%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN953+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN953+1 : TPTP v9.0.0. Released v3.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n011.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 13:02:11 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(p_type, type, (
% 0.11/0.36 p: $i > $o)).
% 0.11/0.36 tff(tptp_fun_X_0_type, type, (
% 0.11/0.36 tptp_fun_X_0: $i)).
% 0.11/0.36 tff(q_type, type, (
% 0.11/0.36 q: $i > $o)).
% 0.11/0.36 tff(1,plain,
% 0.11/0.36 (^[X: $i] : refl((q(X) | (~p(X))) <=> (q(X) | (~p(X))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 (![X: $i] : (q(X) | (~p(X))) <=> ![X: $i] : (q(X) | (~p(X)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 (![X: $i] : (q(X) | (~p(X))) <=> ![X: $i] : (q(X) | (~p(X)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(4,plain,
% 0.11/0.36 ((~(![X: $i] : (p(X) => q(X)) => (![X: $i] : p(X) => ![X: $i] : q(X)))) <=> (~(![X: $i] : q(X) | (~![X: $i] : p(X)) | (~![X: $i] : (q(X) | (~p(X))))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(5,axiom,(~(![X: $i] : (p(X) => q(X)) => (![X: $i] : p(X) => ![X: $i] : q(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.11/0.36 tff(6,plain,
% 0.11/0.36 (~(![X: $i] : q(X) | (~![X: $i] : p(X)) | (~![X: $i] : (q(X) | (~p(X)))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.11/0.36 tff(7,plain,
% 0.11/0.36 (![X: $i] : (q(X) | (~p(X)))),
% 0.11/0.36 inference(or_elim,[status(thm)],[6])).
% 0.11/0.36 tff(8,plain,
% 0.11/0.36 (![X: $i] : (q(X) | (~p(X)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.11/0.36 tff(9,plain,(
% 0.11/0.36 ![X: $i] : (q(X) | (~p(X)))),
% 0.11/0.36 inference(skolemize,[status(sab)],[8])).
% 0.11/0.36 tff(10,plain,
% 0.11/0.36 (![X: $i] : (q(X) | (~p(X)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.11/0.36 tff(11,plain,
% 0.11/0.36 ((~![X: $i] : q(X)) <=> (~![X: $i] : q(X))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(12,plain,
% 0.11/0.36 (~![X: $i] : q(X)),
% 0.11/0.36 inference(or_elim,[status(thm)],[6])).
% 0.11/0.36 tff(13,plain,
% 0.11/0.36 (~![X: $i] : q(X)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.11/0.36 tff(14,plain,
% 0.11/0.36 (~![X: $i] : q(X)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[13, 11])).
% 0.11/0.36 tff(15,plain,
% 0.11/0.36 (~![X: $i] : q(X)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.11/0.36 tff(16,plain,(
% 0.11/0.36 ~q(X!0)),
% 0.11/0.36 inference(skolemize,[status(sab)],[15])).
% 0.11/0.36 tff(17,plain,
% 0.11/0.36 (((~![X: $i] : (q(X) | (~p(X)))) | (q(X!0) | (~p(X!0)))) <=> ((~![X: $i] : (q(X) | (~p(X)))) | q(X!0) | (~p(X!0)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(18,plain,
% 0.11/0.36 ((~![X: $i] : (q(X) | (~p(X)))) | (q(X!0) | (~p(X!0)))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(19,plain,
% 0.11/0.36 ((~![X: $i] : (q(X) | (~p(X)))) | q(X!0) | (~p(X!0))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.11/0.36 tff(20,plain,
% 0.11/0.36 (~p(X!0)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[19, 16, 10])).
% 0.11/0.36 tff(21,plain,
% 0.11/0.36 (^[X: $i] : refl(p(X) <=> p(X))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(22,plain,
% 0.11/0.36 (![X: $i] : p(X) <=> ![X: $i] : p(X)),
% 0.11/0.36 inference(quant_intro,[status(thm)],[21])).
% 0.11/0.36 tff(23,plain,
% 0.11/0.36 (![X: $i] : p(X) <=> ![X: $i] : p(X)),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(24,plain,
% 0.11/0.36 (![X: $i] : p(X)),
% 0.11/0.36 inference(or_elim,[status(thm)],[6])).
% 0.11/0.36 tff(25,plain,
% 0.11/0.36 (![X: $i] : p(X)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.11/0.36 tff(26,plain,(
% 0.11/0.36 ![X: $i] : p(X)),
% 0.11/0.36 inference(skolemize,[status(sab)],[25])).
% 0.11/0.36 tff(27,plain,
% 0.11/0.36 (![X: $i] : p(X)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.11/0.36 tff(28,plain,
% 0.11/0.36 ((~![X: $i] : p(X)) | p(X!0)),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(29,plain,
% 0.11/0.36 ($false),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[28, 27, 20])).
% 0.11/0.36 % SZS output end Proof
% 0.11/0.36 % E exiting
%------------------------------------------------------------------------------