%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN038-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 0.18s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN038-1 : TPTP v9.0.0. Released v1.0.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:26:47 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.18/0.40 % SZS status Unsatisfiable
% 0.18/0.40 % SZS output start Proof
% 0.18/0.40 tff(q_type, type, (
% 0.18/0.40 q: ( $i * $i ) > $o)).
% 0.18/0.40 tff(f_type, type, (
% 0.18/0.40 f: ( $i * $i ) > $i)).
% 0.18/0.40 tff(elem_0_type, type, (
% 0.18/0.40 elem_0: $i)).
% 0.18/0.40 tff(p_type, type, (
% 0.18/0.40 p: ( $i * $i ) > $o)).
% 0.18/0.40 tff(1,assumption,(~q(f(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))), f(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))))), introduced(assumption)).
% 0.18/0.40 tff(2,assumption,(p(elem!0, elem!0)), introduced(assumption)).
% 0.18/0.40 tff(3,assumption,(~q(elem!0, f(elem!0, elem!0))), introduced(assumption)).
% 0.18/0.40 tff(4,plain,
% 0.18/0.40 (^[Y: $i, X: $i] : refl((q(Y, f(X, Y)) | (~p(X, Y)) | (~p(X, f(X, Y)))) <=> (q(Y, f(X, Y)) | (~p(X, Y)) | (~p(X, f(X, Y)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(5,plain,
% 0.18/0.40 (![Y: $i, X: $i] : (q(Y, f(X, Y)) | (~p(X, Y)) | (~p(X, f(X, Y)))) <=> ![Y: $i, X: $i] : (q(Y, f(X, Y)) | (~p(X, Y)) | (~p(X, f(X, Y))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[4])).
% 0.18/0.40 tff(6,plain,
% 0.18/0.40 (![Y: $i, X: $i] : (q(Y, f(X, Y)) | (~p(X, Y)) | (~p(X, f(X, Y)))) <=> ![Y: $i, X: $i] : (q(Y, f(X, Y)) | (~p(X, Y)) | (~p(X, f(X, Y))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(7,plain,
% 0.18/0.40 (^[Y: $i, X: $i] : trans(monotonicity(rewrite(((~p(X, f(X, Y))) | (~p(X, Y))) <=> ((~p(X, Y)) | (~p(X, f(X, Y))))), ((((~p(X, f(X, Y))) | (~p(X, Y))) | q(Y, f(X, Y))) <=> (((~p(X, Y)) | (~p(X, f(X, Y)))) | q(Y, f(X, Y))))), rewrite((((~p(X, Y)) | (~p(X, f(X, Y)))) | q(Y, f(X, Y))) <=> (q(Y, f(X, Y)) | (~p(X, Y)) | (~p(X, f(X, Y))))), ((((~p(X, f(X, Y))) | (~p(X, Y))) | q(Y, f(X, Y))) <=> (q(Y, f(X, Y)) | (~p(X, Y)) | (~p(X, f(X, Y))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(8,plain,
% 0.18/0.40 (![Y: $i, X: $i] : (((~p(X, f(X, Y))) | (~p(X, Y))) | q(Y, f(X, Y))) <=> ![Y: $i, X: $i] : (q(Y, f(X, Y)) | (~p(X, Y)) | (~p(X, f(X, Y))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[7])).
% 0.18/0.40 tff(9,axiom,(![Y: $i, X: $i] : (((~p(X, f(X, Y))) | (~p(X, Y))) | q(Y, f(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_1')).
% 0.18/0.40 tff(10,plain,
% 0.18/0.40 (![Y: $i, X: $i] : (q(Y, f(X, Y)) | (~p(X, Y)) | (~p(X, f(X, Y))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.18/0.40 tff(11,plain,
% 0.18/0.40 (![Y: $i, X: $i] : (q(Y, f(X, Y)) | (~p(X, Y)) | (~p(X, f(X, Y))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.18/0.40 tff(12,plain,(
% 0.18/0.40 ![Y: $i, X: $i] : (q(Y, f(X, Y)) | (~p(X, Y)) | (~p(X, f(X, Y))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[11])).
% 0.18/0.40 tff(13,plain,
% 0.18/0.40 (![Y: $i, X: $i] : (q(Y, f(X, Y)) | (~p(X, Y)) | (~p(X, f(X, Y))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.18/0.40 tff(14,plain,
% 0.18/0.40 (((~![Y: $i, X: $i] : (q(Y, f(X, Y)) | (~p(X, Y)) | (~p(X, f(X, Y))))) | ((~p(elem!0, elem!0)) | (~p(elem!0, f(elem!0, elem!0))) | q(elem!0, f(elem!0, elem!0)))) <=> ((~![Y: $i, X: $i] : (q(Y, f(X, Y)) | (~p(X, Y)) | (~p(X, f(X, Y))))) | (~p(elem!0, elem!0)) | (~p(elem!0, f(elem!0, elem!0))) | q(elem!0, f(elem!0, elem!0)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(15,plain,
% 0.18/0.40 ((q(elem!0, f(elem!0, elem!0)) | (~p(elem!0, elem!0)) | (~p(elem!0, f(elem!0, elem!0)))) <=> ((~p(elem!0, elem!0)) | (~p(elem!0, f(elem!0, elem!0))) | q(elem!0, f(elem!0, elem!0)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(16,plain,
% 0.18/0.40 (((~![Y: $i, X: $i] : (q(Y, f(X, Y)) | (~p(X, Y)) | (~p(X, f(X, Y))))) | (q(elem!0, f(elem!0, elem!0)) | (~p(elem!0, elem!0)) | (~p(elem!0, f(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : (q(Y, f(X, Y)) | (~p(X, Y)) | (~p(X, f(X, Y))))) | ((~p(elem!0, elem!0)) | (~p(elem!0, f(elem!0, elem!0))) | q(elem!0, f(elem!0, elem!0))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[15])).
% 0.18/0.40 tff(17,plain,
% 0.18/0.40 (((~![Y: $i, X: $i] : (q(Y, f(X, Y)) | (~p(X, Y)) | (~p(X, f(X, Y))))) | (q(elem!0, f(elem!0, elem!0)) | (~p(elem!0, elem!0)) | (~p(elem!0, f(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : (q(Y, f(X, Y)) | (~p(X, Y)) | (~p(X, f(X, Y))))) | (~p(elem!0, elem!0)) | (~p(elem!0, f(elem!0, elem!0))) | q(elem!0, f(elem!0, elem!0)))),
% 0.18/0.40 inference(transitivity,[status(thm)],[16, 14])).
% 0.18/0.40 tff(18,plain,
% 0.18/0.40 ((~![Y: $i, X: $i] : (q(Y, f(X, Y)) | (~p(X, Y)) | (~p(X, f(X, Y))))) | (q(elem!0, f(elem!0, elem!0)) | (~p(elem!0, elem!0)) | (~p(elem!0, f(elem!0, elem!0))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(19,plain,
% 0.18/0.40 ((~![Y: $i, X: $i] : (q(Y, f(X, Y)) | (~p(X, Y)) | (~p(X, f(X, Y))))) | (~p(elem!0, elem!0)) | (~p(elem!0, f(elem!0, elem!0))) | q(elem!0, f(elem!0, elem!0))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.18/0.40 tff(20,plain,
% 0.18/0.40 ((~p(elem!0, f(elem!0, elem!0))) | q(elem!0, f(elem!0, elem!0))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[19, 13, 2])).
% 0.18/0.40 tff(21,plain,
% 0.18/0.40 (~p(elem!0, f(elem!0, elem!0))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[20, 3])).
% 0.18/0.40 tff(22,plain,
% 0.18/0.40 (^[Y: $i, X: $i] : refl((q(X, Y) | q(f(X, Y), f(X, Y))) <=> (q(X, Y) | q(f(X, Y), f(X, Y))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(23,plain,
% 0.18/0.40 (![Y: $i, X: $i] : (q(X, Y) | q(f(X, Y), f(X, Y))) <=> ![Y: $i, X: $i] : (q(X, Y) | q(f(X, Y), f(X, Y)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[22])).
% 0.18/0.40 tff(24,plain,
% 0.18/0.40 (![Y: $i, X: $i] : (q(X, Y) | q(f(X, Y), f(X, Y))) <=> ![Y: $i, X: $i] : (q(X, Y) | q(f(X, Y), f(X, Y)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(25,axiom,(![Y: $i, X: $i] : (q(X, Y) | q(f(X, Y), f(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_6')).
% 0.18/0.40 tff(26,plain,
% 0.18/0.40 (![Y: $i, X: $i] : (q(X, Y) | q(f(X, Y), f(X, Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.18/0.40 tff(27,plain,(
% 0.18/0.40 ![Y: $i, X: $i] : (q(X, Y) | q(f(X, Y), f(X, Y)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[26])).
% 0.18/0.40 tff(28,plain,
% 0.18/0.40 (![Y: $i, X: $i] : (q(X, Y) | q(f(X, Y), f(X, Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.18/0.40 tff(29,plain,
% 0.18/0.40 (((~![Y: $i, X: $i] : (q(X, Y) | q(f(X, Y), f(X, Y)))) | (q(elem!0, f(elem!0, elem!0)) | q(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : (q(X, Y) | q(f(X, Y), f(X, Y)))) | q(elem!0, f(elem!0, elem!0)) | q(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(30,plain,
% 0.18/0.40 ((~![Y: $i, X: $i] : (q(X, Y) | q(f(X, Y), f(X, Y)))) | (q(elem!0, f(elem!0, elem!0)) | q(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(31,plain,
% 0.18/0.40 ((~![Y: $i, X: $i] : (q(X, Y) | q(f(X, Y), f(X, Y)))) | q(elem!0, f(elem!0, elem!0)) | q(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.18/0.40 tff(32,plain,
% 0.18/0.40 (q(elem!0, f(elem!0, elem!0)) | q(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[31, 28])).
% 0.18/0.40 tff(33,plain,
% 0.18/0.40 (q(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[32, 3])).
% 0.18/0.40 tff(34,plain,
% 0.18/0.40 (^[Y: $i, X: $i] : refl(((~q(f(X, Y), f(X, Y))) | p(X, Y)) <=> ((~q(f(X, Y), f(X, Y))) | p(X, Y)))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(35,plain,
% 0.18/0.40 (![Y: $i, X: $i] : ((~q(f(X, Y), f(X, Y))) | p(X, Y)) <=> ![Y: $i, X: $i] : ((~q(f(X, Y), f(X, Y))) | p(X, Y))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[34])).
% 0.18/0.40 tff(36,plain,
% 0.18/0.40 (![Y: $i, X: $i] : ((~q(f(X, Y), f(X, Y))) | p(X, Y)) <=> ![Y: $i, X: $i] : ((~q(f(X, Y), f(X, Y))) | p(X, Y))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(37,plain,
% 0.18/0.40 (^[Y: $i, X: $i] : rewrite((p(X, Y) | (~q(f(X, Y), f(X, Y)))) <=> ((~q(f(X, Y), f(X, Y))) | p(X, Y)))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(38,plain,
% 0.18/0.40 (![Y: $i, X: $i] : (p(X, Y) | (~q(f(X, Y), f(X, Y)))) <=> ![Y: $i, X: $i] : ((~q(f(X, Y), f(X, Y))) | p(X, Y))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[37])).
% 0.18/0.40 tff(39,axiom,(![Y: $i, X: $i] : (p(X, Y) | (~q(f(X, Y), f(X, Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_5')).
% 0.18/0.40 tff(40,plain,
% 0.18/0.40 (![Y: $i, X: $i] : ((~q(f(X, Y), f(X, Y))) | p(X, Y))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.18/0.40 tff(41,plain,
% 0.18/0.40 (![Y: $i, X: $i] : ((~q(f(X, Y), f(X, Y))) | p(X, Y))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.18/0.40 tff(42,plain,(
% 0.18/0.40 ![Y: $i, X: $i] : ((~q(f(X, Y), f(X, Y))) | p(X, Y))),
% 0.18/0.40 inference(skolemize,[status(sab)],[41])).
% 0.18/0.40 tff(43,plain,
% 0.18/0.40 (![Y: $i, X: $i] : ((~q(f(X, Y), f(X, Y))) | p(X, Y))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.18/0.40 tff(44,plain,
% 0.18/0.40 (((~![Y: $i, X: $i] : ((~q(f(X, Y), f(X, Y))) | p(X, Y))) | ((~q(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0)))) | p(elem!0, f(elem!0, elem!0)))) <=> ((~![Y: $i, X: $i] : ((~q(f(X, Y), f(X, Y))) | p(X, Y))) | (~q(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0)))) | p(elem!0, f(elem!0, elem!0)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(45,plain,
% 0.18/0.40 ((~![Y: $i, X: $i] : ((~q(f(X, Y), f(X, Y))) | p(X, Y))) | ((~q(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0)))) | p(elem!0, f(elem!0, elem!0)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(46,plain,
% 0.18/0.40 ((~![Y: $i, X: $i] : ((~q(f(X, Y), f(X, Y))) | p(X, Y))) | (~q(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0)))) | p(elem!0, f(elem!0, elem!0))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.18/0.40 tff(47,plain,
% 0.18/0.40 ((~q(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0)))) | p(elem!0, f(elem!0, elem!0))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[46, 43])).
% 0.18/0.40 tff(48,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[47, 33, 21])).
% 0.18/0.40 tff(49,plain,(q(elem!0, f(elem!0, elem!0)) | (~p(elem!0, elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(50,plain,
% 0.18/0.40 (q(elem!0, f(elem!0, elem!0))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[49, 2])).
% 0.18/0.40 tff(51,plain,
% 0.18/0.40 (^[Y: $i, X: $i] : refl(((~p(X, Y)) | p(X, f(X, Y)) | (~q(Y, f(X, Y)))) <=> ((~p(X, Y)) | p(X, f(X, Y)) | (~q(Y, f(X, Y)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(52,plain,
% 0.18/0.40 (![Y: $i, X: $i] : ((~p(X, Y)) | p(X, f(X, Y)) | (~q(Y, f(X, Y)))) <=> ![Y: $i, X: $i] : ((~p(X, Y)) | p(X, f(X, Y)) | (~q(Y, f(X, Y))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[51])).
% 0.18/0.40 tff(53,plain,
% 0.18/0.40 (![Y: $i, X: $i] : ((~p(X, Y)) | p(X, f(X, Y)) | (~q(Y, f(X, Y)))) <=> ![Y: $i, X: $i] : ((~p(X, Y)) | p(X, f(X, Y)) | (~q(Y, f(X, Y))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(54,plain,
% 0.18/0.40 (^[Y: $i, X: $i] : rewrite((((~p(X, Y)) | (~q(Y, f(X, Y)))) | p(X, f(X, Y))) <=> ((~p(X, Y)) | p(X, f(X, Y)) | (~q(Y, f(X, Y)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(55,plain,
% 0.18/0.40 (![Y: $i, X: $i] : (((~p(X, Y)) | (~q(Y, f(X, Y)))) | p(X, f(X, Y))) <=> ![Y: $i, X: $i] : ((~p(X, Y)) | p(X, f(X, Y)) | (~q(Y, f(X, Y))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[54])).
% 0.18/0.40 tff(56,axiom,(![Y: $i, X: $i] : (((~p(X, Y)) | (~q(Y, f(X, Y)))) | p(X, f(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_2')).
% 0.18/0.40 tff(57,plain,
% 0.18/0.40 (![Y: $i, X: $i] : ((~p(X, Y)) | p(X, f(X, Y)) | (~q(Y, f(X, Y))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.18/0.40 tff(58,plain,
% 0.18/0.40 (![Y: $i, X: $i] : ((~p(X, Y)) | p(X, f(X, Y)) | (~q(Y, f(X, Y))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.18/0.40 tff(59,plain,(
% 0.18/0.40 ![Y: $i, X: $i] : ((~p(X, Y)) | p(X, f(X, Y)) | (~q(Y, f(X, Y))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[58])).
% 0.18/0.40 tff(60,plain,
% 0.18/0.40 (![Y: $i, X: $i] : ((~p(X, Y)) | p(X, f(X, Y)) | (~q(Y, f(X, Y))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.18/0.40 tff(61,plain,
% 0.18/0.40 (((~![Y: $i, X: $i] : ((~p(X, Y)) | p(X, f(X, Y)) | (~q(Y, f(X, Y))))) | ((~p(elem!0, elem!0)) | p(elem!0, f(elem!0, elem!0)) | (~q(elem!0, f(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : ((~p(X, Y)) | p(X, f(X, Y)) | (~q(Y, f(X, Y))))) | (~p(elem!0, elem!0)) | p(elem!0, f(elem!0, elem!0)) | (~q(elem!0, f(elem!0, elem!0))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(62,plain,
% 0.18/0.40 ((~![Y: $i, X: $i] : ((~p(X, Y)) | p(X, f(X, Y)) | (~q(Y, f(X, Y))))) | ((~p(elem!0, elem!0)) | p(elem!0, f(elem!0, elem!0)) | (~q(elem!0, f(elem!0, elem!0))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(63,plain,
% 0.18/0.40 ((~![Y: $i, X: $i] : ((~p(X, Y)) | p(X, f(X, Y)) | (~q(Y, f(X, Y))))) | (~p(elem!0, elem!0)) | p(elem!0, f(elem!0, elem!0)) | (~q(elem!0, f(elem!0, elem!0)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.18/0.40 tff(64,plain,
% 0.18/0.40 (p(elem!0, f(elem!0, elem!0)) | (~q(elem!0, f(elem!0, elem!0)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[63, 60, 2])).
% 0.18/0.40 tff(65,plain,
% 0.18/0.40 (p(elem!0, f(elem!0, elem!0))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[64, 50])).
% 0.18/0.40 tff(66,assumption,(~q(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0)))), introduced(assumption)).
% 0.18/0.40 tff(67,assumption,(p(elem!0, f(elem!0, elem!0))), introduced(assumption)).
% 0.18/0.40 tff(68,plain,
% 0.18/0.40 (^[Y: $i, X: $i] : refl(((~p(X, Y)) | q(f(X, Y), f(X, Y)) | (~p(f(X, Y), f(X, Y)))) <=> ((~p(X, Y)) | q(f(X, Y), f(X, Y)) | (~p(f(X, Y), f(X, Y)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(69,plain,
% 0.18/0.40 (![Y: $i, X: $i] : ((~p(X, Y)) | q(f(X, Y), f(X, Y)) | (~p(f(X, Y), f(X, Y)))) <=> ![Y: $i, X: $i] : ((~p(X, Y)) | q(f(X, Y), f(X, Y)) | (~p(f(X, Y), f(X, Y))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[68])).
% 0.18/0.40 tff(70,plain,
% 0.18/0.40 (![Y: $i, X: $i] : ((~p(X, Y)) | q(f(X, Y), f(X, Y)) | (~p(f(X, Y), f(X, Y)))) <=> ![Y: $i, X: $i] : ((~p(X, Y)) | q(f(X, Y), f(X, Y)) | (~p(f(X, Y), f(X, Y))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(71,plain,
% 0.18/0.40 (^[Y: $i, X: $i] : rewrite((((~p(X, Y)) | (~p(f(X, Y), f(X, Y)))) | q(f(X, Y), f(X, Y))) <=> ((~p(X, Y)) | q(f(X, Y), f(X, Y)) | (~p(f(X, Y), f(X, Y)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(72,plain,
% 0.18/0.40 (![Y: $i, X: $i] : (((~p(X, Y)) | (~p(f(X, Y), f(X, Y)))) | q(f(X, Y), f(X, Y))) <=> ![Y: $i, X: $i] : ((~p(X, Y)) | q(f(X, Y), f(X, Y)) | (~p(f(X, Y), f(X, Y))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[71])).
% 0.18/0.40 tff(73,axiom,(![Y: $i, X: $i] : (((~p(X, Y)) | (~p(f(X, Y), f(X, Y)))) | q(f(X, Y), f(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_3')).
% 0.18/0.40 tff(74,plain,
% 0.18/0.40 (![Y: $i, X: $i] : ((~p(X, Y)) | q(f(X, Y), f(X, Y)) | (~p(f(X, Y), f(X, Y))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.18/0.40 tff(75,plain,
% 0.18/0.40 (![Y: $i, X: $i] : ((~p(X, Y)) | q(f(X, Y), f(X, Y)) | (~p(f(X, Y), f(X, Y))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.18/0.40 tff(76,plain,(
% 0.18/0.40 ![Y: $i, X: $i] : ((~p(X, Y)) | q(f(X, Y), f(X, Y)) | (~p(f(X, Y), f(X, Y))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[75])).
% 0.18/0.40 tff(77,plain,
% 0.18/0.40 (![Y: $i, X: $i] : ((~p(X, Y)) | q(f(X, Y), f(X, Y)) | (~p(f(X, Y), f(X, Y))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.18/0.40 tff(78,plain,
% 0.18/0.40 (((~![Y: $i, X: $i] : ((~p(X, Y)) | q(f(X, Y), f(X, Y)) | (~p(f(X, Y), f(X, Y))))) | ((~p(elem!0, f(elem!0, elem!0))) | q(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))) | (~p(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : ((~p(X, Y)) | q(f(X, Y), f(X, Y)) | (~p(f(X, Y), f(X, Y))))) | (~p(elem!0, f(elem!0, elem!0))) | q(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))) | (~p(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(79,plain,
% 0.18/0.40 ((~![Y: $i, X: $i] : ((~p(X, Y)) | q(f(X, Y), f(X, Y)) | (~p(f(X, Y), f(X, Y))))) | ((~p(elem!0, f(elem!0, elem!0))) | q(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))) | (~p(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0)))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(80,plain,
% 0.18/0.40 ((~![Y: $i, X: $i] : ((~p(X, Y)) | q(f(X, Y), f(X, Y)) | (~p(f(X, Y), f(X, Y))))) | (~p(elem!0, f(elem!0, elem!0))) | q(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))) | (~p(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.18/0.40 tff(81,plain,
% 0.18/0.40 (~p(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[80, 77, 67, 66])).
% 0.18/0.40 tff(82,plain,
% 0.18/0.40 (((~![Y: $i, X: $i] : ((~q(f(X, Y), f(X, Y))) | p(X, Y))) | ((~q(f(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))), f(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))))) | p(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : ((~q(f(X, Y), f(X, Y))) | p(X, Y))) | (~q(f(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))), f(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))))) | p(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(83,plain,
% 0.18/0.41 ((~![Y: $i, X: $i] : ((~q(f(X, Y), f(X, Y))) | p(X, Y))) | ((~q(f(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))), f(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))))) | p(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(84,plain,
% 0.18/0.41 ((~![Y: $i, X: $i] : ((~q(f(X, Y), f(X, Y))) | p(X, Y))) | (~q(f(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))), f(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))))) | p(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.18/0.41 tff(85,plain,
% 0.18/0.41 (~q(f(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))), f(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[84, 43, 81])).
% 0.18/0.41 tff(86,plain,
% 0.18/0.41 (((~![Y: $i, X: $i] : (q(X, Y) | q(f(X, Y), f(X, Y)))) | (q(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))) | q(f(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))), f(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : (q(X, Y) | q(f(X, Y), f(X, Y)))) | q(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))) | q(f(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))), f(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(87,plain,
% 0.18/0.41 ((~![Y: $i, X: $i] : (q(X, Y) | q(f(X, Y), f(X, Y)))) | (q(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))) | q(f(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))), f(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0)))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(88,plain,
% 0.18/0.41 ((~![Y: $i, X: $i] : (q(X, Y) | q(f(X, Y), f(X, Y)))) | q(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))) | q(f(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))), f(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.18/0.41 tff(89,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[88, 28, 66, 85])).
% 0.18/0.41 tff(90,plain,(q(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))) | (~p(elem!0, f(elem!0, elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.41 tff(91,plain,
% 0.18/0.41 (q(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[90, 65])).
% 0.18/0.41 tff(92,plain,
% 0.18/0.41 (^[Y: $i, X: $i] : refl(((~q(X, Y)) | (~q(f(X, Y), f(X, Y)))) <=> ((~q(X, Y)) | (~q(f(X, Y), f(X, Y)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(93,plain,
% 0.18/0.41 (![Y: $i, X: $i] : ((~q(X, Y)) | (~q(f(X, Y), f(X, Y)))) <=> ![Y: $i, X: $i] : ((~q(X, Y)) | (~q(f(X, Y), f(X, Y))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[92])).
% 0.18/0.41 tff(94,plain,
% 0.18/0.41 (![Y: $i, X: $i] : ((~q(X, Y)) | (~q(f(X, Y), f(X, Y)))) <=> ![Y: $i, X: $i] : ((~q(X, Y)) | (~q(f(X, Y), f(X, Y))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(95,axiom,(![Y: $i, X: $i] : ((~q(X, Y)) | (~q(f(X, Y), f(X, Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_7')).
% 0.18/0.41 tff(96,plain,
% 0.18/0.41 (![Y: $i, X: $i] : ((~q(X, Y)) | (~q(f(X, Y), f(X, Y))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.18/0.41 tff(97,plain,(
% 0.18/0.41 ![Y: $i, X: $i] : ((~q(X, Y)) | (~q(f(X, Y), f(X, Y))))),
% 0.18/0.41 inference(skolemize,[status(sab)],[96])).
% 0.18/0.41 tff(98,plain,
% 0.18/0.41 (![Y: $i, X: $i] : ((~q(X, Y)) | (~q(f(X, Y), f(X, Y))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.18/0.41 tff(99,plain,
% 0.18/0.41 (((~![Y: $i, X: $i] : ((~q(X, Y)) | (~q(f(X, Y), f(X, Y))))) | ((~q(elem!0, f(elem!0, elem!0))) | (~q(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : ((~q(X, Y)) | (~q(f(X, Y), f(X, Y))))) | (~q(elem!0, f(elem!0, elem!0))) | (~q(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(100,plain,
% 0.18/0.41 ((~![Y: $i, X: $i] : ((~q(X, Y)) | (~q(f(X, Y), f(X, Y))))) | ((~q(elem!0, f(elem!0, elem!0))) | (~q(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0)))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(101,plain,
% 0.18/0.41 ((~![Y: $i, X: $i] : ((~q(X, Y)) | (~q(f(X, Y), f(X, Y))))) | (~q(elem!0, f(elem!0, elem!0))) | (~q(f(elem!0, f(elem!0, elem!0)), f(elem!0, f(elem!0, elem!0))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.18/0.41 tff(102,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[101, 98, 50, 91])).
% 0.18/0.41 tff(103,plain,(~p(elem!0, elem!0)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.41 tff(104,plain,
% 0.18/0.41 (^[Y: $i, X: $i] : refl((p(X, Y) | p(f(X, Y), f(X, Y))) <=> (p(X, Y) | p(f(X, Y), f(X, Y))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(105,plain,
% 0.18/0.41 (![Y: $i, X: $i] : (p(X, Y) | p(f(X, Y), f(X, Y))) <=> ![Y: $i, X: $i] : (p(X, Y) | p(f(X, Y), f(X, Y)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[104])).
% 0.18/0.41 tff(106,plain,
% 0.18/0.41 (![Y: $i, X: $i] : (p(X, Y) | p(f(X, Y), f(X, Y))) <=> ![Y: $i, X: $i] : (p(X, Y) | p(f(X, Y), f(X, Y)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(107,axiom,(![Y: $i, X: $i] : (p(X, Y) | p(f(X, Y), f(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_4')).
% 0.18/0.41 tff(108,plain,
% 0.18/0.41 (![Y: $i, X: $i] : (p(X, Y) | p(f(X, Y), f(X, Y)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.18/0.41 tff(109,plain,(
% 0.18/0.41 ![Y: $i, X: $i] : (p(X, Y) | p(f(X, Y), f(X, Y)))),
% 0.18/0.41 inference(skolemize,[status(sab)],[108])).
% 0.18/0.41 tff(110,plain,
% 0.18/0.41 (![Y: $i, X: $i] : (p(X, Y) | p(f(X, Y), f(X, Y)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.18/0.41 tff(111,plain,
% 0.18/0.41 (((~![Y: $i, X: $i] : (p(X, Y) | p(f(X, Y), f(X, Y)))) | (p(elem!0, elem!0) | p(f(elem!0, elem!0), f(elem!0, elem!0)))) <=> ((~![Y: $i, X: $i] : (p(X, Y) | p(f(X, Y), f(X, Y)))) | p(elem!0, elem!0) | p(f(elem!0, elem!0), f(elem!0, elem!0)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(112,plain,
% 0.18/0.41 ((~![Y: $i, X: $i] : (p(X, Y) | p(f(X, Y), f(X, Y)))) | (p(elem!0, elem!0) | p(f(elem!0, elem!0), f(elem!0, elem!0)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(113,plain,
% 0.18/0.41 ((~![Y: $i, X: $i] : (p(X, Y) | p(f(X, Y), f(X, Y)))) | p(elem!0, elem!0) | p(f(elem!0, elem!0), f(elem!0, elem!0))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.18/0.41 tff(114,plain,
% 0.18/0.41 (p(elem!0, elem!0) | p(f(elem!0, elem!0), f(elem!0, elem!0))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[113, 110])).
% 0.18/0.41 tff(115,plain,
% 0.18/0.41 (p(f(elem!0, elem!0), f(elem!0, elem!0))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[114, 103])).
% 0.18/0.41 tff(116,assumption,(~p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))), introduced(assumption)).
% 0.18/0.41 tff(117,plain,
% 0.18/0.41 (((~![Y: $i, X: $i] : ((~q(f(X, Y), f(X, Y))) | p(X, Y))) | ((~q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))) | p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : ((~q(f(X, Y), f(X, Y))) | p(X, Y))) | (~q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))) | p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(118,plain,
% 0.18/0.41 ((~![Y: $i, X: $i] : ((~q(f(X, Y), f(X, Y))) | p(X, Y))) | ((~q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))) | p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(119,plain,
% 0.18/0.41 ((~![Y: $i, X: $i] : ((~q(f(X, Y), f(X, Y))) | p(X, Y))) | (~q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))) | p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.18/0.41 tff(120,plain,
% 0.18/0.41 (~q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[119, 43, 116])).
% 0.18/0.41 tff(121,assumption,(p(f(elem!0, elem!0), f(elem!0, elem!0))), introduced(assumption)).
% 0.18/0.41 tff(122,plain,
% 0.18/0.42 (((~![Y: $i, X: $i] : ((~p(X, Y)) | p(X, f(X, Y)) | (~q(Y, f(X, Y))))) | ((~p(f(elem!0, elem!0), f(elem!0, elem!0))) | p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))) | (~q(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : ((~p(X, Y)) | p(X, f(X, Y)) | (~q(Y, f(X, Y))))) | (~p(f(elem!0, elem!0), f(elem!0, elem!0))) | p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))) | (~q(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(123,plain,
% 0.18/0.42 ((~![Y: $i, X: $i] : ((~p(X, Y)) | p(X, f(X, Y)) | (~q(Y, f(X, Y))))) | ((~p(f(elem!0, elem!0), f(elem!0, elem!0))) | p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))) | (~q(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(124,plain,
% 0.18/0.42 ((~![Y: $i, X: $i] : ((~p(X, Y)) | p(X, f(X, Y)) | (~q(Y, f(X, Y))))) | (~p(f(elem!0, elem!0), f(elem!0, elem!0))) | p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))) | (~q(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.18/0.42 tff(125,plain,
% 0.18/0.42 (p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))) | (~q(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[124, 60, 121])).
% 0.18/0.42 tff(126,plain,
% 0.18/0.42 (~q(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[125, 116])).
% 0.18/0.42 tff(127,plain,
% 0.18/0.42 (((~![Y: $i, X: $i] : (q(X, Y) | q(f(X, Y), f(X, Y)))) | (q(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))) | q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : (q(X, Y) | q(f(X, Y), f(X, Y)))) | q(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))) | q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(128,plain,
% 0.18/0.42 ((~![Y: $i, X: $i] : (q(X, Y) | q(f(X, Y), f(X, Y)))) | (q(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))) | q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(129,plain,
% 0.18/0.42 ((~![Y: $i, X: $i] : (q(X, Y) | q(f(X, Y), f(X, Y)))) | q(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))) | q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.18/0.42 tff(130,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[129, 28, 126, 120])).
% 0.18/0.42 tff(131,plain,(p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))) | (~p(f(elem!0, elem!0), f(elem!0, elem!0)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.42 tff(132,plain,
% 0.18/0.42 (p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[131, 115])).
% 0.18/0.42 tff(133,plain,
% 0.18/0.42 (((~![Y: $i, X: $i] : (q(Y, f(X, Y)) | (~p(X, Y)) | (~p(X, f(X, Y))))) | ((~p(f(elem!0, elem!0), f(elem!0, elem!0))) | (~p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | q(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))) <=> ((~![Y: $i, X: $i] : (q(Y, f(X, Y)) | (~p(X, Y)) | (~p(X, f(X, Y))))) | (~p(f(elem!0, elem!0), f(elem!0, elem!0))) | (~p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | q(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(134,plain,
% 0.18/0.42 ((q(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))) | (~p(f(elem!0, elem!0), f(elem!0, elem!0))) | (~p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))) <=> ((~p(f(elem!0, elem!0), f(elem!0, elem!0))) | (~p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | q(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(135,plain,
% 0.18/0.42 (((~![Y: $i, X: $i] : (q(Y, f(X, Y)) | (~p(X, Y)) | (~p(X, f(X, Y))))) | (q(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))) | (~p(f(elem!0, elem!0), f(elem!0, elem!0))) | (~p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : (q(Y, f(X, Y)) | (~p(X, Y)) | (~p(X, f(X, Y))))) | ((~p(f(elem!0, elem!0), f(elem!0, elem!0))) | (~p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | q(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[134])).
% 0.18/0.42 tff(136,plain,
% 0.18/0.42 (((~![Y: $i, X: $i] : (q(Y, f(X, Y)) | (~p(X, Y)) | (~p(X, f(X, Y))))) | (q(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))) | (~p(f(elem!0, elem!0), f(elem!0, elem!0))) | (~p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : (q(Y, f(X, Y)) | (~p(X, Y)) | (~p(X, f(X, Y))))) | (~p(f(elem!0, elem!0), f(elem!0, elem!0))) | (~p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | q(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))),
% 0.18/0.42 inference(transitivity,[status(thm)],[135, 133])).
% 0.18/0.42 tff(137,plain,
% 0.18/0.42 ((~![Y: $i, X: $i] : (q(Y, f(X, Y)) | (~p(X, Y)) | (~p(X, f(X, Y))))) | (q(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))) | (~p(f(elem!0, elem!0), f(elem!0, elem!0))) | (~p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(138,plain,
% 0.18/0.42 ((~![Y: $i, X: $i] : (q(Y, f(X, Y)) | (~p(X, Y)) | (~p(X, f(X, Y))))) | (~p(f(elem!0, elem!0), f(elem!0, elem!0))) | (~p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | q(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.18/0.42 tff(139,plain,
% 0.18/0.42 ((~p(f(elem!0, elem!0), f(elem!0, elem!0))) | (~p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | q(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[138, 13])).
% 0.18/0.42 tff(140,plain,
% 0.18/0.42 (q(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[139, 132, 115])).
% 0.18/0.42 tff(141,plain,
% 0.18/0.42 (((~![Y: $i, X: $i] : ((~q(X, Y)) | (~q(f(X, Y), f(X, Y))))) | ((~q(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | (~q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))))) <=> ((~![Y: $i, X: $i] : ((~q(X, Y)) | (~q(f(X, Y), f(X, Y))))) | (~q(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | (~q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(142,plain,
% 0.18/0.42 ((~![Y: $i, X: $i] : ((~q(X, Y)) | (~q(f(X, Y), f(X, Y))))) | ((~q(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | (~q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(143,plain,
% 0.18/0.42 ((~![Y: $i, X: $i] : ((~q(X, Y)) | (~q(f(X, Y), f(X, Y))))) | (~q(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | (~q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.18/0.42 tff(144,plain,
% 0.18/0.42 (~q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[143, 98, 140])).
% 0.18/0.42 tff(145,plain,
% 0.18/0.42 (((~![Y: $i, X: $i] : (q(X, Y) | q(f(X, Y), f(X, Y)))) | (q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | q(f(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))), f(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))))) <=> ((~![Y: $i, X: $i] : (q(X, Y) | q(f(X, Y), f(X, Y)))) | q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | q(f(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))), f(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(146,plain,
% 0.19/0.43 ((~![Y: $i, X: $i] : (q(X, Y) | q(f(X, Y), f(X, Y)))) | (q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | q(f(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))), f(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(147,plain,
% 0.19/0.43 ((~![Y: $i, X: $i] : (q(X, Y) | q(f(X, Y), f(X, Y)))) | q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | q(f(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))), f(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.19/0.43 tff(148,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[147, 28, 144, 1])).
% 0.19/0.43 tff(149,plain,(q(f(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))), f(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(150,plain,
% 0.19/0.43 (((~![Y: $i, X: $i] : ((~q(X, Y)) | (~q(f(X, Y), f(X, Y))))) | ((~q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))) | (~q(f(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))), f(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))))))) <=> ((~![Y: $i, X: $i] : ((~q(X, Y)) | (~q(f(X, Y), f(X, Y))))) | (~q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))) | (~q(f(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))), f(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(151,plain,
% 0.19/0.43 ((~![Y: $i, X: $i] : ((~q(X, Y)) | (~q(f(X, Y), f(X, Y))))) | ((~q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))) | (~q(f(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))), f(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(152,plain,
% 0.19/0.43 ((~![Y: $i, X: $i] : ((~q(X, Y)) | (~q(f(X, Y), f(X, Y))))) | (~q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))) | (~q(f(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))), f(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.19/0.43 tff(153,plain,
% 0.19/0.43 (~q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[152, 98, 149])).
% 0.19/0.43 tff(154,plain,
% 0.19/0.43 (((~![Y: $i, X: $i] : ((~q(f(X, Y), f(X, Y))) | p(X, Y))) | ((~q(f(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))), f(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))))) | p(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : ((~q(f(X, Y), f(X, Y))) | p(X, Y))) | (~q(f(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))), f(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))))) | p(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(155,plain,
% 0.19/0.43 ((~![Y: $i, X: $i] : ((~q(f(X, Y), f(X, Y))) | p(X, Y))) | ((~q(f(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))), f(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))))) | p(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(156,plain,
% 0.19/0.43 ((~![Y: $i, X: $i] : ((~q(f(X, Y), f(X, Y))) | p(X, Y))) | (~q(f(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))), f(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))))) | p(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.19/0.43 tff(157,plain,
% 0.19/0.43 (p(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[156, 43, 149])).
% 0.19/0.43 tff(158,plain,
% 0.19/0.43 (((~![Y: $i, X: $i] : ((~p(X, Y)) | q(f(X, Y), f(X, Y)) | (~p(f(X, Y), f(X, Y))))) | ((~p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | (~p(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))) | q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))))) <=> ((~![Y: $i, X: $i] : ((~p(X, Y)) | q(f(X, Y), f(X, Y)) | (~p(f(X, Y), f(X, Y))))) | (~p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | (~p(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))) | q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(159,plain,
% 0.19/0.43 (((~p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | (~p(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))))) <=> ((~p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | (~p(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))) | q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(160,plain,
% 0.19/0.43 (((~![Y: $i, X: $i] : ((~p(X, Y)) | q(f(X, Y), f(X, Y)) | (~p(f(X, Y), f(X, Y))))) | ((~p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | (~p(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))))) <=> ((~![Y: $i, X: $i] : ((~p(X, Y)) | q(f(X, Y), f(X, Y)) | (~p(f(X, Y), f(X, Y))))) | ((~p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | (~p(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))) | q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[159])).
% 0.19/0.44 tff(161,plain,
% 0.19/0.44 (((~![Y: $i, X: $i] : ((~p(X, Y)) | q(f(X, Y), f(X, Y)) | (~p(f(X, Y), f(X, Y))))) | ((~p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | (~p(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))))) <=> ((~![Y: $i, X: $i] : ((~p(X, Y)) | q(f(X, Y), f(X, Y)) | (~p(f(X, Y), f(X, Y))))) | (~p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | (~p(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))) | q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[160, 158])).
% 0.19/0.44 tff(162,plain,
% 0.19/0.44 ((~![Y: $i, X: $i] : ((~p(X, Y)) | q(f(X, Y), f(X, Y)) | (~p(f(X, Y), f(X, Y))))) | ((~p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | (~p(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(163,plain,
% 0.19/0.44 ((~![Y: $i, X: $i] : ((~p(X, Y)) | q(f(X, Y), f(X, Y)) | (~p(f(X, Y), f(X, Y))))) | (~p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | (~p(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))) | q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.19/0.44 tff(164,plain,
% 0.19/0.44 ((~p(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0)))) | (~p(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))) | q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[163, 77])).
% 0.19/0.44 tff(165,plain,
% 0.19/0.44 ((~p(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))) | q(f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))), f(f(elem!0, elem!0), f(f(elem!0, elem!0), f(elem!0, elem!0))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[164, 132])).
% 0.19/0.44 tff(166,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[165, 157, 153])).
% 0.19/0.44 % SZS output end Proof
% 0.19/0.44 % E exiting
%------------------------------------------------------------------------------