%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN957+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:41:04 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN957+1 : TPTP v9.0.0. Released v3.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.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 13:01:37 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(a_type, type, (
% 0.12/0.37 a: ( $i * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun_Y_0_type, type, (
% 0.12/0.37 tptp_fun_Y_0: $i)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (((~![X: $i] : (~(a(X, X) <=> a(X, Y!0)))) | $false) <=> (~![X: $i] : (~(a(X, X) <=> a(X, Y!0))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 ((~$true) <=> $false),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 ((a(Y!0, Y!0) <=> a(Y!0, Y!0)) <=> $true),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 ((~(a(Y!0, Y!0) <=> a(Y!0, Y!0))) <=> (~$true)),
% 0.12/0.37 inference(monotonicity,[status(thm)],[3])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 ((~(a(Y!0, Y!0) <=> a(Y!0, Y!0))) <=> $false),
% 0.12/0.37 inference(transitivity,[status(thm)],[4, 2])).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (((~![X: $i] : (~(a(X, X) <=> a(X, Y!0)))) | (~(a(Y!0, Y!0) <=> a(Y!0, Y!0)))) <=> ((~![X: $i] : (~(a(X, X) <=> a(X, Y!0)))) | $false)),
% 0.12/0.37 inference(monotonicity,[status(thm)],[5])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (((~![X: $i] : (~(a(X, X) <=> a(X, Y!0)))) | (~(a(Y!0, Y!0) <=> a(Y!0, Y!0)))) <=> (~![X: $i] : (~(a(X, X) <=> a(X, Y!0))))),
% 0.12/0.37 inference(transitivity,[status(thm)],[6, 1])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 ((~![X: $i] : (~(a(X, X) <=> a(X, Y!0)))) | (~(a(Y!0, Y!0) <=> a(Y!0, Y!0)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (~![X: $i] : (~(a(X, X) <=> a(X, Y!0)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (^[X: $i] : refl((~(a(X, X) <=> a(X, Y!0))) <=> (~(a(X, X) <=> a(X, Y!0))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (![X: $i] : (~(a(X, X) <=> a(X, Y!0))) <=> ![X: $i] : (~(a(X, X) <=> a(X, Y!0)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[10])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (?[Y: $i] : ![X: $i] : (~(a(X, X) <=> a(X, Y))) <=> ?[Y: $i] : ![X: $i] : (~(a(X, X) <=> a(X, Y)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 ((~(~?[Y: $i] : ![X: $i] : (~(a(X, X) <=> a(X, Y))))) <=> ?[Y: $i] : ![X: $i] : (~(a(X, X) <=> a(X, Y)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 ((~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X)))) <=> (~?[Y: $i] : ![X: $i] : (~(a(X, X) <=> a(X, Y))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 ((~(~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X))))) <=> (~(~?[Y: $i] : ![X: $i] : (~(a(X, X) <=> a(X, Y)))))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[14])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 ((~(~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X))))) <=> ?[Y: $i] : ![X: $i] : (~(a(X, X) <=> a(X, Y)))),
% 0.12/0.37 inference(transitivity,[status(thm)],[15, 13])).
% 0.12/0.37 tff(17,axiom,(~(~?[Y: $i] : ![X: $i] : (a(X, Y) <=> (~a(X, X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (?[Y: $i] : ![X: $i] : (~(a(X, X) <=> a(X, Y)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (?[Y: $i] : ![X: $i] : (~(a(X, X) <=> a(X, Y)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[18, 12])).
% 0.12/0.37 tff(20,plain,(
% 0.12/0.37 $oeq(![X: $i] : (~(a(X, X) <=> a(X, Y!0))), ![X: $i] : (~(a(X, X) <=> a(X, Y!0))))),
% 0.12/0.37 inference(transitivity,[status(sab)],[19])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 (![X: $i] : (~(a(X, X) <=> a(X, Y!0)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[20, 11])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[21, 9])).
% 0.12/0.37 % SZS output end Proof
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------