%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN052-1 : TPTP v9.0.0. Released v1.0.0.
% 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 05:38:03 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.36s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN052-1 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:27:09 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.36 % SZS status Unsatisfiable
% 0.19/0.36 % SZS output start Proof
% 0.19/0.36 tff(big_f_type, type, (
% 0.19/0.36 big_f: $i > $o)).
% 0.19/0.36 tff(a_type, type, (
% 0.19/0.36 a: $i)).
% 0.19/0.36 tff(p_type, type, (
% 0.19/0.36 p: $o)).
% 0.19/0.36 tff(1,assumption,(~big_f(a)), introduced(assumption)).
% 0.19/0.36 tff(2,plain,
% 0.19/0.36 (^[Y: $i] : refl((p | big_f(Y)) <=> (p | big_f(Y)))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(3,plain,
% 0.19/0.36 (![Y: $i] : (p | big_f(Y)) <=> ![Y: $i] : (p | big_f(Y))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.36 tff(4,plain,
% 0.19/0.36 (![Y: $i] : (p | big_f(Y)) <=> ![Y: $i] : (p | big_f(Y))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(5,plain,
% 0.19/0.36 (^[Y: $i] : rewrite((big_f(Y) | p) <=> (p | big_f(Y)))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(6,plain,
% 0.19/0.36 (![Y: $i] : (big_f(Y) | p) <=> ![Y: $i] : (p | big_f(Y))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[5])).
% 0.19/0.36 tff(7,axiom,(![Y: $i] : (big_f(Y) | p)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_3')).
% 0.19/0.36 tff(8,plain,
% 0.19/0.36 (![Y: $i] : (p | big_f(Y))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.19/0.36 tff(9,plain,
% 0.19/0.36 (![Y: $i] : (p | big_f(Y))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.19/0.36 tff(10,plain,(
% 0.19/0.36 ![Y: $i] : (p | big_f(Y))),
% 0.19/0.36 inference(skolemize,[status(sab)],[9])).
% 0.19/0.36 tff(11,plain,
% 0.19/0.36 (![Y: $i] : (p | big_f(Y))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.19/0.36 tff(12,plain,
% 0.19/0.36 (((~![Y: $i] : (p | big_f(Y))) | (p | big_f(a))) <=> ((~![Y: $i] : (p | big_f(Y))) | p | big_f(a))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(13,plain,
% 0.19/0.36 ((~![Y: $i] : (p | big_f(Y))) | (p | big_f(a))),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(14,plain,
% 0.19/0.36 ((~![Y: $i] : (p | big_f(Y))) | p | big_f(a)),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.36 tff(15,plain,
% 0.19/0.36 (p),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[14, 11, 1])).
% 0.19/0.36 tff(16,plain,
% 0.19/0.36 (^[X: $i] : refl((big_f(X) | (~p)) <=> (big_f(X) | (~p)))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(17,plain,
% 0.19/0.36 (![X: $i] : (big_f(X) | (~p)) <=> ![X: $i] : (big_f(X) | (~p))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.36 tff(18,plain,
% 0.19/0.36 (![X: $i] : (big_f(X) | (~p)) <=> ![X: $i] : (big_f(X) | (~p))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(19,axiom,(![X: $i] : (big_f(X) | (~p))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_2')).
% 0.19/0.36 tff(20,plain,
% 0.19/0.36 (![X: $i] : (big_f(X) | (~p))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.36 tff(21,plain,(
% 0.19/0.36 ![X: $i] : (big_f(X) | (~p))),
% 0.19/0.36 inference(skolemize,[status(sab)],[20])).
% 0.19/0.36 tff(22,plain,
% 0.19/0.36 (![X: $i] : (big_f(X) | (~p))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.19/0.36 tff(23,plain,
% 0.19/0.36 (((~![X: $i] : (big_f(X) | (~p))) | (big_f(a) | (~p))) <=> ((~![X: $i] : (big_f(X) | (~p))) | big_f(a) | (~p))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(24,plain,
% 0.19/0.36 ((~![X: $i] : (big_f(X) | (~p))) | (big_f(a) | (~p))),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(25,plain,
% 0.19/0.36 ((~![X: $i] : (big_f(X) | (~p))) | big_f(a) | (~p)),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.36 tff(26,plain,
% 0.19/0.36 ($false),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[25, 22, 15, 1])).
% 0.19/0.36 tff(27,plain,(big_f(a)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.36 tff(28,plain,
% 0.19/0.36 (((~p) | (~big_f(a))) <=> ((~p) | (~big_f(a)))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(29,axiom,((~p) | (~big_f(a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_4')).
% 0.19/0.36 tff(30,plain,
% 0.19/0.36 ((~p) | (~big_f(a))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.36 tff(31,plain,
% 0.19/0.36 (~p),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[30, 27])).
% 0.19/0.36 tff(32,plain,
% 0.19/0.36 (^[X: $i] : refl((p | (~big_f(X))) <=> (p | (~big_f(X))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(33,plain,
% 0.19/0.36 (![X: $i] : (p | (~big_f(X))) <=> ![X: $i] : (p | (~big_f(X)))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.36 tff(34,plain,
% 0.19/0.36 (![X: $i] : (p | (~big_f(X))) <=> ![X: $i] : (p | (~big_f(X)))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(35,axiom,(![X: $i] : (p | (~big_f(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_1')).
% 0.19/0.36 tff(36,plain,
% 0.19/0.36 (![X: $i] : (p | (~big_f(X)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.36 tff(37,plain,(
% 0.19/0.36 ![X: $i] : (p | (~big_f(X)))),
% 0.19/0.36 inference(skolemize,[status(sab)],[36])).
% 0.19/0.36 tff(38,plain,
% 0.19/0.36 (![X: $i] : (p | (~big_f(X)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.19/0.36 tff(39,plain,
% 0.19/0.36 (((~![X: $i] : (p | (~big_f(X)))) | (p | (~big_f(a)))) <=> ((~![X: $i] : (p | (~big_f(X)))) | p | (~big_f(a)))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(40,plain,
% 0.19/0.36 ((~![X: $i] : (p | (~big_f(X)))) | (p | (~big_f(a)))),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(41,plain,
% 0.19/0.36 ((~![X: $i] : (p | (~big_f(X)))) | p | (~big_f(a))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.36 tff(42,plain,
% 0.19/0.36 ($false),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[41, 38, 31, 27])).
% 0.19/0.36 % SZS output end Proof
% 0.19/0.37 % E exiting
%------------------------------------------------------------------------------