%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN378+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:38:56 AM UTC 2025
% Result : Theorem 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SYN378+1 : TPTP v9.0.0. Released v2.0.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 12:33:25 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.37 % SZS status Theorem
% 0.20/0.37 % SZS output start Proof
% 0.20/0.37 tff(big_p_type, type, (
% 0.20/0.37 big_p: $i > $o)).
% 0.20/0.37 tff(tptp_fun_Y_0_type, type, (
% 0.20/0.37 tptp_fun_Y_0: $i)).
% 0.20/0.37 tff(big_q_type, type, (
% 0.20/0.37 big_q: $i > $o)).
% 0.20/0.37 tff(1,plain,
% 0.20/0.37 (?[Y: $i] : big_q(Y) <=> ?[Y: $i] : big_q(Y)),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(2,plain,
% 0.20/0.37 ((~(![X: $i] : big_p(X) => ((~?[Y: $i] : big_q(Y)) | ?[Z: $i] : (big_p(Z) => big_q(Z))))) <=> (~((~?[Y: $i] : big_q(Y)) | ?[Z: $i] : (big_q(Z) | (~big_p(Z))) | (~![X: $i] : big_p(X))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(3,axiom,(~(![X: $i] : big_p(X) => ((~?[Y: $i] : big_q(Y)) | ?[Z: $i] : (big_p(Z) => big_q(Z))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','x2130')).
% 0.20/0.37 tff(4,plain,
% 0.20/0.37 (~((~?[Y: $i] : big_q(Y)) | ?[Z: $i] : (big_q(Z) | (~big_p(Z))) | (~![X: $i] : big_p(X)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.37 tff(5,plain,
% 0.20/0.37 (?[Y: $i] : big_q(Y)),
% 0.20/0.37 inference(or_elim,[status(thm)],[4])).
% 0.20/0.37 tff(6,plain,
% 0.20/0.37 (?[Y: $i] : big_q(Y)),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.37 tff(7,plain,(
% 0.20/0.37 big_q(Y!0)),
% 0.20/0.37 inference(skolemize,[status(sab)],[6])).
% 0.20/0.37 tff(8,plain,
% 0.20/0.37 ((big_q(Y!0) | (~big_p(Y!0))) | (~big_q(Y!0))),
% 0.20/0.37 inference(tautology,[status(thm)],[])).
% 0.20/0.37 tff(9,plain,
% 0.20/0.37 (big_q(Y!0) | (~big_p(Y!0))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.37 tff(10,plain,
% 0.20/0.37 (^[Z: $i] : refl((~(big_q(Z) | (~big_p(Z)))) <=> (~(big_q(Z) | (~big_p(Z)))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(11,plain,
% 0.20/0.37 (![Z: $i] : (~(big_q(Z) | (~big_p(Z)))) <=> ![Z: $i] : (~(big_q(Z) | (~big_p(Z))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.37 tff(12,plain,
% 0.20/0.37 ((~?[Z: $i] : (big_q(Z) | (~big_p(Z)))) <=> (~?[Z: $i] : (big_q(Z) | (~big_p(Z))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(13,plain,
% 0.20/0.37 (~?[Z: $i] : (big_q(Z) | (~big_p(Z)))),
% 0.20/0.37 inference(or_elim,[status(thm)],[4])).
% 0.20/0.37 tff(14,plain,
% 0.20/0.37 (~?[Z: $i] : (big_q(Z) | (~big_p(Z)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.37 tff(15,plain,
% 0.20/0.37 (~?[Z: $i] : (big_q(Z) | (~big_p(Z)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[14, 12])).
% 0.20/0.37 tff(16,plain,
% 0.20/0.37 (~?[Z: $i] : (big_q(Z) | (~big_p(Z)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.20/0.37 tff(17,plain,
% 0.20/0.37 (^[Z: $i] : refl($oeq((~(big_q(Z) | (~big_p(Z)))), (~(big_q(Z) | (~big_p(Z))))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(18,plain,(
% 0.20/0.37 ![Z: $i] : (~(big_q(Z) | (~big_p(Z))))),
% 0.20/0.37 inference(nnf-neg,[status(sab)],[16, 17])).
% 0.20/0.37 tff(19,plain,
% 0.20/0.37 (![Z: $i] : (~(big_q(Z) | (~big_p(Z))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.20/0.37 tff(20,plain,
% 0.20/0.37 ((~![Z: $i] : (~(big_q(Z) | (~big_p(Z))))) | (~(big_q(Y!0) | (~big_p(Y!0))))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(21,plain,
% 0.20/0.37 ($false),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[20, 19, 9])).
% 0.20/0.37 % SZS output end Proof
% 0.20/0.38 % E exiting
%------------------------------------------------------------------------------