%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN051-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN051-1 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.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 12:26:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(big_f_type, type, (
% 0.12/0.37 big_f: $i > $o)).
% 0.12/0.37 tff(p_type, type, (
% 0.12/0.37 p: $o)).
% 0.12/0.37 tff(b_type, type, (
% 0.12/0.37 b: $i)).
% 0.12/0.37 tff(a_type, type, (
% 0.12/0.37 a: $i)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (^[X: $i] : refl((p | big_f(X)) <=> (p | big_f(X)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (![X: $i] : (p | big_f(X)) <=> ![X: $i] : (p | big_f(X))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (![X: $i] : (p | big_f(X)) <=> ![X: $i] : (p | big_f(X))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(4,axiom,(![X: $i] : (p | big_f(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_3')).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (![X: $i] : (p | big_f(X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.37 tff(6,plain,(
% 0.12/0.37 ![X: $i] : (p | big_f(X))),
% 0.12/0.37 inference(skolemize,[status(sab)],[5])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (![X: $i] : (p | big_f(X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (^[X: $i] : refl(((~p) | (~big_f(X))) <=> ((~p) | (~big_f(X))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (![X: $i] : ((~p) | (~big_f(X))) <=> ![X: $i] : ((~p) | (~big_f(X)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[8])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (![X: $i] : ((~p) | (~big_f(X))) <=> ![X: $i] : ((~p) | (~big_f(X)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (^[X: $i] : rewrite(((~big_f(X)) | (~p)) <=> ((~p) | (~big_f(X))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (![X: $i] : ((~big_f(X)) | (~p)) <=> ![X: $i] : ((~p) | (~big_f(X)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[11])).
% 0.12/0.37 tff(13,axiom,(![X: $i] : ((~big_f(X)) | (~p))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_4')).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (![X: $i] : ((~p) | (~big_f(X)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (![X: $i] : ((~p) | (~big_f(X)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.12/0.37 tff(16,plain,(
% 0.12/0.37 ![X: $i] : ((~p) | (~big_f(X)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[15])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 (![X: $i] : ((~p) | (~big_f(X)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.12/0.37 tff(18,assumption,(p), introduced(assumption)).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (((~p) | big_f(a)) <=> ((~p) | big_f(a))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(20,axiom,((~p) | big_f(a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_1')).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 ((~p) | big_f(a)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 ((~p) | big_f(a)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[21, 19])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 ((~p) | big_f(a)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[22, 19])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 ((~p) | big_f(a)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 ((~p) | big_f(a)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[24, 19])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (big_f(a)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[25, 18])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 (((~![X: $i] : ((~p) | (~big_f(X)))) | ((~p) | (~big_f(a)))) <=> ((~![X: $i] : ((~p) | (~big_f(X)))) | (~p) | (~big_f(a)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 ((~![X: $i] : ((~p) | (~big_f(X)))) | ((~p) | (~big_f(a)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 ((~![X: $i] : ((~p) | (~big_f(X)))) | (~p) | (~big_f(a))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[29, 18, 26, 17])).
% 0.12/0.37 tff(31,plain,(~p), inference(lemma,lemma(discharge,[]))).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 ((p | (~big_f(b))) <=> (p | (~big_f(b)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(33,plain,
% 0.12/0.37 (((~big_f(b)) | p) <=> (p | (~big_f(b)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(34,axiom,((~big_f(b)) | p), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_2')).
% 0.12/0.37 tff(35,plain,
% 0.12/0.37 (p | (~big_f(b))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.12/0.37 tff(36,plain,
% 0.12/0.37 (p | (~big_f(b))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[35, 32])).
% 0.12/0.37 tff(37,plain,
% 0.12/0.37 (~big_f(b)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[36, 31])).
% 0.12/0.37 tff(38,plain,
% 0.12/0.37 (((~![X: $i] : (p | big_f(X))) | (p | big_f(b))) <=> ((~![X: $i] : (p | big_f(X))) | p | big_f(b))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(39,plain,
% 0.12/0.37 ((~![X: $i] : (p | big_f(X))) | (p | big_f(b))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(40,plain,
% 0.12/0.37 ((~![X: $i] : (p | big_f(X))) | p | big_f(b)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.12/0.37 tff(41,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[40, 31, 37, 7])).
% 0.12/0.37 % SZS output end Proof
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------