%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN922+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:41:00 AM UTC 2025
% Result : Theorem 0.20s 0.37s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN922+1 : TPTP v9.0.0. Released v3.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n008.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 13:01:03 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.37 % SZS status Theorem
% 0.20/0.37 % SZS output start Proof
% 0.20/0.37 tff(p_type, type, (
% 0.20/0.37 p: $i > $o)).
% 0.20/0.37 tff(tptp_fun_X_1_type, type, (
% 0.20/0.37 tptp_fun_X_1: $i)).
% 0.20/0.37 tff(q_type, type, (
% 0.20/0.37 q: $i > $o)).
% 0.20/0.37 tff(tptp_fun_X_0_type, type, (
% 0.20/0.37 tptp_fun_X_0: $i)).
% 0.20/0.37 tff(tptp_fun_X_2_type, type, (
% 0.20/0.37 tptp_fun_X_2: $i)).
% 0.20/0.37 tff(1,assumption,(~q(X!0)), introduced(assumption)).
% 0.20/0.37 tff(2,assumption,(![X: $i] : (~((~p(X)) | (~q(X))))), introduced(assumption)).
% 0.20/0.37 tff(3,assumption,((~p(X!1)) | (~q(X!1))), introduced(assumption)).
% 0.20/0.37 tff(4,plain,
% 0.20/0.37 ((~![X: $i] : (~((~p(X)) | (~q(X))))) | (~((~p(X!1)) | (~q(X!1))))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(5,plain,
% 0.20/0.37 ($false),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[4, 2, 3])).
% 0.20/0.37 tff(6,plain,((~((~p(X!1)) | (~q(X!1)))) | (~![X: $i] : (~((~p(X)) | (~q(X)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.37 tff(7,plain,
% 0.20/0.37 (~((~p(X!1)) | (~q(X!1)))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[6, 2])).
% 0.20/0.37 tff(8,plain,
% 0.20/0.37 (((~p(X!1)) | (~q(X!1))) | p(X!1)),
% 0.20/0.37 inference(tautology,[status(thm)],[])).
% 0.20/0.37 tff(9,plain,
% 0.20/0.37 (p(X!1)),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.37 tff(10,assumption,((~p(X!0)) | (~q(X!0))), introduced(assumption)).
% 0.20/0.37 tff(11,plain,
% 0.20/0.37 ((~![X: $i] : (~((~p(X)) | (~q(X))))) | (~((~p(X!0)) | (~q(X!0))))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(12,plain,
% 0.20/0.37 ($false),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[11, 2, 10])).
% 0.20/0.37 tff(13,plain,((~((~p(X!0)) | (~q(X!0)))) | (~![X: $i] : (~((~p(X)) | (~q(X)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.37 tff(14,plain,
% 0.20/0.37 (~((~p(X!0)) | (~q(X!0)))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[13, 2])).
% 0.20/0.37 tff(15,plain,
% 0.20/0.37 (((~p(X!0)) | (~q(X!0))) | p(X!0)),
% 0.20/0.37 inference(tautology,[status(thm)],[])).
% 0.20/0.37 tff(16,plain,
% 0.20/0.37 (p(X!0)),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.20/0.37 tff(17,plain,
% 0.20/0.37 (((~p(X!0)) | (~q(X!0))) | q(X!0)),
% 0.20/0.37 inference(tautology,[status(thm)],[])).
% 0.20/0.37 tff(18,plain,
% 0.20/0.37 (q(X!0)),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[17, 14])).
% 0.20/0.37 tff(19,assumption,(~q(X!2)), introduced(assumption)).
% 0.20/0.37 tff(20,plain,
% 0.20/0.37 (((~p(X!2)) | (~q(X!2))) | q(X!2)),
% 0.20/0.37 inference(tautology,[status(thm)],[])).
% 0.20/0.37 tff(21,plain,
% 0.20/0.37 ((~p(X!2)) | (~q(X!2))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.20/0.37 tff(22,assumption,(![X: $i] : q(X)), introduced(assumption)).
% 0.20/0.37 tff(23,plain,
% 0.20/0.37 ((~![X: $i] : q(X)) | q(X!2)),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(24,plain,
% 0.20/0.37 ($false),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[23, 22, 19])).
% 0.20/0.37 tff(25,plain,((~![X: $i] : q(X)) | q(X!2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.37 tff(26,plain,
% 0.20/0.37 (~![X: $i] : q(X)),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[25, 19])).
% 0.20/0.37 tff(27,plain,
% 0.20/0.37 (((~![X: $i] : p(X)) | (~![X: $i] : q(X))) | ![X: $i] : q(X)),
% 0.20/0.37 inference(tautology,[status(thm)],[])).
% 0.20/0.37 tff(28,plain,
% 0.20/0.37 ((~![X: $i] : p(X)) | (~![X: $i] : q(X))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.20/0.37 tff(29,plain,
% 0.20/0.37 (((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X))))) <=> ((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X)))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(30,plain,
% 0.20/0.37 (((![X: $i] : p(X) & ![X: $i] : q(X)) | ![X: $i] : (p(X) & q(X))) <=> ((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X)))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(31,plain,
% 0.20/0.37 (((![X: $i] : (p(X) & q(X)) | (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(p(X!0) & q(X!0))) | ((~p(X!1)) | (~q(X!2))))) <=> (((![X: $i] : p(X) & ![X: $i] : q(X)) | ![X: $i] : (p(X) & q(X))) & ((~(p(X!0) & q(X!0))) | (~p(X!1)) | (~q(X!2))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(32,plain,
% 0.20/0.37 ((~(![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X)))) <=> (~(![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(33,plain,
% 0.20/0.37 ((![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) <=> (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(34,plain,
% 0.20/0.37 ((~(![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X)))) <=> (~(![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))))),
% 0.20/0.37 inference(monotonicity,[status(thm)],[33])).
% 0.20/0.37 tff(35,plain,
% 0.20/0.37 ((~(![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X)))) <=> (~(![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))))),
% 0.20/0.37 inference(transitivity,[status(thm)],[34, 32])).
% 0.20/0.37 tff(36,axiom,(~(![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.20/0.37 tff(37,plain,
% 0.20/0.37 (~(![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.37 tff(38,plain,
% 0.20/0.37 (~(![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[37, 35])).
% 0.20/0.37 tff(39,plain,
% 0.20/0.37 (~(![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[38, 32])).
% 0.20/0.37 tff(40,plain,
% 0.20/0.37 (~(![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.20/0.37 unexpected number of arguments: (let ((a!1 (lambda ((X $i)) (refl (~ (and (p X) (q X)) (and (p X) (q X))))))
% 0.20/0.37 (a!2 (forall ((X $i)) (and (p X) (q X))))
% 0.20/0.37 (a!4 (lambda ((X $i)) (refl (~ (p X) (p X)))))
% 0.20/0.37 (a!5 (forall ((X $i)) (p X)))
% 0.20/0.37 (a!6 (lambda ((X $i)) (refl (~ (q X) (q X)))))
% 0.20/0.37 (a!7 (forall ((X $i)) (q X)))
% 0.20/0.37 (a!11 (or (not (and (p X!0) (q X!0))) (or (not (p X!1)) (not (q X!2))))))
% 0.20/0.37 (let ((a!3 (~ (not a!2) (not (and (p X!0) (q X!0)))))
% 0.20/0.37 (a!8 (sk (~ (not a!5) (not (p X!1)))))
% 0.20/0.37 (a!9 (sk (~ (not a!7) (not (q X!2)))))
% 0.20/0.37 (a!10 (~ (not (and a!5 a!7)) (or (not (p X!1)) (not (q X!2)))))
% 0.20/0.37 (a!12 (~ (not (= a!2 (and a!5 a!7))) (and (or a!2 (and a!5 a!7)) a!11))))
% 0.20/0.37 (nnf-neg (nnf-pos (proof-bind a!1) (~ a!2 a!2))
% 0.20/0.37 (sk a!3)
% 0.20/0.37 (monotonicity (nnf-pos (proof-bind a!4) (~ a!5 a!5))
% 0.20/0.37 (nnf-pos (proof-bind a!6) (~ a!7 a!7))
% 0.20/0.37 (~ (and a!5 a!7) (and a!5 a!7)))
% 0.20/0.37 (nnf-neg a!8 a!9 a!10)
% 0.20/0.37 a!12)))
% 0.20/0.37 Proof display could not be completed: unexpected number of arguments
% 0.20/0.37 % E exiting
%------------------------------------------------------------------------------