%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN937+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:41:02 AM UTC 2025
% Result : Theorem 0.13s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYN937+1 : TPTP v9.0.0. Released v3.1.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n002.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 13:03:01 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 tff(p_type, type, (
% 0.13/0.38 p: $i > $o)).
% 0.13/0.38 tff(tptp_fun_X_0_type, type, (
% 0.13/0.38 tptp_fun_X_0: $i)).
% 0.13/0.38 tff(c_type, type, (
% 0.13/0.38 c: $o)).
% 0.13/0.38 tff(tptp_fun_X_1_type, type, (
% 0.13/0.38 tptp_fun_X_1: $i)).
% 0.13/0.38 tff(1,assumption,(~(c | (~p(X!1)))), introduced(assumption)).
% 0.13/0.38 tff(2,plain,
% 0.13/0.38 ((c | (~p(X!1))) | p(X!1)),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(3,plain,
% 0.13/0.38 (p(X!1)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.13/0.38 tff(4,plain,
% 0.13/0.38 ((c | (~p(X!1))) | (~c)),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(5,plain,
% 0.13/0.38 (~c),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.13/0.38 tff(6,assumption,(p(X!1)), introduced(assumption)).
% 0.13/0.38 tff(7,assumption,(![X: $i] : (c | (~p(X)))), introduced(assumption)).
% 0.13/0.38 tff(8,assumption,(~c), introduced(assumption)).
% 0.13/0.38 tff(9,plain,
% 0.13/0.38 (((~![X: $i] : (c | (~p(X)))) | (c | (~p(X!1)))) <=> ((~![X: $i] : (c | (~p(X)))) | c | (~p(X!1)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(10,plain,
% 0.13/0.38 ((~![X: $i] : (c | (~p(X)))) | (c | (~p(X!1)))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(11,plain,
% 0.13/0.38 ((~![X: $i] : (c | (~p(X)))) | c | (~p(X!1))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.13/0.38 tff(12,plain,
% 0.13/0.38 ($false),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[11, 8, 7, 6])).
% 0.13/0.38 tff(13,plain,((~![X: $i] : (c | (~p(X)))) | c | (~p(X!1))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.38 tff(14,plain,
% 0.13/0.38 (~![X: $i] : (c | (~p(X)))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[13, 5, 3])).
% 0.13/0.38 tff(15,plain,
% 0.13/0.38 ((c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X))) <=> (c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(16,plain,
% 0.13/0.38 (((![X: $i] : (c | (~p(X))) | (c | ![X: $i] : (~p(X)))) & ((~(c | (~p(X!0)))) | ((~c) & p(X!1)))) <=> ((c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X))) & ((~(c | (~p(X!0)))) | ((~c) & p(X!1))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(17,plain,
% 0.13/0.38 ((~(![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X))))) <=> (~(![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(18,plain,
% 0.13/0.38 ((![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))) <=> (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(19,plain,
% 0.13/0.38 ((~(![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X))))) <=> (~(![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))))),
% 0.13/0.38 inference(monotonicity,[status(thm)],[18])).
% 0.13/0.38 tff(20,plain,
% 0.13/0.38 ((~(![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X))))) <=> (~(![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))))),
% 0.13/0.38 inference(transitivity,[status(thm)],[19, 17])).
% 0.13/0.38 tff(21,plain,
% 0.13/0.38 ((![X: $i] : (p(X) => c) <=> (?[X: $i] : p(X) => c)) <=> (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(22,plain,
% 0.13/0.38 ((~(![X: $i] : (p(X) => c) <=> (?[X: $i] : p(X) => c))) <=> (~(![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))))),
% 0.13/0.38 inference(monotonicity,[status(thm)],[21])).
% 0.13/0.38 tff(23,plain,
% 0.13/0.38 ((~(![X: $i] : (p(X) => c) <=> (?[X: $i] : p(X) => c))) <=> (~(![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))))),
% 0.13/0.38 inference(transitivity,[status(thm)],[22, 17])).
% 0.13/0.38 tff(24,axiom,(~(![X: $i] : (p(X) => c) <=> (?[X: $i] : p(X) => c))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.13/0.38 tff(25,plain,
% 0.13/0.38 (~(![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.13/0.38 tff(26,plain,
% 0.13/0.38 (~(![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[25, 20])).
% 0.13/0.38 tff(27,plain,
% 0.13/0.38 (~(![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[26, 17])).
% 0.13/0.38 tff(28,plain,
% 0.13/0.38 (~(![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.13/0.38 unexpected number of arguments: (let ((a!1 (forall ((X $i)) (or c (not (p X)))))
% 0.13/0.38 (a!3 (not (or c (not (p X!0)))))
% 0.13/0.38 (a!4 (lambda ((X $i)) (refl (~ (not (p X)) (not (p X))))))
% 0.13/0.38 (a!5 (exists ((X $i)) (p X)))
% 0.13/0.38 (a!6 (forall ((X $i)) (not (p X)))))
% 0.13/0.38 (let ((a!2 (nnf-pos (proof-bind (lambda ((X $i))
% 0.13/0.38 (let ((a!1 (~ (or c (not (p X)))
% 0.13/0.38 (or c (not (p X))))))
% 0.13/0.38 (refl a!1))))
% 0.13/0.38 (~ a!1 a!1)))
% 0.13/0.38 (a!7 (monotonicity (refl (~ c c))
% 0.13/0.38 (nnf-neg (proof-bind a!4) (~ (not a!5) a!6))
% 0.13/0.38 (~ (or c (not a!5)) (or c a!6))))
% 0.13/0.38 (a!8 (nnf-neg (sk (~ a!5 (p X!1))) (~ (not (not a!5)) (p X!1))))
% 0.13/0.38 (a!9 (~ (not (or c (not a!5))) (and (not c) (p X!1))))
% 0.13/0.38 (a!11 (not (= a!1 (or c (not a!5)))))
% 0.13/0.38 (a!12 (and (or a!1 (or c a!6)) (or a!3 (and (not c) (p X!1))))))
% 0.13/0.38 (let ((a!10 (nnf-neg (refl (~ (not c) (not c))) a!8 a!9)))
% 0.13/0.38 (nnf-neg a!2 (sk (~ (not a!1) a!3)) a!7 a!10 (~ a!11 a!12)))))
% 0.13/0.38 Proof display could not be completed: unexpected number of arguments
% 0.13/0.38 % E exiting
%------------------------------------------------------------------------------