%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN935+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:41:01 AM UTC 2025
% Result : Theorem 0.21s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYN935+1 : TPTP v9.0.0. Released v3.1.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 13:05:35 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.38 % SZS status Theorem
% 0.21/0.38 % SZS output start Proof
% 0.21/0.38 tff(p_type, type, (
% 0.21/0.38 p: $i > $o)).
% 0.21/0.38 tff(c_type, type, (
% 0.21/0.38 c: $o)).
% 0.21/0.38 tff(tptp_fun_X_0_type, type, (
% 0.21/0.38 tptp_fun_X_0: $i)).
% 0.21/0.38 tff(tptp_fun_X_1_type, type, (
% 0.21/0.38 tptp_fun_X_1: $i)).
% 0.21/0.38 tff(1,assumption,(![X: $i] : (~(c | (~p(X))))), introduced(assumption)).
% 0.21/0.38 tff(2,assumption,(c | (~p(X!1))), introduced(assumption)).
% 0.21/0.38 tff(3,plain,
% 0.21/0.38 ((~![X: $i] : (~(c | (~p(X))))) | (~(c | (~p(X!1))))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(4,plain,
% 0.21/0.38 ($false),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[3, 1, 2])).
% 0.21/0.38 tff(5,plain,((~(c | (~p(X!1)))) | (~![X: $i] : (~(c | (~p(X)))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.38 tff(6,plain,
% 0.21/0.38 (~(c | (~p(X!1)))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[5, 1])).
% 0.21/0.38 tff(7,plain,
% 0.21/0.38 ((c | (~p(X!1))) | p(X!1)),
% 0.21/0.38 inference(tautology,[status(thm)],[])).
% 0.21/0.38 tff(8,plain,
% 0.21/0.38 (p(X!1)),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[7, 6])).
% 0.21/0.38 tff(9,plain,
% 0.21/0.38 ((c | (~p(X!1))) | (~c)),
% 0.21/0.38 inference(tautology,[status(thm)],[])).
% 0.21/0.38 tff(10,plain,
% 0.21/0.38 (~c),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[9, 6])).
% 0.21/0.38 tff(11,plain,
% 0.21/0.38 ((((c | (~p(X!0))) | (c | (~p(X!1)))) & (![X: $i] : (~(c | (~p(X)))) | ((~c) & ![X: $i] : p(X)))) <=> ((c | (~p(X!0)) | (~p(X!1))) & (![X: $i] : (~(c | (~p(X)))) | ((~c) & ![X: $i] : p(X))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(12,plain,
% 0.21/0.38 ((~(?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X))))) <=> (~(?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(13,plain,
% 0.21/0.38 ((?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) <=> (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(14,plain,
% 0.21/0.38 ((~(?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X))))) <=> (~(?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))))),
% 0.21/0.38 inference(monotonicity,[status(thm)],[13])).
% 0.21/0.38 tff(15,plain,
% 0.21/0.38 ((~(?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X))))) <=> (~(?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))))),
% 0.21/0.38 inference(transitivity,[status(thm)],[14, 12])).
% 0.21/0.38 tff(16,plain,
% 0.21/0.38 ((?[X: $i] : (p(X) => c) <=> (![X: $i] : p(X) => c)) <=> (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(17,plain,
% 0.21/0.38 ((~(?[X: $i] : (p(X) => c) <=> (![X: $i] : p(X) => c))) <=> (~(?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))))),
% 0.21/0.38 inference(monotonicity,[status(thm)],[16])).
% 0.21/0.38 tff(18,plain,
% 0.21/0.38 ((~(?[X: $i] : (p(X) => c) <=> (![X: $i] : p(X) => c))) <=> (~(?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))))),
% 0.21/0.38 inference(transitivity,[status(thm)],[17, 12])).
% 0.21/0.38 tff(19,axiom,(~(?[X: $i] : (p(X) => c) <=> (![X: $i] : p(X) => c))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.21/0.38 tff(20,plain,
% 0.21/0.38 (~(?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.21/0.38 tff(21,plain,
% 0.21/0.38 (~(?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.21/0.38 tff(22,plain,
% 0.21/0.38 (~(?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[21, 12])).
% 0.21/0.38 tff(23,plain,
% 0.21/0.38 (~(?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.21/0.38 unexpected number of arguments: (let ((a!1 (exists ((X $i)) (or c (not (p X)))))
% 0.21/0.38 (a!3 (proof-bind (lambda ((X $i))
% 0.21/0.38 (let ((a!1 (not (or c (not (p X))))))
% 0.21/0.38 (refl (~ a!1 a!1))))))
% 0.21/0.38 (a!4 (forall ((X $i)) (not (or c (not (p X))))))
% 0.21/0.38 (a!5 (forall ((X $i)) (p X)))
% 0.21/0.38 (a!8 (lambda ((X $i)) (refl (~ (p X) (p X)))))
% 0.21/0.38 (a!13 (or (or c (not (p X!0))) (or c (not (p X!1))))))
% 0.21/0.38 (let ((a!2 (~ a!1 (or c (not (p X!0)))))
% 0.21/0.38 (a!6 (sk (~ (not a!5) (not (p X!1)))))
% 0.21/0.38 (a!7 (~ (or c (not a!5)) (or c (not (p X!1)))))
% 0.21/0.38 (a!9 (nnf-neg (nnf-pos (proof-bind a!8) (~ a!5 a!5))
% 0.21/0.38 (~ (not (not a!5)) a!5)))
% 0.21/0.38 (a!10 (~ (not (or c (not a!5))) (and (not c) a!5)))
% 0.21/0.38 (a!12 (not (= a!1 (or c (not a!5)))))
% 0.21/0.38 (a!14 (and a!13 (or a!4 (and (not c) a!5)))))
% 0.21/0.38 (let ((a!11 (nnf-neg (refl (~ (not c) (not c))) a!9 a!10)))
% 0.21/0.38 (nnf-neg (sk a!2)
% 0.21/0.38 (nnf-neg a!3 (~ (not a!1) a!4))
% 0.21/0.38 (monotonicity (refl (~ c c)) a!6 a!7)
% 0.21/0.38 a!11
% 0.21/0.38 (~ a!12 a!14)))))
% 0.21/0.38 Proof display could not be completed: unexpected number of arguments
% 0.21/0.38 % E exiting
%------------------------------------------------------------------------------