%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN376+1 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:38:55 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN376+1 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.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 12:37:35 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(big_p_type, type, (
% 0.12/0.37 big_p: $i > $o)).
% 0.12/0.37 tff(tptp_fun_X_2_type, type, (
% 0.12/0.37 tptp_fun_X_2: $i)).
% 0.12/0.37 tff(tptp_fun_X_1_type, type, (
% 0.12/0.37 tptp_fun_X_1: $i)).
% 0.12/0.37 tff(tptp_fun_X_0_type, type, (
% 0.12/0.37 tptp_fun_X_0: $i)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (^[Y: $i] : refl((big_p(Y) <=> big_p(X!2)) <=> (big_p(Y) <=> big_p(X!2)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (![Y: $i] : (big_p(Y) <=> big_p(X!2)) <=> ![Y: $i] : (big_p(Y) <=> big_p(X!2))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (?[X: $i] : ![Y: $i] : (big_p(Y) <=> big_p(X)) <=> ?[X: $i] : ![Y: $i] : (big_p(Y) <=> big_p(X))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 ((~(?[X: $i] : ![Y: $i] : (big_p(Y) <=> big_p(X)) => (![X: $i] : big_p(X) | ![X: $i] : (~big_p(X))))) <=> (~(![X: $i] : big_p(X) | ![X: $i] : (~big_p(X)) | (~?[X: $i] : ![Y: $i] : (big_p(Y) <=> big_p(X)))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(5,axiom,(~(?[X: $i] : ![Y: $i] : (big_p(Y) <=> big_p(X)) => (![X: $i] : big_p(X) | ![X: $i] : (~big_p(X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','x2127')).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (~(![X: $i] : big_p(X) | ![X: $i] : (~big_p(X)) | (~?[X: $i] : ![Y: $i] : (big_p(Y) <=> big_p(X))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (?[X: $i] : ![Y: $i] : (big_p(Y) <=> big_p(X))),
% 0.12/0.37 inference(or_elim,[status(thm)],[6])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (?[X: $i] : ![Y: $i] : (big_p(Y) <=> big_p(X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.37 tff(9,plain,(
% 0.12/0.37 $oeq(![Y: $i] : (big_p(Y) <=> big_p(X!2)), ![Y: $i] : (big_p(Y) <=> big_p(X!2)))),
% 0.12/0.37 inference(transitivity,[status(sab)],[8])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (![Y: $i] : (big_p(Y) <=> big_p(X!2))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 ((~![Y: $i] : (big_p(Y) <=> big_p(X!2))) | (big_p(X!1) <=> big_p(X!2))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (big_p(X!1) <=> big_p(X!2)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 ((~![Y: $i] : (big_p(Y) <=> big_p(X!2))) | (big_p(X!0) <=> big_p(X!2))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (big_p(X!0) <=> big_p(X!2)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[13, 10])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 ((~![X: $i] : big_p(X)) <=> (~![X: $i] : big_p(X))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (~![X: $i] : big_p(X)),
% 0.12/0.37 inference(or_elim,[status(thm)],[6])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 (~![X: $i] : big_p(X)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (~![X: $i] : big_p(X)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[17, 15])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (~![X: $i] : big_p(X)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.12/0.37 tff(20,plain,(
% 0.12/0.37 ~big_p(X!0)),
% 0.12/0.37 inference(skolemize,[status(sab)],[19])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 ((~(big_p(X!0) <=> big_p(X!2))) | big_p(X!0) | (~big_p(X!2))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 ((~(big_p(X!0) <=> big_p(X!2))) | (~big_p(X!2))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 (~big_p(X!2)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[22, 14])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 ((~![X: $i] : (~big_p(X))) <=> (~![X: $i] : (~big_p(X)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (~![X: $i] : (~big_p(X))),
% 0.12/0.37 inference(or_elim,[status(thm)],[6])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (~![X: $i] : (~big_p(X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 (~![X: $i] : (~big_p(X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[26, 24])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 (~![X: $i] : (~big_p(X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.12/0.37 tff(29,plain,(
% 0.12/0.37 big_p(X!1)),
% 0.12/0.37 inference(skolemize,[status(sab)],[28])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 ((~(big_p(X!1) <=> big_p(X!2))) | (~big_p(X!1)) | big_p(X!2)),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 ((~(big_p(X!1) <=> big_p(X!2))) | big_p(X!2)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[31, 23, 12])).
% 0.12/0.37 % SZS output end Proof
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------