%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN036-4 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:38:00 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN036-4 : TPTP v9.0.0. Released v1.0.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n010.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 12:28:12 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.19/0.46 % SZS status Unsatisfiable
% 0.19/0.46 % SZS output start Proof
% 0.19/0.46 tff(q_type, type, (
% 0.19/0.46 q: $i > $o)).
% 0.19/0.46 tff(fz5_type, type, (
% 0.19/0.46 fz5: $i > $i)).
% 0.19/0.46 tff(cw_type, type, (
% 0.19/0.46 cw: $i)).
% 0.19/0.46 tff(p_type, type, (
% 0.19/0.46 p: $i > $o)).
% 0.19/0.46 tff(fy5_type, type, (
% 0.19/0.46 fy5: $i > $i)).
% 0.19/0.46 tff(cx_type, type, (
% 0.19/0.46 cx: $i)).
% 0.19/0.46 tff(fz_type, type, (
% 0.19/0.46 fz: $i > $i)).
% 0.19/0.46 tff(fy_type, type, (
% 0.19/0.46 fy: $i > $i)).
% 0.19/0.46 tff(elem_0_type, type, (
% 0.19/0.46 elem_0: $i)).
% 0.19/0.46 tff(1,assumption,(~p(fy5(cx))), introduced(assumption)).
% 0.19/0.46 tff(2,assumption,(~q(cw)), introduced(assumption)).
% 0.19/0.46 tff(3,assumption,(q(fz(cx))), introduced(assumption)).
% 0.19/0.46 tff(4,assumption,(~p(cx)), introduced(assumption)).
% 0.19/0.46 tff(5,assumption,(~q(fz(cx))), introduced(assumption)).
% 0.19/0.46 tff(6,assumption,(~q(cx)), introduced(assumption)).
% 0.19/0.46 tff(7,plain,
% 0.19/0.46 (^[Y2: $i, W3: $i] : refl((p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3))) <=> (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(8,plain,
% 0.19/0.46 (![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3))) <=> ![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[7])).
% 0.19/0.46 tff(9,plain,
% 0.19/0.46 (![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3))) <=> ![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(10,plain,
% 0.19/0.46 (^[Y2: $i, W3: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~p(Y2)) | p(cx)) <=> (p(cx) | (~p(Y2)))), ((((~p(Y2)) | p(cx)) | q(cw)) <=> ((p(cx) | (~p(Y2))) | q(cw)))), rewrite(((p(cx) | (~p(Y2))) | q(cw)) <=> (p(cx) | q(cw) | (~p(Y2)))), ((((~p(Y2)) | p(cx)) | q(cw)) <=> (p(cx) | q(cw) | (~p(Y2))))), (((((~p(Y2)) | p(cx)) | q(cw)) | q(W3)) <=> ((p(cx) | q(cw) | (~p(Y2))) | q(W3)))), rewrite(((p(cx) | q(cw) | (~p(Y2))) | q(W3)) <=> (p(cx) | q(cw) | q(W3) | (~p(Y2)))), (((((~p(Y2)) | p(cx)) | q(cw)) | q(W3)) <=> (p(cx) | q(cw) | q(W3) | (~p(Y2))))), ((((((~p(Y2)) | p(cx)) | q(cw)) | q(W3)) | q(fz(W3))) <=> ((p(cx) | q(cw) | q(W3) | (~p(Y2))) | q(fz(W3))))), rewrite(((p(cx) | q(cw) | q(W3) | (~p(Y2))) | q(fz(W3))) <=> (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))), ((((((~p(Y2)) | p(cx)) | q(cw)) | q(W3)) | q(fz(W3))) <=> (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(11,plain,
% 0.19/0.46 (![Y2: $i, W3: $i] : (((((~p(Y2)) | p(cx)) | q(cw)) | q(W3)) | q(fz(W3))) <=> ![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.46 tff(12,axiom,(![Y2: $i, W3: $i] : (((((~p(Y2)) | p(cx)) | q(cw)) | q(W3)) | q(fz(W3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_15')).
% 0.19/0.46 tff(13,plain,
% 0.19/0.46 (![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.19/0.46 tff(14,plain,
% 0.19/0.46 (![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.19/0.46 tff(15,plain,(
% 0.19/0.46 ![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[14])).
% 0.19/0.46 tff(16,plain,
% 0.19/0.46 (![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.19/0.46 tff(17,plain,
% 0.19/0.46 (((~![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))) | (p(cx) | q(cw) | q(cx) | (~p(fy5(cx))) | q(fz(cx)))) <=> ((~![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))) | p(cx) | q(cw) | q(cx) | (~p(fy5(cx))) | q(fz(cx)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(18,plain,
% 0.19/0.46 ((~![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))) | (p(cx) | q(cw) | q(cx) | (~p(fy5(cx))) | q(fz(cx)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(19,plain,
% 0.19/0.46 ((~![Y2: $i, W3: $i] : (p(cx) | q(cw) | q(W3) | (~p(Y2)) | q(fz(W3)))) | p(cx) | q(cw) | q(cx) | (~p(fy5(cx))) | q(fz(cx))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.46 tff(20,plain,
% 0.19/0.46 (p(cx) | q(cw) | q(cx) | (~p(fy5(cx))) | q(fz(cx))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[19, 16])).
% 0.19/0.46 tff(21,plain,
% 0.19/0.46 (~p(fy5(cx))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[20, 2, 4, 6, 5])).
% 0.19/0.47 tff(22,plain,
% 0.19/0.47 (^[W9: $i, X7: $i] : refl((p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9))) <=> (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(23,plain,
% 0.19/0.47 (![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9))) <=> ![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.47 tff(24,plain,
% 0.19/0.47 (![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9))) <=> ![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(25,plain,
% 0.19/0.47 (^[W9: $i, X7: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((p(cx) | p(X7)) | p(fy5(X7))) <=> (p(cx) | p(X7) | p(fy5(X7)))), ((((p(cx) | p(X7)) | p(fy5(X7))) | q(cw)) <=> ((p(cx) | p(X7) | p(fy5(X7))) | q(cw)))), rewrite(((p(cx) | p(X7) | p(fy5(X7))) | q(cw)) <=> (p(cx) | q(cw) | p(X7) | p(fy5(X7)))), ((((p(cx) | p(X7)) | p(fy5(X7))) | q(cw)) <=> (p(cx) | q(cw) | p(X7) | p(fy5(X7))))), (((((p(cx) | p(X7)) | p(fy5(X7))) | q(cw)) | q(W9)) <=> ((p(cx) | q(cw) | p(X7) | p(fy5(X7))) | q(W9)))), rewrite(((p(cx) | q(cw) | p(X7) | p(fy5(X7))) | q(W9)) <=> (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)))), (((((p(cx) | p(X7)) | p(fy5(X7))) | q(cw)) | q(W9)) <=> (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7))))), ((((((p(cx) | p(X7)) | p(fy5(X7))) | q(cw)) | q(W9)) | q(fz5(W9))) <=> ((p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7))) | q(fz5(W9))))), rewrite(((p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7))) | q(fz5(W9))) <=> (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))), ((((((p(cx) | p(X7)) | p(fy5(X7))) | q(cw)) | q(W9)) | q(fz5(W9))) <=> (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(26,plain,
% 0.19/0.47 (![W9: $i, X7: $i] : (((((p(cx) | p(X7)) | p(fy5(X7))) | q(cw)) | q(W9)) | q(fz5(W9))) <=> ![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.47 tff(27,axiom,(![W9: $i, X7: $i] : (((((p(cx) | p(X7)) | p(fy5(X7))) | q(cw)) | q(W9)) | q(fz5(W9)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_32')).
% 0.19/0.47 tff(28,plain,
% 0.19/0.47 (![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.47 tff(29,plain,
% 0.19/0.47 (![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.19/0.47 tff(30,plain,(
% 0.19/0.47 ![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[29])).
% 0.19/0.47 tff(31,plain,
% 0.19/0.47 (![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.19/0.47 tff(32,plain,
% 0.19/0.47 (((~![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))) | (p(cx) | q(cw) | q(fz5(cx)) | q(cx) | p(fy5(cx)))) <=> ((~![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))) | p(cx) | q(cw) | q(fz5(cx)) | q(cx) | p(fy5(cx)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(33,plain,
% 0.19/0.47 ((p(cx) | q(cw) | q(cx) | p(cx) | p(fy5(cx)) | q(fz5(cx))) <=> (p(cx) | q(cw) | q(fz5(cx)) | q(cx) | p(fy5(cx)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(34,plain,
% 0.19/0.47 (((~![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))) | (p(cx) | q(cw) | q(cx) | p(cx) | p(fy5(cx)) | q(fz5(cx)))) <=> ((~![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))) | (p(cx) | q(cw) | q(fz5(cx)) | q(cx) | p(fy5(cx))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[33])).
% 0.19/0.47 tff(35,plain,
% 0.19/0.47 (((~![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))) | (p(cx) | q(cw) | q(cx) | p(cx) | p(fy5(cx)) | q(fz5(cx)))) <=> ((~![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))) | p(cx) | q(cw) | q(fz5(cx)) | q(cx) | p(fy5(cx)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[34, 32])).
% 0.19/0.47 tff(36,plain,
% 0.19/0.47 ((~![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))) | (p(cx) | q(cw) | q(cx) | p(cx) | p(fy5(cx)) | q(fz5(cx)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(37,plain,
% 0.19/0.47 ((~![W9: $i, X7: $i] : (p(cx) | q(cw) | q(W9) | p(X7) | p(fy5(X7)) | q(fz5(W9)))) | p(cx) | q(cw) | q(fz5(cx)) | q(cx) | p(fy5(cx))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.47 tff(38,plain,
% 0.19/0.47 (p(cx) | q(cw) | q(fz5(cx)) | q(cx) | p(fy5(cx))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[37, 31])).
% 0.19/0.47 tff(39,plain,
% 0.19/0.47 (q(fz5(cx))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[38, 21, 4, 2, 6])).
% 0.19/0.47 tff(40,plain,
% 0.19/0.47 (^[Z2: $i, X1: $i] : refl((p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1))) <=> (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(41,plain,
% 0.19/0.47 (![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1))) <=> ![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[40])).
% 0.19/0.47 tff(42,plain,
% 0.19/0.47 (![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1))) <=> ![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(43,plain,
% 0.19/0.47 (^[Z2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~q(Z2)) | p(cx)) <=> (p(cx) | (~q(Z2)))), ((((~q(Z2)) | p(cx)) | p(X1)) <=> ((p(cx) | (~q(Z2))) | p(X1)))), rewrite(((p(cx) | (~q(Z2))) | p(X1)) <=> (p(cx) | p(X1) | (~q(Z2)))), ((((~q(Z2)) | p(cx)) | p(X1)) <=> (p(cx) | p(X1) | (~q(Z2))))), (((((~q(Z2)) | p(cx)) | p(X1)) | p(fy(X1))) <=> ((p(cx) | p(X1) | (~q(Z2))) | p(fy(X1))))), rewrite(((p(cx) | p(X1) | (~q(Z2))) | p(fy(X1))) <=> (p(cx) | p(X1) | (~q(Z2)) | p(fy(X1)))), (((((~q(Z2)) | p(cx)) | p(X1)) | p(fy(X1))) <=> (p(cx) | p(X1) | (~q(Z2)) | p(fy(X1))))), ((((((~q(Z2)) | p(cx)) | p(X1)) | p(fy(X1))) | q(cw)) <=> ((p(cx) | p(X1) | (~q(Z2)) | p(fy(X1))) | q(cw)))), rewrite(((p(cx) | p(X1) | (~q(Z2)) | p(fy(X1))) | q(cw)) <=> (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))), ((((((~q(Z2)) | p(cx)) | p(X1)) | p(fy(X1))) | q(cw)) <=> (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(44,plain,
% 0.19/0.47 (![Z2: $i, X1: $i] : (((((~q(Z2)) | p(cx)) | p(X1)) | p(fy(X1))) | q(cw)) <=> ![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[43])).
% 0.19/0.47 tff(45,axiom,(![Z2: $i, X1: $i] : (((((~q(Z2)) | p(cx)) | p(X1)) | p(fy(X1))) | q(cw))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_20')).
% 0.19/0.47 tff(46,plain,
% 0.19/0.47 (![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.47 tff(47,plain,
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% 0.19/0.48 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.19/0.48 tff(100,plain,(
% 0.19/0.48 ![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))),
% 0.19/0.48 inference(skolemize,[status(sab)],[99])).
% 0.19/0.48 tff(101,plain,
% 0.19/0.48 (![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.19/0.48 tff(102,plain,
% 0.19/0.48 (((~![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))) | (p(cx) | (~q(cw)) | q(cx) | (~p(fy(cx))))) <=> ((~![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))) | p(cx) | (~q(cw)) | q(cx) | (~p(fy(cx))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(103,plain,
% 0.19/0.48 ((~![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))) | (p(cx) | (~q(cw)) | q(cx) | (~p(fy(cx))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(104,plain,
% 0.19/0.48 ((~![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))) | p(cx) | (~q(cw)) | q(cx) | (~p(fy(cx)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.48 tff(105,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[104, 101, 4, 73, 6, 91])).
% 0.19/0.48 tff(106,plain,(q(cx) | p(cx) | q(fz(cx))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(107,plain,
% 0.19/0.48 (q(cx)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[106, 5, 4])).
% 0.19/0.48 tff(108,assumption,(q(cx)), introduced(assumption)).
% 0.19/0.48 tff(109,plain,
% 0.19/0.48 (((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | (p(cx) | q(cw) | (~q(cx)) | p(fy(cx)))) <=> ((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | p(cx) | q(cw) | (~q(cx)) | p(fy(cx)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(110,plain,
% 0.19/0.48 ((p(cx) | q(cw) | p(cx) | (~q(cx)) | p(fy(cx))) <=> (p(cx) | q(cw) | (~q(cx)) | p(fy(cx)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(111,plain,
% 0.19/0.48 (((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | (p(cx) | q(cw) | p(cx) | (~q(cx)) | p(fy(cx)))) <=> ((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | (p(cx) | q(cw) | (~q(cx)) | p(fy(cx))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[110])).
% 0.19/0.48 tff(112,plain,
% 0.19/0.48 (((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | (p(cx) | q(cw) | p(cx) | (~q(cx)) | p(fy(cx)))) <=> ((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | p(cx) | q(cw) | (~q(cx)) | p(fy(cx)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[111, 109])).
% 0.19/0.48 tff(113,plain,
% 0.19/0.48 ((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | (p(cx) | q(cw) | p(cx) | (~q(cx)) | p(fy(cx)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(114,plain,
% 0.19/0.48 ((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | p(cx) | q(cw) | (~q(cx)) | p(fy(cx))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.19/0.48 tff(115,plain,
% 0.19/0.48 (p(cx) | q(cw) | (~q(cx)) | p(fy(cx))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[114, 49])).
% 0.19/0.48 tff(116,plain,
% 0.19/0.48 (p(fy(cx))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[115, 2, 4, 108])).
% 0.19/0.48 tff(117,plain,
% 0.19/0.48 (^[Y4: $i, Z4: $i] : refl((p(cx) | q(cw) | (~q(Z4)) | (~p(Y4))) <=> (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(118,plain,
% 0.19/0.48 (![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4))) <=> ![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[117])).
% 0.19/0.48 tff(119,plain,
% 0.19/0.48 (![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4))) <=> ![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(120,plain,
% 0.19/0.48 (^[Y4: $i, Z4: $i] : trans(monotonicity(rewrite((((~p(Y4)) | (~q(Z4))) | p(cx)) <=> (p(cx) | (~q(Z4)) | (~p(Y4)))), (((((~p(Y4)) | (~q(Z4))) | p(cx)) | q(cw)) <=> ((p(cx) | (~q(Z4)) | (~p(Y4))) | q(cw)))), rewrite(((p(cx) | (~q(Z4)) | (~p(Y4))) | q(cw)) <=> (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))), (((((~p(Y4)) | (~q(Z4))) | p(cx)) | q(cw)) <=> (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(121,plain,
% 0.19/0.48 (![Y4: $i, Z4: $i] : ((((~p(Y4)) | (~q(Z4))) | p(cx)) | q(cw)) <=> ![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[120])).
% 0.19/0.48 tff(122,axiom,(![Y4: $i, Z4: $i] : ((((~p(Y4)) | (~q(Z4))) | p(cx)) | q(cw))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_4')).
% 0.19/0.48 tff(123,plain,
% 0.19/0.48 (![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.19/0.48 tff(124,plain,
% 0.19/0.48 (![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.19/0.48 tff(125,plain,(
% 0.19/0.48 ![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))),
% 0.19/0.48 inference(skolemize,[status(sab)],[124])).
% 0.19/0.48 tff(126,plain,
% 0.19/0.48 (![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[125, 118])).
% 0.19/0.48 tff(127,plain,
% 0.19/0.48 (((~![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))) | (p(cx) | q(cw) | (~q(cx)) | (~p(fy(cx))))) <=> ((~![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))) | p(cx) | q(cw) | (~q(cx)) | (~p(fy(cx))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(128,plain,
% 0.19/0.48 ((~![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))) | (p(cx) | q(cw) | (~q(cx)) | (~p(fy(cx))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(129,plain,
% 0.19/0.48 ((~![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))) | p(cx) | q(cw) | (~q(cx)) | (~p(fy(cx)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.19/0.48 tff(130,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[129, 126, 4, 2, 108, 116])).
% 0.19/0.48 tff(131,plain,(q(cw) | p(cx) | (~q(cx))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(132,plain,
% 0.19/0.48 (q(cw)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[131, 107, 4])).
% 0.19/0.48 tff(133,plain,
% 0.19/0.48 (((~![Z1: $i, X1: $i] : (p(cx) | (~q(cw)) | q(Z1) | p(X1) | p(fy(X1)))) | (p(cx) | (~q(cw)) | q(fz(cx)) | p(fy(cx)))) <=> ((~![Z1: $i, X1: $i] : (p(cx) | (~q(cw)) | q(Z1) | p(X1) | p(fy(X1)))) | p(cx) | (~q(cw)) | q(fz(cx)) | p(fy(cx)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(134,plain,
% 0.19/0.48 ((p(cx) | (~q(cw)) | q(fz(cx)) | p(cx) | p(fy(cx))) <=> (p(cx) | (~q(cw)) | q(fz(cx)) | p(fy(cx)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(135,plain,
% 0.19/0.48 (((~![Z1: $i, X1: $i] : (p(cx) | (~q(cw)) | q(Z1) | p(X1) | p(fy(X1)))) | (p(cx) | (~q(cw)) | q(fz(cx)) | p(cx) | p(fy(cx)))) <=> ((~![Z1: $i, X1: $i] : (p(cx) | (~q(cw)) | q(Z1) | p(X1) | p(fy(X1)))) | (p(cx) | (~q(cw)) | q(fz(cx)) | p(fy(cx))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[134])).
% 0.19/0.48 tff(136,plain,
% 0.19/0.48 (((~![Z1: $i, X1: $i] : (p(cx) | (~q(cw)) | q(Z1) | p(X1) | p(fy(X1)))) | (p(cx) | (~q(cw)) | q(fz(cx)) | p(cx) | p(fy(cx)))) <=> ((~![Z1: $i, X1: $i] : (p(cx) | (~q(cw)) | q(Z1) | p(X1) | p(fy(X1)))) | p(cx) | (~q(cw)) | q(fz(cx)) | p(fy(cx)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[135, 133])).
% 0.19/0.48 tff(137,plain,
% 0.19/0.48 ((~![Z1: $i, X1: $i] : (p(cx) | (~q(cw)) | q(Z1) | p(X1) | p(fy(X1)))) | (p(cx) | (~q(cw)) | q(fz(cx)) | p(cx) | p(fy(cx)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(138,plain,
% 0.19/0.48 ((~![Z1: $i, X1: $i] : (p(cx) | (~q(cw)) | q(Z1) | p(X1) | p(fy(X1)))) | p(cx) | (~q(cw)) | q(fz(cx)) | p(fy(cx))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.19/0.48 tff(139,plain,
% 0.19/0.48 (p(cx) | (~q(cw)) | q(fz(cx)) | p(fy(cx))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[138, 83])).
% 0.19/0.48 tff(140,plain,
% 0.19/0.48 (p(fy(cx))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[139, 132, 4, 5])).
% 0.19/0.48 tff(141,plain,
% 0.19/0.48 (((~![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))) | (p(cx) | (~q(cw)) | q(fz(cx)) | (~p(fy(cx))))) <=> ((~![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))) | p(cx) | (~q(cw)) | q(fz(cx)) | (~p(fy(cx))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(142,plain,
% 0.19/0.48 ((~![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))) | (p(cx) | (~q(cw)) | q(fz(cx)) | (~p(fy(cx))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(143,plain,
% 0.19/0.48 ((~![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))) | p(cx) | (~q(cw)) | q(fz(cx)) | (~p(fy(cx)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.19/0.48 tff(144,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[143, 101, 4, 132, 5, 140])).
% 0.19/0.48 tff(145,plain,(q(fz(cx)) | p(cx)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(146,plain,
% 0.19/0.48 (q(fz(cx))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[145, 4])).
% 0.19/0.48 tff(147,assumption,(~q(fz5(cx))), introduced(assumption)).
% 0.19/0.48 tff(148,plain,
% 0.19/0.48 (p(fy5(cx))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[38, 147, 4, 6, 2])).
% 0.19/0.48 tff(149,plain,
% 0.19/0.48 (^[Y4: $i, W9: $i, W6: $i] : refl((p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4))) <=> (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(150,plain,
% 0.19/0.48 (![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4))) <=> ![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[149])).
% 0.19/0.48 tff(151,plain,
% 0.19/0.48 (![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4))) <=> ![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(152,plain,
% 0.19/0.48 (^[Y4: $i, W9: $i, W6: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~p(Y4)) | (~q(W6))) | p(cx)) <=> (p(cx) | (~q(W6)) | (~p(Y4)))), (((((~p(Y4)) | (~q(W6))) | p(cx)) | q(W9)) <=> ((p(cx) | (~q(W6)) | (~p(Y4))) | q(W9)))), rewrite(((p(cx) | (~q(W6)) | (~p(Y4))) | q(W9)) <=> (p(cx) | q(W9) | (~q(W6)) | (~p(Y4)))), (((((~p(Y4)) | (~q(W6))) | p(cx)) | q(W9)) <=> (p(cx) | q(W9) | (~q(W6)) | (~p(Y4))))), ((((((~p(Y4)) | (~q(W6))) | p(cx)) | q(W9)) | q(fz5(W9))) <=> ((p(cx) | q(W9) | (~q(W6)) | (~p(Y4))) | q(fz5(W9))))), rewrite(((p(cx) | q(W9) | (~q(W6)) | (~p(Y4))) | q(fz5(W9))) <=> (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))), ((((((~p(Y4)) | (~q(W6))) | p(cx)) | q(W9)) | q(fz5(W9))) <=> (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(153,plain,
% 0.19/0.48 (![Y4: $i, W9: $i, W6: $i] : (((((~p(Y4)) | (~q(W6))) | p(cx)) | q(W9)) | q(fz5(W9))) <=> ![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[152])).
% 0.19/0.48 tff(154,axiom,(![Y4: $i, W9: $i, W6: $i] : (((((~p(Y4)) | (~q(W6))) | p(cx)) | q(W9)) | q(fz5(W9)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_17')).
% 0.19/0.49 tff(155,plain,
% 0.19/0.49 (![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.19/0.49 tff(156,plain,
% 0.19/0.49 (![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.19/0.49 tff(157,plain,(
% 0.19/0.49 ![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))),
% 0.19/0.49 inference(skolemize,[status(sab)],[156])).
% 0.19/0.49 tff(158,plain,
% 0.19/0.49 (![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[157, 150])).
% 0.19/0.49 tff(159,plain,
% 0.19/0.49 (((~![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))) | (p(cx) | q(fz5(cx)) | q(cx) | (~p(fy5(cx))) | (~q(fz(cx))))) <=> ((~![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))) | p(cx) | q(fz5(cx)) | q(cx) | (~p(fy5(cx))) | (~q(fz(cx))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(160,plain,
% 0.19/0.49 ((p(cx) | q(cx) | (~q(fz(cx))) | q(fz5(cx)) | (~p(fy5(cx)))) <=> (p(cx) | q(fz5(cx)) | q(cx) | (~p(fy5(cx))) | (~q(fz(cx))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(161,plain,
% 0.19/0.49 (((~![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))) | (p(cx) | q(cx) | (~q(fz(cx))) | q(fz5(cx)) | (~p(fy5(cx))))) <=> ((~![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))) | (p(cx) | q(fz5(cx)) | q(cx) | (~p(fy5(cx))) | (~q(fz(cx)))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[160])).
% 0.19/0.49 tff(162,plain,
% 0.19/0.49 (((~![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))) | (p(cx) | q(cx) | (~q(fz(cx))) | q(fz5(cx)) | (~p(fy5(cx))))) <=> ((~![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))) | p(cx) | q(fz5(cx)) | q(cx) | (~p(fy5(cx))) | (~q(fz(cx))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[161, 159])).
% 0.19/0.49 tff(163,plain,
% 0.19/0.49 ((~![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))) | (p(cx) | q(cx) | (~q(fz(cx))) | q(fz5(cx)) | (~p(fy5(cx))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(164,plain,
% 0.19/0.49 ((~![Y4: $i, W9: $i, W6: $i] : (p(cx) | q(W9) | (~q(W6)) | q(fz5(W9)) | (~p(Y4)))) | p(cx) | q(fz5(cx)) | q(cx) | (~p(fy5(cx))) | (~q(fz(cx)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.19/0.49 tff(165,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[164, 158, 4, 147, 6, 148, 146])).
% 0.19/0.49 tff(166,plain,(q(fz5(cx)) | p(cx) | q(cx) | q(cw)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(167,plain,
% 0.19/0.49 (q(fz5(cx))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[166, 2, 6, 4])).
% 0.19/0.49 tff(168,plain,
% 0.19/0.49 (((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | (p(cx) | q(cw) | (~q(fz5(cx))) | p(fy(cx)))) <=> ((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | p(cx) | q(cw) | (~q(fz5(cx))) | p(fy(cx)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(169,plain,
% 0.19/0.49 ((p(cx) | q(cw) | p(cx) | (~q(fz5(cx))) | p(fy(cx))) <=> (p(cx) | q(cw) | (~q(fz5(cx))) | p(fy(cx)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(170,plain,
% 0.19/0.49 (((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | (p(cx) | q(cw) | p(cx) | (~q(fz5(cx))) | p(fy(cx)))) <=> ((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | (p(cx) | q(cw) | (~q(fz5(cx))) | p(fy(cx))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[169])).
% 0.19/0.49 tff(171,plain,
% 0.19/0.49 (((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | (p(cx) | q(cw) | p(cx) | (~q(fz5(cx))) | p(fy(cx)))) <=> ((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | p(cx) | q(cw) | (~q(fz5(cx))) | p(fy(cx)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[170, 168])).
% 0.19/0.49 tff(172,plain,
% 0.19/0.49 ((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | (p(cx) | q(cw) | p(cx) | (~q(fz5(cx))) | p(fy(cx)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(173,plain,
% 0.19/0.49 ((~![Z2: $i, X1: $i] : (p(cx) | q(cw) | p(X1) | (~q(Z2)) | p(fy(X1)))) | p(cx) | q(cw) | (~q(fz5(cx))) | p(fy(cx))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.19/0.49 tff(174,plain,
% 0.19/0.49 (p(cx) | q(cw) | (~q(fz5(cx))) | p(fy(cx))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[173, 49])).
% 0.19/0.49 tff(175,plain,
% 0.19/0.49 (p(fy(cx))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[174, 167, 4, 2])).
% 0.19/0.49 tff(176,plain,
% 0.19/0.49 (((~![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))) | (p(cx) | q(cw) | (~q(fz5(cx))) | (~p(fy(cx))))) <=> ((~![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))) | p(cx) | q(cw) | (~q(fz5(cx))) | (~p(fy(cx))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(177,plain,
% 0.19/0.49 ((~![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))) | (p(cx) | q(cw) | (~q(fz5(cx))) | (~p(fy(cx))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(178,plain,
% 0.19/0.49 ((~![Y4: $i, Z4: $i] : (p(cx) | q(cw) | (~q(Z4)) | (~p(Y4)))) | p(cx) | q(cw) | (~q(fz5(cx))) | (~p(fy(cx)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.19/0.49 tff(179,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[178, 126, 4, 2, 167, 175])).
% 0.19/0.49 tff(180,plain,(q(cw) | p(cx) | q(cx)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(181,plain,
% 0.19/0.49 (q(cw)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[180, 6, 4])).
% 0.19/0.49 tff(182,plain,
% 0.19/0.49 (p(fy(cx))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[90, 181, 4, 6])).
% 0.19/0.49 tff(183,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[104, 101, 4, 181, 6, 182])).
% 0.19/0.49 tff(184,plain,(q(cx) | p(cx)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(185,plain,
% 0.19/0.49 (q(cx)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[184, 4])).
% 0.19/0.49 tff(186,plain,
% 0.19/0.49 (q(cw)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[131, 185, 4])).
% 0.19/0.49 tff(187,plain,
% 0.19/0.49 (^[W3: $i, X1: $i] : refl((p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3)))) <=> (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(188,plain,
% 0.19/0.49 (![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3)))) <=> ![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[187])).
% 0.19/0.49 tff(189,plain,
% 0.19/0.49 (![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3)))) <=> ![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(190,plain,
% 0.19/0.49 (^[W3: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~q(cw)) | (~q(W3))) | (~q(fz(W3)))) <=> ((~q(cw)) | (~q(W3)) | (~q(fz(W3))))), (((((~q(cw)) | (~q(W3))) | (~q(fz(W3)))) | p(cx)) <=> (((~q(cw)) | (~q(W3)) | (~q(fz(W3)))) | p(cx)))), rewrite((((~q(cw)) | (~q(W3)) | (~q(fz(W3)))) | p(cx)) <=> (p(cx) | (~q(cw)) | (~q(W3)) | (~q(fz(W3))))), (((((~q(cw)) | (~q(W3))) | (~q(fz(W3)))) | p(cx)) <=> (p(cx) | (~q(cw)) | (~q(W3)) | (~q(fz(W3)))))), ((((((~q(cw)) | (~q(W3))) | (~q(fz(W3)))) | p(cx)) | p(X1)) <=> ((p(cx) | (~q(cw)) | (~q(W3)) | (~q(fz(W3)))) | p(X1)))), rewrite(((p(cx) | (~q(cw)) | (~q(W3)) | (~q(fz(W3)))) | p(X1)) <=> (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | (~q(fz(W3))))), ((((((~q(cw)) | (~q(W3))) | (~q(fz(W3)))) | p(cx)) | p(X1)) <=> (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | (~q(fz(W3)))))), (((((((~q(cw)) | (~q(W3))) | (~q(fz(W3)))) | p(cx)) | p(X1)) | p(fy(X1))) <=> ((p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | (~q(fz(W3)))) | p(fy(X1))))), rewrite(((p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | (~q(fz(W3)))) | p(fy(X1))) <=> (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))), (((((((~q(cw)) | (~q(W3))) | (~q(fz(W3)))) | p(cx)) | p(X1)) | p(fy(X1))) <=> (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(191,plain,
% 0.19/0.49 (![W3: $i, X1: $i] : ((((((~q(cw)) | (~q(W3))) | (~q(fz(W3)))) | p(cx)) | p(X1)) | p(fy(X1))) <=> ![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[190])).
% 0.19/0.49 tff(192,axiom,(![W3: $i, X1: $i] : ((((((~q(cw)) | (~q(W3))) | (~q(fz(W3)))) | p(cx)) | p(X1)) | p(fy(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_30')).
% 0.19/0.49 tff(193,plain,
% 0.19/0.49 (![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[192, 191])).
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% 0.19/0.49 (![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[193, 189])).
% 0.19/0.49 tff(195,plain,(
% 0.19/0.49 ![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))),
% 0.19/0.49 inference(skolemize,[status(sab)],[194])).
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% 0.19/0.49 inference(modus_ponens,[status(thm)],[195, 188])).
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% 0.19/0.49 (((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | (p(cx) | (~q(cw)) | (~q(cx)) | (~q(fz(cx))) | p(fy(cx)))) <=> ((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | p(cx) | (~q(cw)) | (~q(cx)) | (~q(fz(cx))) | p(fy(cx)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(198,plain,
% 0.19/0.49 ((p(cx) | (~q(cw)) | p(cx) | (~q(cx)) | p(fy(cx)) | (~q(fz(cx)))) <=> (p(cx) | (~q(cw)) | (~q(cx)) | (~q(fz(cx))) | p(fy(cx)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(199,plain,
% 0.19/0.49 (((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | (p(cx) | (~q(cw)) | p(cx) | (~q(cx)) | p(fy(cx)) | (~q(fz(cx))))) <=> ((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | (p(cx) | (~q(cw)) | (~q(cx)) | (~q(fz(cx))) | p(fy(cx))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[198])).
% 0.19/0.49 tff(200,plain,
% 0.19/0.49 (((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | (p(cx) | (~q(cw)) | p(cx) | (~q(cx)) | p(fy(cx)) | (~q(fz(cx))))) <=> ((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | p(cx) | (~q(cw)) | (~q(cx)) | (~q(fz(cx))) | p(fy(cx)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[199, 197])).
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% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(202,plain,
% 0.19/0.49 ((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | p(cx) | (~q(cw)) | (~q(cx)) | (~q(fz(cx))) | p(fy(cx))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[201, 200])).
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% 0.19/0.49 (p(cx) | (~q(cw)) | (~q(cx)) | (~q(fz(cx))) | p(fy(cx))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[202, 196])).
% 0.19/0.49 tff(204,plain,
% 0.19/0.49 (p(fy(cx))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[203, 186, 185, 146, 4])).
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% 0.19/0.49 inference(rewrite,[status(thm)],[])).
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% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
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% 0.19/0.49 ((~![Y4: $i, Z3: $i] : (p(cx) | (~q(cw)) | q(Z3) | (~p(Y4)))) | p(cx) | (~q(cw)) | q(fz5(cx)) | (~p(fy(cx)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[206, 205])).
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% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[207, 101, 4, 186, 147, 204])).
% 0.19/0.49 tff(209,plain,(q(fz5(cx)) | p(cx)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(210,plain,
% 0.19/0.49 (q(fz5(cx))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[209, 4])).
% 0.19/0.49 tff(211,plain,
% 0.19/0.49 (^[Y4: $i, W9: $i] : refl((p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9)))) <=> (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
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% 0.19/0.49 (![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9)))) <=> ![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[211])).
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% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(214,plain,
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% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(215,plain,
% 0.19/0.49 (![Y4: $i, W9: $i] : (((((~p(Y4)) | (~q(cw))) | (~q(W9))) | (~q(fz5(W9)))) | p(cx)) <=> ![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[214])).
% 0.19/0.49 tff(216,axiom,(![Y4: $i, W9: $i] : (((((~p(Y4)) | (~q(cw))) | (~q(W9))) | (~q(fz5(W9)))) | p(cx))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_16')).
% 0.19/0.49 tff(217,plain,
% 0.19/0.49 (![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.19/0.49 tff(218,plain,
% 0.19/0.49 (![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[217, 213])).
% 0.19/0.49 tff(219,plain,(
% 0.19/0.49 ![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))),
% 0.19/0.49 inference(skolemize,[status(sab)],[218])).
% 0.19/0.49 tff(220,plain,
% 0.19/0.49 (![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[219, 212])).
% 0.19/0.49 tff(221,plain,
% 0.19/0.49 (((~![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))) | (p(cx) | (~q(cw)) | (~q(cx)) | (~p(fy5(cx))) | (~q(fz5(cx))))) <=> ((~![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))) | p(cx) | (~q(cw)) | (~q(cx)) | (~p(fy5(cx))) | (~q(fz5(cx))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(222,plain,
% 0.19/0.49 ((~![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))) | (p(cx) | (~q(cw)) | (~q(cx)) | (~p(fy5(cx))) | (~q(fz5(cx))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(223,plain,
% 0.19/0.49 ((~![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))) | p(cx) | (~q(cw)) | (~q(cx)) | (~p(fy5(cx))) | (~q(fz5(cx)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.19/0.49 tff(224,plain,
% 0.19/0.49 (p(cx) | (~q(cw)) | (~q(cx)) | (~p(fy5(cx))) | (~q(fz5(cx)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[223, 220])).
% 0.19/0.49 tff(225,plain,
% 0.19/0.49 (~p(fy5(cx))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[224, 210, 4, 185, 186])).
% 0.19/0.49 tff(226,plain,
% 0.19/0.49 (((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | (p(cx) | (~q(cw)) | (~q(cx)) | p(fy5(cx)) | p(fy(fy5(cx))) | (~q(fz(cx))))) <=> ((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | p(cx) | (~q(cw)) | (~q(cx)) | p(fy5(cx)) | p(fy(fy5(cx))) | (~q(fz(cx))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(227,plain,
% 0.19/0.49 ((p(cx) | (~q(cw)) | p(fy5(cx)) | (~q(cx)) | p(fy(fy5(cx))) | (~q(fz(cx)))) <=> (p(cx) | (~q(cw)) | (~q(cx)) | p(fy5(cx)) | p(fy(fy5(cx))) | (~q(fz(cx))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(228,plain,
% 0.19/0.49 (((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | (p(cx) | (~q(cw)) | p(fy5(cx)) | (~q(cx)) | p(fy(fy5(cx))) | (~q(fz(cx))))) <=> ((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | (p(cx) | (~q(cw)) | (~q(cx)) | p(fy5(cx)) | p(fy(fy5(cx))) | (~q(fz(cx)))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[227])).
% 0.19/0.49 tff(229,plain,
% 0.19/0.49 (((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | (p(cx) | (~q(cw)) | p(fy5(cx)) | (~q(cx)) | p(fy(fy5(cx))) | (~q(fz(cx))))) <=> ((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | p(cx) | (~q(cw)) | (~q(cx)) | p(fy5(cx)) | p(fy(fy5(cx))) | (~q(fz(cx))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[228, 226])).
% 0.19/0.49 tff(230,plain,
% 0.19/0.49 ((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | (p(cx) | (~q(cw)) | p(fy5(cx)) | (~q(cx)) | p(fy(fy5(cx))) | (~q(fz(cx))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(231,plain,
% 0.19/0.49 ((~![W3: $i, X1: $i] : (p(cx) | (~q(cw)) | p(X1) | (~q(W3)) | p(fy(X1)) | (~q(fz(W3))))) | p(cx) | (~q(cw)) | (~q(cx)) | p(fy5(cx)) | p(fy(fy5(cx))) | (~q(fz(cx)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.19/0.49 tff(232,plain,
% 0.19/0.49 (p(cx) | (~q(cw)) | (~q(cx)) | p(fy5(cx)) | p(fy(fy5(cx))) | (~q(fz(cx)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[231, 196])).
% 0.19/0.49 tff(233,plain,
% 0.19/0.49 (p(fy(fy5(cx)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[232, 225, 185, 4, 186, 146])).
% 0.19/0.49 tff(234,plain,
% 0.19/0.49 (((~![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))) | (p(cx) | (~q(cw)) | (~q(cx)) | (~q(fz5(cx))) | (~p(fy(fy5(cx)))))) <=> ((~![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))) | p(cx) | (~q(cw)) | (~q(cx)) | (~q(fz5(cx))) | (~p(fy(fy5(cx)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(235,plain,
% 0.19/0.49 ((p(cx) | (~q(cw)) | (~q(cx)) | (~p(fy(fy5(cx)))) | (~q(fz5(cx)))) <=> (p(cx) | (~q(cw)) | (~q(cx)) | (~q(fz5(cx))) | (~p(fy(fy5(cx)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(236,plain,
% 0.19/0.49 (((~![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))) | (p(cx) | (~q(cw)) | (~q(cx)) | (~p(fy(fy5(cx)))) | (~q(fz5(cx))))) <=> ((~![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))) | (p(cx) | (~q(cw)) | (~q(cx)) | (~q(fz5(cx))) | (~p(fy(fy5(cx))))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[235])).
% 0.19/0.49 tff(237,plain,
% 0.19/0.49 (((~![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))) | (p(cx) | (~q(cw)) | (~q(cx)) | (~p(fy(fy5(cx)))) | (~q(fz5(cx))))) <=> ((~![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))) | p(cx) | (~q(cw)) | (~q(cx)) | (~q(fz5(cx))) | (~p(fy(fy5(cx)))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[236, 234])).
% 0.19/0.49 tff(238,plain,
% 0.19/0.49 ((~![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))) | (p(cx) | (~q(cw)) | (~q(cx)) | (~p(fy(fy5(cx)))) | (~q(fz5(cx))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(239,plain,
% 0.19/0.49 ((~![Y4: $i, W9: $i] : (p(cx) | (~q(cw)) | (~q(W9)) | (~p(Y4)) | (~q(fz5(W9))))) | p(cx) | (~q(cw)) | (~q(cx)) | (~q(fz5(cx))) | (~p(fy(fy5(cx))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.19/0.49 tff(240,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[239, 220, 4, 186, 210, 185, 233])).
% 0.19/0.49 tff(241,plain,(p(cx)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(242,plain,
% 0.19/0.49 (^[X7: $i, Z4: $i] : refl(((~p(cx)) | q(cw) | (~q(Z4)) | (~p(X7)) | (~p(fy5(X7)))) <=> ((~p(cx)) | q(cw) | (~q(Z4)) | (~p(X7)) | (~p(fy5(X7)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(243,plain,
% 0.19/0.49 (![X7: $i, Z4: $i] : ((~p(cx)) | q(cw) | (~q(Z4)) | (~p(X7)) | (~p(fy5(X7)))) <=> ![X7: $i, Z4: $i] : ((~p(cx)) | q(cw) | (~q(Z4)) | (~p(X7)) | (~p(fy5(X7))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[242])).
% 0.19/0.49 tff(244,plain,
% 0.19/0.49 (![X7: $i, Z4: $i] : ((~p(cx)) | q(cw) | (~q(Z4)) | (~p(X7)) | (~p(fy5(X7)))) <=> ![X7: $i, Z4: $i] : ((~p(cx)) | q(cw) | (~q(Z4)) | (~p(X7)) | (~p(fy5(X7))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
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% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(246,plain,
% 0.19/0.50 (![X7: $i, Z4: $i] : (((((~p(cx)) | (~p(X7))) | (~p(fy5(X7)))) | (~q(Z4))) | q(cw)) <=> ![X7: $i, Z4: $i] : ((~p(cx)) | q(cw) | (~q(Z4)) | (~p(X7)) | (~p(fy5(X7))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[245])).
% 0.19/0.50 tff(247,axiom,(![X7: $i, Z4: $i] : (((((~p(cx)) | (~p(X7))) | (~p(fy5(X7)))) | (~q(Z4))) | q(cw))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_6')).
% 0.19/0.50 tff(248,plain,
% 0.19/0.50 (![X7: $i, Z4: $i] : ((~p(cx)) | q(cw) | (~q(Z4)) | (~p(X7)) | (~p(fy5(X7))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.19/0.50 tff(249,plain,
% 0.19/0.50 (![X7: $i, Z4: $i] : ((~p(cx)) | q(cw) | (~q(Z4)) | (~p(X7)) | (~p(fy5(X7))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[248, 244])).
% 0.19/0.50 tff(250,plain,(
% 0.19/0.50 ![X7: $i, Z4: $i] : ((~p(cx)) | q(cw) | (~q(Z4)) | (~p(X7)) | (~p(fy5(X7))))),
% 0.19/0.50 inference(skolemize,[status(sab)],[249])).
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% 0.19/0.50 (![X7: $i, Z4: $i] : ((~p(cx)) | q(cw) | (~q(Z4)) | (~p(X7)) | (~p(fy5(X7))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[250, 243])).
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% 0.19/0.50 inference(rewrite,[status(thm)],[])).
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% 0.19/0.50 (((~p(cx)) | q(cw) | (~q(fz(cx))) | (~p(cx)) | (~p(fy5(cx)))) <=> ((~p(cx)) | q(cw) | (~p(fy5(cx))) | (~q(fz(cx))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
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% 0.19/0.50 (((~![X7: $i, Z4: $i] : ((~p(cx)) | q(cw) | (~q(Z4)) | (~p(X7)) | (~p(fy5(X7))))) | ((~p(cx)) | q(cw) | (~q(fz(cx))) | (~p(cx)) | (~p(fy5(cx))))) <=> ((~![X7: $i, Z4: $i] : ((~p(cx)) | q(cw) | (~q(Z4)) | (~p(X7)) | (~p(fy5(X7))))) | ((~p(cx)) | q(cw) | (~p(fy5(cx))) | (~q(fz(cx)))))),
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% 0.19/0.50 (q(cw) | (~p(fy5(cx))) | (~q(fz(cx)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[257, 251, 241])).
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% 0.19/0.50 (~p(fy5(cx))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[258, 3, 2])).
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% 0.19/0.50 (^[Y3: $i, Z4: $i] : refl(((~p(cx)) | q(cw) | p(Y3) | (~q(Z4))) <=> ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
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% 0.19/0.50 (![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4))) <=> ![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[260])).
% 0.19/0.50 tff(262,plain,
% 0.19/0.50 (![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4))) <=> ![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(263,plain,
% 0.19/0.50 (^[Y3: $i, Z4: $i] : trans(monotonicity(rewrite((((~p(cx)) | (~q(Z4))) | p(Y3)) <=> ((~p(cx)) | p(Y3) | (~q(Z4)))), (((((~p(cx)) | (~q(Z4))) | p(Y3)) | q(cw)) <=> (((~p(cx)) | p(Y3) | (~q(Z4))) | q(cw)))), rewrite((((~p(cx)) | p(Y3) | (~q(Z4))) | q(cw)) <=> ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))), (((((~p(cx)) | (~q(Z4))) | p(Y3)) | q(cw)) <=> ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(264,plain,
% 0.19/0.50 (![Y3: $i, Z4: $i] : ((((~p(cx)) | (~q(Z4))) | p(Y3)) | q(cw)) <=> ![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[263])).
% 0.19/0.50 tff(265,axiom,(![Y3: $i, Z4: $i] : ((((~p(cx)) | (~q(Z4))) | p(Y3)) | q(cw))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_2')).
% 0.19/0.50 tff(266,plain,
% 0.19/0.50 (![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.19/0.50 tff(267,plain,
% 0.19/0.50 (![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[266, 262])).
% 0.19/0.50 tff(268,plain,(
% 0.19/0.50 ![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[267])).
% 0.19/0.50 tff(269,plain,
% 0.19/0.50 (![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[268, 261])).
% 0.19/0.50 tff(270,plain,
% 0.19/0.50 (((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | ((~p(cx)) | q(cw) | p(fy5(cx)) | (~q(fz(cx))))) <=> ((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | (~p(cx)) | q(cw) | p(fy5(cx)) | (~q(fz(cx))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(271,plain,
% 0.19/0.50 ((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | ((~p(cx)) | q(cw) | p(fy5(cx)) | (~q(fz(cx))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(272,plain,
% 0.19/0.50 ((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | (~p(cx)) | q(cw) | p(fy5(cx)) | (~q(fz(cx)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.19/0.50 tff(273,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[272, 269, 241, 2, 259, 3])).
% 0.19/0.50 tff(274,plain,((~q(fz(cx))) | q(cw)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(275,plain,
% 0.19/0.50 (~q(fz(cx))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[274, 2])).
% 0.19/0.50 tff(276,assumption,(~p(fy(cx))), introduced(assumption)).
% 0.19/0.50 tff(277,assumption,(q(elem!0)), introduced(assumption)).
% 0.19/0.50 tff(278,plain,
% 0.19/0.50 (((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | ((~p(cx)) | q(cw) | p(fy(cx)) | (~q(elem!0)))) <=> ((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | (~p(cx)) | q(cw) | p(fy(cx)) | (~q(elem!0)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(279,plain,
% 0.19/0.50 ((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | ((~p(cx)) | q(cw) | p(fy(cx)) | (~q(elem!0)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(280,plain,
% 0.19/0.50 ((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | (~p(cx)) | q(cw) | p(fy(cx)) | (~q(elem!0))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.19/0.50 tff(281,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[280, 269, 241, 2, 277, 276])).
% 0.19/0.50 tff(282,plain,((~q(elem!0)) | q(cw) | p(fy(cx))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(283,plain,
% 0.19/0.50 (~q(elem!0)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[282, 276, 2])).
% 0.19/0.50 tff(284,plain,
% 0.19/0.50 (^[Y1: $i, W3: $i] : refl(((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3))) <=> ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(285,plain,
% 0.19/0.50 (![Y1: $i, W3: $i] : ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3))) <=> ![Y1: $i, W3: $i] : ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[284])).
% 0.19/0.50 tff(286,plain,
% 0.19/0.50 (![Y1: $i, W3: $i] : ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3))) <=> ![Y1: $i, W3: $i] : ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(287,plain,
% 0.19/0.50 (^[Y1: $i, W3: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~p(cx)) | p(Y1)) <=> ((~p(cx)) | p(Y1))), ((((~p(cx)) | p(Y1)) | q(cw)) <=> (((~p(cx)) | p(Y1)) | q(cw)))), rewrite((((~p(cx)) | p(Y1)) | q(cw)) <=> ((~p(cx)) | q(cw) | p(Y1))), ((((~p(cx)) | p(Y1)) | q(cw)) <=> ((~p(cx)) | q(cw) | p(Y1)))), (((((~p(cx)) | p(Y1)) | q(cw)) | q(W3)) <=> (((~p(cx)) | q(cw) | p(Y1)) | q(W3)))), rewrite((((~p(cx)) | q(cw) | p(Y1)) | q(W3)) <=> ((~p(cx)) | q(cw) | p(Y1) | q(W3))), (((((~p(cx)) | p(Y1)) | q(cw)) | q(W3)) <=> ((~p(cx)) | q(cw) | p(Y1) | q(W3)))), ((((((~p(cx)) | p(Y1)) | q(cw)) | q(W3)) | q(fz(W3))) <=> (((~p(cx)) | q(cw) | p(Y1) | q(W3)) | q(fz(W3))))), rewrite((((~p(cx)) | q(cw) | p(Y1) | q(W3)) | q(fz(W3))) <=> ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3)))), ((((((~p(cx)) | p(Y1)) | q(cw)) | q(W3)) | q(fz(W3))) <=> ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3)))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(288,plain,
% 0.19/0.50 (![Y1: $i, W3: $i] : (((((~p(cx)) | p(Y1)) | q(cw)) | q(W3)) | q(fz(W3))) <=> ![Y1: $i, W3: $i] : ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[287])).
% 0.19/0.50 tff(289,axiom,(![Y1: $i, W3: $i] : (((((~p(cx)) | p(Y1)) | q(cw)) | q(W3)) | q(fz(W3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_10')).
% 0.19/0.50 tff(290,plain,
% 0.19/0.50 (![Y1: $i, W3: $i] : ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.19/0.50 tff(291,plain,
% 0.19/0.50 (![Y1: $i, W3: $i] : ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[290, 286])).
% 0.19/0.50 tff(292,plain,(
% 0.19/0.50 ![Y1: $i, W3: $i] : ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[291])).
% 0.19/0.50 tff(293,plain,
% 0.19/0.50 (![Y1: $i, W3: $i] : ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[292, 285])).
% 0.19/0.50 tff(294,plain,
% 0.19/0.50 (((~![Y1: $i, W3: $i] : ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3)))) | ((~p(cx)) | q(cw) | p(fy(elem!0)) | q(cx) | q(fz(cx)))) <=> ((~![Y1: $i, W3: $i] : ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3)))) | (~p(cx)) | q(cw) | p(fy(elem!0)) | q(cx) | q(fz(cx)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(295,plain,
% 0.19/0.50 ((~![Y1: $i, W3: $i] : ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3)))) | ((~p(cx)) | q(cw) | p(fy(elem!0)) | q(cx) | q(fz(cx)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(296,plain,
% 0.19/0.50 ((~![Y1: $i, W3: $i] : ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3)))) | (~p(cx)) | q(cw) | p(fy(elem!0)) | q(cx) | q(fz(cx))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.19/0.50 tff(297,plain,
% 0.19/0.50 (q(cw) | p(fy(elem!0)) | q(cx) | q(fz(cx))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[296, 293, 241])).
% 0.19/0.50 tff(298,plain,
% 0.19/0.50 (p(fy(elem!0))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[297, 5, 2, 6])).
% 0.19/0.50 tff(299,plain,
% 0.19/0.50 (^[W3: $i, X1: $i] : refl(((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1)))) <=> ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1)))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(300,plain,
% 0.19/0.50 (![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1)))) <=> ![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[299])).
% 0.19/0.50 tff(301,plain,
% 0.19/0.50 (![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1)))) <=> ![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(302,plain,
% 0.19/0.50 (^[W3: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~p(cx)) | (~p(X1))) | (~p(fy(X1)))) <=> ((~p(cx)) | (~p(X1)) | (~p(fy(X1))))), (((((~p(cx)) | (~p(X1))) | (~p(fy(X1)))) | q(cw)) <=> (((~p(cx)) | (~p(X1)) | (~p(fy(X1)))) | q(cw)))), rewrite((((~p(cx)) | (~p(X1)) | (~p(fy(X1)))) | q(cw)) <=> ((~p(cx)) | q(cw) | (~p(X1)) | (~p(fy(X1))))), (((((~p(cx)) | (~p(X1))) | (~p(fy(X1)))) | q(cw)) <=> ((~p(cx)) | q(cw) | (~p(X1)) | (~p(fy(X1)))))), ((((((~p(cx)) | (~p(X1))) | (~p(fy(X1)))) | q(cw)) | q(W3)) <=> (((~p(cx)) | q(cw) | (~p(X1)) | (~p(fy(X1)))) | q(W3)))), rewrite((((~p(cx)) | q(cw) | (~p(X1)) | (~p(fy(X1)))) | q(W3)) <=> ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | (~p(fy(X1))))), ((((((~p(cx)) | (~p(X1))) | (~p(fy(X1)))) | q(cw)) | q(W3)) <=> ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | (~p(fy(X1)))))), (((((((~p(cx)) | (~p(X1))) | (~p(fy(X1)))) | q(cw)) | q(W3)) | q(fz(W3))) <=> (((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | (~p(fy(X1)))) | q(fz(W3))))), rewrite((((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | (~p(fy(X1)))) | q(fz(W3))) <=> ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))), (((((((~p(cx)) | (~p(X1))) | (~p(fy(X1)))) | q(cw)) | q(W3)) | q(fz(W3))) <=> ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(303,plain,
% 0.19/0.50 (![W3: $i, X1: $i] : ((((((~p(cx)) | (~p(X1))) | (~p(fy(X1)))) | q(cw)) | q(W3)) | q(fz(W3))) <=> ![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[302])).
% 0.19/0.50 tff(304,axiom,(![W3: $i, X1: $i] : ((((((~p(cx)) | (~p(X1))) | (~p(fy(X1)))) | q(cw)) | q(W3)) | q(fz(W3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_22')).
% 0.19/0.50 tff(305,plain,
% 0.19/0.50 (![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.19/0.50 tff(306,plain,
% 0.19/0.50 (![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[305, 301])).
% 0.19/0.50 tff(307,plain,(
% 0.19/0.50 ![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))),
% 0.19/0.50 inference(skolemize,[status(sab)],[306])).
% 0.19/0.50 tff(308,plain,
% 0.19/0.50 (![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[307, 300])).
% 0.19/0.50 tff(309,plain,
% 0.19/0.50 (((~![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))) | ((~p(cx)) | q(cw) | (~p(fy(elem!0))) | q(cx) | q(fz(cx)) | (~p(fy(fy(elem!0)))))) <=> ((~![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))) | (~p(cx)) | q(cw) | (~p(fy(elem!0))) | q(cx) | q(fz(cx)) | (~p(fy(fy(elem!0)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(310,plain,
% 0.19/0.50 (((~p(cx)) | q(cw) | q(cx) | (~p(fy(elem!0))) | q(fz(cx)) | (~p(fy(fy(elem!0))))) <=> ((~p(cx)) | q(cw) | (~p(fy(elem!0))) | q(cx) | q(fz(cx)) | (~p(fy(fy(elem!0)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(311,plain,
% 0.19/0.50 (((~![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))) | ((~p(cx)) | q(cw) | q(cx) | (~p(fy(elem!0))) | q(fz(cx)) | (~p(fy(fy(elem!0)))))) <=> ((~![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))) | ((~p(cx)) | q(cw) | (~p(fy(elem!0))) | q(cx) | q(fz(cx)) | (~p(fy(fy(elem!0))))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[310])).
% 0.19/0.50 tff(312,plain,
% 0.19/0.50 (((~![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))) | ((~p(cx)) | q(cw) | q(cx) | (~p(fy(elem!0))) | q(fz(cx)) | (~p(fy(fy(elem!0)))))) <=> ((~![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))) | (~p(cx)) | q(cw) | (~p(fy(elem!0))) | q(cx) | q(fz(cx)) | (~p(fy(fy(elem!0)))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[311, 309])).
% 0.19/0.50 tff(313,plain,
% 0.19/0.50 ((~![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))) | ((~p(cx)) | q(cw) | q(cx) | (~p(fy(elem!0))) | q(fz(cx)) | (~p(fy(fy(elem!0)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(314,plain,
% 0.19/0.50 ((~![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))) | (~p(cx)) | q(cw) | (~p(fy(elem!0))) | q(cx) | q(fz(cx)) | (~p(fy(fy(elem!0))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.19/0.50 tff(315,plain,
% 0.19/0.50 (q(cw) | (~p(fy(elem!0))) | q(cx) | q(fz(cx)) | (~p(fy(fy(elem!0))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[314, 308, 241])).
% 0.19/0.50 tff(316,plain,
% 0.19/0.50 (~p(fy(fy(elem!0)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[315, 298, 2, 6, 5])).
% 0.19/0.50 tff(317,plain,
% 0.19/0.50 (((~![Y1: $i, W3: $i] : ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3)))) | ((~p(cx)) | q(cw) | p(elem!0) | q(cx) | q(fz(cx)))) <=> ((~![Y1: $i, W3: $i] : ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3)))) | (~p(cx)) | q(cw) | p(elem!0) | q(cx) | q(fz(cx)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(318,plain,
% 0.19/0.50 ((~![Y1: $i, W3: $i] : ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3)))) | ((~p(cx)) | q(cw) | p(elem!0) | q(cx) | q(fz(cx)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(319,plain,
% 0.19/0.50 ((~![Y1: $i, W3: $i] : ((~p(cx)) | q(cw) | p(Y1) | q(W3) | q(fz(W3)))) | (~p(cx)) | q(cw) | p(elem!0) | q(cx) | q(fz(cx))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.19/0.50 tff(320,plain,
% 0.19/0.50 (q(cw) | p(elem!0) | q(cx) | q(fz(cx))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[319, 293, 241])).
% 0.19/0.50 tff(321,plain,
% 0.19/0.50 (p(elem!0)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[320, 5, 2, 6])).
% 0.19/0.50 tff(322,assumption,(~q(elem!0)), introduced(assumption)).
% 0.19/0.50 tff(323,plain,
% 0.19/0.50 (((~![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))) | ((~p(cx)) | q(cw) | q(elem!0) | (~p(elem!0)) | (~p(fy(elem!0))) | q(fz(elem!0)))) <=> ((~![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))) | (~p(cx)) | q(cw) | q(elem!0) | (~p(elem!0)) | (~p(fy(elem!0))) | q(fz(elem!0)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(324,plain,
% 0.19/0.50 (((~p(cx)) | q(cw) | q(elem!0) | (~p(elem!0)) | q(fz(elem!0)) | (~p(fy(elem!0)))) <=> ((~p(cx)) | q(cw) | q(elem!0) | (~p(elem!0)) | (~p(fy(elem!0))) | q(fz(elem!0)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(325,plain,
% 0.19/0.50 (((~![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))) | ((~p(cx)) | q(cw) | q(elem!0) | (~p(elem!0)) | q(fz(elem!0)) | (~p(fy(elem!0))))) <=> ((~![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))) | ((~p(cx)) | q(cw) | q(elem!0) | (~p(elem!0)) | (~p(fy(elem!0))) | q(fz(elem!0))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[324])).
% 0.19/0.50 tff(326,plain,
% 0.19/0.50 (((~![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))) | ((~p(cx)) | q(cw) | q(elem!0) | (~p(elem!0)) | q(fz(elem!0)) | (~p(fy(elem!0))))) <=> ((~![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))) | (~p(cx)) | q(cw) | q(elem!0) | (~p(elem!0)) | (~p(fy(elem!0))) | q(fz(elem!0)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[325, 323])).
% 0.19/0.50 tff(327,plain,
% 0.19/0.50 ((~![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))) | ((~p(cx)) | q(cw) | q(elem!0) | (~p(elem!0)) | q(fz(elem!0)) | (~p(fy(elem!0))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(328,plain,
% 0.19/0.50 ((~![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))) | (~p(cx)) | q(cw) | q(elem!0) | (~p(elem!0)) | (~p(fy(elem!0))) | q(fz(elem!0))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.19/0.50 tff(329,plain,
% 0.19/0.50 ((~p(cx)) | q(cw) | q(elem!0) | (~p(elem!0)) | (~p(fy(elem!0))) | q(fz(elem!0))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[328, 308])).
% 0.19/0.50 tff(330,plain,
% 0.19/0.50 (q(cw) | q(elem!0) | (~p(elem!0)) | (~p(fy(elem!0))) | q(fz(elem!0))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[329, 241])).
% 0.19/0.50 tff(331,plain,
% 0.19/0.50 (q(fz(elem!0))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[330, 298, 2, 322, 321])).
% 0.19/0.50 tff(332,plain,
% 0.19/0.50 (((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | ((~p(cx)) | q(cw) | p(fy(fy(elem!0))) | (~q(fz(elem!0))))) <=> ((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | (~p(cx)) | q(cw) | p(fy(fy(elem!0))) | (~q(fz(elem!0))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(333,plain,
% 0.19/0.50 ((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | ((~p(cx)) | q(cw) | p(fy(fy(elem!0))) | (~q(fz(elem!0))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(334,plain,
% 0.19/0.50 ((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | (~p(cx)) | q(cw) | p(fy(fy(elem!0))) | (~q(fz(elem!0)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[333, 332])).
% 0.19/0.50 tff(335,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[334, 269, 241, 2, 331, 316])).
% 0.19/0.50 tff(336,plain,(q(fz(cx)) | q(cw) | q(elem!0) | q(cx)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(337,plain,
% 0.19/0.51 (q(fz(cx))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[336, 283, 2, 6])).
% 0.19/0.51 tff(338,plain,
% 0.19/0.51 (((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | ((~p(cx)) | q(cw) | (~q(fz(cx))) | p(fy(cx)))) <=> ((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | (~p(cx)) | q(cw) | (~q(fz(cx))) | p(fy(cx)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(339,plain,
% 0.19/0.51 (((~p(cx)) | q(cw) | p(fy(cx)) | (~q(fz(cx)))) <=> ((~p(cx)) | q(cw) | (~q(fz(cx))) | p(fy(cx)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(340,plain,
% 0.19/0.51 (((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | ((~p(cx)) | q(cw) | p(fy(cx)) | (~q(fz(cx))))) <=> ((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | ((~p(cx)) | q(cw) | (~q(fz(cx))) | p(fy(cx))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[339])).
% 0.19/0.51 tff(341,plain,
% 0.19/0.51 (((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | ((~p(cx)) | q(cw) | p(fy(cx)) | (~q(fz(cx))))) <=> ((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | (~p(cx)) | q(cw) | (~q(fz(cx))) | p(fy(cx)))),
% 0.19/0.51 inference(transitivity,[status(thm)],[340, 338])).
% 0.19/0.51 tff(342,plain,
% 0.19/0.51 ((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | ((~p(cx)) | q(cw) | p(fy(cx)) | (~q(fz(cx))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(343,plain,
% 0.19/0.51 ((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | (~p(cx)) | q(cw) | (~q(fz(cx))) | p(fy(cx))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[342, 341])).
% 0.19/0.51 tff(344,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[343, 269, 241, 2, 337, 276])).
% 0.19/0.51 tff(345,plain,(p(fy(cx)) | q(cw) | q(cx)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(346,plain,
% 0.19/0.51 (p(fy(cx))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[345, 6, 2])).
% 0.19/0.51 tff(347,plain,
% 0.19/0.51 (((~![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))) | ((~p(cx)) | q(cw) | q(cx) | q(fz(cx)) | (~p(fy(cx))))) <=> ((~![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))) | (~p(cx)) | q(cw) | q(cx) | q(fz(cx)) | (~p(fy(cx))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(348,plain,
% 0.19/0.51 (((~p(cx)) | q(cw) | q(cx) | (~p(cx)) | q(fz(cx)) | (~p(fy(cx)))) <=> ((~p(cx)) | q(cw) | q(cx) | q(fz(cx)) | (~p(fy(cx))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(349,plain,
% 0.19/0.51 (((~![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))) | ((~p(cx)) | q(cw) | q(cx) | (~p(cx)) | q(fz(cx)) | (~p(fy(cx))))) <=> ((~![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))) | ((~p(cx)) | q(cw) | q(cx) | q(fz(cx)) | (~p(fy(cx)))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[348])).
% 0.19/0.51 tff(350,plain,
% 0.19/0.51 (((~![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))) | ((~p(cx)) | q(cw) | q(cx) | (~p(cx)) | q(fz(cx)) | (~p(fy(cx))))) <=> ((~![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))) | (~p(cx)) | q(cw) | q(cx) | q(fz(cx)) | (~p(fy(cx))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[349, 347])).
% 0.19/0.51 tff(351,plain,
% 0.19/0.51 ((~![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))) | ((~p(cx)) | q(cw) | q(cx) | (~p(cx)) | q(fz(cx)) | (~p(fy(cx))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(352,plain,
% 0.19/0.51 ((~![W3: $i, X1: $i] : ((~p(cx)) | q(cw) | q(W3) | (~p(X1)) | q(fz(W3)) | (~p(fy(X1))))) | (~p(cx)) | q(cw) | q(cx) | q(fz(cx)) | (~p(fy(cx)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[351, 350])).
% 0.19/0.51 tff(353,plain,
% 0.19/0.51 (q(cw) | q(cx) | q(fz(cx)) | (~p(fy(cx)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[352, 308, 241])).
% 0.19/0.51 tff(354,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[353, 346, 6, 2, 5])).
% 0.19/0.51 tff(355,plain,(q(cx) | q(cw) | q(fz(cx))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(356,plain,
% 0.19/0.51 (q(cx)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[355, 275, 2])).
% 0.19/0.51 tff(357,plain,
% 0.19/0.51 (((~![X7: $i, Z4: $i] : ((~p(cx)) | q(cw) | (~q(Z4)) | (~p(X7)) | (~p(fy5(X7))))) | ((~p(cx)) | q(cw) | (~q(cx)) | (~p(fy5(cx))))) <=> ((~![X7: $i, Z4: $i] : ((~p(cx)) | q(cw) | (~q(Z4)) | (~p(X7)) | (~p(fy5(X7))))) | (~p(cx)) | q(cw) | (~q(cx)) | (~p(fy5(cx))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(358,plain,
% 0.19/0.51 (((~p(cx)) | q(cw) | (~q(cx)) | (~p(cx)) | (~p(fy5(cx)))) <=> ((~p(cx)) | q(cw) | (~q(cx)) | (~p(fy5(cx))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(359,plain,
% 0.19/0.51 (((~![X7: $i, Z4: $i] : ((~p(cx)) | q(cw) | (~q(Z4)) | (~p(X7)) | (~p(fy5(X7))))) | ((~p(cx)) | q(cw) | (~q(cx)) | (~p(cx)) | (~p(fy5(cx))))) <=> ((~![X7: $i, Z4: $i] : ((~p(cx)) | q(cw) | (~q(Z4)) | (~p(X7)) | (~p(fy5(X7))))) | ((~p(cx)) | q(cw) | (~q(cx)) | (~p(fy5(cx)))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[358])).
% 0.19/0.51 tff(360,plain,
% 0.19/0.51 (((~![X7: $i, Z4: $i] : ((~p(cx)) | q(cw) | (~q(Z4)) | (~p(X7)) | (~p(fy5(X7))))) | ((~p(cx)) | q(cw) | (~q(cx)) | (~p(cx)) | (~p(fy5(cx))))) <=> ((~![X7: $i, Z4: $i] : ((~p(cx)) | q(cw) | (~q(Z4)) | (~p(X7)) | (~p(fy5(X7))))) | (~p(cx)) | q(cw) | (~q(cx)) | (~p(fy5(cx))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[359, 357])).
% 0.19/0.51 tff(361,plain,
% 0.19/0.51 ((~![X7: $i, Z4: $i] : ((~p(cx)) | q(cw) | (~q(Z4)) | (~p(X7)) | (~p(fy5(X7))))) | ((~p(cx)) | q(cw) | (~q(cx)) | (~p(cx)) | (~p(fy5(cx))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(362,plain,
% 0.19/0.51 ((~![X7: $i, Z4: $i] : ((~p(cx)) | q(cw) | (~q(Z4)) | (~p(X7)) | (~p(fy5(X7))))) | (~p(cx)) | q(cw) | (~q(cx)) | (~p(fy5(cx)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[361, 360])).
% 0.19/0.51 tff(363,plain,
% 0.19/0.51 (q(cw) | (~q(cx)) | (~p(fy5(cx)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[362, 251, 241])).
% 0.19/0.51 tff(364,plain,
% 0.19/0.51 (~p(fy5(cx))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[363, 356, 2])).
% 0.19/0.51 tff(365,plain,
% 0.19/0.51 (((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | ((~p(cx)) | q(cw) | (~q(cx)) | p(fy5(cx)))) <=> ((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | (~p(cx)) | q(cw) | (~q(cx)) | p(fy5(cx)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(366,plain,
% 0.19/0.51 (((~p(cx)) | q(cw) | p(fy5(cx)) | (~q(cx))) <=> ((~p(cx)) | q(cw) | (~q(cx)) | p(fy5(cx)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(367,plain,
% 0.19/0.51 (((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | ((~p(cx)) | q(cw) | p(fy5(cx)) | (~q(cx)))) <=> ((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | ((~p(cx)) | q(cw) | (~q(cx)) | p(fy5(cx))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[366])).
% 0.19/0.51 tff(368,plain,
% 0.19/0.51 (((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | ((~p(cx)) | q(cw) | p(fy5(cx)) | (~q(cx)))) <=> ((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | (~p(cx)) | q(cw) | (~q(cx)) | p(fy5(cx)))),
% 0.19/0.51 inference(transitivity,[status(thm)],[367, 365])).
% 0.19/0.51 tff(369,plain,
% 0.19/0.51 ((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | ((~p(cx)) | q(cw) | p(fy5(cx)) | (~q(cx)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(370,plain,
% 0.19/0.51 ((~![Y3: $i, Z4: $i] : ((~p(cx)) | q(cw) | p(Y3) | (~q(Z4)))) | (~p(cx)) | q(cw) | (~q(cx)) | p(fy5(cx))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[369, 368])).
% 0.19/0.51 tff(371,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[370, 269, 241, 2, 356, 364])).
% 0.19/0.51 tff(372,plain,(q(cw)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(373,plain,
% 0.19/0.51 (^[W9: $i, Y3: $i] : refl(((~p(cx)) | (~q(cw)) | p(Y3) | (~q(fz5(W9))) | (~q(W9))) <=> ((~p(cx)) | (~q(cw)) | p(Y3) | (~q(fz5(W9))) | (~q(W9))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(374,plain,
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% 0.19/0.51 inference(quant_intro,[status(thm)],[394])).
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% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(421,plain,
% 0.19/0.51 (((~![W9: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)) | (~q(fz5(W9))) | (~q(W9)))) | ((~p(cx)) | (~q(cw)) | (~p(fy5(cx))) | (~p(cx)) | (~q(fz5(cw))) | (~q(cw)))) <=> ((~![W9: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)) | (~q(fz5(W9))) | (~q(W9)))) | ((~p(cx)) | (~q(cw)) | (~p(fy5(cx))) | (~q(fz5(cw)))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[420])).
% 0.19/0.51 tff(422,plain,
% 0.19/0.51 (((~![W9: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)) | (~q(fz5(W9))) | (~q(W9)))) | ((~p(cx)) | (~q(cw)) | (~p(fy5(cx))) | (~p(cx)) | (~q(fz5(cw))) | (~q(cw)))) <=> ((~![W9: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)) | (~q(fz5(W9))) | (~q(W9)))) | (~p(cx)) | (~q(cw)) | (~p(fy5(cx))) | (~q(fz5(cw))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[421, 419])).
% 0.19/0.51 tff(423,plain,
% 0.19/0.51 ((~![W9: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)) | (~q(fz5(W9))) | (~q(W9)))) | ((~p(cx)) | (~q(cw)) | (~p(fy5(cx))) | (~p(cx)) | (~q(fz5(cw))) | (~q(cw)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(424,plain,
% 0.19/0.51 ((~![W9: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)) | (~q(fz5(W9))) | (~q(W9)))) | (~p(cx)) | (~q(cw)) | (~p(fy5(cx))) | (~q(fz5(cw)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[423, 422])).
% 0.19/0.52 tff(425,plain,
% 0.19/0.52 ((~p(fy5(cx))) | (~q(fz5(cw)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[424, 418, 241, 372])).
% 0.19/0.52 tff(426,plain,
% 0.19/0.52 (~q(fz5(cw))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[425, 408])).
% 0.19/0.52 tff(427,plain,
% 0.19/0.52 (^[Z3: $i, X7: $i] : refl(((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7))) <=> ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(428,plain,
% 0.19/0.52 (![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7))) <=> ![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[427])).
% 0.19/0.52 tff(429,plain,
% 0.19/0.52 (![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7))) <=> ![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(430,plain,
% 0.19/0.52 (^[Z3: $i, X7: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~p(cx)) | (~p(X7))) | (~p(fy5(X7)))) <=> ((~p(cx)) | (~p(fy5(X7))) | (~p(X7)))), (((((~p(cx)) | (~p(X7))) | (~p(fy5(X7)))) | (~q(cw))) <=> (((~p(cx)) | (~p(fy5(X7))) | (~p(X7))) | (~q(cw))))), rewrite((((~p(cx)) | (~p(fy5(X7))) | (~p(X7))) | (~q(cw))) <=> ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7)))), (((((~p(cx)) | (~p(X7))) | (~p(fy5(X7)))) | (~q(cw))) <=> ((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7))))), ((((((~p(cx)) | (~p(X7))) | (~p(fy5(X7)))) | (~q(cw))) | q(Z3)) <=> (((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7))) | q(Z3)))), rewrite((((~p(cx)) | (~q(cw)) | (~p(fy5(X7))) | (~p(X7))) | q(Z3)) <=> ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))), ((((((~p(cx)) | (~p(X7))) | (~p(fy5(X7)))) | (~q(cw))) | q(Z3)) <=> ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(431,plain,
% 0.19/0.52 (![Z3: $i, X7: $i] : (((((~p(cx)) | (~p(X7))) | (~p(fy5(X7)))) | (~q(cw))) | q(Z3)) <=> ![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[430])).
% 0.19/0.52 tff(432,axiom,(![Z3: $i, X7: $i] : (((((~p(cx)) | (~p(X7))) | (~p(fy5(X7)))) | (~q(cw))) | q(Z3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_5')).
% 0.19/0.52 tff(433,plain,
% 0.19/0.52 (![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[432, 431])).
% 0.19/0.52 tff(434,plain,
% 0.19/0.52 (![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[433, 429])).
% 0.19/0.52 tff(435,plain,(
% 0.19/0.52 ![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))),
% 0.19/0.52 inference(skolemize,[status(sab)],[434])).
% 0.19/0.52 tff(436,plain,
% 0.19/0.52 (![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[435, 428])).
% 0.19/0.52 tff(437,plain,
% 0.19/0.52 (((~![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))) | ((~p(cx)) | (~q(cw)) | (~p(fy5(cx))) | q(fz5(cw)))) <=> ((~![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))) | (~p(cx)) | (~q(cw)) | (~p(fy5(cx))) | q(fz5(cw)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(438,plain,
% 0.19/0.52 (((~p(cx)) | (~q(cw)) | q(fz5(cw)) | (~p(fy5(cx))) | (~p(cx))) <=> ((~p(cx)) | (~q(cw)) | (~p(fy5(cx))) | q(fz5(cw)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(439,plain,
% 0.19/0.52 (((~![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))) | ((~p(cx)) | (~q(cw)) | q(fz5(cw)) | (~p(fy5(cx))) | (~p(cx)))) <=> ((~![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))) | ((~p(cx)) | (~q(cw)) | (~p(fy5(cx))) | q(fz5(cw))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[438])).
% 0.19/0.52 tff(440,plain,
% 0.19/0.52 (((~![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))) | ((~p(cx)) | (~q(cw)) | q(fz5(cw)) | (~p(fy5(cx))) | (~p(cx)))) <=> ((~![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))) | (~p(cx)) | (~q(cw)) | (~p(fy5(cx))) | q(fz5(cw)))),
% 0.19/0.52 inference(transitivity,[status(thm)],[439, 437])).
% 0.19/0.52 tff(441,plain,
% 0.19/0.52 ((~![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))) | ((~p(cx)) | (~q(cw)) | q(fz5(cw)) | (~p(fy5(cx))) | (~p(cx)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(442,plain,
% 0.19/0.52 ((~![Z3: $i, X7: $i] : ((~p(cx)) | (~q(cw)) | q(Z3) | (~p(fy5(X7))) | (~p(X7)))) | (~p(cx)) | (~q(cw)) | (~p(fy5(cx))) | q(fz5(cw))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[441, 440])).
% 0.19/0.52 tff(443,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[442, 436, 241, 372, 408, 426])).
% 0.19/0.52 % SZS output end Proof
% 0.19/0.52 % E exiting
%------------------------------------------------------------------------------