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. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 : Unsatisfiable 0.13s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COM003-2 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 13:19:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.40 % SZS status Unsatisfiable
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(program_halts2_type, type, (
% 0.13/0.40 program_halts2: ( $i * $i ) > $o)).
% 0.13/0.40 tff(f3_type, type, (
% 0.13/0.40 f3: $i > $i)).
% 0.13/0.40 tff(c1_type, type, (
% 0.13/0.40 c1: $i)).
% 0.13/0.40 tff(halts2_type, type, (
% 0.13/0.40 halts2: ( $i * $i ) > $o)).
% 0.13/0.40 tff(program_not_halts2_type, type, (
% 0.13/0.40 program_not_halts2: ( $i * $i ) > $o)).
% 0.13/0.40 tff(program_not_halts2_halts3_outputs_type, type, (
% 0.13/0.40 program_not_halts2_halts3_outputs: ( $i * $i * $i * $i ) > $o)).
% 0.13/0.40 tff(bad_type, type, (
% 0.13/0.40 bad: $i)).
% 0.13/0.40 tff(program_program_decides_type, type, (
% 0.13/0.40 program_program_decides: $i > $o)).
% 0.13/0.40 tff(algorithm_program_decides_type, type, (
% 0.13/0.40 algorithm_program_decides: $i > $o)).
% 0.13/0.40 tff(c4_type, type, (
% 0.13/0.40 c4: $i)).
% 0.13/0.40 tff(program_halts2_halts3_outputs_type, type, (
% 0.13/0.40 program_halts2_halts3_outputs: ( $i * $i * $i * $i ) > $o)).
% 0.13/0.40 tff(good_type, type, (
% 0.13/0.40 good: $i)).
% 0.13/0.40 tff(1,assumption,(~program_not_halts2_halts3_outputs(c1, f3(c1), f3(c1), bad)), introduced(assumption)).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (algorithm_program_decides(c4) <=> algorithm_program_decides(c4)),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(3,axiom,(algorithm_program_decides(c4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_algorithm_does_not_exist')).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 (algorithm_program_decides(c4)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 (^[X: $i] : refl(((~algorithm_program_decides(X)) | program_program_decides(c1)) <=> ((~algorithm_program_decides(X)) | program_program_decides(c1)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(6,plain,
% 0.13/0.40 (![X: $i] : ((~algorithm_program_decides(X)) | program_program_decides(c1)) <=> ![X: $i] : ((~algorithm_program_decides(X)) | program_program_decides(c1))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[5])).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (![X: $i] : ((~algorithm_program_decides(X)) | program_program_decides(c1)) <=> ![X: $i] : ((~algorithm_program_decides(X)) | program_program_decides(c1))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(8,axiom,(![X: $i] : ((~algorithm_program_decides(X)) | program_program_decides(c1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom1_1')).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (![X: $i] : ((~algorithm_program_decides(X)) | program_program_decides(c1))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.13/0.40 tff(10,plain,(
% 0.13/0.40 ![X: $i] : ((~algorithm_program_decides(X)) | program_program_decides(c1))),
% 0.13/0.40 inference(skolemize,[status(sab)],[9])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 (![X: $i] : ((~algorithm_program_decides(X)) | program_program_decides(c1))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (((~![X: $i] : ((~algorithm_program_decides(X)) | program_program_decides(c1))) | (program_program_decides(c1) | (~algorithm_program_decides(c4)))) <=> ((~![X: $i] : ((~algorithm_program_decides(X)) | program_program_decides(c1))) | program_program_decides(c1) | (~algorithm_program_decides(c4)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (((~algorithm_program_decides(c4)) | program_program_decides(c1)) <=> (program_program_decides(c1) | (~algorithm_program_decides(c4)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 (((~![X: $i] : ((~algorithm_program_decides(X)) | program_program_decides(c1))) | ((~algorithm_program_decides(c4)) | program_program_decides(c1))) <=> ((~![X: $i] : ((~algorithm_program_decides(X)) | program_program_decides(c1))) | (program_program_decides(c1) | (~algorithm_program_decides(c4))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[13])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (((~![X: $i] : ((~algorithm_program_decides(X)) | program_program_decides(c1))) | ((~algorithm_program_decides(c4)) | program_program_decides(c1))) <=> ((~![X: $i] : ((~algorithm_program_decides(X)) | program_program_decides(c1))) | program_program_decides(c1) | (~algorithm_program_decides(c4)))),
% 0.13/0.40 inference(transitivity,[status(thm)],[14, 12])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 ((~![X: $i] : ((~algorithm_program_decides(X)) | program_program_decides(c1))) | ((~algorithm_program_decides(c4)) | program_program_decides(c1))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 ((~![X: $i] : ((~algorithm_program_decides(X)) | program_program_decides(c1))) | program_program_decides(c1) | (~algorithm_program_decides(c4))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (program_program_decides(c1)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[17, 11, 4])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (^[W: $i, Z: $i, Y: $i] : refl(((~program_program_decides(W)) | program_not_halts2_halts3_outputs(W, Y, Z, bad)) <=> ((~program_program_decides(W)) | program_not_halts2_halts3_outputs(W, Y, Z, bad)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 (![W: $i, Z: $i, Y: $i] : ((~program_program_decides(W)) | program_not_halts2_halts3_outputs(W, Y, Z, bad)) <=> ![W: $i, Z: $i, Y: $i] : ((~program_program_decides(W)) | program_not_halts2_halts3_outputs(W, Y, Z, bad))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (![W: $i, Z: $i, Y: $i] : ((~program_program_decides(W)) | program_not_halts2_halts3_outputs(W, Y, Z, bad)) <=> ![W: $i, Z: $i, Y: $i] : ((~program_program_decides(W)) | program_not_halts2_halts3_outputs(W, Y, Z, bad))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(22,axiom,(![W: $i, Z: $i, Y: $i] : ((~program_program_decides(W)) | program_not_halts2_halts3_outputs(W, Y, Z, bad))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom2_2')).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 (![W: $i, Z: $i, Y: $i] : ((~program_program_decides(W)) | program_not_halts2_halts3_outputs(W, Y, Z, bad))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.40 tff(24,plain,(
% 0.20/0.40 ![W: $i, Z: $i, Y: $i] : ((~program_program_decides(W)) | program_not_halts2_halts3_outputs(W, Y, Z, bad))),
% 0.20/0.40 inference(skolemize,[status(sab)],[23])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (![W: $i, Z: $i, Y: $i] : ((~program_program_decides(W)) | program_not_halts2_halts3_outputs(W, Y, Z, bad))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 (((~![W: $i, Z: $i, Y: $i] : ((~program_program_decides(W)) | program_not_halts2_halts3_outputs(W, Y, Z, bad))) | ((~program_program_decides(c1)) | program_not_halts2_halts3_outputs(c1, f3(c1), f3(c1), bad))) <=> ((~![W: $i, Z: $i, Y: $i] : ((~program_program_decides(W)) | program_not_halts2_halts3_outputs(W, Y, Z, bad))) | (~program_program_decides(c1)) | program_not_halts2_halts3_outputs(c1, f3(c1), f3(c1), bad))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 ((~![W: $i, Z: $i, Y: $i] : ((~program_program_decides(W)) | program_not_halts2_halts3_outputs(W, Y, Z, bad))) | ((~program_program_decides(c1)) | program_not_halts2_halts3_outputs(c1, f3(c1), f3(c1), bad))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 ((~![W: $i, Z: $i, Y: $i] : ((~program_program_decides(W)) | program_not_halts2_halts3_outputs(W, Y, Z, bad))) | (~program_program_decides(c1)) | program_not_halts2_halts3_outputs(c1, f3(c1), f3(c1), bad)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[28, 25, 18, 1])).
% 0.20/0.40 tff(30,plain,(program_not_halts2_halts3_outputs(c1, f3(c1), f3(c1), bad)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 (^[W: $i, Z: $i, Y: $i, X: $i] : refl(((~program_not_halts2_halts3_outputs(X, Y, Z, W)) | program_not_halts2(Y, Z)) <=> ((~program_not_halts2_halts3_outputs(X, Y, Z, W)) | program_not_halts2(Y, Z)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 (![W: $i, Z: $i, Y: $i, X: $i] : ((~program_not_halts2_halts3_outputs(X, Y, Z, W)) | program_not_halts2(Y, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~program_not_halts2_halts3_outputs(X, Y, Z, W)) | program_not_halts2(Y, Z))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (![W: $i, Z: $i, Y: $i, X: $i] : ((~program_not_halts2_halts3_outputs(X, Y, Z, W)) | program_not_halts2(Y, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~program_not_halts2_halts3_outputs(X, Y, Z, W)) | program_not_halts2(Y, Z))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(34,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : ((~program_not_halts2_halts3_outputs(X, Y, Z, W)) | program_not_halts2(Y, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','program_not_halts2_halts3_outputs1')).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 (![W: $i, Z: $i, Y: $i, X: $i] : ((~program_not_halts2_halts3_outputs(X, Y, Z, W)) | program_not_halts2(Y, Z))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.40 tff(36,plain,(
% 0.20/0.40 ![W: $i, Z: $i, Y: $i, X: $i] : ((~program_not_halts2_halts3_outputs(X, Y, Z, W)) | program_not_halts2(Y, Z))),
% 0.20/0.40 inference(skolemize,[status(sab)],[35])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 (![W: $i, Z: $i, Y: $i, X: $i] : ((~program_not_halts2_halts3_outputs(X, Y, Z, W)) | program_not_halts2(Y, Z))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~program_not_halts2_halts3_outputs(X, Y, Z, W)) | program_not_halts2(Y, Z))) | ((~program_not_halts2_halts3_outputs(c1, f3(c1), f3(c1), bad)) | program_not_halts2(f3(c1), f3(c1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~program_not_halts2_halts3_outputs(X, Y, Z, W)) | program_not_halts2(Y, Z))) | (~program_not_halts2_halts3_outputs(c1, f3(c1), f3(c1), bad)) | program_not_halts2(f3(c1), f3(c1)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~program_not_halts2_halts3_outputs(X, Y, Z, W)) | program_not_halts2(Y, Z))) | ((~program_not_halts2_halts3_outputs(c1, f3(c1), f3(c1), bad)) | program_not_halts2(f3(c1), f3(c1)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~program_not_halts2_halts3_outputs(X, Y, Z, W)) | program_not_halts2(Y, Z))) | (~program_not_halts2_halts3_outputs(c1, f3(c1), f3(c1), bad)) | program_not_halts2(f3(c1), f3(c1))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 (program_not_halts2(f3(c1), f3(c1))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[40, 37, 30])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 (^[Y: $i, X: $i] : refl(((~halts2(X, Y)) | (~program_not_halts2(X, Y))) <=> ((~halts2(X, Y)) | (~program_not_halts2(X, Y))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~halts2(X, Y)) | (~program_not_halts2(X, Y))) <=> ![Y: $i, X: $i] : ((~halts2(X, Y)) | (~program_not_halts2(X, Y)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[42])).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~halts2(X, Y)) | (~program_not_halts2(X, Y))) <=> ![Y: $i, X: $i] : ((~halts2(X, Y)) | (~program_not_halts2(X, Y)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 (^[Y: $i, X: $i] : rewrite(((~program_not_halts2(X, Y)) | (~halts2(X, Y))) <=> ((~halts2(X, Y)) | (~program_not_halts2(X, Y))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~program_not_halts2(X, Y)) | (~halts2(X, Y))) <=> ![Y: $i, X: $i] : ((~halts2(X, Y)) | (~program_not_halts2(X, Y)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.40 tff(47,axiom,(![Y: $i, X: $i] : ((~program_not_halts2(X, Y)) | (~halts2(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','program_not_halts3a')).
% 0.20/0.40 tff(48,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~halts2(X, Y)) | (~program_not_halts2(X, Y)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.40 tff(49,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~halts2(X, Y)) | (~program_not_halts2(X, Y)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.20/0.40 tff(50,plain,(
% 0.20/0.40 ![Y: $i, X: $i] : ((~halts2(X, Y)) | (~program_not_halts2(X, Y)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[49])).
% 0.20/0.40 tff(51,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~halts2(X, Y)) | (~program_not_halts2(X, Y)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 (((~![Y: $i, X: $i] : ((~halts2(X, Y)) | (~program_not_halts2(X, Y)))) | ((~halts2(f3(c1), f3(c1))) | (~program_not_halts2(f3(c1), f3(c1))))) <=> ((~![Y: $i, X: $i] : ((~halts2(X, Y)) | (~program_not_halts2(X, Y)))) | (~halts2(f3(c1), f3(c1))) | (~program_not_halts2(f3(c1), f3(c1))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(53,plain,
% 0.20/0.40 ((~![Y: $i, X: $i] : ((~halts2(X, Y)) | (~program_not_halts2(X, Y)))) | ((~halts2(f3(c1), f3(c1))) | (~program_not_halts2(f3(c1), f3(c1))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(54,plain,
% 0.20/0.40 ((~![Y: $i, X: $i] : ((~halts2(X, Y)) | (~program_not_halts2(X, Y)))) | (~halts2(f3(c1), f3(c1))) | (~program_not_halts2(f3(c1), f3(c1)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.40 tff(55,plain,
% 0.20/0.40 (~halts2(f3(c1), f3(c1))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[54, 51, 41])).
% 0.20/0.40 tff(56,plain,
% 0.20/0.40 (^[Y: $i, X: $i] : refl(((~program_halts2(X, Y)) | halts2(X, Y)) <=> ((~program_halts2(X, Y)) | halts2(X, Y)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(57,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~program_halts2(X, Y)) | halts2(X, Y)) <=> ![Y: $i, X: $i] : ((~program_halts2(X, Y)) | halts2(X, Y))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[56])).
% 0.20/0.40 tff(58,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~program_halts2(X, Y)) | halts2(X, Y)) <=> ![Y: $i, X: $i] : ((~program_halts2(X, Y)) | halts2(X, Y))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(59,axiom,(![Y: $i, X: $i] : ((~program_halts2(X, Y)) | halts2(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','program_halts3a')).
% 0.20/0.40 tff(60,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~program_halts2(X, Y)) | halts2(X, Y))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.40 tff(61,plain,(
% 0.20/0.40 ![Y: $i, X: $i] : ((~program_halts2(X, Y)) | halts2(X, Y))),
% 0.20/0.40 inference(skolemize,[status(sab)],[60])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 (![Y: $i, X: $i] : ((~program_halts2(X, Y)) | halts2(X, Y))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 (((~![Y: $i, X: $i] : ((~program_halts2(X, Y)) | halts2(X, Y))) | ((~program_halts2(f3(c1), f3(c1))) | halts2(f3(c1), f3(c1)))) <=> ((~![Y: $i, X: $i] : ((~program_halts2(X, Y)) | halts2(X, Y))) | (~program_halts2(f3(c1), f3(c1))) | halts2(f3(c1), f3(c1)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 ((~![Y: $i, X: $i] : ((~program_halts2(X, Y)) | halts2(X, Y))) | ((~program_halts2(f3(c1), f3(c1))) | halts2(f3(c1), f3(c1)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(65,plain,
% 0.20/0.40 ((~![Y: $i, X: $i] : ((~program_halts2(X, Y)) | halts2(X, Y))) | (~program_halts2(f3(c1), f3(c1))) | halts2(f3(c1), f3(c1))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 (~program_halts2(f3(c1), f3(c1))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[65, 62, 55])).
% 0.20/0.40 tff(67,assumption,(~program_halts2_halts3_outputs(c1, f3(c1), f3(c1), good)), introduced(assumption)).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 (^[W: $i, Z: $i, Y: $i] : refl(((~program_program_decides(W)) | program_halts2_halts3_outputs(W, Y, Z, good)) <=> ((~program_program_decides(W)) | program_halts2_halts3_outputs(W, Y, Z, good)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 (![W: $i, Z: $i, Y: $i] : ((~program_program_decides(W)) | program_halts2_halts3_outputs(W, Y, Z, good)) <=> ![W: $i, Z: $i, Y: $i] : ((~program_program_decides(W)) | program_halts2_halts3_outputs(W, Y, Z, good))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 (![W: $i, Z: $i, Y: $i] : ((~program_program_decides(W)) | program_halts2_halts3_outputs(W, Y, Z, good)) <=> ![W: $i, Z: $i, Y: $i] : ((~program_program_decides(W)) | program_halts2_halts3_outputs(W, Y, Z, good))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(71,axiom,(![W: $i, Z: $i, Y: $i] : ((~program_program_decides(W)) | program_halts2_halts3_outputs(W, Y, Z, good))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom2_1')).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 (![W: $i, Z: $i, Y: $i] : ((~program_program_decides(W)) | program_halts2_halts3_outputs(W, Y, Z, good))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.40 tff(73,plain,(
% 0.20/0.40 ![W: $i, Z: $i, Y: $i] : ((~program_program_decides(W)) | program_halts2_halts3_outputs(W, Y, Z, good))),
% 0.20/0.40 inference(skolemize,[status(sab)],[72])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 (![W: $i, Z: $i, Y: $i] : ((~program_program_decides(W)) | program_halts2_halts3_outputs(W, Y, Z, good))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 (((~![W: $i, Z: $i, Y: $i] : ((~program_program_decides(W)) | program_halts2_halts3_outputs(W, Y, Z, good))) | ((~program_program_decides(c1)) | program_halts2_halts3_outputs(c1, f3(c1), f3(c1), good))) <=> ((~![W: $i, Z: $i, Y: $i] : ((~program_program_decides(W)) | program_halts2_halts3_outputs(W, Y, Z, good))) | (~program_program_decides(c1)) | program_halts2_halts3_outputs(c1, f3(c1), f3(c1), good))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(76,plain,
% 0.20/0.41 ((~![W: $i, Z: $i, Y: $i] : ((~program_program_decides(W)) | program_halts2_halts3_outputs(W, Y, Z, good))) | ((~program_program_decides(c1)) | program_halts2_halts3_outputs(c1, f3(c1), f3(c1), good))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(77,plain,
% 0.20/0.41 ((~![W: $i, Z: $i, Y: $i] : ((~program_program_decides(W)) | program_halts2_halts3_outputs(W, Y, Z, good))) | (~program_program_decides(c1)) | program_halts2_halts3_outputs(c1, f3(c1), f3(c1), good)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[77, 74, 18, 67])).
% 0.20/0.41 tff(79,plain,(program_halts2_halts3_outputs(c1, f3(c1), f3(c1), good)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(80,plain,
% 0.20/0.41 (^[W: $i, Z: $i, Y: $i, X: $i] : refl(((~program_halts2_halts3_outputs(X, Y, Z, W)) | program_halts2(Y, Z)) <=> ((~program_halts2_halts3_outputs(X, Y, Z, W)) | program_halts2(Y, Z)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : ((~program_halts2_halts3_outputs(X, Y, Z, W)) | program_halts2(Y, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~program_halts2_halts3_outputs(X, Y, Z, W)) | program_halts2(Y, Z))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : ((~program_halts2_halts3_outputs(X, Y, Z, W)) | program_halts2(Y, Z)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~program_halts2_halts3_outputs(X, Y, Z, W)) | program_halts2(Y, Z))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(83,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : ((~program_halts2_halts3_outputs(X, Y, Z, W)) | program_halts2(Y, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','program_halts2_halts3_outputs1')).
% 0.20/0.41 tff(84,plain,
% 0.20/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : ((~program_halts2_halts3_outputs(X, Y, Z, W)) | program_halts2(Y, Z))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.41 tff(85,plain,(
% 0.20/0.41 ![W: $i, Z: $i, Y: $i, X: $i] : ((~program_halts2_halts3_outputs(X, Y, Z, W)) | program_halts2(Y, Z))),
% 0.20/0.41 inference(skolemize,[status(sab)],[84])).
% 0.20/0.41 tff(86,plain,
% 0.20/0.41 (![W: $i, Z: $i, Y: $i, X: $i] : ((~program_halts2_halts3_outputs(X, Y, Z, W)) | program_halts2(Y, Z))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.20/0.41 tff(87,plain,
% 0.20/0.41 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~program_halts2_halts3_outputs(X, Y, Z, W)) | program_halts2(Y, Z))) | ((~program_halts2_halts3_outputs(c1, f3(c1), f3(c1), good)) | program_halts2(f3(c1), f3(c1)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~program_halts2_halts3_outputs(X, Y, Z, W)) | program_halts2(Y, Z))) | (~program_halts2_halts3_outputs(c1, f3(c1), f3(c1), good)) | program_halts2(f3(c1), f3(c1)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(88,plain,
% 0.20/0.41 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~program_halts2_halts3_outputs(X, Y, Z, W)) | program_halts2(Y, Z))) | ((~program_halts2_halts3_outputs(c1, f3(c1), f3(c1), good)) | program_halts2(f3(c1), f3(c1)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(89,plain,
% 0.20/0.41 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~program_halts2_halts3_outputs(X, Y, Z, W)) | program_halts2(Y, Z))) | (~program_halts2_halts3_outputs(c1, f3(c1), f3(c1), good)) | program_halts2(f3(c1), f3(c1))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.41 tff(90,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[89, 86, 79, 66])).
% 0.20/0.41 % SZS output end Proof
%------------------------------------------------------------------------------