%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN981+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:41:07 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
% 0.07/0.12 % Problem : SYN981+1 : TPTP v9.0.0. Released v3.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n010.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 13:04:12 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_Y_0_type, type, (
% 0.11/0.36 tptp_fun_Y_0: $i)).
% 0.11/0.36 tff(r_type, type, (
% 0.11/0.36 r: $i > $o)).
% 0.11/0.36 tff(q_type, type, (
% 0.11/0.36 q: $i > $o)).
% 0.11/0.36 tff(1,assumption,(r(Y!0) | (~p(Y!0))), introduced(assumption)).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 (^[Z: $i] : refl((~(r(Z) | (~p(Z)))) <=> (~(r(Z) | (~p(Z)))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 (![Z: $i] : (~(r(Z) | (~p(Z)))) <=> ![Z: $i] : (~(r(Z) | (~p(Z))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[2])).
% 0.11/0.36 tff(4,plain,
% 0.11/0.36 ((~?[Z: $i] : (r(Z) | (~p(Z)))) <=> (~?[Z: $i] : (r(Z) | (~p(Z))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(5,plain,
% 0.11/0.36 ((~((![X: $i] : (p(X) => q(X)) & ?[Y: $i] : (q(Y) => r(Y))) => ?[Z: $i] : (p(Z) => r(Z)))) <=> (~((~(![X: $i] : (q(X) | (~p(X))) & ?[Y: $i] : (r(Y) | (~q(Y))))) | ?[Z: $i] : (r(Z) | (~p(Z)))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(6,axiom,(~((![X: $i] : (p(X) => q(X)) & ?[Y: $i] : (q(Y) => r(Y))) => ?[Z: $i] : (p(Z) => r(Z)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.11/0.36 tff(7,plain,
% 0.11/0.36 (~((~(![X: $i] : (q(X) | (~p(X))) & ?[Y: $i] : (r(Y) | (~q(Y))))) | ?[Z: $i] : (r(Z) | (~p(Z))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.11/0.36 tff(8,plain,
% 0.11/0.36 (~?[Z: $i] : (r(Z) | (~p(Z)))),
% 0.11/0.36 inference(or_elim,[status(thm)],[7])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 (~?[Z: $i] : (r(Z) | (~p(Z)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.11/0.36 tff(10,plain,
% 0.11/0.36 (~?[Z: $i] : (r(Z) | (~p(Z)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[9, 4])).
% 0.11/0.36 tff(11,plain,
% 0.11/0.36 (~?[Z: $i] : (r(Z) | (~p(Z)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.11/0.36 tff(12,plain,
% 0.11/0.36 (^[Z: $i] : refl($oeq((~(r(Z) | (~p(Z)))), (~(r(Z) | (~p(Z))))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(13,plain,(
% 0.11/0.36 ![Z: $i] : (~(r(Z) | (~p(Z))))),
% 0.11/0.36 inference(nnf-neg,[status(sab)],[11, 12])).
% 0.11/0.36 tff(14,plain,
% 0.11/0.36 (![Z: $i] : (~(r(Z) | (~p(Z))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[13, 3])).
% 0.11/0.36 tff(15,plain,
% 0.11/0.36 ((~![Z: $i] : (~(r(Z) | (~p(Z))))) | (~(r(Y!0) | (~p(Y!0))))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(16,plain,
% 0.11/0.36 ($false),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[15, 14, 1])).
% 0.11/0.36 tff(17,plain,(~(r(Y!0) | (~p(Y!0)))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.36 tff(18,plain,
% 0.11/0.36 ((r(Y!0) | (~p(Y!0))) | p(Y!0)),
% 0.11/0.36 inference(tautology,[status(thm)],[])).
% 0.11/0.36 tff(19,plain,
% 0.11/0.36 (p(Y!0)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.11/0.36 tff(20,plain,
% 0.11/0.36 ((r(Y!0) | (~p(Y!0))) | (~r(Y!0))),
% 0.11/0.36 inference(tautology,[status(thm)],[])).
% 0.11/0.36 tff(21,plain,
% 0.11/0.36 (~r(Y!0)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[20, 17])).
% 0.11/0.36 tff(22,plain,
% 0.11/0.36 (?[Y: $i] : (r(Y) | (~q(Y))) <=> ?[Y: $i] : (r(Y) | (~q(Y)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(23,plain,
% 0.11/0.36 (![X: $i] : (q(X) | (~p(X))) & ?[Y: $i] : (r(Y) | (~q(Y)))),
% 0.11/0.36 inference(or_elim,[status(thm)],[7])).
% 0.11/0.36 tff(24,plain,
% 0.11/0.36 (?[Y: $i] : (r(Y) | (~q(Y)))),
% 0.11/0.36 inference(and_elim,[status(thm)],[23])).
% 0.11/0.36 tff(25,plain,
% 0.11/0.36 (?[Y: $i] : (r(Y) | (~q(Y)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[24, 22])).
% 0.11/0.36 tff(26,plain,(
% 0.11/0.36 r(Y!0) | (~q(Y!0))),
% 0.11/0.36 inference(skolemize,[status(sab)],[25])).
% 0.11/0.36 tff(27,plain,
% 0.11/0.36 (~q(Y!0)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[26, 21])).
% 0.11/0.36 tff(28,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(29,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)],[28])).
% 0.11/0.36 tff(30,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(31,plain,
% 0.11/0.36 (![X: $i] : (q(X) | (~p(X)))),
% 0.11/0.36 inference(and_elim,[status(thm)],[23])).
% 0.11/0.36 tff(32,plain,
% 0.11/0.36 (![X: $i] : (q(X) | (~p(X)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.11/0.36 tff(33,plain,(
% 0.11/0.36 ![X: $i] : (q(X) | (~p(X)))),
% 0.11/0.36 inference(skolemize,[status(sab)],[32])).
% 0.11/0.36 tff(34,plain,
% 0.11/0.36 (![X: $i] : (q(X) | (~p(X)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.11/0.36 tff(35,plain,
% 0.11/0.36 (((~![X: $i] : (q(X) | (~p(X)))) | (q(Y!0) | (~p(Y!0)))) <=> ((~![X: $i] : (q(X) | (~p(X)))) | q(Y!0) | (~p(Y!0)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(36,plain,
% 0.11/0.36 ((~![X: $i] : (q(X) | (~p(X)))) | (q(Y!0) | (~p(Y!0)))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(37,plain,
% 0.11/0.36 ((~![X: $i] : (q(X) | (~p(X)))) | q(Y!0) | (~p(Y!0))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.11/0.36 tff(38,plain,
% 0.11/0.36 ($false),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[37, 34, 27, 19])).
% 0.11/0.36 % SZS output end Proof
% 0.11/0.36 % E exiting
%------------------------------------------------------------------------------