%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN315-1 : TPTP v9.0.0. Released v1.2.0.
% 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 05:38:43 AM UTC 2025
% Result : Unsatisfiable 0.15s 0.41s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.15 % Problem : SYN315-1 : TPTP v9.0.0. Released v1.2.0.
% 0.08/0.15 % Command : run_E %s %d THM
% 0.15/0.37 % Computer : n013.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri Jun 20 12:30:38 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.15/0.41 % SZS status Unsatisfiable
% 0.15/0.41 % SZS output start Proof
% 0.15/0.41 tff(f_type, type, (
% 0.15/0.41 f: $i > $o)).
% 0.15/0.41 tff(y_type, type, (
% 0.15/0.41 y: $i > $i)).
% 0.15/0.41 tff(elem_7_type, type, (
% 0.15/0.41 elem_7: $i)).
% 0.15/0.41 tff(p_type, type, (
% 0.15/0.41 p: $i > $o)).
% 0.15/0.41 tff(a_type, type, (
% 0.15/0.41 a: $i)).
% 0.15/0.41 tff(elem_0_type, type, (
% 0.15/0.41 elem_0: $i)).
% 0.15/0.41 tff(1,assumption,(~p(a)), introduced(assumption)).
% 0.15/0.41 tff(2,plain,
% 0.15/0.41 (^[X: $i] : refl((p(a) | f(y(X))) <=> (p(a) | f(y(X))))),
% 0.15/0.41 inference(bind,[status(th)],[])).
% 0.15/0.41 tff(3,plain,
% 0.15/0.41 (![X: $i] : (p(a) | f(y(X))) <=> ![X: $i] : (p(a) | f(y(X)))),
% 0.15/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.15/0.41 tff(4,plain,
% 0.15/0.41 (![X: $i] : (p(a) | f(y(X))) <=> ![X: $i] : (p(a) | f(y(X)))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(5,axiom,(![X: $i] : (p(a) | f(y(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause4')).
% 0.15/0.41 tff(6,plain,
% 0.15/0.41 (![X: $i] : (p(a) | f(y(X)))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.15/0.41 tff(7,plain,(
% 0.15/0.41 ![X: $i] : (p(a) | f(y(X)))),
% 0.15/0.41 inference(skolemize,[status(sab)],[6])).
% 0.15/0.41 tff(8,plain,
% 0.15/0.41 (![X: $i] : (p(a) | f(y(X)))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.15/0.41 tff(9,plain,
% 0.15/0.41 (((~![X: $i] : (p(a) | f(y(X)))) | (p(a) | f(y(elem!0)))) <=> ((~![X: $i] : (p(a) | f(y(X)))) | p(a) | f(y(elem!0)))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(10,plain,
% 0.15/0.41 ((~![X: $i] : (p(a) | f(y(X)))) | (p(a) | f(y(elem!0)))),
% 0.15/0.41 inference(quant_inst,[status(thm)],[])).
% 0.15/0.41 tff(11,plain,
% 0.15/0.41 ((~![X: $i] : (p(a) | f(y(X)))) | p(a) | f(y(elem!0))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.15/0.41 tff(12,plain,
% 0.15/0.41 (p(a) | f(y(elem!0))),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[11, 8])).
% 0.15/0.41 tff(13,plain,
% 0.15/0.41 (f(y(elem!0))),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[12, 1])).
% 0.15/0.41 tff(14,plain,
% 0.15/0.41 (^[X: $i] : refl((p(a) | (~f(X))) <=> (p(a) | (~f(X))))),
% 0.15/0.41 inference(bind,[status(th)],[])).
% 0.15/0.41 tff(15,plain,
% 0.15/0.41 (![X: $i] : (p(a) | (~f(X))) <=> ![X: $i] : (p(a) | (~f(X)))),
% 0.15/0.41 inference(quant_intro,[status(thm)],[14])).
% 0.15/0.41 tff(16,plain,
% 0.15/0.41 (![X: $i] : (p(a) | (~f(X))) <=> ![X: $i] : (p(a) | (~f(X)))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(17,plain,
% 0.15/0.41 (^[X: $i] : rewrite(((~f(X)) | p(a)) <=> (p(a) | (~f(X))))),
% 0.15/0.41 inference(bind,[status(th)],[])).
% 0.15/0.41 tff(18,plain,
% 0.15/0.41 (![X: $i] : ((~f(X)) | p(a)) <=> ![X: $i] : (p(a) | (~f(X)))),
% 0.15/0.41 inference(quant_intro,[status(thm)],[17])).
% 0.15/0.41 tff(19,axiom,(![X: $i] : ((~f(X)) | p(a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 0.15/0.41 tff(20,plain,
% 0.15/0.41 (![X: $i] : (p(a) | (~f(X)))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.15/0.41 tff(21,plain,
% 0.15/0.41 (![X: $i] : (p(a) | (~f(X)))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.15/0.41 tff(22,plain,(
% 0.15/0.41 ![X: $i] : (p(a) | (~f(X)))),
% 0.15/0.41 inference(skolemize,[status(sab)],[21])).
% 0.15/0.41 tff(23,plain,
% 0.15/0.41 (![X: $i] : (p(a) | (~f(X)))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.15/0.41 tff(24,plain,
% 0.15/0.41 (((~![X: $i] : (p(a) | (~f(X)))) | (p(a) | (~f(y(elem!0))))) <=> ((~![X: $i] : (p(a) | (~f(X)))) | p(a) | (~f(y(elem!0))))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(25,plain,
% 0.15/0.41 ((~![X: $i] : (p(a) | (~f(X)))) | (p(a) | (~f(y(elem!0))))),
% 0.15/0.41 inference(quant_inst,[status(thm)],[])).
% 0.15/0.41 tff(26,plain,
% 0.15/0.41 ((~![X: $i] : (p(a) | (~f(X)))) | p(a) | (~f(y(elem!0)))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.15/0.41 tff(27,plain,
% 0.15/0.41 ($false),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[26, 23, 1, 13])).
% 0.15/0.41 tff(28,plain,(p(a)), inference(lemma,lemma(discharge,[]))).
% 0.15/0.41 tff(29,plain,
% 0.15/0.41 (^[X: $i] : refl(((~p(a)) | (~f(y(X)))) <=> ((~p(a)) | (~f(y(X)))))),
% 0.15/0.41 inference(bind,[status(th)],[])).
% 0.15/0.41 tff(30,plain,
% 0.15/0.41 (![X: $i] : ((~p(a)) | (~f(y(X)))) <=> ![X: $i] : ((~p(a)) | (~f(y(X))))),
% 0.15/0.41 inference(quant_intro,[status(thm)],[29])).
% 0.15/0.41 tff(31,plain,
% 0.15/0.41 (![X: $i] : ((~p(a)) | (~f(y(X)))) <=> ![X: $i] : ((~p(a)) | (~f(y(X))))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(32,plain,
% 0.15/0.41 (^[X: $i] : rewrite(((~f(y(X))) | (~p(a))) <=> ((~p(a)) | (~f(y(X)))))),
% 0.15/0.41 inference(bind,[status(th)],[])).
% 0.15/0.41 tff(33,plain,
% 0.15/0.41 (![X: $i] : ((~f(y(X))) | (~p(a))) <=> ![X: $i] : ((~p(a)) | (~f(y(X))))),
% 0.15/0.41 inference(quant_intro,[status(thm)],[32])).
% 0.15/0.41 tff(34,axiom,(![X: $i] : ((~f(y(X))) | (~p(a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause3')).
% 0.15/0.41 tff(35,plain,
% 0.15/0.41 (![X: $i] : ((~p(a)) | (~f(y(X))))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.15/0.41 tff(36,plain,
% 0.15/0.41 (![X: $i] : ((~p(a)) | (~f(y(X))))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.15/0.41 tff(37,plain,(
% 0.15/0.41 ![X: $i] : ((~p(a)) | (~f(y(X))))),
% 0.15/0.41 inference(skolemize,[status(sab)],[36])).
% 0.15/0.41 tff(38,plain,
% 0.15/0.41 (![X: $i] : ((~p(a)) | (~f(y(X))))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.15/0.41 tff(39,plain,
% 0.15/0.41 (((~![X: $i] : ((~p(a)) | (~f(y(X))))) | ((~p(a)) | (~f(y(elem!7))))) <=> ((~![X: $i] : ((~p(a)) | (~f(y(X))))) | (~p(a)) | (~f(y(elem!7))))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(40,plain,
% 0.15/0.41 ((~![X: $i] : ((~p(a)) | (~f(y(X))))) | ((~p(a)) | (~f(y(elem!7))))),
% 0.15/0.41 inference(quant_inst,[status(thm)],[])).
% 0.15/0.41 tff(41,plain,
% 0.15/0.41 ((~![X: $i] : ((~p(a)) | (~f(y(X))))) | (~p(a)) | (~f(y(elem!7)))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.15/0.41 tff(42,plain,
% 0.15/0.41 (~f(y(elem!7))),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[41, 38, 28])).
% 0.15/0.41 tff(43,plain,
% 0.15/0.41 (^[X: $i] : refl(((~p(a)) | f(X)) <=> ((~p(a)) | f(X)))),
% 0.15/0.41 inference(bind,[status(th)],[])).
% 0.15/0.41 tff(44,plain,
% 0.15/0.41 (![X: $i] : ((~p(a)) | f(X)) <=> ![X: $i] : ((~p(a)) | f(X))),
% 0.15/0.41 inference(quant_intro,[status(thm)],[43])).
% 0.15/0.41 tff(45,plain,
% 0.15/0.41 (![X: $i] : ((~p(a)) | f(X)) <=> ![X: $i] : ((~p(a)) | f(X))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(46,axiom,(![X: $i] : ((~p(a)) | f(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause2')).
% 0.15/0.41 tff(47,plain,
% 0.15/0.41 (![X: $i] : ((~p(a)) | f(X))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.15/0.41 tff(48,plain,(
% 0.15/0.41 ![X: $i] : ((~p(a)) | f(X))),
% 0.15/0.41 inference(skolemize,[status(sab)],[47])).
% 0.15/0.41 tff(49,plain,
% 0.15/0.41 (![X: $i] : ((~p(a)) | f(X))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.15/0.41 tff(50,plain,
% 0.15/0.41 (((~![X: $i] : ((~p(a)) | f(X))) | ((~p(a)) | f(y(elem!7)))) <=> ((~![X: $i] : ((~p(a)) | f(X))) | (~p(a)) | f(y(elem!7)))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(51,plain,
% 0.15/0.41 ((~![X: $i] : ((~p(a)) | f(X))) | ((~p(a)) | f(y(elem!7)))),
% 0.15/0.41 inference(quant_inst,[status(thm)],[])).
% 0.15/0.41 tff(52,plain,
% 0.15/0.41 ((~![X: $i] : ((~p(a)) | f(X))) | (~p(a)) | f(y(elem!7))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.15/0.41 tff(53,plain,
% 0.15/0.41 ($false),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[52, 49, 28, 42])).
% 0.15/0.41 % SZS output end Proof
% 0.15/0.41 % E exiting
%------------------------------------------------------------------------------