%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM003_1 : TPTP v9.0.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:00:56 AM UTC 2025
% Result : Theorem 0.11s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : COM003_1 : TPTP v9.0.0. Released v5.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 12:21:19 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.38 % SZS status Theorem
% 0.11/0.38 % SZS output start Proof
% 0.11/0.38 tff(halts2_type, type, (
% 0.11/0.38 halts2: ( program * input ) > $o)).
% 0.11/0.38 tff(as_input_type, type, (
% 0.11/0.38 as_input: program > input)).
% 0.11/0.38 tff(tptp_fun_Y_5_type, type, (
% 0.11/0.38 tptp_fun_Y_5: program > program)).
% 0.11/0.38 tff(tptp_fun_V_4_type, type, (
% 0.11/0.38 tptp_fun_V_4: program)).
% 0.11/0.38 tff(outputs_type, type, (
% 0.11/0.38 outputs: ( program * output ) > $o)).
% 0.11/0.38 tff(bad_type, type, (
% 0.11/0.38 bad: output)).
% 0.11/0.38 tff(good_type, type, (
% 0.11/0.38 good: output)).
% 0.11/0.38 tff(halts3_type, type, (
% 0.11/0.38 halts3: ( program * program * input ) > $o)).
% 0.11/0.38 tff(tptp_fun_Y_3_type, type, (
% 0.11/0.38 tptp_fun_Y_3: program > program)).
% 0.11/0.38 tff(tptp_fun_W_2_type, type, (
% 0.11/0.38 tptp_fun_W_2: program)).
% 0.11/0.38 tff(decides_type, type, (
% 0.11/0.38 decides: ( algorithm * program * input ) > $o)).
% 0.11/0.38 tff(elem_9_type, type, (
% 0.11/0.38 elem_9: input)).
% 0.11/0.38 tff(elem_10_type, type, (
% 0.11/0.38 elem_10: program)).
% 0.11/0.38 tff(algorithm_of_type, type, (
% 0.11/0.38 algorithm_of: program > algorithm)).
% 0.11/0.38 tff(tptp_fun_Z_0_type, type, (
% 0.11/0.38 tptp_fun_Z_0: algorithm > input)).
% 0.11/0.38 tff(tptp_fun_Y_1_type, type, (
% 0.11/0.38 tptp_fun_Y_1: algorithm > program)).
% 0.11/0.38 tff(tptp_fun_X1_7_type, type, (
% 0.11/0.38 tptp_fun_X1_7: algorithm)).
% 0.11/0.38 tff(tptp_fun_U_6_type, type, (
% 0.11/0.38 tptp_fun_U_6: program)).
% 0.11/0.38 tff(1,assumption,((~((~halts2(tptp_fun_Y_5(V!4), as_input(tptp_fun_Y_5(V!4)))) | (~((~outputs(V!4, good)) | (~halts2(V!4, as_input(tptp_fun_Y_5(V!4)))))))) | (~(halts2(tptp_fun_Y_5(V!4), as_input(tptp_fun_Y_5(V!4))) | (~((~outputs(V!4, bad)) | (~halts2(V!4, as_input(tptp_fun_Y_5(V!4))))))))), introduced(assumption)).
% 0.11/0.38 tff(2,assumption,((~((~halts2(tptp_fun_Y_3(W!2), as_input(tptp_fun_Y_3(W!2)))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_Y_3(W!2), as_input(tptp_fun_Y_3(W!2)))))))) | (~(halts2(tptp_fun_Y_3(W!2), as_input(tptp_fun_Y_3(W!2))) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_3(W!2), as_input(tptp_fun_Y_3(W!2))))))))), introduced(assumption)).
% 0.11/0.38 tff(3,assumption,(~decides(X1!7, tptp_fun_Y_1(X1!7), tptp_fun_Z_0(X1!7))), introduced(assumption)).
% 0.11/0.38 tff(4,plain,
% 0.11/0.38 (^[Y1: program, Z1: input] : refl(decides(X1!7, Y1, Z1) <=> decides(X1!7, Y1, Z1))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(5,plain,
% 0.11/0.38 (![Y1: program, Z1: input] : decides(X1!7, Y1, Z1) <=> ![Y1: program, Z1: input] : decides(X1!7, Y1, Z1)),
% 0.11/0.38 inference(quant_intro,[status(thm)],[4])).
% 0.11/0.38 tff(6,plain,
% 0.11/0.38 (?[X1: algorithm] : ![Y1: program, Z1: input] : decides(X1, Y1, Z1) <=> ?[X1: algorithm] : ![Y1: program, Z1: input] : decides(X1, Y1, Z1)),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(7,plain,
% 0.11/0.38 ((~(~?[X1: algorithm] : ![Y1: program, Z1: input] : decides(X1, Y1, Z1))) <=> ?[X1: algorithm] : ![Y1: program, Z1: input] : decides(X1, Y1, Z1)),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(8,plain,
% 0.11/0.38 ((~?[X1: algorithm] : ![Y1: program, Z1: input] : decides(X1, Y1, Z1)) <=> (~?[X1: algorithm] : ![Y1: program, Z1: input] : decides(X1, Y1, Z1))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(9,plain,
% 0.11/0.38 ((~(~?[X1: algorithm] : ![Y1: program, Z1: input] : decides(X1, Y1, Z1))) <=> (~(~?[X1: algorithm] : ![Y1: program, Z1: input] : decides(X1, Y1, Z1)))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[8])).
% 0.11/0.38 tff(10,plain,
% 0.11/0.38 ((~(~?[X1: algorithm] : ![Y1: program, Z1: input] : decides(X1, Y1, Z1))) <=> ?[X1: algorithm] : ![Y1: program, Z1: input] : decides(X1, Y1, Z1)),
% 0.11/0.38 inference(transitivity,[status(thm)],[9, 7])).
% 0.11/0.38 tff(11,axiom,(~(~?[X1: algorithm] : ![Y1: program, Z1: input] : decides(X1, Y1, Z1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.11/0.38 tff(12,plain,
% 0.11/0.38 (?[X1: algorithm] : ![Y1: program, Z1: input] : decides(X1, Y1, Z1)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.11/0.38 tff(13,plain,
% 0.11/0.38 (?[X1: algorithm] : ![Y1: program, Z1: input] : decides(X1, Y1, Z1)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[12, 6])).
% 0.11/0.38 tff(14,plain,(
% 0.11/0.38 $oeq(![Y1: program, Z1: input] : decides(X1!7, Y1, Z1), ![Y1: program, Z1: input] : decides(X1!7, Y1, Z1))),
% 0.11/0.38 inference(transitivity,[status(sab)],[13])).
% 0.11/0.38 tff(15,plain,
% 0.11/0.38 (![Y1: program, Z1: input] : decides(X1!7, Y1, Z1)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[14, 5])).
% 0.11/0.38 tff(16,plain,
% 0.11/0.38 ((~![Y1: program, Z1: input] : decides(X1!7, Y1, Z1)) | decides(X1!7, tptp_fun_Y_1(X1!7), tptp_fun_Z_0(X1!7))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(17,plain,
% 0.11/0.39 ($false),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[16, 15, 3])).
% 0.11/0.39 tff(18,plain,(decides(X1!7, tptp_fun_Y_1(X1!7), tptp_fun_Z_0(X1!7))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.39 tff(19,plain,
% 0.11/0.39 ((~![X: algorithm] : (~decides(X, tptp_fun_Y_1(X), tptp_fun_Z_0(X)))) | (~decides(X1!7, tptp_fun_Y_1(X1!7), tptp_fun_Z_0(X1!7)))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(20,plain,
% 0.11/0.39 (~![X: algorithm] : (~decides(X, tptp_fun_Y_1(X), tptp_fun_Z_0(X)))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.11/0.39 tff(21,plain,
% 0.11/0.39 ((![X: algorithm] : (~decides(X, tptp_fun_Y_1(X), tptp_fun_Z_0(X))) | ![Y: program, Z: input] : decides(algorithm_of(W!2), Y, Z)) <=> (![X: algorithm] : (~decides(X, tptp_fun_Y_1(X), tptp_fun_Z_0(X))) | ![Y: program, Z: input] : decides(algorithm_of(W!2), Y, Z))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(22,plain,
% 0.11/0.39 ((![X: algorithm] : (~decides(X, tptp_fun_Y_1(X), tptp_fun_Z_0(X))) | ![Y: program, Z: input] : decides(algorithm_of(W!2), Y, Z)) <=> (![X: algorithm] : (~decides(X, tptp_fun_Y_1(X), tptp_fun_Z_0(X))) | ![Y: program, Z: input] : decides(algorithm_of(W!2), Y, Z))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(23,plain,
% 0.11/0.39 (((~?[X: algorithm] : ![Y: program, Z: input] : decides(X, Y, Z)) | ?[W: program] : ![Y: program, Z: input] : decides(algorithm_of(W), Y, Z)) <=> ((~?[X: algorithm] : ![Y: program, Z: input] : decides(X, Y, Z)) | ?[W: program] : ![Y: program, Z: input] : decides(algorithm_of(W), Y, Z))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(24,plain,
% 0.11/0.39 ((?[X: algorithm] : ![Y: program, Z: input] : decides(X, Y, Z) => ?[W: program] : ![Y: program, Z: input] : decides(algorithm_of(W), Y, Z)) <=> ((~?[X: algorithm] : ![Y: program, Z: input] : decides(X, Y, Z)) | ?[W: program] : ![Y: program, Z: input] : decides(algorithm_of(W), Y, Z))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(25,axiom,(?[X: algorithm] : ![Y: program, Z: input] : decides(X, Y, Z) => ?[W: program] : ![Y: program, Z: input] : decides(algorithm_of(W), Y, Z)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p1')).
% 0.11/0.39 tff(26,plain,
% 0.11/0.39 ((~?[X: algorithm] : ![Y: program, Z: input] : decides(X, Y, Z)) | ?[W: program] : ![Y: program, Z: input] : decides(algorithm_of(W), Y, Z)),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.11/0.39 tff(27,plain,
% 0.11/0.39 ((~?[X: algorithm] : ![Y: program, Z: input] : decides(X, Y, Z)) | ?[W: program] : ![Y: program, Z: input] : decides(algorithm_of(W), Y, Z)),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.11/0.39 tff(28,plain,
% 0.11/0.39 ((~?[X: algorithm] : ![Y: program, Z: input] : decides(X, Y, Z)) | ?[W: program] : ![Y: program, Z: input] : decides(algorithm_of(W), Y, Z)),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.11/0.39 tff(29,plain,
% 0.11/0.39 ((~?[X: algorithm] : ![Y: program, Z: input] : decides(X, Y, Z)) | ?[W: program] : ![Y: program, Z: input] : decides(algorithm_of(W), Y, Z)),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[28, 23])).
% 0.11/0.39 Proof display could not be completed: monotonicity rule is not handled
% 0.11/0.39 % E exiting
%------------------------------------------------------------------------------