%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN051+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:38:03 AM UTC 2025
% Result : Theorem 0.14s 0.40s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SYN051+1 : TPTP v9.0.0. Released v2.0.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 12:27:08 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.14/0.40 % SZS status Theorem
% 0.14/0.40 % SZS output start Proof
% 0.14/0.40 tff(big_f_type, type, (
% 0.14/0.40 big_f: $i > $o)).
% 0.14/0.40 tff(tptp_fun_X_1_type, type, (
% 0.14/0.40 tptp_fun_X_1: $i)).
% 0.14/0.40 tff(p_type, type, (
% 0.14/0.40 p: $o)).
% 0.14/0.40 tff(tptp_fun_X_0_type, type, (
% 0.14/0.40 tptp_fun_X_0: $i)).
% 0.14/0.40 tff(1,assumption,(p), introduced(assumption)).
% 0.14/0.40 tff(2,plain,
% 0.14/0.40 (?[X: $i] : (big_f(X) | (~p)) <=> ?[X: $i] : (big_f(X) | (~p))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(3,plain,
% 0.14/0.40 (^[X: $i] : rewrite((p => big_f(X)) <=> (big_f(X) | (~p)))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(4,plain,
% 0.14/0.40 (?[X: $i] : (p => big_f(X)) <=> ?[X: $i] : (big_f(X) | (~p))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.14/0.40 tff(5,axiom,(?[X: $i] : (p => big_f(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel21_1')).
% 0.14/0.40 tff(6,plain,
% 0.14/0.40 (?[X: $i] : (big_f(X) | (~p))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.14/0.40 tff(7,plain,
% 0.14/0.40 (?[X: $i] : (big_f(X) | (~p))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.14/0.40 tff(8,plain,(
% 0.14/0.40 big_f(X!0) | (~p)),
% 0.14/0.40 inference(skolemize,[status(sab)],[7])).
% 0.14/0.40 tff(9,plain,
% 0.14/0.40 (big_f(X!0)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[8, 1])).
% 0.14/0.40 tff(10,assumption,(p <=> big_f(X!0)), introduced(assumption)).
% 0.14/0.40 tff(11,plain,
% 0.14/0.40 (^[X: $i] : refl((~(p <=> big_f(X))) <=> (~(p <=> big_f(X))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(12,plain,
% 0.14/0.40 (![X: $i] : (~(p <=> big_f(X))) <=> ![X: $i] : (~(p <=> big_f(X)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.14/0.40 tff(13,plain,
% 0.14/0.40 ((~?[X: $i] : (p <=> big_f(X))) <=> (~?[X: $i] : (p <=> big_f(X)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(14,axiom,(~?[X: $i] : (p <=> big_f(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel21')).
% 0.14/0.40 tff(15,plain,
% 0.14/0.40 (~?[X: $i] : (p <=> big_f(X))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.14/0.40 tff(16,plain,
% 0.14/0.40 (~?[X: $i] : (p <=> big_f(X))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[15, 13])).
% 0.14/0.40 tff(17,plain,
% 0.14/0.40 (~?[X: $i] : (p <=> big_f(X))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.14/0.40 tff(18,plain,
% 0.14/0.40 (~?[X: $i] : (p <=> big_f(X))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.14/0.40 tff(19,plain,
% 0.14/0.40 (^[X: $i] : refl($oeq((~(p <=> big_f(X))), (~(p <=> big_f(X)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(20,plain,(
% 0.14/0.40 ![X: $i] : (~(p <=> big_f(X)))),
% 0.14/0.40 inference(nnf-neg,[status(sab)],[18, 19])).
% 0.14/0.40 tff(21,plain,
% 0.14/0.40 (![X: $i] : (~(p <=> big_f(X)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[20, 12])).
% 0.14/0.40 tff(22,plain,
% 0.14/0.40 ((~![X: $i] : (~(p <=> big_f(X)))) | (~(p <=> big_f(X!0)))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(23,plain,
% 0.14/0.40 ($false),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[22, 21, 10])).
% 0.14/0.40 tff(24,plain,(~(p <=> big_f(X!0))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.40 tff(25,plain,
% 0.14/0.40 ((p <=> big_f(X!0)) | (~p) | (~big_f(X!0))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(26,plain,
% 0.14/0.40 ((~p) | (~big_f(X!0))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.14/0.40 tff(27,plain,
% 0.14/0.40 ($false),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[26, 9, 1])).
% 0.14/0.40 tff(28,plain,(~p), inference(lemma,lemma(discharge,[]))).
% 0.14/0.40 tff(29,plain,
% 0.14/0.40 (?[X: $i] : (p | (~big_f(X))) <=> ?[X: $i] : (p | (~big_f(X)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(30,plain,
% 0.14/0.40 (^[X: $i] : rewrite((big_f(X) => p) <=> (p | (~big_f(X))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(31,plain,
% 0.14/0.40 (?[X: $i] : (big_f(X) => p) <=> ?[X: $i] : (p | (~big_f(X)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[30])).
% 0.14/0.40 tff(32,axiom,(?[X: $i] : (big_f(X) => p)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel21_2')).
% 0.14/0.40 tff(33,plain,
% 0.14/0.40 (?[X: $i] : (p | (~big_f(X)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.14/0.40 tff(34,plain,
% 0.14/0.40 (?[X: $i] : (p | (~big_f(X)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.14/0.40 tff(35,plain,(
% 0.14/0.40 p | (~big_f(X!1))),
% 0.14/0.40 inference(skolemize,[status(sab)],[34])).
% 0.14/0.40 tff(36,plain,
% 0.14/0.40 (~big_f(X!1)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[35, 28])).
% 0.14/0.40 tff(37,plain,
% 0.14/0.40 ((p <=> big_f(X!1)) | p | big_f(X!1)),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(38,plain,
% 0.14/0.40 (p <=> big_f(X!1)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[37, 28, 36])).
% 0.14/0.40 tff(39,plain,
% 0.14/0.40 ((~![X: $i] : (~(p <=> big_f(X)))) | (~(p <=> big_f(X!1)))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(40,plain,
% 0.14/0.40 ($false),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[39, 21, 38])).
% 0.14/0.40 % SZS output end Proof
% 0.14/0.40 % E exiting
%------------------------------------------------------------------------------