%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN081-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:38:11 AM UTC 2025
% Result : Unsatisfiable 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SYN081-1 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 12:28:02 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.38 % SZS status Unsatisfiable
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 tff(big_f_type, type, (
% 0.13/0.38 big_f: $i > $o)).
% 0.13/0.38 tff(f_type, type, (
% 0.13/0.38 f: $i > $i)).
% 0.13/0.38 tff(elem_0_type, type, (
% 0.13/0.38 elem_0: $i)).
% 0.13/0.38 tff(1,assumption,(~big_f(f(elem!0))), introduced(assumption)).
% 0.13/0.38 tff(2,plain,
% 0.13/0.38 (^[X: $i] : refl((big_f(f(X)) | big_f(X)) <=> (big_f(f(X)) | big_f(X)))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(3,plain,
% 0.13/0.38 (![X: $i] : (big_f(f(X)) | big_f(X)) <=> ![X: $i] : (big_f(f(X)) | big_f(X))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.38 tff(4,plain,
% 0.13/0.38 (![X: $i] : (big_f(f(X)) | big_f(X)) <=> ![X: $i] : (big_f(f(X)) | big_f(X))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(5,axiom,(![X: $i] : (big_f(f(X)) | big_f(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_2')).
% 0.13/0.38 tff(6,plain,
% 0.13/0.38 (![X: $i] : (big_f(f(X)) | big_f(X))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.13/0.38 tff(7,plain,(
% 0.13/0.38 ![X: $i] : (big_f(f(X)) | big_f(X))),
% 0.13/0.38 inference(skolemize,[status(sab)],[6])).
% 0.13/0.38 tff(8,plain,
% 0.13/0.38 (![X: $i] : (big_f(f(X)) | big_f(X))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.13/0.38 tff(9,plain,
% 0.13/0.38 (((~![X: $i] : (big_f(f(X)) | big_f(X))) | (big_f(f(elem!0)) | big_f(elem!0))) <=> ((~![X: $i] : (big_f(f(X)) | big_f(X))) | big_f(f(elem!0)) | big_f(elem!0))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(10,plain,
% 0.13/0.38 ((~![X: $i] : (big_f(f(X)) | big_f(X))) | (big_f(f(elem!0)) | big_f(elem!0))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(11,plain,
% 0.13/0.38 ((~![X: $i] : (big_f(f(X)) | big_f(X))) | big_f(f(elem!0)) | big_f(elem!0)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.13/0.38 tff(12,plain,
% 0.13/0.38 (big_f(f(elem!0)) | big_f(elem!0)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[11, 8])).
% 0.13/0.38 tff(13,plain,
% 0.13/0.38 (big_f(elem!0)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[12, 1])).
% 0.13/0.38 tff(14,plain,
% 0.13/0.38 (^[X: $i] : refl((big_f(f(X)) | (~big_f(X))) <=> (big_f(f(X)) | (~big_f(X))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(15,plain,
% 0.13/0.38 (![X: $i] : (big_f(f(X)) | (~big_f(X))) <=> ![X: $i] : (big_f(f(X)) | (~big_f(X)))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[14])).
% 0.13/0.38 tff(16,plain,
% 0.13/0.38 (![X: $i] : (big_f(f(X)) | (~big_f(X))) <=> ![X: $i] : (big_f(f(X)) | (~big_f(X)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(17,plain,
% 0.13/0.38 (^[X: $i] : rewrite(((~big_f(X)) | big_f(f(X))) <=> (big_f(f(X)) | (~big_f(X))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(18,plain,
% 0.13/0.38 (![X: $i] : ((~big_f(X)) | big_f(f(X))) <=> ![X: $i] : (big_f(f(X)) | (~big_f(X)))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[17])).
% 0.13/0.38 tff(19,axiom,(![X: $i] : ((~big_f(X)) | big_f(f(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.13/0.38 tff(20,plain,
% 0.13/0.38 (![X: $i] : (big_f(f(X)) | (~big_f(X)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.13/0.38 tff(21,plain,
% 0.13/0.38 (![X: $i] : (big_f(f(X)) | (~big_f(X)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.13/0.38 tff(22,plain,(
% 0.13/0.38 ![X: $i] : (big_f(f(X)) | (~big_f(X)))),
% 0.13/0.38 inference(skolemize,[status(sab)],[21])).
% 0.13/0.38 tff(23,plain,
% 0.13/0.38 (![X: $i] : (big_f(f(X)) | (~big_f(X)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.13/0.38 tff(24,plain,
% 0.13/0.38 (((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | (big_f(f(elem!0)) | (~big_f(elem!0)))) <=> ((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | big_f(f(elem!0)) | (~big_f(elem!0)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(25,plain,
% 0.13/0.38 ((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | (big_f(f(elem!0)) | (~big_f(elem!0)))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(26,plain,
% 0.13/0.38 ((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | big_f(f(elem!0)) | (~big_f(elem!0))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.13/0.38 tff(27,plain,
% 0.13/0.38 ($false),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[26, 23, 1, 13])).
% 0.13/0.38 tff(28,plain,(big_f(f(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.38 tff(29,plain,
% 0.13/0.38 (^[X: $i] : refl(((~big_f(X)) | (~big_f(f(X)))) <=> ((~big_f(X)) | (~big_f(f(X)))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(30,plain,
% 0.13/0.38 (![X: $i] : ((~big_f(X)) | (~big_f(f(X)))) <=> ![X: $i] : ((~big_f(X)) | (~big_f(f(X))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[29])).
% 0.13/0.38 tff(31,plain,
% 0.13/0.38 (![X: $i] : ((~big_f(X)) | (~big_f(f(X)))) <=> ![X: $i] : ((~big_f(X)) | (~big_f(f(X))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(32,axiom,(![X: $i] : ((~big_f(X)) | (~big_f(f(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_1')).
% 0.13/0.38 tff(33,plain,
% 0.13/0.38 (![X: $i] : ((~big_f(X)) | (~big_f(f(X))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.13/0.38 tff(34,plain,(
% 0.13/0.38 ![X: $i] : ((~big_f(X)) | (~big_f(f(X))))),
% 0.13/0.38 inference(skolemize,[status(sab)],[33])).
% 0.13/0.38 tff(35,plain,
% 0.13/0.38 (![X: $i] : ((~big_f(X)) | (~big_f(f(X))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.13/0.38 tff(36,plain,
% 0.13/0.38 (((~![X: $i] : ((~big_f(X)) | (~big_f(f(X))))) | ((~big_f(f(elem!0))) | (~big_f(f(f(elem!0)))))) <=> ((~![X: $i] : ((~big_f(X)) | (~big_f(f(X))))) | (~big_f(f(elem!0))) | (~big_f(f(f(elem!0)))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(37,plain,
% 0.13/0.38 ((~![X: $i] : ((~big_f(X)) | (~big_f(f(X))))) | ((~big_f(f(elem!0))) | (~big_f(f(f(elem!0)))))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(38,plain,
% 0.13/0.38 ((~![X: $i] : ((~big_f(X)) | (~big_f(f(X))))) | (~big_f(f(elem!0))) | (~big_f(f(f(elem!0))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.13/0.38 tff(39,plain,
% 0.13/0.38 (~big_f(f(f(elem!0)))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[38, 35, 28])).
% 0.13/0.38 tff(40,plain,
% 0.13/0.38 (((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | (big_f(f(f(elem!0))) | (~big_f(f(elem!0))))) <=> ((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | big_f(f(f(elem!0))) | (~big_f(f(elem!0))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(41,plain,
% 0.13/0.38 ((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | (big_f(f(f(elem!0))) | (~big_f(f(elem!0))))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(42,plain,
% 0.13/0.38 ((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | big_f(f(f(elem!0))) | (~big_f(f(elem!0)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.13/0.38 tff(43,plain,
% 0.13/0.38 ($false),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[42, 23, 28, 39])).
% 0.13/0.38 % SZS output end Proof
% 0.13/0.38 % E exiting
%------------------------------------------------------------------------------