%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN367+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:38:54 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
% 0.03/0.11 % Problem : SYN367+1 : TPTP v9.0.0. Released v2.0.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n013.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 12:32:38 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.19/0.36 % SZS status Theorem
% 0.19/0.36 % SZS output start Proof
% 0.19/0.36 tff(big_q_type, type, (
% 0.19/0.36 big_q: $i > $o)).
% 0.19/0.36 tff(tptp_fun_X_1_type, type, (
% 0.19/0.36 tptp_fun_X_1: $i)).
% 0.19/0.36 tff(p_type, type, (
% 0.19/0.36 p: $o)).
% 0.19/0.36 tff(big_r_type, type, (
% 0.19/0.36 big_r: $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 ((~![X: $i] : big_r(X)) <=> (~![X: $i] : big_r(X))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(2,plain,
% 0.19/0.36 ((~(![X: $i] : ((p & big_q(X)) | ((~p) & big_r(X))) => (![X: $i] : big_q(X) | ![X: $i] : big_r(X)))) <=> (~(![X: $i] : big_q(X) | ![X: $i] : big_r(X) | (~![X: $i] : ((p & big_q(X)) | ((~p) & big_r(X))))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(3,axiom,(~(![X: $i] : ((p & big_q(X)) | ((~p) & big_r(X))) => (![X: $i] : big_q(X) | ![X: $i] : big_r(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','x2118')).
% 0.19/0.36 tff(4,plain,
% 0.19/0.36 (~(![X: $i] : big_q(X) | ![X: $i] : big_r(X) | (~![X: $i] : ((p & big_q(X)) | ((~p) & big_r(X)))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.36 tff(5,plain,
% 0.19/0.36 (~![X: $i] : big_r(X)),
% 0.19/0.36 inference(or_elim,[status(thm)],[4])).
% 0.19/0.36 tff(6,plain,
% 0.19/0.36 (~![X: $i] : big_r(X)),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.36 tff(7,plain,
% 0.19/0.36 (~![X: $i] : big_r(X)),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.19/0.36 tff(8,plain,
% 0.19/0.36 (~![X: $i] : big_r(X)),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.19/0.36 tff(9,plain,(
% 0.19/0.36 ~big_r(X!1)),
% 0.19/0.36 inference(skolemize,[status(sab)],[8])).
% 0.19/0.36 tff(10,plain,
% 0.19/0.36 ((p | (~big_r(X!1))) | big_r(X!1)),
% 0.19/0.36 inference(tautology,[status(thm)],[])).
% 0.19/0.36 tff(11,plain,
% 0.19/0.36 (p | (~big_r(X!1))),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.19/0.36 tff(12,plain,
% 0.19/0.36 (^[X: $i] : refl(((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X))))) <=> ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X))))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(13,plain,
% 0.19/0.36 (![X: $i] : ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X))))) <=> ![X: $i] : ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X)))))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.36 tff(14,plain,
% 0.19/0.36 (^[X: $i] : trans(monotonicity(rewrite((p & big_q(X)) <=> (~((~p) | (~big_q(X))))), rewrite(((~p) & big_r(X)) <=> (~(p | (~big_r(X))))), (((p & big_q(X)) | ((~p) & big_r(X))) <=> ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X))))))), rewrite(((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X))))) <=> ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X)))))), (((p & big_q(X)) | ((~p) & big_r(X))) <=> ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X)))))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(15,plain,
% 0.19/0.36 (![X: $i] : ((p & big_q(X)) | ((~p) & big_r(X))) <=> ![X: $i] : ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X)))))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.36 tff(16,plain,
% 0.19/0.36 (![X: $i] : ((p & big_q(X)) | ((~p) & big_r(X))) <=> ![X: $i] : ((p & big_q(X)) | ((~p) & big_r(X)))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(17,plain,
% 0.19/0.36 (![X: $i] : ((p & big_q(X)) | ((~p) & big_r(X)))),
% 0.19/0.36 inference(or_elim,[status(thm)],[4])).
% 0.19/0.36 tff(18,plain,
% 0.19/0.36 (![X: $i] : ((p & big_q(X)) | ((~p) & big_r(X)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.36 tff(19,plain,(
% 0.19/0.36 ![X: $i] : ((p & big_q(X)) | ((~p) & big_r(X)))),
% 0.19/0.36 inference(skolemize,[status(sab)],[18])).
% 0.19/0.36 tff(20,plain,
% 0.19/0.36 (![X: $i] : ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X)))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.19/0.36 tff(21,plain,
% 0.19/0.36 (![X: $i] : ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X)))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.19/0.36 tff(22,plain,
% 0.19/0.36 (((~![X: $i] : ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X)))))) | ((~((~p) | (~big_q(X!1)))) | (~(p | (~big_r(X!1)))))) <=> ((~![X: $i] : ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X)))))) | (~((~p) | (~big_q(X!1)))) | (~(p | (~big_r(X!1)))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(23,plain,
% 0.19/0.36 ((~![X: $i] : ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X)))))) | ((~((~p) | (~big_q(X!1)))) | (~(p | (~big_r(X!1)))))),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(24,plain,
% 0.19/0.36 ((~![X: $i] : ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X)))))) | (~((~p) | (~big_q(X!1)))) | (~(p | (~big_r(X!1))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.19/0.36 tff(25,plain,
% 0.19/0.36 (~((~p) | (~big_q(X!1)))),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[24, 21, 11])).
% 0.19/0.36 tff(26,plain,
% 0.19/0.36 ((~![X: $i] : big_q(X)) <=> (~![X: $i] : big_q(X))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(27,plain,
% 0.19/0.36 (~![X: $i] : big_q(X)),
% 0.19/0.36 inference(or_elim,[status(thm)],[4])).
% 0.19/0.36 tff(28,plain,
% 0.19/0.36 (~![X: $i] : big_q(X)),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.36 tff(29,plain,
% 0.19/0.36 (~![X: $i] : big_q(X)),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[28, 26])).
% 0.19/0.36 tff(30,plain,
% 0.19/0.36 (~![X: $i] : big_q(X)),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.19/0.36 tff(31,plain,(
% 0.19/0.36 ~big_q(X!0)),
% 0.19/0.36 inference(skolemize,[status(sab)],[30])).
% 0.19/0.36 tff(32,plain,
% 0.19/0.36 (((~p) | (~big_q(X!0))) | big_q(X!0)),
% 0.19/0.36 inference(tautology,[status(thm)],[])).
% 0.19/0.36 tff(33,plain,
% 0.19/0.36 ((~p) | (~big_q(X!0))),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.19/0.36 tff(34,plain,
% 0.19/0.36 (((~![X: $i] : ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X)))))) | ((~((~p) | (~big_q(X!0)))) | (~(p | (~big_r(X!0)))))) <=> ((~![X: $i] : ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X)))))) | (~((~p) | (~big_q(X!0)))) | (~(p | (~big_r(X!0)))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(35,plain,
% 0.19/0.36 ((~![X: $i] : ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X)))))) | ((~((~p) | (~big_q(X!0)))) | (~(p | (~big_r(X!0)))))),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(36,plain,
% 0.19/0.36 ((~![X: $i] : ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X)))))) | (~((~p) | (~big_q(X!0)))) | (~(p | (~big_r(X!0))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.36 tff(37,plain,
% 0.19/0.36 (~(p | (~big_r(X!0)))),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[36, 21, 33])).
% 0.19/0.36 tff(38,plain,
% 0.19/0.36 ((p | (~big_r(X!0))) | (~p)),
% 0.19/0.36 inference(tautology,[status(thm)],[])).
% 0.19/0.36 tff(39,plain,
% 0.19/0.36 (~p),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.19/0.36 tff(40,plain,
% 0.19/0.36 (((~p) | (~big_q(X!1))) | p),
% 0.19/0.36 inference(tautology,[status(thm)],[])).
% 0.19/0.36 tff(41,plain,
% 0.19/0.36 ($false),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[40, 39, 25])).
% 0.19/0.36 % SZS output end Proof
% 0.19/0.36 % E exiting
%------------------------------------------------------------------------------