%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN976+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:41:06 AM UTC 2025
% Result : Theorem 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN976+1 : TPTP v9.0.0. Released v3.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.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 13:02:18 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.37 % SZS status Theorem
% 0.20/0.37 % SZS output start Proof
% 0.20/0.37 tff(q_type, type, (
% 0.20/0.37 q: $i > $o)).
% 0.20/0.37 tff(tptp_fun_A_1_type, type, (
% 0.20/0.37 tptp_fun_A_1: $i)).
% 0.20/0.37 tff(p_type, type, (
% 0.20/0.37 p: $i > $o)).
% 0.20/0.37 tff(k!0_type, type, (
% 0.20/0.37 k!0: $o)).
% 0.20/0.37 tff(g_type, type, (
% 0.20/0.37 g: $o)).
% 0.20/0.37 tff(f_type, type, (
% 0.20/0.37 f: $o)).
% 0.20/0.37 tff(1,plain,
% 0.20/0.37 (((~q(A!1)) & (k!0 & ![X: $i] : (p(X) & q(X)))) <=> ((~q(A!1)) & k!0 & ![X: $i] : (p(X) & q(X)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(2,plain,
% 0.20/0.37 ((k!0 & ![X: $i] : (p(X) & q(X))) <=> (k!0 & ![X: $i] : (p(X) & q(X)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(3,plain,
% 0.20/0.37 (((~q(A!1)) & (k!0 & ![X: $i] : (p(X) & q(X)))) <=> ((~q(A!1)) & (k!0 & ![X: $i] : (p(X) & q(X))))),
% 0.20/0.37 inference(monotonicity,[status(thm)],[2])).
% 0.20/0.37 tff(4,plain,
% 0.20/0.37 (((~q(A!1)) & (k!0 & ![X: $i] : (p(X) & q(X)))) <=> ((~q(A!1)) & k!0 & ![X: $i] : (p(X) & q(X)))),
% 0.20/0.37 inference(transitivity,[status(thm)],[3, 1])).
% 0.20/0.37 tff(5,plain,
% 0.20/0.37 ((~![A: $i] : (q(A) | (~((f | g) & ![X: $i] : (p(X) & q(X)))))) <=> (~![A: $i] : (q(A) | (~(k!0 & ![X: $i] : (p(X) & q(X))))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(6,plain,
% 0.20/0.37 ((~![A: $i] : (q(A) | (~((f | g) & ![X: $i] : (p(X) & q(X)))))) <=> (~![A: $i] : (q(A) | (~((f | g) & ![X: $i] : (p(X) & q(X))))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(7,plain,
% 0.20/0.37 ((~![A: $i] : (((f | g) & ![X: $i] : (p(X) & q(X))) => q(A))) <=> (~![A: $i] : (q(A) | (~((f | g) & ![X: $i] : (p(X) & q(X))))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(8,axiom,(~![A: $i] : (((f | g) & ![X: $i] : (p(X) & q(X))) => q(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.20/0.37 tff(9,plain,
% 0.20/0.37 (~![A: $i] : (q(A) | (~((f | g) & ![X: $i] : (p(X) & q(X)))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.37 tff(10,plain,
% 0.20/0.37 (~![A: $i] : (q(A) | (~((f | g) & ![X: $i] : (p(X) & q(X)))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.20/0.37 tff(11,plain,
% 0.20/0.37 (~![A: $i] : (q(A) | (~((f | g) & ![X: $i] : (p(X) & q(X)))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.20/0.37 tff(12,plain,
% 0.20/0.37 (~![A: $i] : (q(A) | (~((f | g) & ![X: $i] : (p(X) & q(X)))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.20/0.37 tff(13,plain,
% 0.20/0.37 (~![A: $i] : (q(A) | (~(k!0 & ![X: $i] : (p(X) & q(X)))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.20/0.37 tff(14,plain,
% 0.20/0.37 ((~q(A!1)) & k!0 & ![X: $i] : (p(X) & q(X))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[13, 4])).
% 0.20/0.37 tff(15,plain,
% 0.20/0.37 (~q(A!1)),
% 0.20/0.37 inference(and_elim,[status(thm)],[14])).
% 0.20/0.37 tff(16,plain,
% 0.20/0.37 (((~p(A!1)) | (~q(A!1))) | q(A!1)),
% 0.20/0.37 inference(tautology,[status(thm)],[])).
% 0.20/0.37 tff(17,plain,
% 0.20/0.37 ((~p(A!1)) | (~q(A!1))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.20/0.37 tff(18,plain,
% 0.20/0.37 (^[X: $i] : refl((~((~p(X)) | (~q(X)))) <=> (~((~p(X)) | (~q(X)))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(19,plain,
% 0.20/0.37 (![X: $i] : (~((~p(X)) | (~q(X)))) <=> ![X: $i] : (~((~p(X)) | (~q(X))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.37 tff(20,plain,
% 0.20/0.37 (^[X: $i] : rewrite((p(X) & q(X)) <=> (~((~p(X)) | (~q(X)))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(21,plain,
% 0.20/0.37 (![X: $i] : (p(X) & q(X)) <=> ![X: $i] : (~((~p(X)) | (~q(X))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[20])).
% 0.20/0.37 tff(22,plain,
% 0.20/0.37 (![X: $i] : (p(X) & q(X))),
% 0.20/0.37 inference(and_elim,[status(thm)],[14])).
% 0.20/0.37 tff(23,plain,
% 0.20/0.37 (![X: $i] : (~((~p(X)) | (~q(X))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.37 tff(24,plain,
% 0.20/0.37 (![X: $i] : (~((~p(X)) | (~q(X))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.20/0.37 tff(25,plain,
% 0.20/0.37 ((~![X: $i] : (~((~p(X)) | (~q(X))))) | (~((~p(A!1)) | (~q(A!1))))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(26,plain,
% 0.20/0.37 ($false),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[25, 24, 17])).
% 0.20/0.37 % SZS output end Proof
% 0.20/0.37 % E exiting
%------------------------------------------------------------------------------