%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN721+1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:39:54 AM UTC 2025
% Result : Theorem 0.18s 0.36s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN721+1 : TPTP v9.0.0. Released v2.5.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n006.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 12:40:20 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.18/0.36 % SZS status Theorem
% 0.18/0.36 % SZS output start Proof
% 0.18/0.36 tff(r_type, type, (
% 0.18/0.36 r: ( $i * $i ) > $o)).
% 0.18/0.36 tff(a_type, type, (
% 0.18/0.36 a: $i)).
% 0.18/0.36 tff(q_type, type, (
% 0.18/0.36 q: ( $i * $i ) > $o)).
% 0.18/0.36 tff(b_type, type, (
% 0.18/0.36 b: $i)).
% 0.18/0.36 tff(1,assumption,(![Y: $i] : (~r(a, Y))), introduced(assumption)).
% 0.18/0.36 tff(2,plain,
% 0.18/0.36 (r(a, b) <=> r(a, b)),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(3,plain,
% 0.18/0.36 ((~(((r(a, b) & ![X: $i] : (?[Y: $i] : r(X, Y) => q(X, X))) & ![U: $i, V: $i] : (q(U, V) => ![Z: $i] : r(Z, V))) => ?[W: $i] : (r(b, W) & q(W, a)))) <=> (~((~(r(a, b) & ![X: $i] : ((~?[Y: $i] : r(X, Y)) | q(X, X)) & ![U: $i, V: $i] : ((~q(U, V)) | ![Z: $i] : r(Z, V)))) | ?[W: $i] : (r(b, W) & q(W, a))))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(4,axiom,(~(((r(a, b) & ![X: $i] : (?[Y: $i] : r(X, Y) => q(X, X))) & ![U: $i, V: $i] : (q(U, V) => ![Z: $i] : r(Z, V))) => ?[W: $i] : (r(b, W) & q(W, a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lx1')).
% 0.18/0.36 tff(5,plain,
% 0.18/0.36 (~((~(r(a, b) & ![X: $i] : ((~?[Y: $i] : r(X, Y)) | q(X, X)) & ![U: $i, V: $i] : ((~q(U, V)) | ![Z: $i] : r(Z, V)))) | ?[W: $i] : (r(b, W) & q(W, a)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.18/0.36 tff(6,plain,
% 0.18/0.36 (r(a, b) & ![X: $i] : ((~?[Y: $i] : r(X, Y)) | q(X, X)) & ![U: $i, V: $i] : ((~q(U, V)) | ![Z: $i] : r(Z, V))),
% 0.18/0.36 inference(or_elim,[status(thm)],[5])).
% 0.18/0.36 tff(7,plain,
% 0.18/0.36 (r(a, b)),
% 0.18/0.36 inference(and_elim,[status(thm)],[6])).
% 0.18/0.36 tff(8,plain,
% 0.18/0.36 (r(a, b)),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.18/0.36 tff(9,plain,
% 0.18/0.36 ((~![Y: $i] : (~r(a, Y))) | (~r(a, b))),
% 0.18/0.36 inference(quant_inst,[status(thm)],[])).
% 0.18/0.36 tff(10,plain,
% 0.18/0.36 ($false),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.18/0.36 tff(11,plain,(~![Y: $i] : (~r(a, Y))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.36 tff(12,plain,
% 0.18/0.36 (^[X: $i] : refl((q(X, X) | ![Y: $i] : (~r(X, Y))) <=> (q(X, X) | ![Y: $i] : (~r(X, Y))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(13,plain,
% 0.18/0.36 (![X: $i] : (q(X, X) | ![Y: $i] : (~r(X, Y))) <=> ![X: $i] : (q(X, X) | ![Y: $i] : (~r(X, Y)))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[12])).
% 0.18/0.36 tff(14,plain,
% 0.18/0.36 (^[X: $i] : rewrite((q(X, X) | ![Y: $i] : (~r(X, Y))) <=> (q(X, X) | ![Y: $i] : (~r(X, Y))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(15,plain,
% 0.18/0.36 (![X: $i] : (q(X, X) | ![Y: $i] : (~r(X, Y))) <=> ![X: $i] : (q(X, X) | ![Y: $i] : (~r(X, Y)))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[14])).
% 0.18/0.36 tff(16,plain,
% 0.18/0.36 (![X: $i] : (q(X, X) | ![Y: $i] : (~r(X, Y))) <=> ![X: $i] : (q(X, X) | ![Y: $i] : (~r(X, Y)))),
% 0.18/0.36 inference(transitivity,[status(thm)],[15, 13])).
% 0.18/0.36 tff(17,plain,
% 0.18/0.36 (^[X: $i] : rewrite((![Y: $i] : (~r(X, Y)) | q(X, X)) <=> (q(X, X) | ![Y: $i] : (~r(X, Y))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(18,plain,
% 0.18/0.36 (![X: $i] : (![Y: $i] : (~r(X, Y)) | q(X, X)) <=> ![X: $i] : (q(X, X) | ![Y: $i] : (~r(X, Y)))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[17])).
% 0.18/0.36 tff(19,plain,
% 0.18/0.36 (![X: $i] : ((~?[Y: $i] : r(X, Y)) | q(X, X)) <=> ![X: $i] : ((~?[Y: $i] : r(X, Y)) | q(X, X))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(20,plain,
% 0.18/0.36 (![X: $i] : ((~?[Y: $i] : r(X, Y)) | q(X, X))),
% 0.18/0.36 inference(and_elim,[status(thm)],[6])).
% 0.18/0.36 tff(21,plain,
% 0.18/0.36 (![X: $i] : ((~?[Y: $i] : r(X, Y)) | q(X, X))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.18/0.36 tff(22,plain,(
% 0.18/0.36 ![X: $i] : (![Y: $i] : (~r(X, Y)) | q(X, X))),
% 0.18/0.36 inference(skolemize,[status(sab)],[21])).
% 0.18/0.36 tff(23,plain,
% 0.18/0.36 (![X: $i] : (q(X, X) | ![Y: $i] : (~r(X, Y)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.18/0.36 tff(24,plain,
% 0.18/0.36 (![X: $i] : (q(X, X) | ![Y: $i] : (~r(X, Y)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.18/0.36 tff(25,plain,
% 0.18/0.36 (((~![X: $i] : (q(X, X) | ![Y: $i] : (~r(X, Y)))) | (q(a, a) | ![Y: $i] : (~r(a, Y)))) <=> ((~![X: $i] : (q(X, X) | ![Y: $i] : (~r(X, Y)))) | q(a, a) | ![Y: $i] : (~r(a, Y)))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(26,plain,
% 0.18/0.36 ((~![X: $i] : (q(X, X) | ![Y: $i] : (~r(X, Y)))) | (q(a, a) | ![Y: $i] : (~r(a, Y)))),
% 0.18/0.36 inference(quant_inst,[status(thm)],[])).
% 0.18/0.36 tff(27,plain,
% 0.18/0.36 ((~![X: $i] : (q(X, X) | ![Y: $i] : (~r(X, Y)))) | q(a, a) | ![Y: $i] : (~r(a, Y))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.18/0.37 tff(28,plain,
% 0.18/0.37 (q(a, a) | ![Y: $i] : (~r(a, Y))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[27, 24])).
% 0.18/0.37 tff(29,plain,
% 0.18/0.37 (q(a, a)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[28, 11])).
% 0.18/0.37 tff(30,plain,
% 0.18/0.37 (^[U: $i, V: $i] : refl(((~q(U, V)) | ![Z: $i] : r(Z, V)) <=> ((~q(U, V)) | ![Z: $i] : r(Z, V)))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(31,plain,
% 0.18/0.37 (![U: $i, V: $i] : ((~q(U, V)) | ![Z: $i] : r(Z, V)) <=> ![U: $i, V: $i] : ((~q(U, V)) | ![Z: $i] : r(Z, V))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[30])).
% 0.18/0.37 tff(32,plain,
% 0.18/0.37 (^[U: $i, V: $i] : rewrite(((~q(U, V)) | ![Z: $i] : r(Z, V)) <=> ((~q(U, V)) | ![Z: $i] : r(Z, V)))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(33,plain,
% 0.18/0.37 (![U: $i, V: $i] : ((~q(U, V)) | ![Z: $i] : r(Z, V)) <=> ![U: $i, V: $i] : ((~q(U, V)) | ![Z: $i] : r(Z, V))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[32])).
% 0.18/0.37 tff(34,plain,
% 0.18/0.37 (![U: $i, V: $i] : ((~q(U, V)) | ![Z: $i] : r(Z, V)) <=> ![U: $i, V: $i] : ((~q(U, V)) | ![Z: $i] : r(Z, V))),
% 0.18/0.37 inference(transitivity,[status(thm)],[33, 31])).
% 0.18/0.37 tff(35,plain,
% 0.18/0.37 (![U: $i, V: $i] : ((~q(U, V)) | ![Z: $i] : r(Z, V)) <=> ![U: $i, V: $i] : ((~q(U, V)) | ![Z: $i] : r(Z, V))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(36,plain,
% 0.18/0.37 (![U: $i, V: $i] : ((~q(U, V)) | ![Z: $i] : r(Z, V))),
% 0.18/0.37 inference(and_elim,[status(thm)],[6])).
% 0.18/0.37 tff(37,plain,
% 0.18/0.37 (![U: $i, V: $i] : ((~q(U, V)) | ![Z: $i] : r(Z, V))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.18/0.37 tff(38,plain,(
% 0.18/0.37 ![U: $i, V: $i] : ((~q(U, V)) | ![Z: $i] : r(Z, V))),
% 0.18/0.37 inference(skolemize,[status(sab)],[37])).
% 0.18/0.37 tff(39,plain,
% 0.18/0.37 (![U: $i, V: $i] : ((~q(U, V)) | ![Z: $i] : r(Z, V))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.18/0.37 tff(40,plain,
% 0.18/0.37 (((~![U: $i, V: $i] : ((~q(U, V)) | ![Z: $i] : r(Z, V))) | ((~q(a, a)) | ![Z: $i] : r(Z, a))) <=> ((~![U: $i, V: $i] : ((~q(U, V)) | ![Z: $i] : r(Z, V))) | (~q(a, a)) | ![Z: $i] : r(Z, a))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(41,plain,
% 0.18/0.37 ((~![U: $i, V: $i] : ((~q(U, V)) | ![Z: $i] : r(Z, V))) | ((~q(a, a)) | ![Z: $i] : r(Z, a))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(42,plain,
% 0.18/0.37 ((~![U: $i, V: $i] : ((~q(U, V)) | ![Z: $i] : r(Z, V))) | (~q(a, a)) | ![Z: $i] : r(Z, a)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.18/0.37 tff(43,plain,
% 0.18/0.37 (![Z: $i] : r(Z, a)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[42, 39, 29])).
% 0.18/0.37 tff(44,plain,
% 0.18/0.37 (^[W: $i] : refl(((~r(b, W)) | (~q(W, a))) <=> ((~r(b, W)) | (~q(W, a))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(45,plain,
% 0.18/0.37 (![W: $i] : ((~r(b, W)) | (~q(W, a))) <=> ![W: $i] : ((~r(b, W)) | (~q(W, a)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[44])).
% 0.18/0.37 tff(46,plain,
% 0.18/0.37 (^[W: $i] : trans(monotonicity(rewrite((r(b, W) & q(W, a)) <=> (~((~r(b, W)) | (~q(W, a))))), ((~(r(b, W) & q(W, a))) <=> (~(~((~r(b, W)) | (~q(W, a))))))), rewrite((~(~((~r(b, W)) | (~q(W, a))))) <=> ((~r(b, W)) | (~q(W, a)))), ((~(r(b, W) & q(W, a))) <=> ((~r(b, W)) | (~q(W, a)))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(47,plain,
% 0.18/0.37 (![W: $i] : (~(r(b, W) & q(W, a))) <=> ![W: $i] : ((~r(b, W)) | (~q(W, a)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[46])).
% 0.18/0.37 tff(48,plain,
% 0.18/0.37 ((~?[W: $i] : (r(b, W) & q(W, a))) <=> (~?[W: $i] : (r(b, W) & q(W, a)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(49,plain,
% 0.18/0.37 (~?[W: $i] : (r(b, W) & q(W, a))),
% 0.18/0.37 inference(or_elim,[status(thm)],[5])).
% 0.18/0.37 tff(50,plain,
% 0.18/0.37 (~?[W: $i] : (r(b, W) & q(W, a))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.18/0.37 tff(51,plain,
% 0.18/0.37 (~?[W: $i] : (r(b, W) & q(W, a))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[50, 48])).
% 0.18/0.37 tff(52,plain,
% 0.18/0.37 (~?[W: $i] : (r(b, W) & q(W, a))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[51, 48])).
% 0.18/0.37 tff(53,plain,
% 0.18/0.37 (^[W: $i] : refl($oeq((~(r(b, W) & q(W, a))), (~(r(b, W) & q(W, a)))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(54,plain,(
% 0.18/0.37 ![W: $i] : (~(r(b, W) & q(W, a)))),
% 0.18/0.37 inference(nnf-neg,[status(sab)],[52, 53])).
% 0.18/0.37 tff(55,plain,
% 0.18/0.37 (![W: $i] : ((~r(b, W)) | (~q(W, a)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.18/0.37 tff(56,plain,
% 0.18/0.37 (![W: $i] : ((~r(b, W)) | (~q(W, a)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[55, 45])).
% 0.18/0.37 tff(57,plain,
% 0.18/0.37 (((~![W: $i] : ((~r(b, W)) | (~q(W, a)))) | ((~r(b, a)) | (~q(a, a)))) <=> ((~![W: $i] : ((~r(b, W)) | (~q(W, a)))) | (~r(b, a)) | (~q(a, a)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(58,plain,
% 0.18/0.37 ((~![W: $i] : ((~r(b, W)) | (~q(W, a)))) | ((~r(b, a)) | (~q(a, a)))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(59,plain,
% 0.18/0.37 ((~![W: $i] : ((~r(b, W)) | (~q(W, a)))) | (~r(b, a)) | (~q(a, a))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.18/0.37 tff(60,plain,
% 0.18/0.37 ((~r(b, a)) | (~q(a, a))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[59, 56])).
% 0.18/0.37 tff(61,plain,
% 0.18/0.37 (~r(b, a)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[60, 29])).
% 0.18/0.37 tff(62,plain,
% 0.18/0.37 ((~![Z: $i] : r(Z, a)) | r(b, a)),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(63,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[62, 61, 43])).
% 0.18/0.37 % SZS output end Proof
% 0.18/0.37 % E exiting
%------------------------------------------------------------------------------