TSTP Solution File: SYN965+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN965+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 : Fri Sep 30 00:01:25 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYN965+1 : TPTP v8.1.0. Released v3.1.0.
% 0.13/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Sep 5 09:42:48 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.20/0.35 Usage: tptp [options] [-file:]file
% 0.20/0.35 -h, -? prints this message.
% 0.20/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.20/0.35 -m, -model generate model.
% 0.20/0.35 -p, -proof generate proof.
% 0.20/0.35 -c, -core generate unsat core of named formulas.
% 0.20/0.35 -st, -statistics display statistics.
% 0.20/0.35 -t:timeout set timeout (in second).
% 0.20/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.20/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.20/0.35 -<param>:<value> configuration parameter and value.
% 0.20/0.35 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(p_type, type, (
% 0.20/0.40 p: ( $i * $i ) > $o)).
% 0.20/0.40 tff(tptp_fun_X_0_type, type, (
% 0.20/0.40 tptp_fun_X_0: $i > $i)).
% 0.20/0.40 tff(elem_1_type, type, (
% 0.20/0.40 elem_1: $i)).
% 0.20/0.40 tff(1,assumption,((~p(elem!1, tptp_fun_X_0(elem!1))) | (~p(tptp_fun_X_0(elem!1), elem!1)) | p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))), introduced(assumption)).
% 0.20/0.40 tff(2,assumption,(~((~p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, tptp_fun_X_0(elem!1)))))), introduced(assumption)).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (((~p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, tptp_fun_X_0(elem!1))))) | ![W: $i] : (~p(W, tptp_fun_X_0(elem!1)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (![W: $i] : (~p(W, tptp_fun_X_0(elem!1)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[3, 2])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (((~p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, tptp_fun_X_0(elem!1))))) | p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[5, 2])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 ((~![W: $i] : (~p(W, tptp_fun_X_0(elem!1)))) | (~p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[7, 6, 4])).
% 0.20/0.40 tff(9,plain,((~p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, tptp_fun_X_0(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (^[Z: $i, Y: $i] : refl(((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y)))))) <=> ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y)))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y)))))) <=> ![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (^[Z: $i, Y: $i] : rewrite(((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y)))))) <=> ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y)))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y)))))) <=> ![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y)))))) <=> ![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[13, 11])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (^[Z: $i, Y: $i] : rewrite(((~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z)))) | (p(Y, tptp_fun_X_0(Z)) & ![W: $i] : (~p(W, Y)))) <=> ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y)))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (![Z: $i, Y: $i] : ((~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z)))) | (p(Y, tptp_fun_X_0(Z)) & ![W: $i] : (~p(W, Y)))) <=> ![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (![Z: $i] : ![Y: $i] : ((~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z)))) | (p(Y, tptp_fun_X_0(Z)) & ![W: $i] : (~p(W, Y)))) <=> ![Z: $i, Y: $i] : ((~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z)))) | (p(Y, tptp_fun_X_0(Z)) & ![W: $i] : (~p(W, Y))))),
% 0.20/0.40 inference(pull_quant,[status(thm)],[])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (^[Z: $i] : quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite(((~(~p(Y, tptp_fun_X_0(Z)))) & ![W: $i] : (~p(W, Y))) <=> (p(Y, tptp_fun_X_0(Z)) & ![W: $i] : (~p(W, Y)))), ((((~(~p(Y, tptp_fun_X_0(Z)))) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z))))) <=> ((p(Y, tptp_fun_X_0(Z)) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z))))))), rewrite(((p(Y, tptp_fun_X_0(Z)) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z))))) <=> ((~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z)))) | (p(Y, tptp_fun_X_0(Z)) & ![W: $i] : (~p(W, Y))))), ((((~(~p(Y, tptp_fun_X_0(Z)))) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z))))) <=> ((~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z)))) | (p(Y, tptp_fun_X_0(Z)) & ![W: $i] : (~p(W, Y))))))), (![Y: $i] : (((~(~p(Y, tptp_fun_X_0(Z)))) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z))))) <=> ![Y: $i] : ((~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z)))) | (p(Y, tptp_fun_X_0(Z)) & ![W: $i] : (~p(W, Y))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (![Z: $i] : ![Y: $i] : (((~(~p(Y, tptp_fun_X_0(Z)))) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z))))) <=> ![Z: $i] : ![Y: $i] : ((~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z)))) | (p(Y, tptp_fun_X_0(Z)) & ![W: $i] : (~p(W, Y))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 (![Z: $i] : ![Y: $i] : (((~(~p(Y, tptp_fun_X_0(Z)))) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z))))) <=> ![Z: $i, Y: $i] : ((~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z)))) | (p(Y, tptp_fun_X_0(Z)) & ![W: $i] : (~p(W, Y))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[19, 17])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 ((~?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X)))) <=> (~?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 ((~?[Z: $i] : ![X: $i] : ?[Y: $i] : ((p(Y, X) => ?[W: $i] : p(W, Y)) & ((p(Z, Y) & p(Y, Z)) => p(Y, X)))) <=> (~?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(23,axiom,(~?[Z: $i] : ![X: $i] : ?[Y: $i] : ((p(Y, X) => ?[W: $i] : p(W, Y)) & ((p(Z, Y) & p(Y, Z)) => p(Y, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 (~?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (~?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 (~?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 (~?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (~?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[27, 21])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (~?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (~?[Z: $i] : ![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[29, 21])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 (^[Z: $i] : trans(sk($oeq((~![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X)))), (~?[Y: $i] : (((~p(Y, tptp_fun_X_0(Z))) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z))))))), nnf_neg(proof_bind(^[Y: $i] : nnf_neg(nnf_neg(refl($oeq((~(~p(Y, tptp_fun_X_0(Z)))), (~(~p(Y, tptp_fun_X_0(Z)))))), nnf_neg(proof_bind(^[W: $i] : refl($oeq((~p(W, Y)), (~p(W, Y))))), $oeq((~?[W: $i] : p(W, Y)), ![W: $i] : (~p(W, Y)))), $oeq((~((~p(Y, tptp_fun_X_0(Z))) | ?[W: $i] : p(W, Y))), ((~(~p(Y, tptp_fun_X_0(Z)))) & ![W: $i] : (~p(W, Y))))), refl($oeq((~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z)))), (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z)))))), $oeq((~(((~p(Y, tptp_fun_X_0(Z))) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z))))), (((~(~p(Y, tptp_fun_X_0(Z)))) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z)))))))), $oeq((~?[Y: $i] : (((~p(Y, tptp_fun_X_0(Z))) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z))))), ![Y: $i] : (((~(~p(Y, tptp_fun_X_0(Z)))) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z))))))), $oeq((~![X: $i] : ?[Y: $i] : (((~p(Y, X)) | ?[W: $i] : p(W, Y)) & ((~(p(Z, Y) & p(Y, Z))) | p(Y, X)))), ![Y: $i] : (((~(~p(Y, tptp_fun_X_0(Z)))) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(32,plain,(
% 0.20/0.41 ![Z: $i] : ![Y: $i] : (((~(~p(Y, tptp_fun_X_0(Z)))) & ![W: $i] : (~p(W, Y))) | (~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z)))))),
% 0.20/0.41 inference(nnf-neg,[status(sab)],[30, 31])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (![Z: $i, Y: $i] : ((~((~(p(Z, Y) & p(Y, Z))) | p(Y, tptp_fun_X_0(Z)))) | (p(Y, tptp_fun_X_0(Z)) & ![W: $i] : (~p(W, Y))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[32, 20])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[33, 16])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[34, 14])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~p(tptp_fun_X_0(elem!1), elem!1)) | p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1)))) | (~((~p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, tptp_fun_X_0(elem!1)))))))) <=> ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | (~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~p(tptp_fun_X_0(elem!1), elem!1)) | p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1)))) | (~((~p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, tptp_fun_X_0(elem!1)))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 (((~((~p(tptp_fun_X_0(elem!1), elem!1)) | p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1)) | (~p(elem!1, tptp_fun_X_0(elem!1))))) | (~((~p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, tptp_fun_X_0(elem!1))))))) <=> ((~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~p(tptp_fun_X_0(elem!1), elem!1)) | p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1)))) | (~((~p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, tptp_fun_X_0(elem!1)))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(tptp_fun_X_0(elem!1), elem!1)) | p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1)) | (~p(elem!1, tptp_fun_X_0(elem!1))))) | (~((~p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, tptp_fun_X_0(elem!1)))))))) <=> ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~p(tptp_fun_X_0(elem!1), elem!1)) | p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1)))) | (~((~p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, tptp_fun_X_0(elem!1))))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[37])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(tptp_fun_X_0(elem!1), elem!1)) | p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1)) | (~p(elem!1, tptp_fun_X_0(elem!1))))) | (~((~p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, tptp_fun_X_0(elem!1)))))))) <=> ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | (~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~p(tptp_fun_X_0(elem!1), elem!1)) | p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1)))) | (~((~p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, tptp_fun_X_0(elem!1)))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[38, 36])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(tptp_fun_X_0(elem!1), elem!1)) | p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1)) | (~p(elem!1, tptp_fun_X_0(elem!1))))) | (~((~p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, tptp_fun_X_0(elem!1)))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | (~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~p(tptp_fun_X_0(elem!1), elem!1)) | p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1)))) | (~((~p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, tptp_fun_X_0(elem!1))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[41, 35, 9, 1])).
% 0.20/0.41 tff(43,plain,(~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~p(tptp_fun_X_0(elem!1), elem!1)) | p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(44,assumption,(~![W: $i] : (~p(W, elem!1))), introduced(assumption)).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (((~p(elem!1, tptp_fun_X_0(tptp_fun_X_0(elem!1)))) | (~![W: $i] : (~p(W, elem!1)))) | ![W: $i] : (~p(W, elem!1))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 ((~p(elem!1, tptp_fun_X_0(tptp_fun_X_0(elem!1)))) | (~![W: $i] : (~p(W, elem!1)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (((~p(elem!1, tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, elem!1)))) | ![W: $i] : (~p(W, elem!1))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 ((~p(elem!1, tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, elem!1)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[47, 44])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(elem!1, elem!1)) | p(elem!1, tptp_fun_X_0(elem!1)))) | (~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, elem!1))))))) <=> ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | (~((~p(elem!1, elem!1)) | p(elem!1, tptp_fun_X_0(elem!1)))) | (~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, elem!1))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 (((~((~p(elem!1, elem!1)) | p(elem!1, tptp_fun_X_0(elem!1)) | (~p(elem!1, elem!1)))) | (~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, elem!1)))))) <=> ((~((~p(elem!1, elem!1)) | p(elem!1, tptp_fun_X_0(elem!1)))) | (~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, elem!1))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(elem!1, elem!1)) | p(elem!1, tptp_fun_X_0(elem!1)) | (~p(elem!1, elem!1)))) | (~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, elem!1))))))) <=> ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(elem!1, elem!1)) | p(elem!1, tptp_fun_X_0(elem!1)))) | (~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, elem!1)))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[50])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 (((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(elem!1, elem!1)) | p(elem!1, tptp_fun_X_0(elem!1)) | (~p(elem!1, elem!1)))) | (~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, elem!1))))))) <=> ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | (~((~p(elem!1, elem!1)) | p(elem!1, tptp_fun_X_0(elem!1)))) | (~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, elem!1))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[51, 49])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(elem!1, elem!1)) | p(elem!1, tptp_fun_X_0(elem!1)) | (~p(elem!1, elem!1)))) | (~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, elem!1))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | (~((~p(elem!1, elem!1)) | p(elem!1, tptp_fun_X_0(elem!1)))) | (~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, elem!1)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 ((~((~p(elem!1, elem!1)) | p(elem!1, tptp_fun_X_0(elem!1)))) | (~((~p(elem!1, tptp_fun_X_0(elem!1))) | (~![W: $i] : (~p(W, elem!1)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[54, 35])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 (~((~p(elem!1, elem!1)) | p(elem!1, tptp_fun_X_0(elem!1)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[55, 48])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (((~p(elem!1, elem!1)) | p(elem!1, tptp_fun_X_0(elem!1))) | (~p(elem!1, tptp_fun_X_0(elem!1)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (~p(elem!1, tptp_fun_X_0(elem!1))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 (((~p(elem!1, tptp_fun_X_0(elem!1))) | p(elem!1, tptp_fun_X_0(tptp_fun_X_0(elem!1))) | (~p(tptp_fun_X_0(elem!1), elem!1))) | p(elem!1, tptp_fun_X_0(elem!1))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 ((~p(elem!1, tptp_fun_X_0(elem!1))) | p(elem!1, tptp_fun_X_0(tptp_fun_X_0(elem!1))) | (~p(tptp_fun_X_0(elem!1), elem!1))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 (((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(elem!1, tptp_fun_X_0(elem!1))) | p(elem!1, tptp_fun_X_0(tptp_fun_X_0(elem!1))) | (~p(tptp_fun_X_0(elem!1), elem!1)))) | (~((~p(elem!1, tptp_fun_X_0(tptp_fun_X_0(elem!1)))) | (~![W: $i] : (~p(W, elem!1))))))) <=> ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | (~((~p(elem!1, tptp_fun_X_0(elem!1))) | p(elem!1, tptp_fun_X_0(tptp_fun_X_0(elem!1))) | (~p(tptp_fun_X_0(elem!1), elem!1)))) | (~((~p(elem!1, tptp_fun_X_0(tptp_fun_X_0(elem!1)))) | (~![W: $i] : (~p(W, elem!1))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | ((~((~p(elem!1, tptp_fun_X_0(elem!1))) | p(elem!1, tptp_fun_X_0(tptp_fun_X_0(elem!1))) | (~p(tptp_fun_X_0(elem!1), elem!1)))) | (~((~p(elem!1, tptp_fun_X_0(tptp_fun_X_0(elem!1)))) | (~![W: $i] : (~p(W, elem!1))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 ((~![Z: $i, Y: $i] : ((~((~p(Y, Z)) | p(Y, tptp_fun_X_0(Z)) | (~p(Z, Y)))) | (~((~p(Y, tptp_fun_X_0(Z))) | (~![W: $i] : (~p(W, Y))))))) | (~((~p(elem!1, tptp_fun_X_0(elem!1))) | p(elem!1, tptp_fun_X_0(tptp_fun_X_0(elem!1))) | (~p(tptp_fun_X_0(elem!1), elem!1)))) | (~((~p(elem!1, tptp_fun_X_0(tptp_fun_X_0(elem!1)))) | (~![W: $i] : (~p(W, elem!1)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[63, 35, 60, 46])).
% 0.20/0.42 tff(65,plain,(![W: $i] : (~p(W, elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(66,assumption,(p(tptp_fun_X_0(elem!1), elem!1)), introduced(assumption)).
% 0.20/0.42 tff(67,assumption,(![W: $i] : (~p(W, elem!1))), introduced(assumption)).
% 0.20/0.42 tff(68,plain,
% 0.20/0.42 ((~![W: $i] : (~p(W, elem!1))) | (~p(tptp_fun_X_0(elem!1), elem!1))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[68, 67, 66])).
% 0.20/0.42 tff(70,plain,((~p(tptp_fun_X_0(elem!1), elem!1)) | (~![W: $i] : (~p(W, elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(71,plain,
% 0.20/0.42 (~p(tptp_fun_X_0(elem!1), elem!1)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[70, 65])).
% 0.20/0.42 tff(72,plain,
% 0.20/0.42 (((~p(elem!1, tptp_fun_X_0(elem!1))) | (~p(tptp_fun_X_0(elem!1), elem!1)) | p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))) | p(tptp_fun_X_0(elem!1), elem!1)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(73,plain,
% 0.20/0.42 ((~p(elem!1, tptp_fun_X_0(elem!1))) | (~p(tptp_fun_X_0(elem!1), elem!1)) | p(tptp_fun_X_0(elem!1), tptp_fun_X_0(elem!1))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[73, 43])).
% 0.20/0.42 % SZS output end Proof
%------------------------------------------------------------------------------