%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN936+1 : TPTP v9.0.0. Released v3.1.0.
% 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 05:41:02 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN936+1 : TPTP v9.0.0. Released v3.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 13:03:12 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(p_type, type, (
% 0.12/0.37 p: $i > $o)).
% 0.12/0.37 tff(tptp_fun_X_1_type, type, (
% 0.12/0.37 tptp_fun_X_1: $i)).
% 0.12/0.37 tff(k!0_type, type, (
% 0.12/0.37 k!0: $o)).
% 0.12/0.37 tff(tptp_fun_X_2_type, type, (
% 0.12/0.37 tptp_fun_X_2: $i)).
% 0.12/0.37 tff(c_type, type, (
% 0.12/0.37 c: $o)).
% 0.12/0.37 tff(1,assumption,(~(k!0 | p(X!2))), introduced(assumption)).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 ((k!0 | p(X!2)) | (~p(X!2))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (~p(X!2)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 ((k!0 | p(X!2)) | (~k!0)),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (~k!0),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.12/0.37 tff(6,assumption,(~p(X!2)), introduced(assumption)).
% 0.12/0.37 tff(7,assumption,(![X: $i] : p(X)), introduced(assumption)).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 ((~![X: $i] : p(X)) | p(X!2)),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[8, 7, 6])).
% 0.12/0.37 tff(10,plain,((~![X: $i] : p(X)) | p(X!2)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (~![X: $i] : p(X)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[10, 3])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 ((![X: $i] : p(X) | k!0 | ![X: $i] : (k!0 | p(X))) <=> (k!0 | ![X: $i] : p(X) | ![X: $i] : (k!0 | p(X)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 ((![X: $i] : p(X) | k!0 | ![X: $i] : (k!0 | p(X))) <=> (![X: $i] : p(X) | k!0 | ![X: $i] : (k!0 | p(X)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (((![X: $i] : (k!0 | p(X)) | (k!0 | ![X: $i] : p(X))) & ((~(k!0 | p(X!1))) | ((~k!0) & (~p(X!2))))) <=> ((![X: $i] : p(X) | k!0 | ![X: $i] : (k!0 | p(X))) & ((~(k!0 | p(X!1))) | ((~k!0) & (~p(X!2)))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 ((~(![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X)))) <=> (~(![X: $i] : (k!0 | p(X)) <=> (k!0 | ![X: $i] : p(X))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 ((~(![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X)))) <=> (~(![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 ((![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) <=> (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 ((~(![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X)))) <=> (~(![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[17])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 ((~(![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X)))) <=> (~(![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))))),
% 0.12/0.37 inference(transitivity,[status(thm)],[18, 16])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 ((![X: $i] : (c => p(X)) <=> (c => ![X: $i] : p(X))) <=> (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 ((~(![X: $i] : (c => p(X)) <=> (c => ![X: $i] : p(X)))) <=> (~(![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[20])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 ((~(![X: $i] : (c => p(X)) <=> (c => ![X: $i] : p(X)))) <=> (~(![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))))),
% 0.12/0.37 inference(transitivity,[status(thm)],[21, 16])).
% 0.12/0.37 tff(23,axiom,(~(![X: $i] : (c => p(X)) <=> (c => ![X: $i] : p(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 (~(![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (~(![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[24, 19])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (~(![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[25, 16])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 (~(![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 (~(![X: $i] : (k!0 | p(X)) <=> (k!0 | ![X: $i] : p(X)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[27, 15])).
% 0.12/0.37 unexpected number of arguments: (let ((a!1 (lambda ((X $i)) (refl (~ (or k!0 (p X)) (or k!0 (p X))))))
% 0.12/0.37 (a!2 (forall ((X $i)) (or k!0 (p X))))
% 0.12/0.37 (a!4 (lambda ((X $i)) (refl (~ (p X) (p X)))))
% 0.12/0.37 (a!5 (forall ((X $i)) (p X)))
% 0.12/0.37 (a!9 (or (not (or k!0 (p X!1))) (and (not k!0) (not (p X!2))))))
% 0.12/0.37 (let ((a!3 (~ (not a!2) (not (or k!0 (p X!1)))))
% 0.12/0.37 (a!6 (sk (~ (not a!5) (not (p X!2)))))
% 0.12/0.37 (a!7 (~ (not (or k!0 a!5)) (and (not k!0) (not (p X!2)))))
% 0.12/0.37 (a!10 (~ (not (= a!2 (or k!0 a!5))) (and (or a!2 (or k!0 a!5)) a!9))))
% 0.12/0.37 (let ((a!8 (nnf-neg (refl (~ (not k!0) (not k!0))) a!6 a!7)))
% 0.12/0.37 (nnf-neg (nnf-pos (proof-bind a!1) (~ a!2 a!2))
% 0.12/0.37 (sk a!3)
% 0.12/0.37 (monotonicity (refl (~ k!0 k!0))
% 0.12/0.37 (nnf-pos (proof-bind a!4) (~ a!5 a!5))
% 0.12/0.37 (~ (or k!0 a!5) (or k!0 a!5)))
% 0.12/0.37 a!8
% 0.12/0.37 a!10))))
% 0.12/0.37 Proof display could not be completed: unexpected number of arguments
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------