%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN357+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:38:53 AM UTC 2025
% Result : Theorem 0.19s 0.36s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN357+1 : TPTP v9.0.0. Released v2.0.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n001.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % 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 12:36:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.36 % SZS status Theorem
% 0.19/0.36 % SZS output start Proof
% 0.19/0.36 tff(big_p_type, type, (
% 0.19/0.36 big_p: $i > $o)).
% 0.19/0.36 tff(tptp_fun_X_0_type, type, (
% 0.19/0.36 tptp_fun_X_0: $i)).
% 0.19/0.36 tff(1,plain,
% 0.19/0.36 (((~![Y: $i] : (~(big_p(Y) | (~big_p(X!0))))) | $false) <=> (~![Y: $i] : (~(big_p(Y) | (~big_p(X!0)))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(2,plain,
% 0.19/0.36 ((~$true) <=> $false),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(3,plain,
% 0.19/0.36 ((big_p(X!0) | (~big_p(X!0))) <=> $true),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(4,plain,
% 0.19/0.36 ((~(big_p(X!0) | (~big_p(X!0)))) <=> (~$true)),
% 0.19/0.36 inference(monotonicity,[status(thm)],[3])).
% 0.19/0.36 tff(5,plain,
% 0.19/0.36 ((~(big_p(X!0) | (~big_p(X!0)))) <=> $false),
% 0.19/0.36 inference(transitivity,[status(thm)],[4, 2])).
% 0.19/0.36 tff(6,plain,
% 0.19/0.36 (((~![Y: $i] : (~(big_p(Y) | (~big_p(X!0))))) | (~(big_p(X!0) | (~big_p(X!0))))) <=> ((~![Y: $i] : (~(big_p(Y) | (~big_p(X!0))))) | $false)),
% 0.19/0.36 inference(monotonicity,[status(thm)],[5])).
% 0.19/0.36 tff(7,plain,
% 0.19/0.36 (((~![Y: $i] : (~(big_p(Y) | (~big_p(X!0))))) | (~(big_p(X!0) | (~big_p(X!0))))) <=> (~![Y: $i] : (~(big_p(Y) | (~big_p(X!0)))))),
% 0.19/0.36 inference(transitivity,[status(thm)],[6, 1])).
% 0.19/0.36 tff(8,plain,
% 0.19/0.36 ((~![Y: $i] : (~(big_p(Y) | (~big_p(X!0))))) | (~(big_p(X!0) | (~big_p(X!0))))),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(9,plain,
% 0.19/0.36 (~![Y: $i] : (~(big_p(Y) | (~big_p(X!0))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.36 tff(10,plain,
% 0.19/0.36 (^[Y: $i] : refl((~(big_p(Y) | (~big_p(X!0)))) <=> (~(big_p(Y) | (~big_p(X!0)))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(11,plain,
% 0.19/0.36 (![Y: $i] : (~(big_p(Y) | (~big_p(X!0)))) <=> ![Y: $i] : (~(big_p(Y) | (~big_p(X!0))))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.36 tff(12,plain,
% 0.19/0.36 ((~![X: $i] : ?[Y: $i] : (big_p(Y) | (~big_p(X)))) <=> (~![X: $i] : ?[Y: $i] : (big_p(Y) | (~big_p(X))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(13,plain,
% 0.19/0.36 ((~![X: $i] : ?[Y: $i] : (big_p(X) => big_p(Y))) <=> (~![X: $i] : ?[Y: $i] : (big_p(Y) | (~big_p(X))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(14,axiom,(~![X: $i] : ?[Y: $i] : (big_p(X) => big_p(Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','x2108')).
% 0.19/0.36 tff(15,plain,
% 0.19/0.36 (~![X: $i] : ?[Y: $i] : (big_p(Y) | (~big_p(X)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.36 tff(16,plain,
% 0.19/0.36 (~![X: $i] : ?[Y: $i] : (big_p(Y) | (~big_p(X)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.19/0.36 tff(17,plain,
% 0.19/0.36 (~![X: $i] : ?[Y: $i] : (big_p(Y) | (~big_p(X)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.36 tff(18,plain,
% 0.19/0.36 (~![X: $i] : ?[Y: $i] : (big_p(Y) | (~big_p(X)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.19/0.36 tff(19,plain,(
% 0.19/0.36 $oeq((~?[Y: $i] : (big_p(Y) | (~big_p(X!0)))), ![Y: $i] : (~(big_p(Y) | (~big_p(X!0)))))),
% 0.19/0.36 inference(transitivity,[status(sab)],[18])).
% 0.19/0.36 tff(20,plain,
% 0.19/0.36 (![Y: $i] : (~(big_p(Y) | (~big_p(X!0))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[19, 11])).
% 0.19/0.36 tff(21,plain,
% 0.19/0.36 ($false),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[20, 9])).
% 0.19/0.36 % SZS output end Proof
% 0.19/0.37 % E exiting
%------------------------------------------------------------------------------