%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN009-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:37:57 AM UTC 2025
% Result : Unsatisfiable 0.10s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYN009-1 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.10/0.32 % Computer : n014.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Fri Jun 20 12:26:24 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.10/0.37 % SZS status Unsatisfiable
% 0.10/0.37 % SZS output start Proof
% 0.10/0.37 tff(q_type, type, (
% 0.10/0.37 q: ( $i * $i * $i ) > $o)).
% 0.10/0.37 tff(c_type, type, (
% 0.10/0.37 c: $i)).
% 0.10/0.37 tff(p_type, type, (
% 0.10/0.37 p: ( $i * $i * $i ) > $o)).
% 0.10/0.37 tff(r_type, type, (
% 0.10/0.37 r: ( $i * $i * $i ) > $o)).
% 0.10/0.37 tff(s_type, type, (
% 0.10/0.37 s: $i > $o)).
% 0.10/0.37 tff(1,assumption,(p(c, c, c)), introduced(assumption)).
% 0.10/0.37 tff(2,plain,
% 0.10/0.37 (^[Y: $i, X: $i] : refl((~p(c, X, Y)) <=> (~p(c, X, Y)))),
% 0.10/0.37 inference(bind,[status(th)],[])).
% 0.10/0.37 tff(3,plain,
% 0.10/0.37 (![Y: $i, X: $i] : (~p(c, X, Y)) <=> ![Y: $i, X: $i] : (~p(c, X, Y))),
% 0.10/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.10/0.37 tff(4,plain,
% 0.10/0.37 (![Y: $i, X: $i] : (~p(c, X, Y)) <=> ![Y: $i, X: $i] : (~p(c, X, Y))),
% 0.10/0.37 inference(rewrite,[status(thm)],[])).
% 0.10/0.37 tff(5,axiom,(![Y: $i, X: $i] : (~p(c, X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_1')).
% 0.10/0.37 tff(6,plain,
% 0.10/0.37 (![Y: $i, X: $i] : (~p(c, X, Y))),
% 0.10/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.10/0.37 tff(7,plain,(
% 0.10/0.37 ![Y: $i, X: $i] : (~p(c, X, Y))),
% 0.10/0.37 inference(skolemize,[status(sab)],[6])).
% 0.10/0.37 tff(8,plain,
% 0.10/0.37 (![Y: $i, X: $i] : (~p(c, X, Y))),
% 0.10/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.10/0.37 tff(9,plain,
% 0.10/0.37 ((~![Y: $i, X: $i] : (~p(c, X, Y))) | (~p(c, c, c))),
% 0.10/0.37 inference(quant_inst,[status(thm)],[])).
% 0.10/0.37 tff(10,plain,
% 0.10/0.37 ($false),
% 0.10/0.37 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.10/0.37 tff(11,plain,(~p(c, c, c)), inference(lemma,lemma(discharge,[]))).
% 0.10/0.37 tff(12,plain,
% 0.10/0.37 (^[Y: $i, X: $i] : refl((~r(X, Y, c)) <=> (~r(X, Y, c)))),
% 0.10/0.37 inference(bind,[status(th)],[])).
% 0.10/0.37 tff(13,plain,
% 0.10/0.37 (![Y: $i, X: $i] : (~r(X, Y, c)) <=> ![Y: $i, X: $i] : (~r(X, Y, c))),
% 0.10/0.37 inference(quant_intro,[status(thm)],[12])).
% 0.10/0.37 tff(14,plain,
% 0.10/0.37 (![Y: $i, X: $i] : (~r(X, Y, c)) <=> ![Y: $i, X: $i] : (~r(X, Y, c))),
% 0.10/0.37 inference(rewrite,[status(thm)],[])).
% 0.10/0.37 tff(15,axiom,(![Y: $i, X: $i] : (~r(X, Y, c))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_3')).
% 0.10/0.37 tff(16,plain,
% 0.10/0.37 (![Y: $i, X: $i] : (~r(X, Y, c))),
% 0.10/0.37 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.10/0.37 tff(17,plain,(
% 0.10/0.37 ![Y: $i, X: $i] : (~r(X, Y, c))),
% 0.10/0.37 inference(skolemize,[status(sab)],[16])).
% 0.10/0.37 tff(18,plain,
% 0.10/0.37 (![Y: $i, X: $i] : (~r(X, Y, c))),
% 0.10/0.37 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.10/0.37 tff(19,plain,
% 0.10/0.37 ((~![Y: $i, X: $i] : (~r(X, Y, c))) | (~r(c, c, c))),
% 0.10/0.37 inference(quant_inst,[status(thm)],[])).
% 0.10/0.37 tff(20,plain,
% 0.10/0.37 (~r(c, c, c)),
% 0.10/0.37 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.10/0.37 tff(21,plain,
% 0.10/0.37 (^[Z: $i, Y: $i, X: $i] : refl((r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X))) <=> (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X))))),
% 0.10/0.37 inference(bind,[status(th)],[])).
% 0.10/0.37 tff(22,plain,
% 0.10/0.37 (![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X))) <=> ![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))),
% 0.10/0.37 inference(quant_intro,[status(thm)],[21])).
% 0.10/0.37 tff(23,plain,
% 0.10/0.37 (![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X))) <=> ![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))),
% 0.10/0.37 inference(rewrite,[status(thm)],[])).
% 0.10/0.37 tff(24,plain,
% 0.10/0.37 (^[Z: $i, Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~s(X)) | (~s(Y))) | (~s(Z))) <=> ((~s(Z)) | (~s(Y)) | (~s(X)))), (((((~s(X)) | (~s(Y))) | (~s(Z))) | p(X, Y, Z)) <=> (((~s(Z)) | (~s(Y)) | (~s(X))) | p(X, Y, Z)))), rewrite((((~s(Z)) | (~s(Y)) | (~s(X))) | p(X, Y, Z)) <=> (p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))), (((((~s(X)) | (~s(Y))) | (~s(Z))) | p(X, Y, Z)) <=> (p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X))))), ((((((~s(X)) | (~s(Y))) | (~s(Z))) | p(X, Y, Z)) | q(X, Y, Z)) <=> ((p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X))) | q(X, Y, Z)))), rewrite(((p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X))) | q(X, Y, Z)) <=> (q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))), ((((((~s(X)) | (~s(Y))) | (~s(Z))) | p(X, Y, Z)) | q(X, Y, Z)) <=> (q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X))))), (((((((~s(X)) | (~s(Y))) | (~s(Z))) | p(X, Y, Z)) | q(X, Y, Z)) | r(X, Y, Z)) <=> ((q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X))) | r(X, Y, Z)))), rewrite(((q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X))) | r(X, Y, Z)) <=> (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))), (((((((~s(X)) | (~s(Y))) | (~s(Z))) | p(X, Y, Z)) | q(X, Y, Z)) | r(X, Y, Z)) <=> (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))))),
% 0.10/0.37 inference(bind,[status(th)],[])).
% 0.10/0.37 tff(25,plain,
% 0.10/0.37 (![Z: $i, Y: $i, X: $i] : ((((((~s(X)) | (~s(Y))) | (~s(Z))) | p(X, Y, Z)) | q(X, Y, Z)) | r(X, Y, Z)) <=> ![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))),
% 0.10/0.37 inference(quant_intro,[status(thm)],[24])).
% 0.10/0.37 tff(26,axiom,(![Z: $i, Y: $i, X: $i] : ((((((~s(X)) | (~s(Y))) | (~s(Z))) | p(X, Y, Z)) | q(X, Y, Z)) | r(X, Y, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_7')).
% 0.10/0.37 tff(27,plain,
% 0.10/0.37 (![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))),
% 0.10/0.37 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.10/0.37 tff(28,plain,
% 0.10/0.37 (![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))),
% 0.10/0.37 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.10/0.37 tff(29,plain,(
% 0.10/0.37 ![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))),
% 0.10/0.37 inference(skolemize,[status(sab)],[28])).
% 0.10/0.37 tff(30,plain,
% 0.10/0.37 (![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))),
% 0.10/0.37 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.10/0.37 tff(31,plain,
% 0.10/0.37 (s(c) <=> s(c)),
% 0.10/0.37 inference(rewrite,[status(thm)],[])).
% 0.10/0.37 tff(32,axiom,(s(c)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_6')).
% 0.10/0.37 tff(33,plain,
% 0.10/0.37 (s(c)),
% 0.10/0.37 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.10/0.37 tff(34,plain,
% 0.10/0.37 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))) | ((~s(c)) | r(c, c, c) | q(c, c, c) | p(c, c, c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))) | (~s(c)) | r(c, c, c) | q(c, c, c) | p(c, c, c))),
% 0.10/0.37 inference(rewrite,[status(thm)],[])).
% 0.10/0.37 tff(35,plain,
% 0.10/0.37 ((r(c, c, c) | q(c, c, c) | p(c, c, c) | (~s(c)) | (~s(c)) | (~s(c))) <=> ((~s(c)) | r(c, c, c) | q(c, c, c) | p(c, c, c))),
% 0.10/0.37 inference(rewrite,[status(thm)],[])).
% 0.10/0.37 tff(36,plain,
% 0.10/0.37 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))) | (r(c, c, c) | q(c, c, c) | p(c, c, c) | (~s(c)) | (~s(c)) | (~s(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))) | ((~s(c)) | r(c, c, c) | q(c, c, c) | p(c, c, c)))),
% 0.10/0.37 inference(monotonicity,[status(thm)],[35])).
% 0.10/0.37 tff(37,plain,
% 0.10/0.37 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))) | (r(c, c, c) | q(c, c, c) | p(c, c, c) | (~s(c)) | (~s(c)) | (~s(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))) | (~s(c)) | r(c, c, c) | q(c, c, c) | p(c, c, c))),
% 0.10/0.37 inference(transitivity,[status(thm)],[36, 34])).
% 0.10/0.37 tff(38,plain,
% 0.10/0.37 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))) | (r(c, c, c) | q(c, c, c) | p(c, c, c) | (~s(c)) | (~s(c)) | (~s(c)))),
% 0.10/0.37 inference(quant_inst,[status(thm)],[])).
% 0.10/0.37 tff(39,plain,
% 0.10/0.37 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))) | (~s(c)) | r(c, c, c) | q(c, c, c) | p(c, c, c)),
% 0.10/0.37 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.10/0.37 tff(40,plain,
% 0.10/0.37 (q(c, c, c) | p(c, c, c)),
% 0.10/0.37 inference(unit_resolution,[status(thm)],[39, 33, 30, 20])).
% 0.10/0.37 tff(41,plain,
% 0.10/0.37 (q(c, c, c)),
% 0.10/0.37 inference(unit_resolution,[status(thm)],[40, 11])).
% 0.10/0.37 tff(42,plain,
% 0.10/0.37 (^[Y: $i, X: $i] : refl((~q(X, c, Y)) <=> (~q(X, c, Y)))),
% 0.10/0.37 inference(bind,[status(th)],[])).
% 0.10/0.37 tff(43,plain,
% 0.10/0.37 (![Y: $i, X: $i] : (~q(X, c, Y)) <=> ![Y: $i, X: $i] : (~q(X, c, Y))),
% 0.10/0.37 inference(quant_intro,[status(thm)],[42])).
% 0.10/0.37 tff(44,plain,
% 0.10/0.37 (![Y: $i, X: $i] : (~q(X, c, Y)) <=> ![Y: $i, X: $i] : (~q(X, c, Y))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(45,axiom,(![Y: $i, X: $i] : (~q(X, c, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_2')).
% 0.18/0.37 tff(46,plain,
% 0.18/0.37 (![Y: $i, X: $i] : (~q(X, c, Y))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.18/0.37 tff(47,plain,(
% 0.18/0.37 ![Y: $i, X: $i] : (~q(X, c, Y))),
% 0.18/0.37 inference(skolemize,[status(sab)],[46])).
% 0.18/0.37 tff(48,plain,
% 0.18/0.37 (![Y: $i, X: $i] : (~q(X, c, Y))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.18/0.37 tff(49,plain,
% 0.18/0.37 ((~![Y: $i, X: $i] : (~q(X, c, Y))) | (~q(c, c, c))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(50,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[49, 48, 41])).
% 0.18/0.37 % SZS output end Proof
% 0.18/0.38 % E exiting
%------------------------------------------------------------------------------