%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN413+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:39:01 AM UTC 2025
% Result : Theorem 0.18s 0.44s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN413+1 : TPTP v9.0.0. Released v2.0.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n014.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 12:33:39 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.44 % SZS status Theorem
% 0.18/0.44 % SZS output start Proof
% 0.18/0.44 tff(f_type, type, (
% 0.18/0.44 f: ( $i * $i ) > $o)).
% 0.18/0.44 tff(tptp_fun_Y_1_type, type, (
% 0.18/0.44 tptp_fun_Y_1: $i > $i)).
% 0.18/0.44 tff(tptp_fun_V_0_type, type, (
% 0.18/0.44 tptp_fun_V_0: $i)).
% 0.18/0.44 tff(1,assumption,(~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))), introduced(assumption)).
% 0.18/0.44 tff(2,assumption,(((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), V!0)) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))) <=> f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(V!0))), introduced(assumption)).
% 0.18/0.44 tff(3,plain,
% 0.18/0.44 (^[Z: $i, X: $i] : refl((~(((~f(X, Z)) | f(X, X)) <=> f(X, tptp_fun_Y_1(Z)))) <=> (~(((~f(X, Z)) | f(X, X)) <=> f(X, tptp_fun_Y_1(Z)))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(4,plain,
% 0.18/0.44 (![Z: $i, X: $i] : (~(((~f(X, Z)) | f(X, X)) <=> f(X, tptp_fun_Y_1(Z)))) <=> ![Z: $i, X: $i] : (~(((~f(X, Z)) | f(X, X)) <=> f(X, tptp_fun_Y_1(Z))))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[3])).
% 0.18/0.44 tff(5,plain,
% 0.18/0.44 (^[Z: $i, X: $i] : trans(trans(monotonicity(rewrite((f(X, Z) & (~f(X, X))) <=> (~((~f(X, Z)) | f(X, X)))), ((f(X, tptp_fun_Y_1(Z)) <=> (f(X, Z) & (~f(X, X)))) <=> (f(X, tptp_fun_Y_1(Z)) <=> (~((~f(X, Z)) | f(X, X)))))), rewrite((f(X, tptp_fun_Y_1(Z)) <=> (~((~f(X, Z)) | f(X, X)))) <=> (~(((~f(X, Z)) | f(X, X)) <=> f(X, tptp_fun_Y_1(Z))))), ((f(X, tptp_fun_Y_1(Z)) <=> (f(X, Z) & (~f(X, X)))) <=> (~(((~f(X, Z)) | f(X, X)) <=> f(X, tptp_fun_Y_1(Z)))))), rewrite((~(((~f(X, Z)) | f(X, X)) <=> f(X, tptp_fun_Y_1(Z)))) <=> (~(((~f(X, Z)) | f(X, X)) <=> f(X, tptp_fun_Y_1(Z))))), ((f(X, tptp_fun_Y_1(Z)) <=> (f(X, Z) & (~f(X, X)))) <=> (~(((~f(X, Z)) | f(X, X)) <=> f(X, tptp_fun_Y_1(Z))))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(6,plain,
% 0.18/0.44 (![Z: $i, X: $i] : (f(X, tptp_fun_Y_1(Z)) <=> (f(X, Z) & (~f(X, X)))) <=> ![Z: $i, X: $i] : (~(((~f(X, Z)) | f(X, X)) <=> f(X, tptp_fun_Y_1(Z))))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[5])).
% 0.18/0.44 tff(7,plain,
% 0.18/0.44 (![Z: $i] : ![X: $i] : (f(X, tptp_fun_Y_1(Z)) <=> (f(X, Z) & (~f(X, X)))) <=> ![Z: $i, X: $i] : (f(X, tptp_fun_Y_1(Z)) <=> (f(X, Z) & (~f(X, X))))),
% 0.18/0.44 inference(pull_quant,[status(thm)],[])).
% 0.18/0.44 tff(8,plain,
% 0.18/0.44 (![Z: $i] : ?[Y: $i] : ![X: $i] : (f(X, Y) <=> (f(X, Z) & (~f(X, X)))) <=> ![Z: $i] : ?[Y: $i] : ![X: $i] : (f(X, Y) <=> (f(X, Z) & (~f(X, X))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(9,plain,
% 0.18/0.44 ((~(![Z: $i] : ?[Y: $i] : ![X: $i] : (f(X, Y) <=> (f(X, Z) & (~f(X, X)))) => (~?[V: $i] : ![U: $i] : f(U, V)))) <=> (~((~?[V: $i] : ![U: $i] : f(U, V)) | (~![Z: $i] : ?[Y: $i] : ![X: $i] : (f(X, Y) <=> (f(X, Z) & (~f(X, X)))))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(10,axiom,(~(![Z: $i] : ?[Y: $i] : ![X: $i] : (f(X, Y) <=> (f(X, Z) & (~f(X, X)))) => (~?[V: $i] : ![U: $i] : f(U, V)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','kalish256')).
% 0.18/0.44 tff(11,plain,
% 0.18/0.44 (~((~?[V: $i] : ![U: $i] : f(U, V)) | (~![Z: $i] : ?[Y: $i] : ![X: $i] : (f(X, Y) <=> (f(X, Z) & (~f(X, X))))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.18/0.44 tff(12,plain,
% 0.18/0.44 (![Z: $i] : ?[Y: $i] : ![X: $i] : (f(X, Y) <=> (f(X, Z) & (~f(X, X))))),
% 0.18/0.44 inference(or_elim,[status(thm)],[11])).
% 0.18/0.44 tff(13,plain,
% 0.18/0.44 (![Z: $i] : ?[Y: $i] : ![X: $i] : (f(X, Y) <=> (f(X, Z) & (~f(X, X))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.18/0.44 tff(14,plain,(
% 0.18/0.44 ![Z: $i] : ![X: $i] : (f(X, tptp_fun_Y_1(Z)) <=> (f(X, Z) & (~f(X, X))))),
% 0.18/0.44 inference(skolemize,[status(sab)],[13])).
% 0.18/0.44 tff(15,plain,
% 0.18/0.44 (![Z: $i, X: $i] : (f(X, tptp_fun_Y_1(Z)) <=> (f(X, Z) & (~f(X, X))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.18/0.44 tff(16,plain,
% 0.18/0.44 (![Z: $i, X: $i] : (~(((~f(X, Z)) | f(X, X)) <=> f(X, tptp_fun_Y_1(Z))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[15, 6])).
% 0.18/0.44 tff(17,plain,
% 0.18/0.44 (![Z: $i, X: $i] : (~(((~f(X, Z)) | f(X, X)) <=> f(X, tptp_fun_Y_1(Z))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[16, 4])).
% 0.18/0.44 tff(18,plain,
% 0.18/0.44 ((~![Z: $i, X: $i] : (~(((~f(X, Z)) | f(X, X)) <=> f(X, tptp_fun_Y_1(Z))))) | (~(((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), V!0)) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))) <=> f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(V!0))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(19,plain,
% 0.18/0.44 ($false),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[18, 17, 2])).
% 0.18/0.44 tff(20,plain,(~(((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), V!0)) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))) <=> f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(V!0)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.44 tff(21,assumption,(~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), V!0)), introduced(assumption)).
% 0.18/0.44 tff(22,plain,
% 0.18/0.44 (^[U: $i] : refl(f(U, V!0) <=> f(U, V!0))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(23,plain,
% 0.18/0.44 (![U: $i] : f(U, V!0) <=> ![U: $i] : f(U, V!0)),
% 0.18/0.44 inference(quant_intro,[status(thm)],[22])).
% 0.18/0.44 tff(24,plain,
% 0.18/0.44 (?[V: $i] : ![U: $i] : f(U, V) <=> ?[V: $i] : ![U: $i] : f(U, V)),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(25,plain,
% 0.18/0.44 (?[V: $i] : ![U: $i] : f(U, V)),
% 0.18/0.44 inference(or_elim,[status(thm)],[11])).
% 0.18/0.44 tff(26,plain,
% 0.18/0.44 (?[V: $i] : ![U: $i] : f(U, V)),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.18/0.44 tff(27,plain,(
% 0.18/0.44 $oeq(![U: $i] : f(U, V!0), ![U: $i] : f(U, V!0))),
% 0.18/0.44 inference(transitivity,[status(sab)],[26])).
% 0.18/0.44 tff(28,plain,
% 0.18/0.44 (![U: $i] : f(U, V!0)),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.18/0.44 tff(29,plain,
% 0.18/0.44 ((~![U: $i] : f(U, V!0)) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), V!0)),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(30,plain,
% 0.18/0.44 ($false),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[29, 28, 21])).
% 0.18/0.44 tff(31,plain,(f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), V!0)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.44 tff(32,plain,
% 0.18/0.44 ((~((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), V!0)) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))))) | (~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), V!0)) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(33,plain,
% 0.18/0.44 (~((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), V!0)) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[32, 1, 31])).
% 0.18/0.44 tff(34,plain,
% 0.18/0.44 ((((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), V!0)) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))) <=> f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(V!0))) | ((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), V!0)) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(V!0))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(35,plain,
% 0.18/0.44 (f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(V!0))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[34, 33, 20])).
% 0.18/0.44 tff(36,plain,
% 0.18/0.44 ((~((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(V!0))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))))) | (~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(V!0))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(37,plain,
% 0.18/0.44 (~((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(V!0))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[36, 35, 1])).
% 0.18/0.45 tff(38,assumption,(((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))) <=> f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))), introduced(assumption)).
% 0.18/0.45 tff(39,plain,
% 0.18/0.45 ((~![Z: $i, X: $i] : (~(((~f(X, Z)) | f(X, X)) <=> f(X, tptp_fun_Y_1(Z))))) | (~(((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))) <=> f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(40,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[39, 17, 38])).
% 0.18/0.45 tff(41,plain,(~(((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))) <=> f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.45 tff(42,plain,
% 0.18/0.45 ((((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))) <=> f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))) | ((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(43,plain,
% 0.18/0.45 (((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.18/0.45 tff(44,plain,
% 0.18/0.45 ((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[43, 1])).
% 0.18/0.45 tff(45,plain,
% 0.18/0.45 ((~((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))))) | (~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(46,plain,
% 0.18/0.45 (~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[45, 44, 1])).
% 0.18/0.45 tff(47,assumption,(((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(V!0)))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))) <=> f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))), introduced(assumption)).
% 0.18/0.45 tff(48,plain,
% 0.18/0.45 ((~![Z: $i, X: $i] : (~(((~f(X, Z)) | f(X, X)) <=> f(X, tptp_fun_Y_1(Z))))) | (~(((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(V!0)))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))) <=> f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(49,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[48, 17, 47])).
% 0.18/0.45 tff(50,plain,(~(((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(V!0)))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))) <=> f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.45 tff(51,plain,
% 0.18/0.45 ((((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(V!0)))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))) <=> f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))) | ((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(V!0)))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(52,plain,
% 0.18/0.45 (((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(V!0)))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.18/0.45 tff(53,plain,
% 0.18/0.45 ((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(V!0)))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[52, 46])).
% 0.18/0.45 tff(54,plain,
% 0.18/0.45 ((~((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(V!0)))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))))) | (~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(V!0)))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(55,plain,
% 0.18/0.45 (~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(V!0)))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[54, 53, 1])).
% 0.18/0.45 tff(56,assumption,(((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(V!0))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))) <=> f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), introduced(assumption)).
% 0.18/0.45 tff(57,plain,
% 0.18/0.45 ((~![Z: $i, X: $i] : (~(((~f(X, Z)) | f(X, X)) <=> f(X, tptp_fun_Y_1(Z))))) | (~(((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(V!0))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))) <=> f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(58,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[57, 17, 56])).
% 0.18/0.45 tff(59,plain,(~(((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(V!0))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))) <=> f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(V!0))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.45 tff(60,plain,
% 0.18/0.45 ((((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(V!0))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))) <=> f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(V!0)))) | ((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(V!0))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(V!0)))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(61,plain,
% 0.18/0.45 (((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(V!0))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(V!0)))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.18/0.45 tff(62,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[61, 55, 37])).
% 0.18/0.45 tff(63,plain,(f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.45 tff(64,plain,
% 0.18/0.45 (((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))) | (~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(65,plain,
% 0.18/0.45 ((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.18/0.45 tff(66,plain,
% 0.18/0.45 ((((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))) <=> f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))))) | (~((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))))) | (~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))))),
% 0.18/0.45 inference(tautology,[status(thm)],[])).
% 0.18/0.45 tff(67,plain,
% 0.18/0.45 ((~((~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))) | f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))))) | (~f(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0)))), tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(tptp_fun_Y_1(V!0))))))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[66, 41])).
% 0.18/0.45 tff(68,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[67, 65, 63])).
% 0.18/0.45 % SZS output end Proof
% 0.18/0.45 % E exiting
%------------------------------------------------------------------------------