%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN724+1 : TPTP v9.0.0. Released v2.5.0.
% 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 05:39:55 AM UTC 2025
% Result : Theorem 0.12s 0.36s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN724+1 : TPTP v9.0.0. Released v2.5.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n010.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 12:42:42 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % SZS output start Proof
% 0.12/0.36 tff(r_type, type, (
% 0.12/0.36 r: $i > $o)).
% 0.12/0.36 tff(tptp_fun_X_1_type, type, (
% 0.12/0.36 tptp_fun_X_1: $i)).
% 0.12/0.36 tff(s_type, type, (
% 0.12/0.36 s: $i > $o)).
% 0.12/0.36 tff(tptp_fun_X_0_type, type, (
% 0.12/0.36 tptp_fun_X_0: $i)).
% 0.12/0.36 tff(1,assumption,(~(s(X!0) | (~r(X!0)))), introduced(assumption)).
% 0.12/0.36 tff(2,plain,
% 0.12/0.36 ((s(X!0) | (~r(X!0))) | r(X!0)),
% 0.12/0.36 inference(tautology,[status(thm)],[])).
% 0.12/0.36 tff(3,plain,
% 0.12/0.36 (r(X!0)),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.12/0.36 tff(4,plain,
% 0.12/0.36 ((s(X!0) | (~r(X!0))) | (~s(X!0))),
% 0.12/0.36 inference(tautology,[status(thm)],[])).
% 0.12/0.36 tff(5,plain,
% 0.12/0.36 (~s(X!0)),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.12/0.36 tff(6,assumption,(~s(X!0)), introduced(assumption)).
% 0.12/0.36 tff(7,plain,
% 0.12/0.36 (((~r(X!0)) | (~s(X!0))) | s(X!0)),
% 0.12/0.36 inference(tautology,[status(thm)],[])).
% 0.12/0.36 tff(8,plain,
% 0.12/0.36 ((~r(X!0)) | (~s(X!0))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[7, 6])).
% 0.12/0.36 tff(9,assumption,(r(X!0)), introduced(assumption)).
% 0.12/0.36 tff(10,plain,
% 0.12/0.36 ((((~r(X!0)) | (~s(X!0))) <=> r(X!0)) | (~((~r(X!0)) | (~s(X!0)))) | (~r(X!0))),
% 0.12/0.36 inference(tautology,[status(thm)],[])).
% 0.12/0.36 tff(11,plain,
% 0.12/0.36 (((~r(X!0)) | (~s(X!0))) <=> r(X!0)),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[10, 9, 8])).
% 0.12/0.36 tff(12,assumption,(![X: $i] : (~(((~r(X)) | (~s(X))) <=> r(X)))), introduced(assumption)).
% 0.12/0.36 tff(13,plain,
% 0.12/0.36 ((~![X: $i] : (~(((~r(X)) | (~s(X))) <=> r(X)))) | (~(((~r(X!0)) | (~s(X!0))) <=> r(X!0)))),
% 0.12/0.36 inference(quant_inst,[status(thm)],[])).
% 0.12/0.36 tff(14,plain,
% 0.12/0.36 ($false),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[13, 12, 11])).
% 0.12/0.36 tff(15,plain,((~![X: $i] : (~(((~r(X)) | (~s(X))) <=> r(X)))) | (~r(X!0)) | s(X!0)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.36 tff(16,plain,
% 0.12/0.36 (~![X: $i] : (~(((~r(X)) | (~s(X))) <=> r(X)))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[15, 3, 5])).
% 0.12/0.36 tff(17,plain,
% 0.12/0.36 ((![X: $i] : (~(((~r(X)) | (~s(X))) <=> r(X))) | ![X: $i] : (s(X) | (~r(X)))) <=> (![X: $i] : (~(((~r(X)) | (~s(X))) <=> r(X))) | ![X: $i] : (s(X) | (~r(X))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(18,plain,
% 0.12/0.36 ((![X: $i] : ((r(X) & s(X)) <=> r(X)) | ![X: $i] : (s(X) | (~r(X)))) <=> (![X: $i] : (~(((~r(X)) | (~s(X))) <=> r(X))) | ![X: $i] : (s(X) | (~r(X))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(19,plain,
% 0.12/0.36 (((![X: $i] : (s(X) | (~r(X))) | ![X: $i] : ((r(X) & s(X)) <=> r(X))) & ((~(s(X!0) | (~r(X!0)))) | (~((r(X!1) & s(X!1)) <=> r(X!1))))) <=> ((![X: $i] : ((r(X) & s(X)) <=> r(X)) | ![X: $i] : (s(X) | (~r(X)))) & ((~(s(X!0) | (~r(X!0)))) | (~((r(X!1) & s(X!1)) <=> r(X!1)))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(20,plain,
% 0.12/0.36 ((~(![X: $i] : (s(X) | (~r(X))) <=> ![X: $i] : ((r(X) & s(X)) <=> r(X)))) <=> (~(![X: $i] : (s(X) | (~r(X))) <=> ![X: $i] : ((r(X) & s(X)) <=> r(X))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(21,plain,
% 0.12/0.36 ((![X: $i] : (s(X) | (~r(X))) <=> ![X: $i] : ((r(X) & s(X)) <=> r(X))) <=> (![X: $i] : (s(X) | (~r(X))) <=> ![X: $i] : ((r(X) & s(X)) <=> r(X)))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(22,plain,
% 0.12/0.36 ((~(![X: $i] : (s(X) | (~r(X))) <=> ![X: $i] : ((r(X) & s(X)) <=> r(X)))) <=> (~(![X: $i] : (s(X) | (~r(X))) <=> ![X: $i] : ((r(X) & s(X)) <=> r(X))))),
% 0.12/0.36 inference(monotonicity,[status(thm)],[21])).
% 0.12/0.36 tff(23,plain,
% 0.12/0.36 ((~(![X: $i] : (s(X) | (~r(X))) <=> ![X: $i] : ((r(X) & s(X)) <=> r(X)))) <=> (~(![X: $i] : (s(X) | (~r(X))) <=> ![X: $i] : ((r(X) & s(X)) <=> r(X))))),
% 0.12/0.36 inference(transitivity,[status(thm)],[22, 20])).
% 0.12/0.36 tff(24,plain,
% 0.12/0.36 ((![X: $i] : (r(X) => s(X)) <=> ![X: $i] : ((r(X) & s(X)) <=> r(X))) <=> (![X: $i] : (s(X) | (~r(X))) <=> ![X: $i] : ((r(X) & s(X)) <=> r(X)))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(25,plain,
% 0.12/0.36 ((~(![X: $i] : (r(X) => s(X)) <=> ![X: $i] : ((r(X) & s(X)) <=> r(X)))) <=> (~(![X: $i] : (s(X) | (~r(X))) <=> ![X: $i] : ((r(X) & s(X)) <=> r(X))))),
% 0.12/0.36 inference(monotonicity,[status(thm)],[24])).
% 0.12/0.36 tff(26,plain,
% 0.12/0.36 ((~(![X: $i] : (r(X) => s(X)) <=> ![X: $i] : ((r(X) & s(X)) <=> r(X)))) <=> (~(![X: $i] : (s(X) | (~r(X))) <=> ![X: $i] : ((r(X) & s(X)) <=> r(X))))),
% 0.12/0.36 inference(transitivity,[status(thm)],[25, 20])).
% 0.12/0.36 tff(27,axiom,(~(![X: $i] : (r(X) => s(X)) <=> ![X: $i] : ((r(X) & s(X)) <=> r(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm31')).
% 0.12/0.36 tff(28,plain,
% 0.12/0.36 (~(![X: $i] : (s(X) | (~r(X))) <=> ![X: $i] : ((r(X) & s(X)) <=> r(X)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.12/0.36 tff(29,plain,
% 0.12/0.36 (~(![X: $i] : (s(X) | (~r(X))) <=> ![X: $i] : ((r(X) & s(X)) <=> r(X)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[28, 23])).
% 0.12/0.36 tff(30,plain,
% 0.12/0.36 (~(![X: $i] : (s(X) | (~r(X))) <=> ![X: $i] : ((r(X) & s(X)) <=> r(X)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[29, 20])).
% 0.12/0.36 tff(31,plain,
% 0.12/0.36 (~(![X: $i] : (s(X) | (~r(X))) <=> ![X: $i] : ((r(X) & s(X)) <=> r(X)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.12/0.36 unexpected number of arguments: (let ((a!1 (forall ((X $i)) (or (s X) (not (r X)))))
% 0.12/0.36 (a!3 (not (or (s X!0) (not (r X!0)))))
% 0.12/0.36 (a!4 (forall ((X $i)) (= (and (r X) (s X)) (r X))))
% 0.12/0.36 (a!6 (not (= (and (r X!1) (s X!1)) (r X!1)))))
% 0.12/0.36 (let ((a!2 (nnf-pos (proof-bind (lambda ((X $i))
% 0.12/0.36 (let ((a!1 (~ (or (s X) (not (r X)))
% 0.12/0.36 (or (s X) (not (r X))))))
% 0.12/0.36 (refl a!1))))
% 0.12/0.36 (~ a!1 a!1)))
% 0.12/0.36 (a!5 (nnf-pos (proof-bind (lambda ((X $i))
% 0.12/0.36 (let ((a!1 (~ (= (and (r X) (s X)) (r X))
% 0.12/0.36 (= (and (r X) (s X)) (r X)))))
% 0.12/0.36 (refl a!1))))
% 0.12/0.36 (~ a!4 a!4))))
% 0.12/0.36 (nnf-neg a!2
% 0.12/0.36 (sk (~ (not a!1) a!3))
% 0.12/0.36 a!5
% 0.12/0.36 (sk (~ (not a!4) a!6))
% 0.12/0.36 (~ (not (= a!1 a!4)) (and (or a!1 a!4) (or a!3 a!6))))))
% 0.12/0.36 Proof display could not be completed: unexpected number of arguments
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------