%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN934+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 05:41:01 AM UTC 2025
% Result : Theorem 0.19s 0.37s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : SYN934+1 : TPTP v9.0.0. Released v3.1.0.
% 0.02/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.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 13:01:18 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(p_type, type, (
% 0.19/0.37 p: $i > $o)).
% 0.19/0.37 tff(elem_3_type, type, (
% 0.19/0.37 elem_3: $i)).
% 0.19/0.37 tff(k!0_type, type, (
% 0.19/0.37 k!0: $o)).
% 0.19/0.37 tff(tptp_fun_X_2_type, type, (
% 0.19/0.37 tptp_fun_X_2: $i)).
% 0.19/0.37 tff(tptp_fun_X_1_type, type, (
% 0.19/0.37 tptp_fun_X_1: $i)).
% 0.19/0.37 tff(c_type, type, (
% 0.19/0.37 c: $o)).
% 0.19/0.37 tff(1,assumption,(~k!0), introduced(assumption)).
% 0.19/0.37 tff(2,assumption,(![X: $i] : (~(k!0 | p(X)))), introduced(assumption)).
% 0.19/0.37 tff(3,assumption,(k!0 | p(X!1)), introduced(assumption)).
% 0.19/0.37 tff(4,plain,
% 0.19/0.37 ((~![X: $i] : (~(k!0 | p(X)))) | (~(k!0 | p(X!1)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(5,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[4, 2, 3])).
% 0.19/0.37 tff(6,plain,((~(k!0 | p(X!1))) | (~![X: $i] : (~(k!0 | p(X))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(7,plain,
% 0.19/0.37 (~(k!0 | p(X!1))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[6, 2])).
% 0.19/0.37 tff(8,plain,
% 0.19/0.37 ((k!0 | p(X!1)) | (~p(X!1))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(9,plain,
% 0.19/0.37 (~p(X!1)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.37 tff(10,plain,
% 0.19/0.37 ((((k!0 | p(X!1)) | (k!0 | p(X!2))) & (![X: $i] : (~(k!0 | p(X))) | ((~k!0) & ![X: $i] : (~p(X))))) <=> ((k!0 | p(X!1) | p(X!2)) & (![X: $i] : (~(k!0 | p(X))) | ((~k!0) & ![X: $i] : (~p(X)))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(11,plain,
% 0.19/0.37 ((~(?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X)))) <=> (~(?[X: $i] : (k!0 | p(X)) <=> (k!0 | ?[X: $i] : p(X))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(12,plain,
% 0.19/0.37 ((~(?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X)))) <=> (~(?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(13,plain,
% 0.19/0.37 ((?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) <=> (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(14,plain,
% 0.19/0.37 ((~(?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X)))) <=> (~(?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[13])).
% 0.19/0.37 tff(15,plain,
% 0.19/0.37 ((~(?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X)))) <=> (~(?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))))),
% 0.19/0.37 inference(transitivity,[status(thm)],[14, 12])).
% 0.19/0.37 tff(16,plain,
% 0.19/0.37 ((?[X: $i] : (c => p(X)) <=> (c => ?[X: $i] : p(X))) <=> (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(17,plain,
% 0.19/0.37 ((~(?[X: $i] : (c => p(X)) <=> (c => ?[X: $i] : p(X)))) <=> (~(?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[16])).
% 0.19/0.37 tff(18,plain,
% 0.19/0.37 ((~(?[X: $i] : (c => p(X)) <=> (c => ?[X: $i] : p(X)))) <=> (~(?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))))),
% 0.19/0.37 inference(transitivity,[status(thm)],[17, 12])).
% 0.19/0.37 tff(19,axiom,(~(?[X: $i] : (c => p(X)) <=> (c => ?[X: $i] : p(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.19/0.37 tff(20,plain,
% 0.19/0.37 (~(?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.37 tff(21,plain,
% 0.19/0.37 (~(?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.19/0.37 tff(22,plain,
% 0.19/0.37 (~(?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[21, 12])).
% 0.19/0.37 tff(23,plain,
% 0.19/0.37 (~(?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.19/0.37 tff(24,plain,
% 0.19/0.37 (~(?[X: $i] : (k!0 | p(X)) <=> (k!0 | ?[X: $i] : p(X)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[23, 11])).
% 0.19/0.37 unexpected number of arguments: (let ((a!1 (exists ((X $i)) (or k!0 (p X))))
% 0.19/0.37 (a!3 (forall ((X $i)) (not (or k!0 (p X)))))
% 0.19/0.37 (a!5 (exists ((X $i)) (p X)))
% 0.19/0.37 (a!7 (lambda ((X $i)) (refl (~ (not (p X)) (not (p X))))))
% 0.19/0.37 (a!8 (forall ((X $i)) (not (p X)))))
% 0.19/0.37 (let ((a!2 (sk (~ a!1 (or k!0 (p X!1)))))
% 0.19/0.37 (a!4 (nnf-neg (proof-bind (lambda ((X $i))
% 0.19/0.37 (let ((a!1 (~ (not (or k!0 (p X)))
% 0.19/0.37 (not (or k!0 (p X))))))
% 0.19/0.37 (refl a!1))))
% 0.19/0.37 (~ (not a!1) a!3)))
% 0.19/0.37 (a!6 (monotonicity (refl (~ k!0 k!0))
% 0.19/0.37 (sk (~ a!5 (p X!2)))
% 0.19/0.37 (~ (or k!0 a!5) (or k!0 (p X!2)))))
% 0.19/0.37 (a!9 (nnf-neg (refl (~ (not k!0) (not k!0)))
% 0.19/0.37 (nnf-neg (proof-bind a!7) (~ (not a!5) a!8))
% 0.19/0.37 (~ (not (or k!0 a!5)) (and (not k!0) a!8))))
% 0.19/0.37 (a!10 (and (or (or k!0 (p X!1)) (or k!0 (p X!2)))
% 0.19/0.37 (or a!3 (and (not k!0) a!8)))))
% 0.19/0.37 (let ((a!11 (~ (not (= a!1 (or k!0 a!5))) a!10)))
% 0.19/0.37 (nnf-neg a!2 a!4 a!6 a!9 a!11))))
% 0.19/0.37 Proof display could not be completed: unexpected number of arguments
% 0.19/0.37 % E exiting
%------------------------------------------------------------------------------