%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN945+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:41:03 AM UTC 2025
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN945+1 : TPTP v9.0.0. Released v3.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.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 13:02:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % SZS output start Proof
% 0.12/0.36 tff(p_type, type, (
% 0.12/0.36 p: $i > $o)).
% 0.12/0.36 tff(tptp_fun_A_1_type, type, (
% 0.12/0.36 tptp_fun_A_1: $i)).
% 0.12/0.36 tff(tptp_fun_B_0_type, type, (
% 0.12/0.36 tptp_fun_B_0: $i)).
% 0.12/0.36 tff(1,assumption,(~p(B!0)), introduced(assumption)).
% 0.12/0.36 tff(2,plain,
% 0.12/0.36 (^[X: $i] : refl(p(X) <=> p(X))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(3,plain,
% 0.12/0.36 (![X: $i] : p(X) <=> ![X: $i] : p(X)),
% 0.12/0.36 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.36 tff(4,plain,
% 0.12/0.36 (![X: $i] : p(X) <=> ![X: $i] : p(X)),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(5,plain,
% 0.12/0.36 ((~(![X: $i] : p(X) => ![A: $i, B: $i] : (p(A) & p(B)))) <=> (~((~![X: $i] : p(X)) | ![A: $i, B: $i] : (p(A) & p(B))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(6,axiom,(~(![X: $i] : p(X) => ![A: $i, B: $i] : (p(A) & p(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.12/0.36 tff(7,plain,
% 0.12/0.36 (~((~![X: $i] : p(X)) | ![A: $i, B: $i] : (p(A) & p(B)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.12/0.36 tff(8,plain,
% 0.12/0.36 (![X: $i] : p(X)),
% 0.12/0.36 inference(or_elim,[status(thm)],[7])).
% 0.12/0.36 tff(9,plain,
% 0.12/0.36 (![X: $i] : p(X)),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.12/0.36 tff(10,plain,(
% 0.12/0.36 ![X: $i] : p(X)),
% 0.12/0.36 inference(skolemize,[status(sab)],[9])).
% 0.12/0.36 tff(11,plain,
% 0.12/0.36 (![X: $i] : p(X)),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.12/0.36 tff(12,plain,
% 0.12/0.36 ((~![X: $i] : p(X)) | p(B!0)),
% 0.12/0.36 inference(quant_inst,[status(thm)],[])).
% 0.12/0.36 tff(13,plain,
% 0.12/0.36 ($false),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[12, 11, 1])).
% 0.12/0.36 tff(14,plain,(p(B!0)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.36 tff(15,plain,
% 0.12/0.36 ((~(~((~p(A!1)) | (~p(B!0))))) <=> ((~p(A!1)) | (~p(B!0)))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(16,plain,
% 0.12/0.36 ((p(A!1) & p(B!0)) <=> (~((~p(A!1)) | (~p(B!0))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(17,plain,
% 0.12/0.36 ((~(p(A!1) & p(B!0))) <=> (~(~((~p(A!1)) | (~p(B!0)))))),
% 0.12/0.36 inference(monotonicity,[status(thm)],[16])).
% 0.12/0.36 tff(18,plain,
% 0.12/0.36 ((~(p(A!1) & p(B!0))) <=> ((~p(A!1)) | (~p(B!0)))),
% 0.12/0.36 inference(transitivity,[status(thm)],[17, 15])).
% 0.12/0.36 tff(19,plain,
% 0.12/0.36 ((~![A: $i, B: $i] : (p(A) & p(B))) <=> (~![A: $i, B: $i] : (p(A) & p(B)))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(20,plain,
% 0.12/0.36 (~![A: $i, B: $i] : (p(A) & p(B))),
% 0.12/0.36 inference(or_elim,[status(thm)],[7])).
% 0.12/0.36 tff(21,plain,
% 0.12/0.36 (~![A: $i, B: $i] : (p(A) & p(B))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.12/0.36 tff(22,plain,
% 0.12/0.36 (~![A: $i, B: $i] : (p(A) & p(B))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[21, 19])).
% 0.12/0.36 tff(23,plain,
% 0.12/0.36 (~![A: $i, B: $i] : (p(A) & p(B))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[22, 19])).
% 0.12/0.36 tff(24,plain,(
% 0.12/0.36 ~(p(A!1) & p(B!0))),
% 0.12/0.36 inference(skolemize,[status(sab)],[23])).
% 0.12/0.36 tff(25,plain,
% 0.12/0.36 ((~p(A!1)) | (~p(B!0))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[24, 18])).
% 0.12/0.36 tff(26,plain,
% 0.12/0.36 (~p(A!1)),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[25, 14])).
% 0.12/0.36 tff(27,plain,
% 0.12/0.36 ((~![X: $i] : p(X)) | p(A!1)),
% 0.12/0.36 inference(quant_inst,[status(thm)],[])).
% 0.12/0.36 tff(28,plain,
% 0.12/0.36 ($false),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[27, 11, 26])).
% 0.12/0.36 % SZS output end Proof
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------