (~big_q(f4(X16))))),
% 22.77/22.93      inference(quant_intro,[status(thm)],[1419])).
% 22.77/22.93  tff(1421,plain,
% 22.77/22.93      (![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | big_p(c19) | (~big_q(f4(X16)))) <=> ![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | big_p(c19) | (~big_q(f4(X16))))),
% 22.77/22.93      inference(rewrite,[status(thm)],[])).
% 22.77/22.93  tff(1422,plain,
% 22.77/22.93      (^[X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(c11)) | big_p(X7)) <=> (big_p(X7) | (~big_p(c11)))), ((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) <=> ((big_p(X7) | (~big_p(c11))) | (~big_q(X8))))), rewrite(((big_p(X7) | (~big_p(c11))) | (~big_q(X8))) <=> ((~big_q(X8)) | big_p(X7) | (~big_p(c11)))), ((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) <=> ((~big_q(X8)) | big_p(X7) | (~big_p(c11))))), (((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) <=> (((~big_q(X8)) | big_p(X7) | (~big_p(c11))) | big_p(X9)))), rewrite((((~big_q(X8)) | big_p(X7) | (~big_p(c11))) | big_p(X9)) <=> ((~big_q(X8)) | big_p(X9) | big_p(X7) | (~big_p(c11)))), (((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) <=> ((~big_q(X8)) | big_p(X9) | big_p(X7) | (~big_p(c11))))), ((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) <=> (((~big_q(X8)) | big_p(X9) | big_p(X7) | (~big_p(c11))) | (~big_q(f4(X16)))))), rewrite((((~big_q(X8)) | big_p(X9) | big_p(X7) | (~big_p(c11))) | (~big_q(f4(X16)))) <=> ((~big_q(X8)) | big_p(X9) | big_p(X7) | (~big_p(c11)) | (~big_q(f4(X16))))), ((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) <=> ((~big_q(X8)) | big_p(X9) | big_p(X7) | (~big_p(c11)) | (~big_q(f4(X16)))))), (((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) <=> (((~big_q(X8)) | big_p(X9) | big_p(X7) | (~big_p(c11)) | (~big_q(f4(X16)))) | (~big_q(X16))))), rewrite((((~big_q(X8)) | big_p(X9) | big_p(X7) | (~big_p(c11)) | (~big_q(f4(X16)))) | (~big_q(X16))) <=> ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | (~big_q(f4(X16))))), (((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) <=> ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | (~big_q(f4(X16)))))), ((((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) | big_p(c19)) <=> (((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | (~big_q(f4(X16)))) | big_p(c19)))), rewrite((((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | (~big_q(f4(X16)))) | big_p(c19)) <=> ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | big_p(c19) | (~big_q(f4(X16))))), ((((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) | big_p(c19)) <=> ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | big_p(c19) | (~big_q(f4(X16)))))), (((((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) | big_p(c19)) | big_q(X17)) <=> (((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | big_p(c19) | (~big_q(f4(X16)))) | big_q(X17)))), rewrite((((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | big_p(c19) | (~big_q(f4(X16)))) | big_q(X17)) <=> ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | big_p(c19) | (~big_q(f4(X16))))), (((((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) | big_p(c19)) | big_q(X17)) <=> ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | big_p(c19) | (~big_q(f4(X16))))))),
% 22.77/22.93      inference(bind,[status(th)],[])).
% 22.77/22.93  tff(1423,plain,
% 22.77/22.93      (![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) | big_p(c19)) | big_q(X17)) <=> ![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | big_p(c19) | (~big_q(f4(X16))))),
% 22.77/22.93      inference(quant_intro,[status(thm)],[1422])).
% 22.77/22.93  tff(1424,axiom,(![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((((((((~big_p(c11)) | big_p(X7)) | (~big_q(X8))) | big_p(X9)) | (~big_q(f4(X16)))) | (~big_q(X16))) | big_p(c19)) | big_q(X17))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_71')).
% 22.77/22.93  tff(1425,plain,
% 22.77/22.93      (![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | big_p(c19) | (~big_q(f4(X16))))),
% 22.77/22.93      inference(modus_ponens,[status(thm)],[1424, 1423])).
% 22.77/22.93  tff(1426,plain,
% 22.77/22.93      (![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | big_p(c19) | (~big_q(f4(X16))))),
% 22.77/22.93      inference(modus_ponens,[status(thm)],[1425, 1421])).
% 22.77/22.93  tff(1427,plain,(
% 22.77/22.93      ![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | big_p(c19) | (~big_q(f4(X16))))),
% 22.77/22.93      inference(skolemize,[status(sab)],[1426])).
% 22.77/22.93  tff(1428,plain,
% 22.77/22.93      (![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | big_p(c19) | (~big_q(f4(X16))))),
% 22.77/22.93      inference(modus_ponens,[status(thm)],[1427, 1420])).
% 22.77/22.93  tff(1429,plain,
% 22.77/22.93      (((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | big_p(c19) | (~big_q(f4(X16))))) | ((~big_p(c11)) | big_q(c20) | big_p(c19) | (~big_q(elem!0)) | (~big_q(f4(elem!0))))) <=> ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | big_p(c19) | (~big_q(f4(X16))))) | (~big_p(c11)) | big_q(c20) | big_p(c19) | (~big_q(elem!0)) | (~big_q(f4(elem!0))))),
% 22.77/22.93      inference(rewrite,[status(thm)],[])).
% 22.77/22.93  tff(1430,plain,
% 22.77/22.93      (((~big_q(elem!0)) | big_p(c19) | big_q(c20) | (~big_q(elem!0)) | big_p(c19) | (~big_p(c11)) | big_p(c19) | (~big_q(f4(elem!0)))) <=> ((~big_p(c11)) | big_q(c20) | big_p(c19) | (~big_q(elem!0)) | (~big_q(f4(elem!0))))),
% 22.77/22.93      inference(rewrite,[status(thm)],[])).
% 22.77/22.93  tff(1431,plain,
% 22.77/22.93      (((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | big_p(c19) | (~big_q(f4(X16))))) | ((~big_q(elem!0)) | big_p(c19) | big_q(c20) | (~big_q(elem!0)) | big_p(c19) | (~big_p(c11)) | big_p(c19) | (~big_q(f4(elem!0))))) <=> ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | big_p(c19) | (~big_q(f4(X16))))) | ((~big_p(c11)) | big_q(c20) | big_p(c19) | (~big_q(elem!0)) | (~big_q(f4(elem!0)))))),
% 22.77/22.93      inference(monotonicity,[status(thm)],[1430])).
% 22.77/22.93  tff(1432,plain,
% 22.77/22.93      (((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | big_p(c19) | (~big_q(f4(X16))))) | ((~big_q(elem!0)) | big_p(c19) | big_q(c20) | (~big_q(elem!0)) | big_p(c19) | (~big_p(c11)) | big_p(c19) | (~big_q(f4(elem!0))))) <=> ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | big_p(c19) | (~big_q(f4(X16))))) | (~big_p(c11)) | big_q(c20) | big_p(c19) | (~big_q(elem!0)) | (~big_q(f4(elem!0))))),
% 22.77/22.93      inference(transitivity,[status(thm)],[1431, 1429])).
% 22.77/22.93  tff(1433,plain,
% 22.77/22.93      ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | big_p(c19) | (~big_q(f4(X16))))) | ((~big_q(elem!0)) | big_p(c19) | big_q(c20) | (~big_q(elem!0)) | big_p(c19) | (~big_p(c11)) | big_p(c19) | (~big_q(f4(elem!0))))),
% 22.77/22.93      inference(quant_inst,[status(thm)],[])).
% 22.77/22.93  tff(1434,plain,
% 22.77/22.93      ((~![X9: $i, X17: $i, X16: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | big_q(X17) | (~big_q(X16)) | big_p(X7) | (~big_p(c11)) | big_p(c19) | (~big_q(f4(X16))))) | (~big_p(c11)) | big_q(c20) | big_p(c19) | (~big_q(elem!0)) | (~big_q(f4(elem!0)))),
% 22.77/22.93      inference(modus_ponens,[status(thm)],[1433, 1432])).
% 22.77/22.93  tff(1435,plain,
% 22.77/22.93      ($false),
% 22.77/22.93      inference(unit_resolution,[status(thm)],[1434, 1428, 307, 1299, 1411, 1418, 1367])).
% 22.77/22.93  tff(1436,plain,(big_p(c19)), inference(lemma,lemma(discharge,[]))).
% 22.77/22.93  tff(1437,plain,
% 22.77/22.93      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | (~big_q(c16)) | big_p(c15) | big_q(f4(elem!0)) | (~big_q(elem!0)) | (~big_p(c19)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_p(c15) | big_q(f4(elem!0)) | (~big_q(elem!0)) | (~big_p(c19)))),
% 22.77/22.93      inference(rewrite,[status(thm)],[])).
% 22.77/22.93  tff(1438,plain,
% 22.77/22.93      (((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | big_p(c15) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(c15)) <=> ((~big_p(c11)) | (~big_q(c16)) | big_p(c15) | big_q(f4(elem!0)) | (~big_q(elem!0)) | (~big_p(c19)))),
% 22.77/22.93      inference(rewrite,[status(thm)],[])).
% 22.77/22.93  tff(1439,plain,
% 22.77/22.93      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | big_p(c15) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(c15))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | (~big_q(c16)) | big_p(c15) | big_q(f4(elem!0)) | (~big_q(elem!0)) | (~big_p(c19))))),
% 22.77/22.93      inference(monotonicity,[status(thm)],[1438])).
% 22.77/22.93  tff(1440,plain,
% 22.77/22.93      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | big_p(c15) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(c15))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_p(c15) | big_q(f4(elem!0)) | (~big_q(elem!0)) | (~big_p(c19)))),
% 22.77/22.93      inference(transitivity,[status(thm)],[1439, 1437])).
% 22.77/22.93  tff(1441,plain,
% 22.77/22.93      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | big_p(c15) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(c15))),
% 22.77/22.93      inference(quant_inst,[status(thm)],[])).
% 22.77/22.93  tff(1442,plain,
% 22.77/22.93      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_p(c15) | big_q(f4(elem!0)) | (~big_q(elem!0)) | (~big_p(c19))),
% 22.77/22.93      inference(modus_ponens,[status(thm)],[1441, 1440])).
% 22.77/22.93  tff(1443,plain,
% 22.77/22.93      ($false),
% 22.77/22.93      inference(unit_resolution,[status(thm)],[1442, 354, 1436, 1299, 306, 1402, 986, 1367])).
% 22.77/22.93  tff(1444,plain,(big_p(c15) | big_q(f4(elem!0))), inference(lemma,lemma(discharge,[]))).
% 22.77/22.93  tff(1445,plain,
% 22.77/22.93      (big_q(f4(elem!0))),
% 22.77/22.93      inference(unit_resolution,[status(thm)],[1444, 986])).
% 22.77/22.93  tff(1446,plain,
% 22.77/22.93      (((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_p(c11)) | (~big_q(c20)) | big_p(c15) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(c19)))) <=> ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | (~big_p(c11)) | (~big_q(c20)) | big_p(c15) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(c19)))),
% 22.77/22.93      inference(rewrite,[status(thm)],[])).
% 22.77/22.93  tff(1447,plain,
% 22.77/22.93      (((~big_q(f4(elem!0))) | big_p(c15) | (~big_q(elem!0)) | big_p(c15) | (~big_p(c19)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(elem!0)))) <=> ((~big_p(c11)) | (~big_q(c20)) | big_p(c15) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(c19)))),
% 22.77/22.93      inference(rewrite,[status(thm)],[])).
% 22.77/22.93  tff(1448,plain,
% 22.77/22.93      (((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_q(f4(elem!0))) | big_p(c15) | (~big_q(elem!0)) | big_p(c15) | (~big_p(c19)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(elem!0))))) <=> ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_p(c11)) | (~big_q(c20)) | big_p(c15) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(c19))))),
% 22.77/22.93      inference(monotonicity,[status(thm)],[1447])).
% 22.77/22.93  tff(1449,plain,
% 22.77/22.93      (((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_q(f4(elem!0))) | big_p(c15) | (~big_q(elem!0)) | big_p(c15) | (~big_p(c19)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(elem!0))))) <=> ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | (~big_p(c11)) | (~big_q(c20)) | big_p(c15) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(c19)))),
% 22.77/22.94      inference(transitivity,[status(thm)],[1448, 1446])).
% 22.77/22.94  tff(1450,plain,
% 22.77/22.94      ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_q(f4(elem!0))) | big_p(c15) | (~big_q(elem!0)) | big_p(c15) | (~big_p(c19)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(elem!0))))),
% 22.77/22.94      inference(quant_inst,[status(thm)],[])).
% 22.77/22.94  tff(1451,plain,
% 22.77/22.94      ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | (~big_p(c11)) | (~big_q(c20)) | big_p(c15) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(c19))),
% 22.77/22.94      inference(modus_ponens,[status(thm)],[1450, 1449])).
% 22.77/22.94  tff(1452,plain,
% 22.77/22.94      (~big_q(c20)),
% 22.77/22.94      inference(unit_resolution,[status(thm)],[1451, 747, 1436, 1299, 1445, 986, 1367])).
% 22.77/22.94  tff(1453,plain,
% 22.77/22.94      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | big_q(c20) | (~big_q(c16)) | big_p(c15) | (~big_q(elem!0)) | (~big_p(c19)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | big_q(c20) | (~big_q(c16)) | big_p(c15) | (~big_q(elem!0)) | (~big_p(c19)))),
% 22.77/22.94      inference(rewrite,[status(thm)],[])).
% 22.77/22.94  tff(1454,plain,
% 22.77/22.94      (((~big_q(elem!0)) | big_q(c20) | big_q(c20) | big_p(c15) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(c15)) <=> ((~big_p(c11)) | big_q(c20) | (~big_q(c16)) | big_p(c15) | (~big_q(elem!0)) | (~big_p(c19)))),
% 22.77/22.94      inference(rewrite,[status(thm)],[])).
% 22.77/22.94  tff(1455,plain,
% 22.77/22.94      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c20) | big_q(c20) | big_p(c15) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(c15))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | big_q(c20) | (~big_q(c16)) | big_p(c15) | (~big_q(elem!0)) | (~big_p(c19))))),
% 22.77/22.94      inference(monotonicity,[status(thm)],[1454])).
% 22.77/22.94  tff(1456,plain,
% 22.77/22.94      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c20) | big_q(c20) | big_p(c15) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(c15))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | big_q(c20) | (~big_q(c16)) | big_p(c15) | (~big_q(elem!0)) | (~big_p(c19)))),
% 22.77/22.94      inference(transitivity,[status(thm)],[1455, 1453])).
% 22.77/22.94  tff(1457,plain,
% 22.77/22.94      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c20) | big_q(c20) | big_p(c15) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(c15))),
% 22.77/22.94      inference(quant_inst,[status(thm)],[])).
% 22.77/22.94  tff(1458,plain,
% 22.77/22.94      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | big_q(c20) | (~big_q(c16)) | big_p(c15) | (~big_q(elem!0)) | (~big_p(c19))),
% 22.77/22.94      inference(modus_ponens,[status(thm)],[1457, 1456])).
% 22.77/22.94  tff(1459,plain,
% 22.77/22.94      ($false),
% 22.77/22.94      inference(unit_resolution,[status(thm)],[1458, 354, 1436, 1299, 1402, 986, 1452, 1367])).
% 22.77/22.94  tff(1460,plain,(big_p(c15)), inference(lemma,lemma(discharge,[]))).
% 22.77/22.94  tff(1461,plain,
% 22.77/22.94      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | (~big_q(c16)) | big_q(f4(elem!0)) | big_p(f3(elem!0)) | (~big_q(elem!0)) | (~big_p(c19)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_q(f4(elem!0)) | big_p(f3(elem!0)) | (~big_q(elem!0)) | (~big_p(c19)))),
% 22.77/22.94      inference(rewrite,[status(thm)],[])).
% 22.77/22.94  tff(1462,plain,
% 22.77/22.94      (((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | big_p(f3(elem!0)) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(f3(elem!0))) <=> ((~big_p(c11)) | (~big_q(c16)) | big_q(f4(elem!0)) | big_p(f3(elem!0)) | (~big_q(elem!0)) | (~big_p(c19)))),
% 22.77/22.94      inference(rewrite,[status(thm)],[])).
% 22.77/22.94  tff(1463,plain,
% 22.77/22.94      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | big_p(f3(elem!0)) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(f3(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | (~big_q(c16)) | big_q(f4(elem!0)) | big_p(f3(elem!0)) | (~big_q(elem!0)) | (~big_p(c19))))),
% 22.77/22.94      inference(monotonicity,[status(thm)],[1462])).
% 22.77/22.94  tff(1464,plain,
% 22.77/22.94      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | big_p(f3(elem!0)) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(f3(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_q(f4(elem!0)) | big_p(f3(elem!0)) | (~big_q(elem!0)) | (~big_p(c19)))),
% 22.77/22.94      inference(transitivity,[status(thm)],[1463, 1461])).
% 22.77/22.94  tff(1465,plain,
% 22.77/22.94      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | big_p(f3(elem!0)) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(f3(elem!0)))),
% 22.77/22.94      inference(quant_inst,[status(thm)],[])).
% 22.77/22.94  tff(1466,plain,
% 22.77/22.94      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | (~big_q(c16)) | big_q(f4(elem!0)) | big_p(f3(elem!0)) | (~big_q(elem!0)) | (~big_p(c19))),
% 22.77/22.94      inference(modus_ponens,[status(thm)],[1465, 1464])).
% 22.77/22.94  tff(1467,plain,
% 22.77/22.94      ($false),
% 22.77/22.94      inference(unit_resolution,[status(thm)],[1466, 354, 1436, 1299, 306, 820, 1402, 1367])).
% 22.77/22.94  tff(1468,plain,(big_p(f3(elem!0)) | big_q(f4(elem!0))), inference(lemma,lemma(discharge,[]))).
% 22.77/22.94  tff(1469,plain,
% 22.77/22.94      (big_p(f3(elem!0))),
% 22.77/22.94      inference(unit_resolution,[status(thm)],[1468, 306])).
% 22.77/22.94  tff(1470,plain,
% 22.77/22.94      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(c16)) | (~big_p(c15)) | big_q(f4(elem!0)) | (~big_q(elem!0)) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (~big_q(c16)) | (~big_p(c15)) | big_q(f4(elem!0)) | (~big_q(elem!0)) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))),
% 22.77/22.94      inference(rewrite,[status(thm)],[])).
% 22.77/22.94  tff(1471,plain,
% 22.77/22.94      (((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | (~big_p(elem!0)) | (~big_q(c16)) | (~big_p(f3(elem!0))) | (~big_p(c15)) | (~big_p(f3(elem!0)))) <=> ((~big_q(c16)) | (~big_p(c15)) | big_q(f4(elem!0)) | (~big_q(elem!0)) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))),
% 22.77/22.94      inference(rewrite,[status(thm)],[])).
% 22.77/22.94  tff(1472,plain,
% 22.77/22.94      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | (~big_p(elem!0)) | (~big_q(c16)) | (~big_p(f3(elem!0))) | (~big_p(c15)) | (~big_p(f3(elem!0))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(c16)) | (~big_p(c15)) | big_q(f4(elem!0)) | (~big_q(elem!0)) | (~big_p(f3(elem!0))) | (~big_p(elem!0))))),
% 22.77/22.94      inference(monotonicity,[status(thm)],[1471])).
% 22.77/22.94  tff(1473,plain,
% 22.77/22.94      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | (~big_p(elem!0)) | (~big_q(c16)) | (~big_p(f3(elem!0))) | (~big_p(c15)) | (~big_p(f3(elem!0))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (~big_q(c16)) | (~big_p(c15)) | big_q(f4(elem!0)) | (~big_q(elem!0)) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))),
% 22.77/22.94      inference(transitivity,[status(thm)],[1472, 1470])).
% 22.77/22.94  tff(1474,plain,
% 22.77/22.94      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(elem!0)) | big_q(f4(elem!0)) | big_q(f4(elem!0)) | (~big_p(elem!0)) | (~big_q(c16)) | (~big_p(f3(elem!0))) | (~big_p(c15)) | (~big_p(f3(elem!0))))),
% 22.77/22.94      inference(quant_inst,[status(thm)],[])).
% 22.77/22.94  tff(1475,plain,
% 22.77/22.94      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (~big_q(c16)) | (~big_p(c15)) | big_q(f4(elem!0)) | (~big_q(elem!0)) | (~big_p(f3(elem!0))) | (~big_p(elem!0))),
% 22.77/22.94      inference(modus_ponens,[status(thm)],[1474, 1473])).
% 22.77/22.94  tff(1476,plain,
% 22.77/22.94      ($false),
% 22.77/22.94      inference(unit_resolution,[status(thm)],[1475, 1222, 1299, 306, 1469, 762, 1402, 1460])).
% 22.77/22.94  tff(1477,plain,(big_q(f4(elem!0))), inference(lemma,lemma(discharge,[]))).
% 22.77/22.94  tff(1478,plain,
% 22.77/22.94      (((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_p(c11)) | (~big_q(c20)) | big_p(f3(elem!0)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(c19)))) <=> ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | (~big_p(c11)) | (~big_q(c20)) | big_p(f3(elem!0)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(c19)))),
% 22.77/22.94      inference(rewrite,[status(thm)],[])).
% 22.77/22.94  tff(1479,plain,
% 22.77/22.94      (((~big_q(elem!0)) | big_p(f3(elem!0)) | (~big_q(elem!0)) | big_p(f3(elem!0)) | (~big_p(c19)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(elem!0)))) <=> ((~big_p(c11)) | (~big_q(c20)) | big_p(f3(elem!0)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(c19)))),
% 22.77/22.94      inference(rewrite,[status(thm)],[])).
% 22.77/22.94  tff(1480,plain,
% 22.77/22.94      (((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_q(elem!0)) | big_p(f3(elem!0)) | (~big_q(elem!0)) | big_p(f3(elem!0)) | (~big_p(c19)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(elem!0))))) <=> ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_p(c11)) | (~big_q(c20)) | big_p(f3(elem!0)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(c19))))),
% 22.77/22.94      inference(monotonicity,[status(thm)],[1479])).
% 22.77/22.94  tff(1481,plain,
% 22.77/22.94      (((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_q(elem!0)) | big_p(f3(elem!0)) | (~big_q(elem!0)) | big_p(f3(elem!0)) | (~big_p(c19)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(elem!0))))) <=> ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | (~big_p(c11)) | (~big_q(c20)) | big_p(f3(elem!0)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(c19)))),
% 22.77/22.94      inference(transitivity,[status(thm)],[1480, 1478])).
% 22.77/22.94  tff(1482,plain,
% 22.77/22.94      ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | ((~big_q(elem!0)) | big_p(f3(elem!0)) | (~big_q(elem!0)) | big_p(f3(elem!0)) | (~big_p(c19)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(elem!0))))),
% 22.77/22.94      inference(quant_inst,[status(thm)],[])).
% 22.77/22.94  tff(1483,plain,
% 22.77/22.94      ((~![X9: $i, X16: $i, X18: $i, X7: $i, X8: $i] : ((~big_q(X8)) | big_p(X9) | (~big_q(X16)) | big_p(X7) | (~big_p(X18)) | (~big_p(c11)) | (~big_q(c20)) | (~big_q(f4(X16))))) | (~big_p(c11)) | (~big_q(c20)) | big_p(f3(elem!0)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(c19))),
% 22.77/22.94      inference(modus_ponens,[status(thm)],[1482, 1481])).
% 22.77/22.94  tff(1484,plain,
% 22.77/22.94      (~big_q(c20)),
% 22.77/22.94      inference(unit_resolution,[status(thm)],[1483, 747, 1436, 1299, 1477, 820, 1367])).
% 22.77/22.94  tff(1485,plain,
% 22.77/22.94      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | big_q(c20) | (~big_q(c16)) | big_p(f3(elem!0)) | (~big_q(elem!0)) | (~big_p(c19)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | big_q(c20) | (~big_q(c16)) | big_p(f3(elem!0)) | (~big_q(elem!0)) | (~big_p(c19)))),
% 22.77/22.94      inference(rewrite,[status(thm)],[])).
% 22.77/22.94  tff(1486,plain,
% 22.77/22.94      (((~big_q(elem!0)) | big_q(c20) | big_q(c20) | big_p(f3(elem!0)) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(f3(elem!0))) <=> ((~big_p(c11)) | big_q(c20) | (~big_q(c16)) | big_p(f3(elem!0)) | (~big_q(elem!0)) | (~big_p(c19)))),
% 22.77/22.94      inference(rewrite,[status(thm)],[])).
% 22.77/22.94  tff(1487,plain,
% 22.77/22.94      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c20) | big_q(c20) | big_p(f3(elem!0)) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(f3(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_p(c11)) | big_q(c20) | (~big_q(c16)) | big_p(f3(elem!0)) | (~big_q(elem!0)) | (~big_p(c19))))),
% 22.77/22.94      inference(monotonicity,[status(thm)],[1486])).
% 22.77/22.94  tff(1488,plain,
% 22.77/22.94      (((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c20) | big_q(c20) | big_p(f3(elem!0)) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(f3(elem!0)))) <=> ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | big_q(c20) | (~big_q(c16)) | big_p(f3(elem!0)) | (~big_q(elem!0)) | (~big_p(c19)))),
% 22.77/22.94      inference(transitivity,[status(thm)],[1487, 1485])).
% 22.77/22.94  tff(1489,plain,
% 22.77/22.94      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | ((~big_q(elem!0)) | big_q(c20) | big_q(c20) | big_p(f3(elem!0)) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(c19)) | big_p(f3(elem!0)))),
% 22.77/22.94      inference(quant_inst,[status(thm)],[])).
% 22.77/22.94  tff(1490,plain,
% 22.77/22.94      ((~![X9: $i, X14: $i, X13: $i, X7: $i, X15: $i, X8: $i] : ((~big_q(X8)) | big_q(X15) | big_q(X13) | big_p(X7) | (~big_p(c11)) | (~big_q(c16)) | (~big_p(X14)) | big_p(X9))) | (~big_p(c11)) | big_q(c20) | (~big_q(c16)) | big_p(f3(elem!0)) | (~big_q(elem!0)) | (~big_p(c19))),
% 22.77/22.94      inference(modus_ponens,[status(thm)],[1489, 1488])).
% 22.77/22.94  tff(1491,plain,
% 22.77/22.94      ($false),
% 22.77/22.94      inference(unit_resolution,[status(thm)],[1490, 354, 1436, 1299, 820, 1402, 1484, 1367])).
% 22.77/22.94  tff(1492,plain,(big_p(f3(elem!0))), inference(lemma,lemma(discharge,[]))).
% 22.77/22.94  tff(1493,plain,
% 22.77/22.94      (^[X12: $i, X10: $i, X16: $i, X18: $i] : refl(((~big_p(X18)) | (~big_q(X12)) | (~big_q(X16)) | (~big_p(X10)) | (~big_q(c20)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10)))) <=> ((~big_p(X18)) | (~big_q(X12)) | (~big_q(X16)) | (~big_p(X10)) | (~big_q(c20)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10)))))),
% 22.77/22.94      inference(bind,[status(th)],[])).
% 22.77/22.94  tff(1494,plain,
% 22.77/22.94      (![X12: $i, X10: $i, X16: $i, X18: $i] : ((~big_p(X18)) | (~big_q(X12)) | (~big_q(X16)) | (~big_p(X10)) | (~big_q(c20)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10)))) <=> ![X12: $i, X10: $i, X16: $i, X18: $i] : ((~big_p(X18)) | (~big_q(X12)) | (~big_q(X16)) | (~big_p(X10)) | (~big_q(c20)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10))))),
% 22.77/22.94      inference(quant_intro,[status(thm)],[1493])).
% 22.77/22.94  tff(1495,plain,
% 22.77/22.94      (![X12: $i, X10: $i, X16: $i, X18: $i] : ((~big_p(X18)) | (~big_q(X12)) | (~big_q(X16)) | (~big_p(X10)) | (~big_q(c20)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10)))) <=> ![X12: $i, X10: $i, X16: $i, X18: $i] : ((~big_p(X18)) | (~big_q(X12)) | (~big_q(X16)) | (~big_p(X10)) | (~big_q(c20)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10))))),
% 22.77/22.94      inference(rewrite,[status(thm)],[])).
% 22.77/22.94  tff(1496,plain,
% 22.77/22.94      (^[X12: $i, X10: $i, X16: $i, X18: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) <=> ((~big_q(X12)) | (~big_p(X10)) | (~big_p(f3(X10))))), (((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) <=> (((~big_q(X12)) | (~big_p(X10)) | (~big_p(f3(X10)))) | (~big_p(c15))))), rewrite((((~big_q(X12)) | (~big_p(X10)) | (~big_p(f3(X10)))) | (~big_p(c15))) <=> ((~big_q(X12)) | (~big_p(X10)) | (~big_p(c15)) | (~big_p(f3(X10))))), (((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) <=> ((~big_q(X12)) | (~big_p(X10)) | (~big_p(c15)) | (~big_p(f3(X10)))))), ((((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) | (~big_q(f4(X16)))) <=> (((~big_q(X12)) | (~big_p(X10)) | (~big_p(c15)) | (~big_p(f3(X10)))) | (~big_q(f4(X16)))))), rewrite((((~big_q(X12)) | (~big_p(X10)) | (~big_p(c15)) | (~big_p(f3(X10)))) | (~big_q(f4(X16)))) <=> ((~big_q(X12)) | (~big_p(X10)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10))))), ((((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) | (~big_q(f4(X16)))) <=> ((~big_q(X12)) | (~big_p(X10)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10)))))), (((((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) | (~big_q(f4(X16)))) | (~big_q(X16))) <=> (((~big_q(X12)) | (~big_p(X10)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10)))) | (~big_q(X16))))), rewrite((((~big_q(X12)) | (~big_p(X10)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10)))) | (~big_q(X16))) <=> ((~big_q(X12)) | (~big_q(X16)) | (~big_p(X10)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10))))), (((((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) | (~big_q(f4(X16)))) | (~big_q(X16))) <=> ((~big_q(X12)) | (~big_q(X16)) | (~big_p(X10)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10)))))), ((((((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) | (~big_q(f4(X16)))) | (~big_q(X16))) | (~big_p(X18))) <=> (((~big_q(X12)) | (~big_q(X16)) | (~big_p(X10)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10)))) | (~big_p(X18))))), rewrite((((~big_q(X12)) | (~big_q(X16)) | (~big_p(X10)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10)))) | (~big_p(X18))) <=> ((~big_p(X18)) | (~big_q(X12)) | (~big_q(X16)) | (~big_p(X10)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10))))), ((((((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) | (~big_q(f4(X16)))) | (~big_q(X16))) | (~big_p(X18))) <=> ((~big_p(X18)) | (~big_q(X12)) | (~big_q(X16)) | (~big_p(X10)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10)))))), (((((((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) | (~big_q(f4(X16)))) | (~big_q(X16))) | (~big_p(X18))) | (~big_q(c20))) <=> (((~big_p(X18)) | (~big_q(X12)) | (~big_q(X16)) | (~big_p(X10)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10)))) | (~big_q(c20))))), rewrite((((~big_p(X18)) | (~big_q(X12)) | (~big_q(X16)) | (~big_p(X10)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10)))) | (~big_q(c20))) <=> ((~big_p(X18)) | (~big_q(X12)) | (~big_q(X16)) | (~big_p(X10)) | (~big_q(c20)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10))))), (((((((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) | (~big_q(f4(X16)))) | (~big_q(X16))) | (~big_p(X18))) | (~big_q(c20))) <=> ((~big_p(X18)) | (~big_q(X12)) | (~big_q(X16)) | (~big_p(X10)) | (~big_q(c20)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10))))))),
% 22.77/22.94      inference(bind,[status(th)],[])).
% 22.77/22.94  tff(1497,plain,
% 22.77/22.94      (![X12: $i, X10: $i, X16: $i, X18: $i] : ((((((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) | (~big_q(f4(X16)))) | (~big_q(X16))) | (~big_p(X18))) | (~big_q(c20))) <=> ![X12: $i, X10: $i, X16: $i, X18: $i] : ((~big_p(X18)) | (~big_q(X12)) | (~big_q(X16)) | (~big_p(X10)) | (~big_q(c20)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10))))),
% 22.77/22.94      inference(quant_intro,[status(thm)],[1496])).
% 22.77/22.94  tff(1498,axiom,(![X12: $i, X10: $i, X16: $i, X18: $i] : ((((((((~big_p(X10)) | (~big_p(f3(X10)))) | (~big_q(X12))) | (~big_p(c15))) | (~big_q(f4(X16)))) | (~big_q(X16))) | (~big_p(X18))) | (~big_q(c20)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_128')).
% 22.77/22.94  tff(1499,plain,
% 22.77/22.94      (![X12: $i, X10: $i, X16: $i, X18: $i] : ((~big_p(X18)) | (~big_q(X12)) | (~big_q(X16)) | (~big_p(X10)) | (~big_q(c20)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10))))),
% 22.77/22.94      inference(modus_ponens,[status(thm)],[1498, 1497])).
% 22.77/22.94  tff(1500,plain,
% 22.77/22.94      (![X12: $i, X10: $i, X16: $i, X18: $i] : ((~big_p(X18)) | (~big_q(X12)) | (~big_q(X16)) | (~big_p(X10)) | (~big_q(c20)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10))))),
% 22.77/22.94      inference(modus_ponens,[status(thm)],[1499, 1495])).
% 22.77/22.94  tff(1501,plain,(
% 22.77/22.94      ![X12: $i, X10: $i, X16: $i, X18: $i] : ((~big_p(X18)) | (~big_q(X12)) | (~big_q(X16)) | (~big_p(X10)) | (~big_q(c20)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10))))),
% 22.77/22.94      inference(skolemize,[status(sab)],[1500])).
% 22.77/22.94  tff(1502,plain,
% 22.77/22.94      (![X12: $i, X10: $i, X16: $i, X18: $i] : ((~big_p(X18)) | (~big_q(X12)) | (~big_q(X16)) | (~big_p(X10)) | (~big_q(c20)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10))))),
% 22.77/22.94      inference(modus_ponens,[status(thm)],[1501, 1494])).
% 22.77/22.94  tff(1503,plain,
% 22.77/22.94      (((~![X12: $i, X10: $i, X16: $i, X18: $i] : ((~big_p(X18)) | (~big_q(X12)) | (~big_q(X16)) | (~big_p(X10)) | (~big_q(c20)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(c20)) | (~big_p(c15)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))) <=> ((~![X12: $i, X10: $i, X16: $i, X18: $i] : ((~big_p(X18)) | (~big_q(X12)) | (~big_q(X16)) | (~big_p(X10)) | (~big_q(c20)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10))))) | (~big_q(c20)) | (~big_p(c15)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))),
% 22.77/22.94      inference(rewrite,[status(thm)],[])).
% 22.77/22.94  tff(1504,plain,
% 22.77/22.94      (((~big_p(elem!0)) | (~big_q(elem!0)) | (~big_q(elem!0)) | (~big_p(elem!0)) | (~big_q(c20)) | (~big_q(f4(elem!0))) | (~big_p(c15)) | (~big_p(f3(elem!0)))) <=> ((~big_q(c20)) | (~big_p(c15)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))),
% 22.77/22.94      inference(rewrite,[status(thm)],[])).
% 22.77/22.94  tff(1505,plain,
% 22.77/22.94      (((~![X12: $i, X10: $i, X16: $i, X18: $i] : ((~big_p(X18)) | (~big_q(X12)) | (~big_q(X16)) | (~big_p(X10)) | (~big_q(c20)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_p(elem!0)) | (~big_q(elem!0)) | (~big_q(elem!0)) | (~big_p(elem!0)) | (~big_q(c20)) | (~big_q(f4(elem!0))) | (~big_p(c15)) | (~big_p(f3(elem!0))))) <=> ((~![X12: $i, X10: $i, X16: $i, X18: $i] : ((~big_p(X18)) | (~big_q(X12)) | (~big_q(X16)) | (~big_p(X10)) | (~big_q(c20)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(c20)) | (~big_p(c15)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(f3(elem!0))) | (~big_p(elem!0))))),
% 22.77/22.94      inference(monotonicity,[status(thm)],[1504])).
% 22.77/22.94  tff(1506,plain,
% 22.77/22.94      (((~![X12: $i, X10: $i, X16: $i, X18: $i] : ((~big_p(X18)) | (~big_q(X12)) | (~big_q(X16)) | (~big_p(X10)) | (~big_q(c20)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_p(elem!0)) | (~big_q(elem!0)) | (~big_q(elem!0)) | (~big_p(elem!0)) | (~big_q(c20)) | (~big_q(f4(elem!0))) | (~big_p(c15)) | (~big_p(f3(elem!0))))) <=> ((~![X12: $i, X10: $i, X16: $i, X18: $i] : ((~big_p(X18)) | (~big_q(X12)) | (~big_q(X16)) | (~big_p(X10)) | (~big_q(c20)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10))))) | (~big_q(c20)) | (~big_p(c15)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))),
% 22.77/22.94      inference(transitivity,[status(thm)],[1505, 1503])).
% 22.77/22.94  tff(1507,plain,
% 22.77/22.94      ((~![X12: $i, X10: $i, X16: $i, X18: $i] : ((~big_p(X18)) | (~big_q(X12)) | (~big_q(X16)) | (~big_p(X10)) | (~big_q(c20)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_p(elem!0)) | (~big_q(elem!0)) | (~big_q(elem!0)) | (~big_p(elem!0)) | (~big_q(c20)) | (~big_q(f4(elem!0))) | (~big_p(c15)) | (~big_p(f3(elem!0))))),
% 22.77/22.94      inference(quant_inst,[status(thm)],[])).
% 22.77/22.94  tff(1508,plain,
% 22.77/22.94      ((~![X12: $i, X10: $i, X16: $i, X18: $i] : ((~big_p(X18)) | (~big_q(X12)) | (~big_q(X16)) | (~big_p(X10)) | (~big_q(c20)) | (~big_q(f4(X16))) | (~big_p(c15)) | (~big_p(f3(X10))))) | (~big_q(c20)) | (~big_p(c15)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(f3(elem!0))) | (~big_p(elem!0))),
% 22.77/22.94      inference(modus_ponens,[status(thm)],[1507, 1506])).
% 22.77/22.94  tff(1509,plain,
% 22.77/22.94      ((~big_q(c20)) | (~big_p(c15)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(f3(elem!0))) | (~big_p(elem!0))),
% 22.77/22.95      inference(unit_resolution,[status(thm)],[1508, 1502])).
% 22.77/22.95  tff(1510,plain,
% 22.77/22.95      ((~big_q(c20)) | (~big_p(c15)) | (~big_q(elem!0)) | (~big_q(f4(elem!0))) | (~big_p(f3(elem!0)))),
% 22.77/22.95      inference(unit_resolution,[status(thm)],[1509, 762])).
% 22.77/22.95  tff(1511,plain,
% 22.77/22.95      ((~big_q(c20)) | (~big_p(c15)) | (~big_q(f4(elem!0))) | (~big_p(f3(elem!0)))),
% 22.77/22.95      inference(unit_resolution,[status(thm)],[1510, 1299])).
% 22.77/22.95  tff(1512,plain,
% 22.77/22.95      (~big_q(c20)),
% 22.77/22.95      inference(unit_resolution,[status(thm)],[1511, 1492, 1477, 1460])).
% 22.77/22.95  tff(1513,plain,
% 22.77/22.95      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (big_q(c20) | (~big_q(c16)) | (~big_p(c15)) | (~big_q(elem!0)) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | big_q(c20) | (~big_q(c16)) | (~big_p(c15)) | (~big_q(elem!0)) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))),
% 22.77/22.95      inference(rewrite,[status(thm)],[])).
% 22.77/22.95  tff(1514,plain,
% 22.77/22.95      (((~big_q(elem!0)) | big_q(c20) | big_q(c20) | (~big_p(elem!0)) | (~big_q(c16)) | (~big_p(f3(elem!0))) | (~big_p(c15)) | (~big_p(f3(elem!0)))) <=> (big_q(c20) | (~big_q(c16)) | (~big_p(c15)) | (~big_q(elem!0)) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))),
% 22.77/22.95      inference(rewrite,[status(thm)],[])).
% 22.77/22.95  tff(1515,plain,
% 22.77/22.95      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(elem!0)) | big_q(c20) | big_q(c20) | (~big_p(elem!0)) | (~big_q(c16)) | (~big_p(f3(elem!0))) | (~big_p(c15)) | (~big_p(f3(elem!0))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | (big_q(c20) | (~big_q(c16)) | (~big_p(c15)) | (~big_q(elem!0)) | (~big_p(f3(elem!0))) | (~big_p(elem!0))))),
% 22.77/22.95      inference(monotonicity,[status(thm)],[1514])).
% 22.77/22.95  tff(1516,plain,
% 22.77/22.95      (((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(elem!0)) | big_q(c20) | big_q(c20) | (~big_p(elem!0)) | (~big_q(c16)) | (~big_p(f3(elem!0))) | (~big_p(c15)) | (~big_p(f3(elem!0))))) <=> ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | big_q(c20) | (~big_q(c16)) | (~big_p(c15)) | (~big_q(elem!0)) | (~big_p(f3(elem!0))) | (~big_p(elem!0)))),
% 22.77/22.95      inference(transitivity,[status(thm)],[1515, 1513])).
% 22.77/22.95  tff(1517,plain,
% 22.77/22.95      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | ((~big_q(elem!0)) | big_q(c20) | big_q(c20) | (~big_p(elem!0)) | (~big_q(c16)) | (~big_p(f3(elem!0))) | (~big_p(c15)) | (~big_p(f3(elem!0))))),
% 22.77/22.95      inference(quant_inst,[status(thm)],[])).
% 22.77/22.95  tff(1518,plain,
% 22.77/22.95      ((~![X14: $i, X12: $i, X13: $i, X10: $i, X15: $i] : ((~big_q(X12)) | big_q(X15) | big_q(X13) | (~big_p(X10)) | (~big_q(c16)) | (~big_p(X14)) | (~big_p(c15)) | (~big_p(f3(X10))))) | big_q(c20) | (~big_q(c16)) | (~big_p(c15)) | (~big_q(elem!0)) | (~big_p(f3(elem!0))) | (~big_p(elem!0))),
% 22.77/22.95      inference(modus_ponens,[status(thm)],[1517, 1516])).
% 22.77/22.95  tff(1519,plain,
% 22.77/22.95      ($false),
% 22.77/22.95      inference(unit_resolution,[status(thm)],[1518, 1222, 1299, 1492, 762, 1402, 1460, 1512])).
% 22.77/22.95  % SZS output end Proof
% 22.77/22.99  % E exiting
%------------------------------------------------------------------------------