TSTP Solution File: COM003+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : COM003+2 : TPTP v8.1.0. Bugfixed v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 : Tue Sep 6 18:05:42 EDT 2022
% Result : Theorem 0.96s 0.91s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COM003+2 : TPTP v8.1.0. Bugfixed v2.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 30 13:26:05 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.96/0.91 % SZS status Theorem
% 0.96/0.91 % SZS output start Proof
% 0.96/0.91 tff(outputs_type, type, (
% 0.96/0.91 outputs: ( $i * $i ) > $o)).
% 0.96/0.91 tff(good_type, type, (
% 0.96/0.91 good: $i)).
% 0.96/0.91 tff(tptp_fun_U_6_type, type, (
% 0.96/0.91 tptp_fun_U_6: $i)).
% 0.96/0.91 tff(halts2_type, type, (
% 0.96/0.91 halts2: ( $i * $i ) > $o)).
% 0.96/0.91 tff(halts2_outputs_type, type, (
% 0.96/0.91 halts2_outputs: ( $i * $i * $i ) > $o)).
% 0.96/0.91 tff(program_type, type, (
% 0.96/0.91 program: $i > $o)).
% 0.96/0.91 tff(program_halts2_type, type, (
% 0.96/0.91 program_halts2: ( $i * $i ) > $o)).
% 0.96/0.91 tff(program_not_halts2_halts2_outputs_type, type, (
% 0.96/0.91 program_not_halts2_halts2_outputs: ( $i * $i * $i ) > $o)).
% 0.96/0.91 tff(bad_type, type, (
% 0.96/0.91 bad: $i)).
% 0.96/0.91 tff(tptp_fun_Y_5_type, type, (
% 0.96/0.91 tptp_fun_Y_5: $i > $i)).
% 0.96/0.91 tff(program_halts2_halts2_outputs_type, type, (
% 0.96/0.91 program_halts2_halts2_outputs: ( $i * $i * $i ) > $o)).
% 0.96/0.91 tff(tptp_fun_V_4_type, type, (
% 0.96/0.91 tptp_fun_V_4: $i)).
% 0.96/0.91 tff(program_not_halts2_halts3_outputs_type, type, (
% 0.96/0.91 program_not_halts2_halts3_outputs: ( $i * $i * $i * $i ) > $o)).
% 0.96/0.91 tff(tptp_fun_Y_3_type, type, (
% 0.96/0.91 tptp_fun_Y_3: $i > $i)).
% 0.96/0.91 tff(program_halts2_halts3_outputs_type, type, (
% 0.96/0.91 program_halts2_halts3_outputs: ( $i * $i * $i * $i ) > $o)).
% 0.96/0.91 tff(tptp_fun_W_2_type, type, (
% 0.96/0.91 tptp_fun_W_2: $i)).
% 0.96/0.91 tff(program_program_decides_type, type, (
% 0.96/0.91 program_program_decides: $i > $o)).
% 0.96/0.91 tff(algorithm_program_decides_type, type, (
% 0.96/0.91 algorithm_program_decides: $i > $o)).
% 0.96/0.91 tff(program_decides_type, type, (
% 0.96/0.91 program_decides: $i > $o)).
% 0.96/0.91 tff(program_not_halts2_type, type, (
% 0.96/0.91 program_not_halts2: ( $i * $i ) > $o)).
% 0.96/0.91 tff(1,assumption,(~(program_halts2(U!6, U!6) <=> (~((~program(U!6)) | (~halts2(U!6, U!6)))))), introduced(assumption)).
% 0.96/0.91 tff(2,plain,
% 0.96/0.91 (^[X: $i, Y: $i] : refl((program_halts2(X, Y) <=> (~((~program(X)) | (~halts2(X, Y))))) <=> (program_halts2(X, Y) <=> (~((~program(X)) | (~halts2(X, Y))))))),
% 0.96/0.91 inference(bind,[status(th)],[])).
% 0.96/0.91 tff(3,plain,
% 0.96/0.91 (![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)))))),
% 0.96/0.91 inference(quant_intro,[status(thm)],[2])).
% 0.96/0.91 tff(4,plain,
% 0.96/0.91 (^[X: $i, Y: $i] : rewrite((program_halts2(X, Y) <=> (program(X) & halts2(X, Y))) <=> (program_halts2(X, Y) <=> (~((~program(X)) | (~halts2(X, Y))))))),
% 0.96/0.91 inference(bind,[status(th)],[])).
% 0.96/0.91 tff(5,plain,
% 0.96/0.91 (![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)))))),
% 0.96/0.91 inference(quant_intro,[status(thm)],[4])).
% 0.96/0.91 tff(6,plain,
% 0.96/0.91 (![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)))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(7,axiom,(![X: $i, Y: $i] : (program_halts2(X, Y) <=> (program(X) & halts2(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','program_halts2_def')).
% 0.96/0.91 tff(8,plain,
% 0.96/0.91 (![X: $i, Y: $i] : (program_halts2(X, Y) <=> (program(X) & halts2(X, Y)))),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.96/0.91 tff(9,plain,(
% 0.96/0.91 ![X: $i, Y: $i] : (program_halts2(X, Y) <=> (program(X) & halts2(X, Y)))),
% 0.96/0.91 inference(skolemize,[status(sab)],[8])).
% 0.96/0.91 tff(10,plain,
% 0.96/0.91 (![X: $i, Y: $i] : (program_halts2(X, Y) <=> (~((~program(X)) | (~halts2(X, Y)))))),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.96/0.91 tff(11,plain,
% 0.96/0.91 (![X: $i, Y: $i] : (program_halts2(X, Y) <=> (~((~program(X)) | (~halts2(X, Y)))))),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.96/0.91 tff(12,plain,
% 0.96/0.91 ((~![X: $i, Y: $i] : (program_halts2(X, Y) <=> (~((~program(X)) | (~halts2(X, Y)))))) | (program_halts2(U!6, U!6) <=> (~((~program(U!6)) | (~halts2(U!6, U!6)))))),
% 0.96/0.91 inference(quant_inst,[status(thm)],[])).
% 0.96/0.91 tff(13,plain,
% 0.96/0.91 ($false),
% 0.96/0.91 inference(unit_resolution,[status(thm)],[12, 11, 1])).
% 0.96/0.91 tff(14,plain,(program_halts2(U!6, U!6) <=> (~((~program(U!6)) | (~halts2(U!6, U!6))))), inference(lemma,lemma(discharge,[]))).
% 0.96/0.91 tff(15,assumption,(halts2(U!6, U!6)), introduced(assumption)).
% 0.96/0.91 tff(16,assumption,((~program_halts2_halts2_outputs(V!4, tptp_fun_Y_5(V!4), good)) | (~program_not_halts2_halts2_outputs(V!4, tptp_fun_Y_5(V!4), bad))), introduced(assumption)).
% 0.96/0.91 tff(17,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)).
% 0.96/0.91 tff(18,plain,
% 0.96/0.91 (^[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))))))),
% 0.96/0.91 inference(bind,[status(th)],[])).
% 0.96/0.91 tff(19,plain,
% 0.96/0.91 (![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)))))),
% 0.96/0.91 inference(quant_intro,[status(thm)],[18])).
% 0.96/0.91 tff(20,plain,
% 0.96/0.91 (^[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))))))),
% 0.96/0.91 inference(bind,[status(th)],[])).
% 0.96/0.91 tff(21,plain,
% 0.96/0.91 (![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)))))),
% 0.96/0.91 inference(quant_intro,[status(thm)],[20])).
% 0.96/0.91 tff(22,plain,
% 0.96/0.91 (![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)))))),
% 0.96/0.91 inference(transitivity,[status(thm)],[21, 19])).
% 0.96/0.91 tff(23,plain,
% 0.96/0.91 (^[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))))))),
% 0.96/0.91 inference(bind,[status(th)],[])).
% 0.96/0.91 tff(24,plain,
% 0.96/0.91 (![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)))))),
% 0.96/0.91 inference(quant_intro,[status(thm)],[23])).
% 0.96/0.91 tff(25,plain,
% 0.96/0.91 (![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)))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(26,plain,
% 0.96/0.91 (^[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))))),
% 0.96/0.91 inference(bind,[status(th)],[])).
% 0.96/0.91 tff(27,plain,
% 0.96/0.91 (![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)))),
% 0.96/0.91 inference(quant_intro,[status(thm)],[26])).
% 0.96/0.91 tff(28,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/sandbox2/benchmark/theBenchmark.p','p2')).
% 0.96/0.91 tff(29,plain,
% 0.96/0.91 (![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)))),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.96/0.91 tff(30,plain,
% 0.96/0.91 (![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)))),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.96/0.91 tff(31,plain,(
% 0.96/0.91 ![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)))),
% 0.96/0.91 inference(skolemize,[status(sab)],[30])).
% 0.96/0.91 tff(32,plain,
% 0.96/0.91 (![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)))))),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.96/0.91 tff(33,plain,
% 0.96/0.91 (![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)))))),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[32, 22])).
% 0.96/0.91 tff(34,plain,
% 0.96/0.91 (?[W: $i] : program_program_decides(W) <=> ?[W: $i] : program_program_decides(W)),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(35,plain,
% 0.96/0.91 (($false | ?[W: $i] : program_program_decides(W)) <=> ?[W: $i] : program_program_decides(W)),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(36,plain,
% 0.96/0.91 ((~$true) <=> $false),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(37,plain,
% 0.96/0.91 ((~(~?[X: $i] : algorithm_program_decides(X))) <=> ?[X: $i] : algorithm_program_decides(X)),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(38,axiom,(~(~?[X: $i] : algorithm_program_decides(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.96/0.91 tff(39,plain,
% 0.96/0.91 (?[X: $i] : algorithm_program_decides(X)),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.96/0.91 tff(40,plain,
% 0.96/0.91 (?[X: $i] : algorithm_program_decides(X) <=> $true),
% 0.96/0.91 inference(iff_true,[status(thm)],[39])).
% 0.96/0.91 tff(41,plain,
% 0.96/0.91 ((~?[X: $i] : algorithm_program_decides(X)) <=> (~$true)),
% 0.96/0.91 inference(monotonicity,[status(thm)],[40])).
% 0.96/0.91 tff(42,plain,
% 0.96/0.91 ((~?[X: $i] : algorithm_program_decides(X)) <=> $false),
% 0.96/0.91 inference(transitivity,[status(thm)],[41, 36])).
% 0.96/0.91 tff(43,plain,
% 0.96/0.91 (((~?[X: $i] : algorithm_program_decides(X)) | ?[W: $i] : program_program_decides(W)) <=> ($false | ?[W: $i] : program_program_decides(W))),
% 0.96/0.91 inference(monotonicity,[status(thm)],[42])).
% 0.96/0.91 tff(44,plain,
% 0.96/0.91 (((~?[X: $i] : algorithm_program_decides(X)) | ?[W: $i] : program_program_decides(W)) <=> ?[W: $i] : program_program_decides(W)),
% 0.96/0.91 inference(transitivity,[status(thm)],[43, 35])).
% 0.96/0.91 tff(45,plain,
% 0.96/0.91 (((~?[X: $i] : algorithm_program_decides(X)) | ?[W: $i] : program_program_decides(W)) <=> ((~?[X: $i] : algorithm_program_decides(X)) | ?[W: $i] : program_program_decides(W))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(46,plain,
% 0.96/0.91 ((?[X: $i] : algorithm_program_decides(X) => ?[W: $i] : program_program_decides(W)) <=> ((~?[X: $i] : algorithm_program_decides(X)) | ?[W: $i] : program_program_decides(W))),
% 0.96/0.91 inference(rewrite,[status(thm)],[])).
% 0.96/0.91 tff(47,axiom,(?[X: $i] : algorithm_program_decides(X) => ?[W: $i] : program_program_decides(W)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p1')).
% 0.96/0.91 tff(48,plain,
% 0.96/0.91 ((~?[X: $i] : algorithm_program_decides(X)) | ?[W: $i] : program_program_decides(W)),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.96/0.91 tff(49,plain,
% 0.96/0.91 ((~?[X: $i] : algorithm_program_decides(X)) | ?[W: $i] : program_program_decides(W)),
% 0.96/0.91 inference(modus_ponens,[status(thm)],[48, 45])).
% 0.96/0.91 tff(50,plain,
% 0.96/0.91 (?[W: $i] : program_program_decides(W)),
% 0.96/0.92 inference(modus_ponens,[status(thm)],[49, 44])).
% 0.96/0.92 tff(51,plain,
% 0.96/0.92 (?[W: $i] : program_program_decides(W)),
% 0.96/0.92 inference(modus_ponens,[status(thm)],[50, 34])).
% 0.96/0.92 tff(52,plain,(
% 0.96/0.92 program_program_decides(W!2)),
% 0.96/0.92 inference(skolemize,[status(sab)],[51])).
% 0.96/0.92 tff(53,plain,
% 0.96/0.92 (((~![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)))))) | ((~program_program_decides(W!2)) | ![Y: $i, Z: $i] : (~((~program_halts2_halts3_outputs(W!2, Y, Z, good)) | (~program_not_halts2_halts3_outputs(W!2, 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)))))) | (~program_program_decides(W!2)) | ![Y: $i, Z: $i] : (~((~program_halts2_halts3_outputs(W!2, Y, Z, good)) | (~program_not_halts2_halts3_outputs(W!2, Y, Z, bad)))))),
% 0.96/0.92 inference(rewrite,[status(thm)],[])).
% 0.96/0.92 tff(54,plain,
% 0.96/0.92 ((~![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)))))) | ((~program_program_decides(W!2)) | ![Y: $i, Z: $i] : (~((~program_halts2_halts3_outputs(W!2, Y, Z, good)) | (~program_not_halts2_halts3_outputs(W!2, Y, Z, bad)))))),
% 0.96/0.92 inference(quant_inst,[status(thm)],[])).
% 0.96/0.92 tff(55,plain,
% 0.96/0.92 ((~![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)))))) | (~program_program_decides(W!2)) | ![Y: $i, Z: $i] : (~((~program_halts2_halts3_outputs(W!2, Y, Z, good)) | (~program_not_halts2_halts3_outputs(W!2, Y, Z, bad))))),
% 0.96/0.92 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.96/0.92 tff(56,plain,
% 0.96/0.92 (![Y: $i, Z: $i] : (~((~program_halts2_halts3_outputs(W!2, Y, Z, good)) | (~program_not_halts2_halts3_outputs(W!2, Y, Z, bad))))),
% 0.96/0.92 inference(unit_resolution,[status(thm)],[55, 52, 33])).
% 0.96/0.92 tff(57,plain,
% 0.96/0.92 ((~![Y: $i, Z: $i] : (~((~program_halts2_halts3_outputs(W!2, Y, Z, good)) | (~program_not_halts2_halts3_outputs(W!2, Y, Z, bad))))) | (~((~program_halts2_halts3_outputs(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2), good)) | (~program_not_halts2_halts3_outputs(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2), bad))))),
% 0.96/0.92 inference(quant_inst,[status(thm)],[])).
% 0.96/0.92 tff(58,plain,
% 0.96/0.92 ($false),
% 0.96/0.92 inference(unit_resolution,[status(thm)],[57, 56, 17])).
% 0.96/0.92 tff(59,plain,(~((~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)))), inference(lemma,lemma(discharge,[]))).
% 0.96/0.92 tff(60,plain,
% 0.96/0.92 (((~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))) | program_not_halts2_halts3_outputs(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2), bad)),
% 0.96/0.92 inference(tautology,[status(thm)],[])).
% 0.96/0.92 tff(61,plain,
% 0.96/0.92 (program_not_halts2_halts3_outputs(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2), bad)),
% 0.96/0.92 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.96/0.92 tff(62,plain,
% 0.96/0.92 (((~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))) | program_halts2_halts3_outputs(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2), good)),
% 0.96/0.92 inference(tautology,[status(thm)],[])).
% 0.96/0.92 tff(63,plain,
% 0.96/0.92 (program_halts2_halts3_outputs(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2), good)),
% 0.96/0.92 inference(unit_resolution,[status(thm)],[62, 59])).
% 0.96/0.92 tff(64,plain,
% 0.96/0.92 (^[X: $i] : refl((program_program_decides(X) <=> (~((~program(X)) | (~program_decides(X))))) <=> (program_program_decides(X) <=> (~((~program(X)) | (~program_decides(X))))))),
% 0.96/0.92 inference(bind,[status(th)],[])).
% 0.96/0.92 tff(65,plain,
% 0.96/0.92 (![X: $i] : (program_program_decides(X) <=> (~((~program(X)) | (~program_decides(X))))) <=> ![X: $i] : (program_program_decides(X) <=> (~((~program(X)) | (~program_decides(X)))))),
% 0.96/0.92 inference(quant_intro,[status(thm)],[64])).
% 0.96/0.92 tff(66,plain,
% 0.96/0.92 (^[X: $i] : rewrite((program_program_decides(X) <=> (program(X) & program_decides(X))) <=> (program_program_decides(X) <=> (~((~program(X)) | (~program_decides(X))))))),
% 0.96/0.92 inference(bind,[status(th)],[])).
% 0.96/0.92 tff(67,plain,
% 0.96/0.92 (![X: $i] : (program_program_decides(X) <=> (program(X) & program_decides(X))) <=> ![X: $i] : (program_program_decides(X) <=> (~((~program(X)) | (~program_decides(X)))))),
% 0.96/0.92 inference(quant_intro,[status(thm)],[66])).
% 0.96/0.92 tff(68,plain,
% 0.96/0.92 (![X: $i] : (program_program_decides(X) <=> (program(X) & program_decides(X))) <=> ![X: $i] : (program_program_decides(X) <=> (program(X) & program_decides(X)))),
% 0.96/0.92 inference(rewrite,[status(thm)],[])).
% 0.96/0.92 tff(69,axiom,(![X: $i] : (program_program_decides(X) <=> (program(X) & program_decides(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','program_program_decides_def')).
% 0.96/0.92 tff(70,plain,
% 0.96/0.92 (![X: $i] : (program_program_decides(X) <=> (program(X) & program_decides(X)))),
% 0.96/0.92 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.96/0.92 tff(71,plain,(
% 0.96/0.92 ![X: $i] : (program_program_decides(X) <=> (program(X) & program_decides(X)))),
% 0.96/0.92 inference(skolemize,[status(sab)],[70])).
% 0.96/0.92 tff(72,plain,
% 0.96/0.92 (![X: $i] : (program_program_decides(X) <=> (~((~program(X)) | (~program_decides(X)))))),
% 0.96/0.92 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.96/0.92 tff(73,plain,
% 0.96/0.92 (![X: $i] : (program_program_decides(X) <=> (~((~program(X)) | (~program_decides(X)))))),
% 0.96/0.92 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.96/0.92 tff(74,plain,
% 0.96/0.92 ((~![X: $i] : (program_program_decides(X) <=> (~((~program(X)) | (~program_decides(X)))))) | (program_program_decides(W!2) <=> (~((~program(W!2)) | (~program_decides(W!2)))))),
% 0.96/0.92 inference(quant_inst,[status(thm)],[])).
% 0.96/0.92 tff(75,plain,
% 0.96/0.92 (program_program_decides(W!2) <=> (~((~program(W!2)) | (~program_decides(W!2))))),
% 0.96/0.92 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.96/0.92 tff(76,plain,
% 0.96/0.92 ((~(program_program_decides(W!2) <=> (~((~program(W!2)) | (~program_decides(W!2)))))) | (~program_program_decides(W!2)) | (~((~program(W!2)) | (~program_decides(W!2))))),
% 0.96/0.92 inference(tautology,[status(thm)],[])).
% 0.96/0.92 tff(77,plain,
% 0.96/0.92 ((~(program_program_decides(W!2) <=> (~((~program(W!2)) | (~program_decides(W!2)))))) | (~((~program(W!2)) | (~program_decides(W!2))))),
% 0.96/0.92 inference(unit_resolution,[status(thm)],[76, 52])).
% 0.96/0.92 tff(78,plain,
% 0.96/0.92 (~((~program(W!2)) | (~program_decides(W!2)))),
% 0.96/0.92 inference(unit_resolution,[status(thm)],[77, 75])).
% 0.96/0.92 tff(79,plain,
% 0.96/0.92 (((~program(W!2)) | (~program_decides(W!2))) | program(W!2)),
% 0.96/0.92 inference(tautology,[status(thm)],[])).
% 0.96/0.92 tff(80,plain,
% 0.96/0.92 (program(W!2)),
% 0.96/0.92 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.96/0.92 tff(81,assumption,(![W: $i] : ((~program(W)) | (~program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good)) | (~program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad)))), introduced(assumption)).
% 0.96/0.92 tff(82,plain,
% 0.96/0.92 (((~![W: $i] : ((~program(W)) | (~program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good)) | (~program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad)))) | ((~program(W!2)) | (~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)))) <=> ((~![W: $i] : ((~program(W)) | (~program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good)) | (~program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad)))) | (~program(W!2)) | (~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)))),
% 0.96/0.92 inference(rewrite,[status(thm)],[])).
% 0.96/0.92 tff(83,plain,
% 0.96/0.92 ((~![W: $i] : ((~program(W)) | (~program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good)) | (~program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad)))) | ((~program(W!2)) | (~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)))),
% 0.96/0.92 inference(quant_inst,[status(thm)],[])).
% 0.96/0.92 tff(84,plain,
% 0.96/0.92 ((~![W: $i] : ((~program(W)) | (~program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good)) | (~program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad)))) | (~program(W!2)) | (~program_halts2_halts3_outputs(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2), good)) | (~program_not_halts2_halts3_outputs(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2), bad))),
% 0.96/0.92 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.96/0.92 tff(85,plain,
% 0.96/0.92 ($false),
% 0.96/0.92 inference(unit_resolution,[status(thm)],[84, 81, 80, 63, 61])).
% 0.96/0.92 tff(86,plain,(~![W: $i] : ((~program(W)) | (~program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good)) | (~program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad)))), inference(lemma,lemma(discharge,[]))).
% 0.96/0.92 tff(87,plain,
% 0.96/0.92 ((![W: $i] : ((~program(W)) | (~program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good)) | (~program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad))) | (~((~program(V!4)) | (~![Y: $i] : (~((~program_halts2_halts2_outputs(V!4, Y, good)) | (~program_not_halts2_halts2_outputs(V!4, Y, bad)))))))) <=> (![W: $i] : ((~program(W)) | (~program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good)) | (~program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad))) | (~((~program(V!4)) | (~![Y: $i] : (~((~program_halts2_halts2_outputs(V!4, Y, good)) | (~program_not_halts2_halts2_outputs(V!4, Y, bad))))))))),
% 0.96/0.92 inference(rewrite,[status(thm)],[])).
% 0.96/0.92 tff(88,plain,
% 0.96/0.92 ((![W: $i] : ((~program(W)) | (~program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good)) | (~program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad))) | (~((~program(V!4)) | (~![Y: $i] : (~((~program_halts2_halts2_outputs(V!4, Y, good)) | (~program_not_halts2_halts2_outputs(V!4, Y, bad)))))))) <=> (![W: $i] : ((~program(W)) | (~program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good)) | (~program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad))) | (~((~program(V!4)) | (~![Y: $i] : (~((~program_halts2_halts2_outputs(V!4, Y, good)) | (~program_not_halts2_halts2_outputs(V!4, Y, bad))))))))),
% 0.96/0.92 inference(rewrite,[status(thm)],[])).
% 0.96/0.92 tff(89,plain,
% 0.96/0.92 ((program(V!4) & ![Y: $i] : (~((~program_halts2_halts2_outputs(V!4, Y, good)) | (~program_not_halts2_halts2_outputs(V!4, Y, bad))))) <=> (~((~program(V!4)) | (~![Y: $i] : (~((~program_halts2_halts2_outputs(V!4, Y, good)) | (~program_not_halts2_halts2_outputs(V!4, Y, bad)))))))),
% 0.96/0.92 inference(rewrite,[status(thm)],[])).
% 0.96/0.92 tff(90,plain,
% 0.96/0.92 (^[Y: $i] : rewrite((program_halts2_halts2_outputs(V!4, Y, good) & program_not_halts2_halts2_outputs(V!4, Y, bad)) <=> (~((~program_halts2_halts2_outputs(V!4, Y, good)) | (~program_not_halts2_halts2_outputs(V!4, Y, bad)))))),
% 0.96/0.92 inference(bind,[status(th)],[])).
% 0.96/0.92 tff(91,plain,
% 0.96/0.92 (![Y: $i] : (program_halts2_halts2_outputs(V!4, Y, good) & program_not_halts2_halts2_outputs(V!4, Y, bad)) <=> ![Y: $i] : (~((~program_halts2_halts2_outputs(V!4, Y, good)) | (~program_not_halts2_halts2_outputs(V!4, Y, bad))))),
% 0.96/0.92 inference(quant_intro,[status(thm)],[90])).
% 0.96/0.92 tff(92,plain,
% 0.96/0.92 ((program(V!4) & ![Y: $i] : (program_halts2_halts2_outputs(V!4, Y, good) & program_not_halts2_halts2_outputs(V!4, Y, bad))) <=> (program(V!4) & ![Y: $i] : (~((~program_halts2_halts2_outputs(V!4, Y, good)) | (~program_not_halts2_halts2_outputs(V!4, Y, bad)))))),
% 0.96/0.92 inference(monotonicity,[status(thm)],[91])).
% 0.96/0.92 tff(93,plain,
% 0.96/0.92 ((program(V!4) & ![Y: $i] : (program_halts2_halts2_outputs(V!4, Y, good) & program_not_halts2_halts2_outputs(V!4, Y, bad))) <=> (~((~program(V!4)) | (~![Y: $i] : (~((~program_halts2_halts2_outputs(V!4, Y, good)) | (~program_not_halts2_halts2_outputs(V!4, Y, bad)))))))),
% 0.96/0.92 inference(transitivity,[status(thm)],[92, 89])).
% 0.96/0.92 tff(94,plain,
% 0.96/0.92 (^[W: $i] : trans(monotonicity(trans(monotonicity(rewrite((program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good) & program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad)) <=> (~((~program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good)) | (~program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad))))), ((~(program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good) & program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad))) <=> (~(~((~program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good)) | (~program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad))))))), rewrite((~(~((~program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good)) | (~program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad))))) <=> ((~program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good)) | (~program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad)))), ((~(program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good) & program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad))) <=> ((~program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good)) | (~program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad))))), (((~program(W)) | (~(program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good) & program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad)))) <=> ((~program(W)) | ((~program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good)) | (~program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad)))))), rewrite(((~program(W)) | ((~program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good)) | (~program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad)))) <=> ((~program(W)) | (~program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good)) | (~program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad)))), (((~program(W)) | (~(program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good) & program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad)))) <=> ((~program(W)) | (~program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good)) | (~program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad)))))),
% 0.96/0.92 inference(bind,[status(th)],[])).
% 0.96/0.92 tff(95,plain,
% 0.96/0.92 (![W: $i] : ((~program(W)) | (~(program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good) & program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad)))) <=> ![W: $i] : ((~program(W)) | (~program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good)) | (~program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad)))),
% 0.96/0.92 inference(quant_intro,[status(thm)],[94])).
% 0.96/0.92 tff(96,plain,
% 0.96/0.92 ((![W: $i] : ((~program(W)) | (~(program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good) & program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad)))) | (program(V!4) & ![Y: $i] : (program_halts2_halts2_outputs(V!4, Y, good) & program_not_halts2_halts2_outputs(V!4, Y, bad)))) <=> (![W: $i] : ((~program(W)) | (~program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good)) | (~program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad))) | (~((~program(V!4)) | (~![Y: $i] : (~((~program_halts2_halts2_outputs(V!4, Y, good)) | (~program_not_halts2_halts2_outputs(V!4, Y, bad))))))))),
% 0.96/0.92 inference(monotonicity,[status(thm)],[95, 93])).
% 0.96/0.92 tff(97,plain,
% 0.96/0.92 ((![W: $i] : ((~program(W)) | (~(program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good) & program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad)))) | (program(V!4) & ![Y: $i] : (program_halts2_halts2_outputs(V!4, Y, good) & program_not_halts2_halts2_outputs(V!4, Y, bad)))) <=> (![W: $i] : ((~program(W)) | (~program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good)) | (~program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad))) | (~((~program(V!4)) | (~![Y: $i] : (~((~program_halts2_halts2_outputs(V!4, Y, good)) | (~program_not_halts2_halts2_outputs(V!4, Y, bad))))))))),
% 0.96/0.92 inference(transitivity,[status(thm)],[96, 88])).
% 0.96/0.92 tff(98,plain,
% 0.96/0.92 ((![W: $i] : ((~program(W)) | (~(program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good) & program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad)))) | (program(V!4) & ![Y: $i] : (program_halts2_halts2_outputs(V!4, Y, good) & program_not_halts2_halts2_outputs(V!4, Y, bad)))) <=> (![W: $i] : ((~program(W)) | (~(program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good) & program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad)))) | (program(V!4) & ![Y: $i] : (program_halts2_halts2_outputs(V!4, Y, good) & program_not_halts2_halts2_outputs(V!4, Y, bad))))),
% 0.96/0.92 inference(rewrite,[status(thm)],[])).
% 0.96/0.92 tff(99,plain,
% 0.96/0.92 ((program(V!4) & ![Y: $i] : (program_halts2_halts2_outputs(V!4, Y, good) & program_not_halts2_halts2_outputs(V!4, Y, bad))) <=> (program(V!4) & ![Y: $i] : (program_halts2_halts2_outputs(V!4, Y, good) & program_not_halts2_halts2_outputs(V!4, Y, bad)))),
% 0.96/0.92 inference(rewrite,[status(thm)],[])).
% 0.96/0.92 tff(100,plain,
% 0.96/0.92 ((![W: $i] : ((~program(W)) | (~(program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good) & program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad)))) | (program(V!4) & ![Y: $i] : (program_halts2_halts2_outputs(V!4, Y, good) & program_not_halts2_halts2_outputs(V!4, Y, bad)))) <=> (![W: $i] : ((~program(W)) | (~(program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good) & program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad)))) | (program(V!4) & ![Y: $i] : (program_halts2_halts2_outputs(V!4, Y, good) & program_not_halts2_halts2_outputs(V!4, Y, bad))))),
% 0.96/0.92 inference(monotonicity,[status(thm)],[99])).
% 0.96/0.92 tff(101,plain,
% 0.96/0.92 ((![W: $i] : ((~program(W)) | (~(program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good) & program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad)))) | (program(V!4) & ![Y: $i] : (program_halts2_halts2_outputs(V!4, Y, good) & program_not_halts2_halts2_outputs(V!4, Y, bad)))) <=> (![W: $i] : ((~program(W)) | (~(program_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), good) & program_not_halts2_halts3_outputs(W, tptp_fun_Y_3(W), tptp_fun_Y_3(W), bad)))) | (program(V!4) & ![Y: $i] : (program_halts2_halts2_outputs(V!4, Y, good) & program_not_halts2_halts2_outputs(V!4, Y, bad))))),
% 0.96/0.92 inference(transitivity,[status(thm)],[100, 98])).
% 0.96/0.92 tff(102,plain,
% 0.96/0.92 ((~?[W: $i] : (program(W) & ![Y: $i] : (program_halts2_halts3_outputs(W, Y, Y, good) & program_not_halts2_halts3_outputs(W, Y, Y, bad)))) <=> (~?[W: $i] : (program(W) & ![Y: $i] : (program_halts2_halts3_outputs(W, Y, Y, good) & program_not_halts2_halts3_outputs(W, Y, Y, bad))))),
% 0.96/0.92 inference(rewrite,[status(thm)],[])).
% 0.96/0.92 tff(103,plain,
% 0.96/0.92 (((~?[W: $i] : (program(W) & ![Y: $i] : (program_halts2_halts3_outputs(W, Y, Y, good) & program_not_halts2_halts3_outputs(W, Y, Y, bad)))) | ?[V: $i] : (program(V) & ![Y: $i] : (program_halts2_halts2_outputs(V, Y, good) & program_not_halts2_halts2_outputs(V, Y, bad)))) <=> ((~?[W: $i] : (program(W) & ![Y: $i] : (program_halts2_halts3_outputs(W, Y, Y, good) & program_not_halts2_halts3_outputs(W, Y, Y, bad)))) | ?[V: $i] : (program(V) & ![Y: $i] : (program_halts2_halts2_outputs(V, Y, good) & program_not_halts2_halts2_outputs(V, Y, bad))))),
% 0.96/0.92 inference(monotonicity,[status(thm)],[102])).
% 0.96/0.92 tff(104,plain,
% 0.96/0.92 (((~?[W: $i] : (program(W) & ![Y: $i] : (program_halts2_halts3_outputs(W, Y, Y, good) & program_not_halts2_halts3_outputs(W, Y, Y, bad)))) | ?[V: $i] : (program(V) & ![Y: $i] : (program_halts2_halts2_outputs(V, Y, good) & program_not_halts2_halts2_outputs(V, Y, bad)))) <=> ((~?[W: $i] : (program(W) & ![Y: $i] : (program_halts2_halts3_outputs(W, Y, Y, good) & program_not_halts2_halts3_outputs(W, Y, Y, bad)))) | ?[V: $i] : (program(V) & ![Y: $i] : (program_halts2_halts2_outputs(V, Y, good) & program_not_halts2_halts2_outputs(V, Y, bad))))),
% 0.96/0.93 inference(rewrite,[status(thm)],[])).
% 0.96/0.93 tff(105,plain,
% 0.96/0.93 ((?[W: $i] : (program(W) & ![Y: $i] : (program_halts2_halts3_outputs(W, Y, Y, good) & program_not_halts2_halts3_outputs(W, Y, Y, bad))) => ?[V: $i] : (program(V) & ![Y: $i] : (program_halts2_halts2_outputs(V, Y, good) & program_not_halts2_halts2_outputs(V, Y, bad)))) <=> ((~?[W: $i] : (program(W) & ![Y: $i] : (program_halts2_halts3_outputs(W, Y, Y, good) & program_not_halts2_halts3_outputs(W, Y, Y, bad)))) | ?[V: $i] : (program(V) & ![Y: $i] : (program_halts2_halts2_outputs(V, Y, good) & program_not_halts2_halts2_outputs(V, Y, bad))))),
% 0.96/0.93 inference(rewrite,[status(thm)],[])).
% 0.96/0.93 tff(106,axiom,(?[W: $i] : (program(W) & ![Y: $i] : (program_halts2_halts3_outputs(W, Y, Y, good) & program_not_halts2_halts3_outputs(W, Y, Y, bad))) => ?[V: $i] : (program(V) & ![Y: $i] : (program_halts2_halts2_outputs(V, Y, good) & program_not_halts2_halts2_outputs(V, Y, bad)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3')).
% 0.96/0.93 tff(107,plain,
% 0.96/0.93 ((~?[W: $i] : (program(W) & ![Y: $i] : (program_halts2_halts3_outputs(W, Y, Y, good) & program_not_halts2_halts3_outputs(W, Y, Y, bad)))) | ?[V: $i] : (program(V) & ![Y: $i] : (program_halts2_halts2_outputs(V, Y, good) & program_not_halts2_halts2_outputs(V, Y, bad)))),
% 0.96/0.93 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.96/0.93 tff(108,plain,
% 0.96/0.93 ((~?[W: $i] : (program(W) & ![Y: $i] : (program_halts2_halts3_outputs(W, Y, Y, good) & program_not_halts2_halts3_outputs(W, Y, Y, bad)))) | ?[V: $i] : (program(V) & ![Y: $i] : (program_halts2_halts2_outputs(V, Y, good) & program_not_halts2_halts2_outputs(V, Y, bad)))),
% 0.96/0.93 inference(modus_ponens,[status(thm)],[107, 104])).
% 0.96/0.93 tff(109,plain,
% 0.96/0.93 ((~?[W: $i] : (program(W) & ![Y: $i] : (program_halts2_halts3_outputs(W, Y, Y, good) & program_not_halts2_halts3_outputs(W, Y, Y, bad)))) | ?[V: $i] : (program(V) & ![Y: $i] : (program_halts2_halts2_outputs(V, Y, good) & program_not_halts2_halts2_outputs(V, Y, bad)))),
% 0.96/0.93 inference(modus_ponens,[status(thm)],[108, 103])).
% 0.96/0.93 tff(110,plain,
% 0.96/0.93 ((~?[W: $i] : (program(W) & ![Y: $i] : (program_halts2_halts3_outputs(W, Y, Y, good) & program_not_halts2_halts3_outputs(W, Y, Y, bad)))) | ?[V: $i] : (program(V) & ![Y: $i] : (program_halts2_halts2_outputs(V, Y, good) & program_not_halts2_halts2_outputs(V, Y, bad)))),
% 0.96/0.93 inference(modus_ponens,[status(thm)],[109, 104])).
% 0.96/0.93 tff(111,plain,
% 0.96/0.93 ((~?[W: $i] : (program(W) & ![Y: $i] : (program_halts2_halts3_outputs(W, Y, Y, good) & program_not_halts2_halts3_outputs(W, Y, Y, bad)))) | ?[V: $i] : (program(V) & ![Y: $i] : (program_halts2_halts2_outputs(V, Y, good) & program_not_halts2_halts2_outputs(V, Y, bad)))),
% 0.96/0.93 inference(modus_ponens,[status(thm)],[110, 104])).
% 0.96/0.93 tff(112,plain,
% 0.96/0.93 ((~?[W: $i] : (program(W) & ![Y: $i] : (program_halts2_halts3_outputs(W, Y, Y, good) & program_not_halts2_halts3_outputs(W, Y, Y, bad)))) | ?[V: $i] : (program(V) & ![Y: $i] : (program_halts2_halts2_outputs(V, Y, good) & program_not_halts2_halts2_outputs(V, Y, bad)))),
% 0.96/0.93 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.96/0.93 tff(113,plain,
% 0.96/0.93 ((~?[W: $i] : (program(W) & ![Y: $i] : (program_halts2_halts3_outputs(W, Y, Y, good) & program_not_halts2_halts3_outputs(W, Y, Y, bad)))) | ?[V: $i] : (program(V) & ![Y: $i] : (program_halts2_halts2_outputs(V, Y, good) & program_not_halts2_halts2_outputs(V, Y, bad)))),
% 0.96/0.93 inference(modus_ponens,[status(thm)],[112, 104])).
% 0.96/0.93 tff(114,plain,
% 0.96/0.93 ((~?[W: $i] : (program(W) & ![Y: $i] : (program_halts2_halts3_outputs(W, Y, Y, good) & program_not_halts2_halts3_outputs(W, Y, Y, bad)))) | ?[V: $i] : (program(V) & ![Y: $i] : (program_halts2_halts2_outputs(V, Y, good) & program_not_halts2_halts2_outputs(V, Y, bad)))),
% 0.96/0.93 inference(modus_ponens,[status(thm)],[113, 103])).
% 0.96/0.93 Proof display could not be completed: monotonicity rule is not handled
%------------------------------------------------------------------------------