%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN971+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 05:41:05 AM UTC 2025
% Result : Theorem 0.18s 0.36s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SYN971+1 : TPTP v9.0.0. Released v3.1.0.
% 0.02/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.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
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 13:03:35 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.36 % SZS status Theorem
% 0.18/0.36 % SZS output start Proof
% 0.18/0.36 tff(p_type, type, (
% 0.18/0.36 p: $i > $o)).
% 0.18/0.36 tff(tptp_fun_X_0_type, type, (
% 0.18/0.36 tptp_fun_X_0: $i)).
% 0.18/0.36 tff(1,plain,
% 0.18/0.36 (((~![Y: $i] : (~(p(Y) | (~p(X!0))))) | $false) <=> (~![Y: $i] : (~(p(Y) | (~p(X!0)))))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(2,plain,
% 0.18/0.36 ((~$true) <=> $false),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(3,plain,
% 0.18/0.36 ((p(X!0) | (~p(X!0))) <=> $true),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(4,plain,
% 0.18/0.36 ((~(p(X!0) | (~p(X!0)))) <=> (~$true)),
% 0.18/0.36 inference(monotonicity,[status(thm)],[3])).
% 0.18/0.36 tff(5,plain,
% 0.18/0.36 ((~(p(X!0) | (~p(X!0)))) <=> $false),
% 0.18/0.36 inference(transitivity,[status(thm)],[4, 2])).
% 0.18/0.36 tff(6,plain,
% 0.18/0.36 (((~![Y: $i] : (~(p(Y) | (~p(X!0))))) | (~(p(X!0) | (~p(X!0))))) <=> ((~![Y: $i] : (~(p(Y) | (~p(X!0))))) | $false)),
% 0.18/0.36 inference(monotonicity,[status(thm)],[5])).
% 0.18/0.36 tff(7,plain,
% 0.18/0.36 (((~![Y: $i] : (~(p(Y) | (~p(X!0))))) | (~(p(X!0) | (~p(X!0))))) <=> (~![Y: $i] : (~(p(Y) | (~p(X!0)))))),
% 0.18/0.36 inference(transitivity,[status(thm)],[6, 1])).
% 0.18/0.36 tff(8,plain,
% 0.18/0.36 ((~![Y: $i] : (~(p(Y) | (~p(X!0))))) | (~(p(X!0) | (~p(X!0))))),
% 0.18/0.36 inference(quant_inst,[status(thm)],[])).
% 0.18/0.36 tff(9,plain,
% 0.18/0.36 (~![Y: $i] : (~(p(Y) | (~p(X!0))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.18/0.36 tff(10,plain,
% 0.18/0.36 (^[Y: $i] : refl((~(p(Y) | (~p(X!0)))) <=> (~(p(Y) | (~p(X!0)))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(11,plain,
% 0.18/0.36 (![Y: $i] : (~(p(Y) | (~p(X!0)))) <=> ![Y: $i] : (~(p(Y) | (~p(X!0))))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[10])).
% 0.18/0.36 tff(12,plain,
% 0.18/0.36 (^[Y: $i] : rewrite(((~p(Y)) & p(X!0)) <=> (~(p(Y) | (~p(X!0)))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(13,plain,
% 0.18/0.36 (![Y: $i] : ((~p(Y)) & p(X!0)) <=> ![Y: $i] : (~(p(Y) | (~p(X!0))))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[12])).
% 0.18/0.36 tff(14,plain,
% 0.18/0.36 ((~?[Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) <=> (~?[Y: $i] : (p(Y) | (~?[X: $i] : p(X))))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(15,plain,
% 0.18/0.36 ((~?[Y: $i] : (?[X: $i] : p(X) => p(Y))) <=> (~?[Y: $i] : (p(Y) | (~?[X: $i] : p(X))))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(16,axiom,(~?[Y: $i] : (?[X: $i] : p(X) => p(Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.18/0.36 tff(17,plain,
% 0.18/0.36 (~?[Y: $i] : (p(Y) | (~?[X: $i] : p(X)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.18/0.36 tff(18,plain,
% 0.18/0.36 (~?[Y: $i] : (p(Y) | (~?[X: $i] : p(X)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.18/0.36 tff(19,plain,
% 0.18/0.36 (~?[Y: $i] : (p(Y) | (~?[X: $i] : p(X)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.18/0.36 tff(20,plain,
% 0.18/0.36 (~?[Y: $i] : (p(Y) | (~?[X: $i] : p(X)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.18/0.36 tff(21,plain,
% 0.18/0.36 (^[Y: $i] : nnf_neg(refl($oeq((~p(Y)), (~p(Y)))), nnf_neg(sk($oeq(?[X: $i] : p(X), p(X!0))), $oeq((~(~?[X: $i] : p(X))), p(X!0))), $oeq((~(p(Y) | (~?[X: $i] : p(X)))), ((~p(Y)) & p(X!0))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(22,plain,(
% 0.18/0.36 ![Y: $i] : ((~p(Y)) & p(X!0))),
% 0.18/0.36 inference(nnf-neg,[status(sab)],[20, 21])).
% 0.18/0.36 tff(23,plain,
% 0.18/0.36 (![Y: $i] : (~(p(Y) | (~p(X!0))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[22, 13])).
% 0.18/0.36 tff(24,plain,
% 0.18/0.36 (![Y: $i] : (~(p(Y) | (~p(X!0))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[23, 11])).
% 0.18/0.36 tff(25,plain,
% 0.18/0.36 ($false),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[24, 9])).
% 0.18/0.36 % SZS output end Proof
% 0.18/0.36 % E exiting
%------------------------------------------------------------------------------