%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM003+2 : TPTP v9.0.0. Bugfixed v2.2.0.
% 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 05:00:56 AM UTC 2025
% Result : Theorem 0.46s 0.65s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : COM003+2 : TPTP v9.0.0. Bugfixed v2.2.0.
% 0.05/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.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 : Thu Jun 19 12:24:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.46/0.65 % SZS status Theorem
% 0.46/0.65 % SZS output start Proof
% 0.46/0.65 tff(program_not_halts2_type, type, (
% 0.46/0.65 program_not_halts2: ( $i * $i ) > $o)).
% 0.46/0.65 tff(tptp_fun_U_6_type, type, (
% 0.46/0.65 tptp_fun_U_6: $i)).
% 0.46/0.65 tff(halts2_type, type, (
% 0.46/0.65 halts2: ( $i * $i ) > $o)).
% 0.46/0.65 tff(program_type, type, (
% 0.46/0.65 program: $i > $o)).
% 0.46/0.65 tff(program_halts2_type, type, (
% 0.46/0.65 program_halts2: ( $i * $i ) > $o)).
% 0.46/0.65 tff(program_not_halts2_halts2_outputs_type, type, (
% 0.46/0.65 program_not_halts2_halts2_outputs: ( $i * $i * $i ) > $o)).
% 0.46/0.65 tff(good_type, type, (
% 0.46/0.65 good: $i)).
% 0.46/0.65 tff(bad_type, type, (
% 0.46/0.65 bad: $i)).
% 0.46/0.65 tff(tptp_fun_Y_5_type, type, (
% 0.46/0.65 tptp_fun_Y_5: $i > $i)).
% 0.46/0.65 tff(program_halts2_halts2_outputs_type, type, (
% 0.46/0.65 program_halts2_halts2_outputs: ( $i * $i * $i ) > $o)).
% 0.46/0.65 tff(tptp_fun_V_4_type, type, (
% 0.46/0.65 tptp_fun_V_4: $i)).
% 0.46/0.65 tff(program_not_halts2_halts3_outputs_type, type, (
% 0.46/0.65 program_not_halts2_halts3_outputs: ( $i * $i * $i * $i ) > $o)).
% 0.46/0.65 tff(tptp_fun_Y_3_type, type, (
% 0.46/0.65 tptp_fun_Y_3: $i > $i)).
% 0.46/0.65 tff(program_halts2_halts3_outputs_type, type, (
% 0.46/0.65 program_halts2_halts3_outputs: ( $i * $i * $i * $i ) > $o)).
% 0.46/0.66 tff(tptp_fun_W_2_type, type, (
% 0.46/0.66 tptp_fun_W_2: $i)).
% 0.46/0.66 tff(program_program_decides_type, type, (
% 0.46/0.66 program_program_decides: $i > $o)).
% 0.46/0.66 tff(algorithm_program_decides_type, type, (
% 0.46/0.66 algorithm_program_decides: $i > $o)).
% 0.46/0.66 tff(tptp_fun_X_7_type, type, (
% 0.46/0.66 tptp_fun_X_7: $i)).
% 0.46/0.66 tff(program_decides_type, type, (
% 0.46/0.66 program_decides: $i > $o)).
% 0.46/0.66 tff(halts2_outputs_type, type, (
% 0.46/0.66 halts2_outputs: ( $i * $i * $i ) > $o)).
% 0.46/0.66 tff(outputs_type, type, (
% 0.46/0.66 outputs: ( $i * $i ) > $o)).
% 0.46/0.66 tff(1,assumption,(((~program(U!6)) | (~halts2(U!6, U!6))) <=> program_halts2(U!6, U!6)), introduced(assumption)).
% 0.46/0.66 tff(2,plain,
% 0.46/0.66 (^[X: $i, Y: $i] : refl((~(((~program(X)) | (~halts2(X, Y))) <=> program_halts2(X, Y))) <=> (~(((~program(X)) | (~halts2(X, Y))) <=> program_halts2(X, Y))))),
% 0.46/0.66 inference(bind,[status(th)],[])).
% 0.46/0.66 tff(3,plain,
% 0.46/0.66 (![X: $i, Y: $i] : (~(((~program(X)) | (~halts2(X, Y))) <=> program_halts2(X, Y))) <=> ![X: $i, Y: $i] : (~(((~program(X)) | (~halts2(X, Y))) <=> program_halts2(X, Y)))),
% 0.46/0.66 inference(quant_intro,[status(thm)],[2])).
% 0.46/0.66 tff(4,plain,
% 0.46/0.66 (^[X: $i, Y: $i] : trans(trans(monotonicity(rewrite((program(X) & halts2(X, Y)) <=> (~((~program(X)) | (~halts2(X, Y))))), ((program_halts2(X, Y) <=> (program(X) & halts2(X, Y))) <=> (program_halts2(X, Y) <=> (~((~program(X)) | (~halts2(X, Y))))))), rewrite((program_halts2(X, Y) <=> (~((~program(X)) | (~halts2(X, Y))))) <=> (~(((~program(X)) | (~halts2(X, Y))) <=> program_halts2(X, Y)))), ((program_halts2(X, Y) <=> (program(X) & halts2(X, Y))) <=> (~(((~program(X)) | (~halts2(X, Y))) <=> program_halts2(X, Y))))), rewrite((~(((~program(X)) | (~halts2(X, Y))) <=> program_halts2(X, Y))) <=> (~(((~program(X)) | (~halts2(X, Y))) <=> program_halts2(X, Y)))), ((program_halts2(X, Y) <=> (program(X) & halts2(X, Y))) <=> (~(((~program(X)) | (~halts2(X, Y))) <=> program_halts2(X, Y)))))),
% 0.46/0.66 inference(bind,[status(th)],[])).
% 0.46/0.66 tff(5,plain,
% 0.46/0.66 (![X: $i, Y: $i] : (program_halts2(X, Y) <=> (program(X) & halts2(X, Y))) <=> ![X: $i, Y: $i] : (~(((~program(X)) | (~halts2(X, Y))) <=> program_halts2(X, Y)))),
% 0.46/0.66 inference(quant_intro,[status(thm)],[4])).
% 0.46/0.66 tff(6,plain,
% 0.46/0.66 (![X: $i, Y: $i] : (program_halts2(X, Y) <=> (program(X) & halts2(X, Y))) <=> ![X: $i, Y: $i] : (program_halts2(X, Y) <=> (program(X) & halts2(X, Y)))),
% 0.46/0.66 inference(rewrite,[status(thm)],[])).
% 0.46/0.66 tff(7,axiom,(![X: $i, Y: $i] : (program_halts2(X, Y) <=> (program(X) & halts2(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','program_halts2_def')).
% 0.46/0.66 tff(8,plain,
% 0.46/0.66 (![X: $i, Y: $i] : (program_halts2(X, Y) <=> (program(X) & halts2(X, Y)))),
% 0.46/0.66 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.46/0.66 tff(9,plain,(
% 0.46/0.66 ![X: $i, Y: $i] : (program_halts2(X, Y) <=> (program(X) & halts2(X, Y)))),
% 0.46/0.66 inference(skolemize,[status(sab)],[8])).
% 0.46/0.66 tff(10,plain,
% 0.46/0.66 (![X: $i, Y: $i] : (~(((~program(X)) | (~halts2(X, Y))) <=> program_halts2(X, Y)))),
% 0.46/0.66 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.46/0.66 tff(11,plain,
% 0.46/0.66 (![X: $i, Y: $i] : (~(((~program(X)) | (~halts2(X, Y))) <=> program_halts2(X, Y)))),
% 0.46/0.66 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.46/0.66 tff(12,plain,
% 0.46/0.66 ((~![X: $i, Y: $i] : (~(((~program(X)) | (~halts2(X, Y))) <=> program_halts2(X, Y)))) | (~(((~program(U!6)) | (~halts2(U!6, U!6))) <=> program_halts2(U!6, U!6)))),
% 0.46/0.66 inference(quant_inst,[status(thm)],[])).
% 0.46/0.66 tff(13,plain,
% 0.46/0.66 ($false),
% 0.46/0.66 inference(unit_resolution,[status(thm)],[12, 11, 1])).
% 0.46/0.66 tff(14,plain,(~(((~program(U!6)) | (~halts2(U!6, U!6))) <=> program_halts2(U!6, U!6))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.66 tff(15,assumption,(program_halts2(U!6, U!6)), introduced(assumption)).
% 0.46/0.66 tff(16,assumption,((~program_halts2_halts3_outputs(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2), good)) | (~program_not_halts2_halts3_outputs(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2), bad))), introduced(assumption)).
% 0.46/0.66 tff(17,plain,
% 0.46/0.66 (^[W: $i] : refl(((~program_program_decides(W)) | ![Y: $i, Z: $i] : (~((~program_halts2_halts3_outputs(W, Y, Z, good)) | (~program_not_halts2_halts3_outputs(W, Y, Z, bad))))) <=> ((~program_program_decides(W)) | ![Y: $i, Z: $i] : (~((~program_halts2_halts3_outputs(W, Y, Z, good)) | (~program_not_halts2_halts3_outputs(W, Y, Z, bad))))))),
% 0.46/0.66 inference(bind,[status(th)],[])).
% 0.46/0.66 tff(18,plain,
% 0.46/0.66 (![W: $i] : ((~program_program_decides(W)) | ![Y: $i, Z: $i] : (~((~program_halts2_halts3_outputs(W, Y, Z, good)) | (~program_not_halts2_halts3_outputs(W, Y, Z, bad))))) <=> ![W: $i] : ((~program_program_decides(W)) | ![Y: $i, Z: $i] : (~((~program_halts2_halts3_outputs(W, Y, Z, good)) | (~program_not_halts2_halts3_outputs(W, Y, Z, bad)))))),
% 0.46/0.66 inference(quant_intro,[status(thm)],[17])).
% 0.46/0.66 tff(19,plain,
% 0.46/0.66 (^[W: $i] : rewrite(((~program_program_decides(W)) | ![Y: $i, Z: $i] : (~((~program_halts2_halts3_outputs(W, Y, Z, good)) | (~program_not_halts2_halts3_outputs(W, Y, Z, bad))))) <=> ((~program_program_decides(W)) | ![Y: $i, Z: $i] : (~((~program_halts2_halts3_outputs(W, Y, Z, good)) | (~program_not_halts2_halts3_outputs(W, Y, Z, bad))))))),
% 0.46/0.66 inference(bind,[status(th)],[])).
% 0.46/0.66 tff(20,plain,
% 0.46/0.66 (![W: $i] : ((~program_program_decides(W)) | ![Y: $i, Z: $i] : (~((~program_halts2_halts3_outputs(W, Y, Z, good)) | (~program_not_halts2_halts3_outputs(W, Y, Z, bad))))) <=> ![W: $i] : ((~program_program_decides(W)) | ![Y: $i, Z: $i] : (~((~program_halts2_halts3_outputs(W, Y, Z, good)) | (~program_not_halts2_halts3_outputs(W, Y, Z, bad)))))),
% 0.46/0.66 inference(quant_intro,[status(thm)],[19])).
% 0.46/0.66 tff(21,plain,
% 0.46/0.66 (![W: $i] : ((~program_program_decides(W)) | ![Y: $i, Z: $i] : (~((~program_halts2_halts3_outputs(W, Y, Z, good)) | (~program_not_halts2_halts3_outputs(W, Y, Z, bad))))) <=> ![W: $i] : ((~program_program_decides(W)) | ![Y: $i, Z: $i] : (~((~program_halts2_halts3_outputs(W, Y, Z, good)) | (~program_not_halts2_halts3_outputs(W, Y, Z, bad)))))),
% 0.46/0.66 inference(transitivity,[status(thm)],[20, 18])).
% 0.46/0.66 tff(22,plain,
% 0.46/0.66 (^[W: $i] : rewrite(((~program_program_decides(W)) | ![Y: $i, Z: $i] : (program_halts2_halts3_outputs(W, Y, Z, good) & program_not_halts2_halts3_outputs(W, Y, Z, bad))) <=> ((~program_program_decides(W)) | ![Y: $i, Z: $i] : (~((~program_halts2_halts3_outputs(W, Y, Z, good)) | (~program_not_halts2_halts3_outputs(W, Y, Z, bad))))))),
% 0.46/0.66 inference(bind,[status(th)],[])).
% 0.46/0.66 tff(23,plain,
% 0.46/0.66 (![W: $i] : ((~program_program_decides(W)) | ![Y: $i, Z: $i] : (program_halts2_halts3_outputs(W, Y, Z, good) & program_not_halts2_halts3_outputs(W, Y, Z, bad))) <=> ![W: $i] : ((~program_program_decides(W)) | ![Y: $i, Z: $i] : (~((~program_halts2_halts3_outputs(W, Y, Z, good)) | (~program_not_halts2_halts3_outputs(W, Y, Z, bad)))))),
% 0.46/0.66 inference(quant_intro,[status(thm)],[22])).
% 0.46/0.66 tff(24,plain,
% 0.46/0.66 (![W: $i] : ((~program_program_decides(W)) | ![Y: $i, Z: $i] : (program_halts2_halts3_outputs(W, Y, Z, good) & program_not_halts2_halts3_outputs(W, Y, Z, bad))) <=> ![W: $i] : ((~program_program_decides(W)) | ![Y: $i, Z: $i] : (program_halts2_halts3_outputs(W, Y, Z, good) & program_not_halts2_halts3_outputs(W, Y, Z, bad)))),
% 0.46/0.66 inference(rewrite,[status(thm)],[])).
% 0.46/0.66 tff(25,plain,
% 0.46/0.66 (^[W: $i] : rewrite((program_program_decides(W) => ![Y: $i, Z: $i] : (program_halts2_halts3_outputs(W, Y, Z, good) & program_not_halts2_halts3_outputs(W, Y, Z, bad))) <=> ((~program_program_decides(W)) | ![Y: $i, Z: $i] : (program_halts2_halts3_outputs(W, Y, Z, good) & program_not_halts2_halts3_outputs(W, Y, Z, bad))))),
% 0.46/0.66 inference(bind,[status(th)],[])).
% 0.46/0.66 tff(26,plain,
% 0.46/0.66 (![W: $i] : (program_program_decides(W) => ![Y: $i, Z: $i] : (program_halts2_halts3_outputs(W, Y, Z, good) & program_not_halts2_halts3_outputs(W, Y, Z, bad))) <=> ![W: $i] : ((~program_program_decides(W)) | ![Y: $i, Z: $i] : (program_halts2_halts3_outputs(W, Y, Z, good) & program_not_halts2_halts3_outputs(W, Y, Z, bad)))),
% 0.46/0.66 inference(quant_intro,[status(thm)],[25])).
% 0.46/0.66 tff(27,axiom,(![W: $i] : (program_program_decides(W) => ![Y: $i, Z: $i] : (program_halts2_halts3_outputs(W, Y, Z, good) & program_not_halts2_halts3_outputs(W, Y, Z, bad)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2')).
% 0.46/0.66 tff(28,plain,
% 0.46/0.66 (![W: $i] : ((~program_program_decides(W)) | ![Y: $i, Z: $i] : (program_halts2_halts3_outputs(W, Y, Z, good) & program_not_halts2_halts3_outputs(W, Y, Z, bad)))),
% 0.46/0.66 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.46/0.66 tff(29,plain,
% 0.46/0.66 (![W: $i] : ((~program_program_decides(W)) | ![Y: $i, Z: $i] : (program_halts2_halts3_outputs(W, Y, Z, good) & program_not_halts2_halts3_outputs(W, Y, Z, bad)))),
% 0.46/0.66 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.46/0.66 tff(30,plain,(
% 0.46/0.66 ![W: $i] : ((~program_program_decides(W)) | ![Y: $i, Z: $i] : (program_halts2_halts3_outputs(W, Y, Z, good) & program_not_halts2_halts3_outputs(W, Y, Z, bad)))),
% 0.46/0.66 inference(skolemize,[status(sab)],[29])).
% 0.46/0.66 tff(31,plain,
% 0.46/0.66 (![W: $i] : ((~program_program_decides(W)) | ![Y: $i, Z: $i] : (~((~program_halts2_halts3_outputs(W, Y, Z, good)) | (~program_not_halts2_halts3_outputs(W, Y, Z, bad)))))),
% 0.46/0.66 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.46/0.66 tff(32,plain,
% 0.46/0.66 (![W: $i] : ((~program_program_decides(W)) | ![Y: $i, Z: $i] : (~((~program_halts2_halts3_outputs(W, Y, Z, good)) | (~program_not_halts2_halts3_outputs(W, Y, Z, bad)))))),
% 0.46/0.66 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.46/0.66 tff(33,plain,
% 0.46/0.66 (?[X: $i] : algorithm_program_decides(X) <=> ?[X: $i] : algorithm_program_decides(X)),
% 0.46/0.66 inference(rewrite,[status(thm)],[])).
% 0.46/0.66 tff(34,plain,
% 0.46/0.66 ((~(~?[X: $i] : algorithm_program_decides(X))) <=> ?[X: $i] : algorithm_program_decides(X)),
% 0.46/0.66 inference(rewrite,[status(thm)],[])).
% 0.46/0.66 tff(35,axiom,(~(~?[X: $i] : algorithm_program_decides(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.46/0.66 tff(36,plain,
% 0.46/0.66 (?[X: $i] : algorithm_program_decides(X)),
% 0.46/0.66 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.46/0.66 tff(37,plain,
% 0.46/0.66 (?[X: $i] : algorithm_program_decides(X)),
% 0.46/0.66 inference(modus_ponens,[status(thm)],[36, 33])).
% 0.46/0.66 tff(38,plain,(
% 0.46/0.66 algorithm_program_decides(X!7)),
% 0.46/0.66 inference(skolemize,[status(sab)],[37])).
% 0.46/0.66 tff(39,assumption,(![X: $i] : (~algorithm_program_decides(X))), introduced(assumption)).
% 0.46/0.66 tff(40,plain,
% 0.46/0.66 ((~![X: $i] : (~algorithm_program_decides(X))) | (~algorithm_program_decides(X!7))),
% 0.46/0.66 inference(quant_inst,[status(thm)],[])).
% 0.46/0.66 tff(41,plain,
% 0.46/0.66 ($false),
% 0.46/0.66 inference(unit_resolution,[status(thm)],[40, 39, 38])).
% 0.46/0.66 tff(42,plain,(~![X: $i] : (~algorithm_program_decides(X))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.66 tff(43,plain,
% 0.46/0.66 ((![X: $i] : (~algorithm_program_decides(X)) | program_program_decides(W!2)) <=> (program_program_decides(W!2) | ![X: $i] : (~algorithm_program_decides(X)))),
% 0.46/0.66 inference(rewrite,[status(thm)],[])).
% 0.46/0.66 tff(44,plain,
% 0.46/0.66 ((![X: $i] : (~algorithm_program_decides(X)) | program_program_decides(W!2)) <=> (![X: $i] : (~algorithm_program_decides(X)) | program_program_decides(W!2))),
% 0.46/0.66 inference(rewrite,[status(thm)],[])).
% 0.46/0.66 tff(45,plain,
% 0.46/0.66 ((![X: $i] : (~algorithm_program_decides(X)) | program_program_decides(W!2)) <=> (![X: $i] : (~algorithm_program_decides(X)) | program_program_decides(W!2))),
% 0.46/0.66 inference(rewrite,[status(thm)],[])).
% 0.46/0.66 tff(46,plain,
% 0.46/0.66 (((~?[X: $i] : algorithm_program_decides(X)) | ?[W: $i] : program_program_decides(W)) <=> ((~?[X: $i] : algorithm_program_decides(X)) | ?[W: $i] : program_program_decides(W))),
% 0.46/0.66 inference(rewrite,[status(thm)],[])).
% 0.46/0.66 tff(47,plain,
% 0.46/0.66 ((?[X: $i] : algorithm_program_decides(X) => ?[W: $i] : program_program_decides(W)) <=> ((~?[X: $i] : algorithm_program_decides(X)) | ?[W: $i] : program_program_decides(W))),
% 0.46/0.66 inference(rewrite,[status(thm)],[])).
% 0.46/0.66 tff(48,axiom,(?[X: $i] : algorithm_program_decides(X) => ?[W: $i] : program_program_decides(W)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p1')).
% 0.46/0.66 tff(49,plain,
% 0.46/0.66 ((~?[X: $i] : algorithm_program_decides(X)) | ?[W: $i] : program_program_decides(W)),
% 0.46/0.66 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.46/0.66 tff(50,plain,
% 0.46/0.66 ((~?[X: $i] : algorithm_program_decides(X)) | ?[W: $i] : program_program_decides(W)),
% 0.46/0.66 inference(modus_ponens,[status(thm)],[49, 46])).
% 0.46/0.66 tff(51,plain,
% 0.46/0.66 ((~?[X: $i] : algorithm_program_decides(X)) | ?[W: $i] : program_program_decides(W)),
% 0.46/0.66 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.46/0.66 tff(52,plain,
% 0.46/0.66 ((~?[X: $i] : algorithm_program_decides(X)) | ?[W: $i] : program_program_decides(W)),
% 0.46/0.66 inference(modus_ponens,[status(thm)],[51, 46])).
% 0.46/0.66 Proof display could not be completed: monotonicity rule is not handled
% 0.46/0.66 % E exiting
%------------------------------------------------------------------------------