%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN380+1 : TPTP v9.0.0. Released v2.0.0.
% 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 05:38:56 AM UTC 2025
% Result : Theorem 0.20s 0.36s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN380+1 : TPTP v9.0.0. Released v2.0.0.
% 0.00/0.12 % 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 12:32:52 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.36 % SZS status Theorem
% 0.20/0.36 % SZS output start Proof
% 0.20/0.36 tff(big_r_type, type, (
% 0.20/0.36 big_r: ( $i * $i ) > $o)).
% 0.20/0.36 tff(tptp_fun_Z_0_type, type, (
% 0.20/0.36 tptp_fun_Z_0: $i)).
% 0.20/0.36 tff(big_q_type, type, (
% 0.20/0.36 big_q: ( $i * $i ) > $o)).
% 0.20/0.36 tff(1,assumption,(big_r(Z!0, Z!0)), introduced(assumption)).
% 0.20/0.36 tff(2,plain,
% 0.20/0.36 (^[W: $i] : refl((~big_r(W, W)) <=> (~big_r(W, W)))),
% 0.20/0.36 inference(bind,[status(th)],[])).
% 0.20/0.36 tff(3,plain,
% 0.20/0.36 (![W: $i] : (~big_r(W, W)) <=> ![W: $i] : (~big_r(W, W))),
% 0.20/0.36 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.36 tff(4,plain,
% 0.20/0.36 (![W: $i] : (~big_r(W, W)) <=> ![W: $i] : (~big_r(W, W))),
% 0.20/0.36 inference(rewrite,[status(thm)],[])).
% 0.20/0.36 tff(5,plain,
% 0.20/0.36 ((~(![W: $i] : (~big_r(W, W)) => ?[X: $i, Y: $i] : ((~big_r(X, Y)) & (big_q(Y, X) => ![Z: $i] : big_q(Z, Z))))) <=> (~((~![W: $i] : (~big_r(W, W))) | ?[X: $i, Y: $i] : ((~big_r(X, Y)) & ((~big_q(Y, X)) | ![Z: $i] : big_q(Z, Z)))))),
% 0.20/0.36 inference(rewrite,[status(thm)],[])).
% 0.20/0.36 tff(6,axiom,(~(![W: $i] : (~big_r(W, W)) => ?[X: $i, Y: $i] : ((~big_r(X, Y)) & (big_q(Y, X) => ![Z: $i] : big_q(Z, Z))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','x2132')).
% 0.20/0.36 tff(7,plain,
% 0.20/0.36 (~((~![W: $i] : (~big_r(W, W))) | ?[X: $i, Y: $i] : ((~big_r(X, Y)) & ((~big_q(Y, X)) | ![Z: $i] : big_q(Z, Z))))),
% 0.20/0.36 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.36 tff(8,plain,
% 0.20/0.36 (![W: $i] : (~big_r(W, W))),
% 0.20/0.36 inference(or_elim,[status(thm)],[7])).
% 0.20/0.36 tff(9,plain,
% 0.20/0.36 (![W: $i] : (~big_r(W, W))),
% 0.20/0.36 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.36 tff(10,plain,(
% 0.20/0.36 ![W: $i] : (~big_r(W, W))),
% 0.20/0.36 inference(skolemize,[status(sab)],[9])).
% 0.20/0.36 tff(11,plain,
% 0.20/0.36 (![W: $i] : (~big_r(W, W))),
% 0.20/0.36 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.20/0.36 tff(12,plain,
% 0.20/0.36 ((~![W: $i] : (~big_r(W, W))) | (~big_r(Z!0, Z!0))),
% 0.20/0.36 inference(quant_inst,[status(thm)],[])).
% 0.20/0.36 tff(13,plain,
% 0.20/0.36 ($false),
% 0.20/0.36 inference(unit_resolution,[status(thm)],[12, 11, 1])).
% 0.20/0.36 tff(14,plain,(~big_r(Z!0, Z!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.36 tff(15,plain,
% 0.20/0.36 (^[X: $i, Y: $i] : refl((big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0)))) <=> (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0)))))),
% 0.20/0.36 inference(bind,[status(th)],[])).
% 0.20/0.36 tff(16,plain,
% 0.20/0.36 (![X: $i, Y: $i] : (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0)))) <=> ![X: $i, Y: $i] : (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0))))),
% 0.20/0.36 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.36 tff(17,plain,
% 0.20/0.36 (^[X: $i, Y: $i] : trans(monotonicity(rewrite((big_q(Y, X) & (~big_q(Z!0, Z!0))) <=> (~((~big_q(Y, X)) | big_q(Z!0, Z!0)))), ((big_r(X, Y) | (big_q(Y, X) & (~big_q(Z!0, Z!0)))) <=> (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0)))))), rewrite((big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0)))) <=> (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0))))), ((big_r(X, Y) | (big_q(Y, X) & (~big_q(Z!0, Z!0)))) <=> (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0))))))),
% 0.20/0.36 inference(bind,[status(th)],[])).
% 0.20/0.36 tff(18,plain,
% 0.20/0.36 (![X: $i, Y: $i] : (big_r(X, Y) | (big_q(Y, X) & (~big_q(Z!0, Z!0)))) <=> ![X: $i, Y: $i] : (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0))))),
% 0.20/0.36 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.36 tff(19,plain,
% 0.20/0.36 ((~?[X: $i, Y: $i] : ((~big_r(X, Y)) & ((~big_q(Y, X)) | ![Z: $i] : big_q(Z, Z)))) <=> (~?[X: $i, Y: $i] : ((~big_r(X, Y)) & ((~big_q(Y, X)) | ![Z: $i] : big_q(Z, Z))))),
% 0.20/0.36 inference(rewrite,[status(thm)],[])).
% 0.20/0.36 tff(20,plain,
% 0.20/0.36 (~?[X: $i, Y: $i] : ((~big_r(X, Y)) & ((~big_q(Y, X)) | ![Z: $i] : big_q(Z, Z)))),
% 0.20/0.36 inference(or_elim,[status(thm)],[7])).
% 0.20/0.36 tff(21,plain,
% 0.20/0.36 (~?[X: $i, Y: $i] : ((~big_r(X, Y)) & ((~big_q(Y, X)) | ![Z: $i] : big_q(Z, Z)))),
% 0.20/0.36 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.36 tff(22,plain,
% 0.20/0.36 (~?[X: $i, Y: $i] : ((~big_r(X, Y)) & ((~big_q(Y, X)) | ![Z: $i] : big_q(Z, Z)))),
% 0.20/0.36 inference(modus_ponens,[status(thm)],[21, 19])).
% 0.20/0.36 tff(23,plain,
% 0.20/0.36 (~?[X: $i, Y: $i] : ((~big_r(X, Y)) & ((~big_q(Y, X)) | ![Z: $i] : big_q(Z, Z)))),
% 0.20/0.36 inference(modus_ponens,[status(thm)],[22, 19])).
% 0.20/0.36 tff(24,plain,
% 0.20/0.36 (^[X: $i, Y: $i] : nnf_neg(refl($oeq(big_r(X, Y), big_r(X, Y))), nnf_neg(refl($oeq(big_q(Y, X), big_q(Y, X))), sk($oeq((~![Z: $i] : big_q(Z, Z)), (~big_q(Z!0, Z!0)))), $oeq((~((~big_q(Y, X)) | ![Z: $i] : big_q(Z, Z))), (big_q(Y, X) & (~big_q(Z!0, Z!0))))), $oeq((~((~big_r(X, Y)) & ((~big_q(Y, X)) | ![Z: $i] : big_q(Z, Z)))), (big_r(X, Y) | (big_q(Y, X) & (~big_q(Z!0, Z!0))))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(25,plain,(
% 0.20/0.37 ![X: $i, Y: $i] : (big_r(X, Y) | (big_q(Y, X) & (~big_q(Z!0, Z!0))))),
% 0.20/0.37 inference(nnf-neg,[status(sab)],[23, 24])).
% 0.20/0.37 tff(26,plain,
% 0.20/0.37 (![X: $i, Y: $i] : (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.20/0.37 tff(27,plain,
% 0.20/0.37 (![X: $i, Y: $i] : (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.20/0.37 tff(28,plain,
% 0.20/0.37 (((~![X: $i, Y: $i] : (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0))))) | big_r(Z!0, Z!0)) <=> ((~![X: $i, Y: $i] : (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0))))) | big_r(Z!0, Z!0))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(29,plain,
% 0.20/0.37 ((big_r(Z!0, Z!0) | $false) <=> big_r(Z!0, Z!0)),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(30,plain,
% 0.20/0.37 ((~$true) <=> $false),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(31,plain,
% 0.20/0.37 (((~big_q(Z!0, Z!0)) | big_q(Z!0, Z!0)) <=> $true),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(32,plain,
% 0.20/0.37 ((~((~big_q(Z!0, Z!0)) | big_q(Z!0, Z!0))) <=> (~$true)),
% 0.20/0.37 inference(monotonicity,[status(thm)],[31])).
% 0.20/0.37 tff(33,plain,
% 0.20/0.37 ((~((~big_q(Z!0, Z!0)) | big_q(Z!0, Z!0))) <=> $false),
% 0.20/0.37 inference(transitivity,[status(thm)],[32, 30])).
% 0.20/0.37 tff(34,plain,
% 0.20/0.37 ((big_r(Z!0, Z!0) | (~((~big_q(Z!0, Z!0)) | big_q(Z!0, Z!0)))) <=> (big_r(Z!0, Z!0) | $false)),
% 0.20/0.37 inference(monotonicity,[status(thm)],[33])).
% 0.20/0.37 tff(35,plain,
% 0.20/0.37 ((big_r(Z!0, Z!0) | (~((~big_q(Z!0, Z!0)) | big_q(Z!0, Z!0)))) <=> big_r(Z!0, Z!0)),
% 0.20/0.37 inference(transitivity,[status(thm)],[34, 29])).
% 0.20/0.37 tff(36,plain,
% 0.20/0.37 (((~![X: $i, Y: $i] : (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0))))) | (big_r(Z!0, Z!0) | (~((~big_q(Z!0, Z!0)) | big_q(Z!0, Z!0))))) <=> ((~![X: $i, Y: $i] : (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0))))) | big_r(Z!0, Z!0))),
% 0.20/0.37 inference(monotonicity,[status(thm)],[35])).
% 0.20/0.37 tff(37,plain,
% 0.20/0.37 (((~![X: $i, Y: $i] : (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0))))) | (big_r(Z!0, Z!0) | (~((~big_q(Z!0, Z!0)) | big_q(Z!0, Z!0))))) <=> ((~![X: $i, Y: $i] : (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0))))) | big_r(Z!0, Z!0))),
% 0.20/0.37 inference(transitivity,[status(thm)],[36, 28])).
% 0.20/0.37 tff(38,plain,
% 0.20/0.37 ((~![X: $i, Y: $i] : (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0))))) | (big_r(Z!0, Z!0) | (~((~big_q(Z!0, Z!0)) | big_q(Z!0, Z!0))))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(39,plain,
% 0.20/0.37 ((~![X: $i, Y: $i] : (big_r(X, Y) | (~((~big_q(Y, X)) | big_q(Z!0, Z!0))))) | big_r(Z!0, Z!0)),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.20/0.37 tff(40,plain,
% 0.20/0.37 ($false),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[39, 27, 14])).
% 0.20/0.37 % SZS output end Proof
% 0.20/0.37 % E exiting
%------------------------------------------------------------------------------