TSTP Solution File: COM003-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : COM003-1 : TPTP v8.1.0. Bugfixed v1.0.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 0.20s 0.51s
% Output : Proof 0.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COM003-1 : TPTP v8.1.0. Bugfixed v1.0.1.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n015.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 13:30:36 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.51 % SZS status Unsatisfiable
% 0.20/0.51 % SZS output start Proof
% 0.20/0.51 tff(halts2_type, type, (
% 0.20/0.51 halts2: ( $i * $i ) > $o)).
% 0.20/0.51 tff(f6_type, type, (
% 0.20/0.51 f6: $i > $i)).
% 0.20/0.51 tff(c2_type, type, (
% 0.20/0.51 c2: $i)).
% 0.20/0.51 tff(outputs_type, type, (
% 0.20/0.51 outputs: ( $i * $i ) > $o)).
% 0.20/0.51 tff(good_type, type, (
% 0.20/0.51 good: $i)).
% 0.20/0.51 tff(c1_type, type, (
% 0.20/0.51 c1: $i)).
% 0.20/0.51 tff(program_type, type, (
% 0.20/0.51 program: $i > $o)).
% 0.20/0.51 tff(f4_type, type, (
% 0.20/0.51 f4: $i > $i)).
% 0.20/0.51 tff(decides_type, type, (
% 0.20/0.51 decides: ( $i * $i * $i ) > $o)).
% 0.20/0.51 tff(f3_type, type, (
% 0.20/0.51 f3: $i > $i)).
% 0.20/0.51 tff(f5_type, type, (
% 0.20/0.51 f5: $i > $i)).
% 0.20/0.51 tff(f1_type, type, (
% 0.20/0.51 f1: $i > $i)).
% 0.20/0.51 tff(c4_type, type, (
% 0.20/0.51 c4: $i)).
% 0.20/0.51 tff(f2_type, type, (
% 0.20/0.51 f2: $i > $i)).
% 0.20/0.51 tff(algorithm_type, type, (
% 0.20/0.51 algorithm: $i > $o)).
% 0.20/0.51 tff(c3_type, type, (
% 0.20/0.51 c3: $i)).
% 0.20/0.51 tff(bad_type, type, (
% 0.20/0.51 bad: $i)).
% 0.20/0.51 tff(halts3_type, type, (
% 0.20/0.51 halts3: ( $i * $i * $i ) > $o)).
% 0.20/0.51 tff(1,assumption,(~outputs(c1, good)), introduced(assumption)).
% 0.20/0.51 tff(2,assumption,(~program(f5(c1))), introduced(assumption)).
% 0.20/0.51 tff(3,assumption,(~program(c1)), introduced(assumption)).
% 0.20/0.51 tff(4,plain,
% 0.20/0.51 (algorithm(c4) <=> algorithm(c4)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(5,axiom,(algorithm(c4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a_deciding_algorithm')).
% 0.20/0.51 tff(6,plain,
% 0.20/0.51 (algorithm(c4)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.51 tff(7,plain,
% 0.20/0.51 (^[X: $i] : refl((program(c1) | (~algorithm(X)) | (~decides(X, f2(X), f1(X)))) <=> (program(c1) | (~algorithm(X)) | (~decides(X, f2(X), f1(X)))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(8,plain,
% 0.20/0.51 (![X: $i] : (program(c1) | (~algorithm(X)) | (~decides(X, f2(X), f1(X)))) <=> ![X: $i] : (program(c1) | (~algorithm(X)) | (~decides(X, f2(X), f1(X))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[7])).
% 0.20/0.51 tff(9,plain,
% 0.20/0.51 (![X: $i] : (program(c1) | (~algorithm(X)) | (~decides(X, f2(X), f1(X)))) <=> ![X: $i] : (program(c1) | (~algorithm(X)) | (~decides(X, f2(X), f1(X))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(10,plain,
% 0.20/0.51 (^[X: $i] : rewrite((((~algorithm(X)) | (~decides(X, f2(X), f1(X)))) | program(c1)) <=> (program(c1) | (~algorithm(X)) | (~decides(X, f2(X), f1(X)))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(11,plain,
% 0.20/0.51 (![X: $i] : (((~algorithm(X)) | (~decides(X, f2(X), f1(X)))) | program(c1)) <=> ![X: $i] : (program(c1) | (~algorithm(X)) | (~decides(X, f2(X), f1(X))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.51 tff(12,axiom,(![X: $i] : (((~algorithm(X)) | (~decides(X, f2(X), f1(X)))) | program(c1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_1_3')).
% 0.20/0.51 tff(13,plain,
% 0.20/0.51 (![X: $i] : (program(c1) | (~algorithm(X)) | (~decides(X, f2(X), f1(X))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.20/0.51 tff(14,plain,
% 0.20/0.51 (![X: $i] : (program(c1) | (~algorithm(X)) | (~decides(X, f2(X), f1(X))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.20/0.51 tff(15,plain,(
% 0.20/0.51 ![X: $i] : (program(c1) | (~algorithm(X)) | (~decides(X, f2(X), f1(X))))),
% 0.20/0.51 inference(skolemize,[status(sab)],[14])).
% 0.20/0.51 tff(16,plain,
% 0.20/0.51 (![X: $i] : (program(c1) | (~algorithm(X)) | (~decides(X, f2(X), f1(X))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.20/0.51 tff(17,plain,
% 0.20/0.51 (((~![X: $i] : (program(c1) | (~algorithm(X)) | (~decides(X, f2(X), f1(X))))) | (program(c1) | (~algorithm(c4)) | (~decides(c4, f2(c4), f1(c4))))) <=> ((~![X: $i] : (program(c1) | (~algorithm(X)) | (~decides(X, f2(X), f1(X))))) | program(c1) | (~algorithm(c4)) | (~decides(c4, f2(c4), f1(c4))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(18,plain,
% 0.20/0.51 ((~![X: $i] : (program(c1) | (~algorithm(X)) | (~decides(X, f2(X), f1(X))))) | (program(c1) | (~algorithm(c4)) | (~decides(c4, f2(c4), f1(c4))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(19,plain,
% 0.20/0.51 ((~![X: $i] : (program(c1) | (~algorithm(X)) | (~decides(X, f2(X), f1(X))))) | program(c1) | (~algorithm(c4)) | (~decides(c4, f2(c4), f1(c4)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.51 tff(20,plain,
% 0.20/0.51 (program(c1) | (~decides(c4, f2(c4), f1(c4)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[19, 16, 6])).
% 0.20/0.51 tff(21,plain,
% 0.20/0.51 (~decides(c4, f2(c4), f1(c4))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[20, 3])).
% 0.20/0.51 tff(22,plain,
% 0.20/0.51 (^[X: $i] : refl((program(c1) | program(f2(X)) | (~algorithm(X))) <=> (program(c1) | program(f2(X)) | (~algorithm(X))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(23,plain,
% 0.20/0.51 (![X: $i] : (program(c1) | program(f2(X)) | (~algorithm(X))) <=> ![X: $i] : (program(c1) | program(f2(X)) | (~algorithm(X)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.51 tff(24,plain,
% 0.20/0.51 (![X: $i] : (program(c1) | program(f2(X)) | (~algorithm(X))) <=> ![X: $i] : (program(c1) | program(f2(X)) | (~algorithm(X)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(25,plain,
% 0.20/0.51 (^[X: $i] : rewrite((((~algorithm(X)) | program(f2(X))) | program(c1)) <=> (program(c1) | program(f2(X)) | (~algorithm(X))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(26,plain,
% 0.20/0.51 (![X: $i] : (((~algorithm(X)) | program(f2(X))) | program(c1)) <=> ![X: $i] : (program(c1) | program(f2(X)) | (~algorithm(X)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.51 tff(27,axiom,(![X: $i] : (((~algorithm(X)) | program(f2(X))) | program(c1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_1_1')).
% 0.20/0.51 tff(28,plain,
% 0.20/0.51 (![X: $i] : (program(c1) | program(f2(X)) | (~algorithm(X)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.51 tff(29,plain,
% 0.20/0.51 (![X: $i] : (program(c1) | program(f2(X)) | (~algorithm(X)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.20/0.51 tff(30,plain,(
% 0.20/0.51 ![X: $i] : (program(c1) | program(f2(X)) | (~algorithm(X)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[29])).
% 0.20/0.51 tff(31,plain,
% 0.20/0.51 (![X: $i] : (program(c1) | program(f2(X)) | (~algorithm(X)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.20/0.51 tff(32,plain,
% 0.20/0.51 (((~![X: $i] : (program(c1) | program(f2(X)) | (~algorithm(X)))) | (program(c1) | program(f2(c4)) | (~algorithm(c4)))) <=> ((~![X: $i] : (program(c1) | program(f2(X)) | (~algorithm(X)))) | program(c1) | program(f2(c4)) | (~algorithm(c4)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(33,plain,
% 0.20/0.51 ((~![X: $i] : (program(c1) | program(f2(X)) | (~algorithm(X)))) | (program(c1) | program(f2(c4)) | (~algorithm(c4)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(34,plain,
% 0.20/0.51 ((~![X: $i] : (program(c1) | program(f2(X)) | (~algorithm(X)))) | program(c1) | program(f2(c4)) | (~algorithm(c4))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.51 tff(35,plain,
% 0.20/0.51 (program(c1) | program(f2(c4))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[34, 31, 6])).
% 0.20/0.51 tff(36,plain,
% 0.20/0.51 (program(f2(c4))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[35, 3])).
% 0.20/0.51 tff(37,plain,
% 0.20/0.51 (^[Y1: $i, Z1: $i] : refl(((~program(Y1)) | decides(c4, Y1, Z1)) <=> ((~program(Y1)) | decides(c4, Y1, Z1)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(38,plain,
% 0.20/0.51 (![Y1: $i, Z1: $i] : ((~program(Y1)) | decides(c4, Y1, Z1)) <=> ![Y1: $i, Z1: $i] : ((~program(Y1)) | decides(c4, Y1, Z1))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.51 tff(39,plain,
% 0.20/0.51 (![Y1: $i, Z1: $i] : ((~program(Y1)) | decides(c4, Y1, Z1)) <=> ![Y1: $i, Z1: $i] : ((~program(Y1)) | decides(c4, Y1, Z1))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(40,axiom,(![Y1: $i, Z1: $i] : ((~program(Y1)) | decides(c4, Y1, Z1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_the_algorithm_doesnt_exist')).
% 0.20/0.51 tff(41,plain,
% 0.20/0.51 (![Y1: $i, Z1: $i] : ((~program(Y1)) | decides(c4, Y1, Z1))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.51 tff(42,plain,(
% 0.20/0.51 ![Y1: $i, Z1: $i] : ((~program(Y1)) | decides(c4, Y1, Z1))),
% 0.20/0.51 inference(skolemize,[status(sab)],[41])).
% 0.20/0.51 tff(43,plain,
% 0.20/0.51 (![Y1: $i, Z1: $i] : ((~program(Y1)) | decides(c4, Y1, Z1))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.20/0.51 tff(44,plain,
% 0.20/0.51 (((~![Y1: $i, Z1: $i] : ((~program(Y1)) | decides(c4, Y1, Z1))) | ((~program(f2(c4))) | decides(c4, f2(c4), f1(c4)))) <=> ((~![Y1: $i, Z1: $i] : ((~program(Y1)) | decides(c4, Y1, Z1))) | (~program(f2(c4))) | decides(c4, f2(c4), f1(c4)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(45,plain,
% 0.20/0.51 ((~![Y1: $i, Z1: $i] : ((~program(Y1)) | decides(c4, Y1, Z1))) | ((~program(f2(c4))) | decides(c4, f2(c4), f1(c4)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(46,plain,
% 0.20/0.51 ((~![Y1: $i, Z1: $i] : ((~program(Y1)) | decides(c4, Y1, Z1))) | (~program(f2(c4))) | decides(c4, f2(c4), f1(c4))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.51 tff(47,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[46, 43, 36, 21])).
% 0.20/0.51 tff(48,plain,(program(c1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(49,plain,
% 0.20/0.51 (^[W: $i] : refl((program(c2) | program(f5(W)) | (~program(W))) <=> (program(c2) | program(f5(W)) | (~program(W))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(50,plain,
% 0.20/0.51 (![W: $i] : (program(c2) | program(f5(W)) | (~program(W))) <=> ![W: $i] : (program(c2) | program(f5(W)) | (~program(W)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.51 tff(51,plain,
% 0.20/0.51 (![W: $i] : (program(c2) | program(f5(W)) | (~program(W))) <=> ![W: $i] : (program(c2) | program(f5(W)) | (~program(W)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(52,plain,
% 0.20/0.51 (^[W: $i] : rewrite((((~program(W)) | program(f5(W))) | program(c2)) <=> (program(c2) | program(f5(W)) | (~program(W))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(53,plain,
% 0.20/0.51 (![W: $i] : (((~program(W)) | program(f5(W))) | program(c2)) <=> ![W: $i] : (program(c2) | program(f5(W)) | (~program(W)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.51 tff(54,axiom,(![W: $i] : (((~program(W)) | program(f5(W))) | program(c2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_3_1')).
% 0.20/0.51 tff(55,plain,
% 0.20/0.51 (![W: $i] : (program(c2) | program(f5(W)) | (~program(W)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.51 tff(56,plain,
% 0.20/0.51 (![W: $i] : (program(c2) | program(f5(W)) | (~program(W)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.20/0.51 tff(57,plain,(
% 0.20/0.51 ![W: $i] : (program(c2) | program(f5(W)) | (~program(W)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[56])).
% 0.20/0.51 tff(58,plain,
% 0.20/0.51 (![W: $i] : (program(c2) | program(f5(W)) | (~program(W)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.20/0.51 tff(59,plain,
% 0.20/0.51 (((~![W: $i] : (program(c2) | program(f5(W)) | (~program(W)))) | (program(c2) | (~program(c1)) | program(f5(c1)))) <=> ((~![W: $i] : (program(c2) | program(f5(W)) | (~program(W)))) | program(c2) | (~program(c1)) | program(f5(c1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(60,plain,
% 0.20/0.51 ((program(c2) | program(f5(c1)) | (~program(c1))) <=> (program(c2) | (~program(c1)) | program(f5(c1)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(61,plain,
% 0.20/0.51 (((~![W: $i] : (program(c2) | program(f5(W)) | (~program(W)))) | (program(c2) | program(f5(c1)) | (~program(c1)))) <=> ((~![W: $i] : (program(c2) | program(f5(W)) | (~program(W)))) | (program(c2) | (~program(c1)) | program(f5(c1))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[60])).
% 0.20/0.51 tff(62,plain,
% 0.20/0.51 (((~![W: $i] : (program(c2) | program(f5(W)) | (~program(W)))) | (program(c2) | program(f5(c1)) | (~program(c1)))) <=> ((~![W: $i] : (program(c2) | program(f5(W)) | (~program(W)))) | program(c2) | (~program(c1)) | program(f5(c1)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[61, 59])).
% 0.20/0.51 tff(63,plain,
% 0.20/0.51 ((~![W: $i] : (program(c2) | program(f5(W)) | (~program(W)))) | (program(c2) | program(f5(c1)) | (~program(c1)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(64,plain,
% 0.20/0.51 ((~![W: $i] : (program(c2) | program(f5(W)) | (~program(W)))) | program(c2) | (~program(c1)) | program(f5(c1))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.51 tff(65,plain,
% 0.20/0.51 (program(c2) | program(f5(c1))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[64, 58, 48])).
% 0.20/0.51 tff(66,plain,
% 0.20/0.51 (program(c2)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[65, 2])).
% 0.20/0.51 tff(67,assumption,(~program(c3)), introduced(assumption)).
% 0.20/0.51 tff(68,plain,
% 0.20/0.51 (^[V: $i] : refl(((~program(V)) | program(c3) | program(f6(V))) <=> ((~program(V)) | program(c3) | program(f6(V))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(69,plain,
% 0.20/0.51 (![V: $i] : ((~program(V)) | program(c3) | program(f6(V))) <=> ![V: $i] : ((~program(V)) | program(c3) | program(f6(V)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.51 tff(70,plain,
% 0.20/0.51 (![V: $i] : ((~program(V)) | program(c3) | program(f6(V))) <=> ![V: $i] : ((~program(V)) | program(c3) | program(f6(V)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(71,plain,
% 0.20/0.51 (^[V: $i] : rewrite((((~program(V)) | program(f6(V))) | program(c3)) <=> ((~program(V)) | program(c3) | program(f6(V))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(72,plain,
% 0.20/0.51 (![V: $i] : (((~program(V)) | program(f6(V))) | program(c3)) <=> ![V: $i] : ((~program(V)) | program(c3) | program(f6(V)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[71])).
% 0.20/0.51 tff(73,axiom,(![V: $i] : (((~program(V)) | program(f6(V))) | program(c3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_4_1')).
% 0.20/0.51 tff(74,plain,
% 0.20/0.51 (![V: $i] : ((~program(V)) | program(c3) | program(f6(V)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.20/0.51 tff(75,plain,
% 0.20/0.51 (![V: $i] : ((~program(V)) | program(c3) | program(f6(V)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.20/0.51 tff(76,plain,(
% 0.20/0.51 ![V: $i] : ((~program(V)) | program(c3) | program(f6(V)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[75])).
% 0.20/0.51 tff(77,plain,
% 0.20/0.51 (![V: $i] : ((~program(V)) | program(c3) | program(f6(V)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.20/0.51 tff(78,plain,
% 0.20/0.51 (((~![V: $i] : ((~program(V)) | program(c3) | program(f6(V)))) | (program(c3) | (~program(c2)) | program(f6(c2)))) <=> ((~![V: $i] : ((~program(V)) | program(c3) | program(f6(V)))) | program(c3) | (~program(c2)) | program(f6(c2)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(79,plain,
% 0.20/0.51 (((~program(c2)) | program(c3) | program(f6(c2))) <=> (program(c3) | (~program(c2)) | program(f6(c2)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(80,plain,
% 0.20/0.51 (((~![V: $i] : ((~program(V)) | program(c3) | program(f6(V)))) | ((~program(c2)) | program(c3) | program(f6(c2)))) <=> ((~![V: $i] : ((~program(V)) | program(c3) | program(f6(V)))) | (program(c3) | (~program(c2)) | program(f6(c2))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[79])).
% 0.20/0.51 tff(81,plain,
% 0.20/0.51 (((~![V: $i] : ((~program(V)) | program(c3) | program(f6(V)))) | ((~program(c2)) | program(c3) | program(f6(c2)))) <=> ((~![V: $i] : ((~program(V)) | program(c3) | program(f6(V)))) | program(c3) | (~program(c2)) | program(f6(c2)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[80, 78])).
% 0.20/0.51 tff(82,plain,
% 0.20/0.51 ((~![V: $i] : ((~program(V)) | program(c3) | program(f6(V)))) | ((~program(c2)) | program(c3) | program(f6(c2)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(83,plain,
% 0.20/0.51 ((~![V: $i] : ((~program(V)) | program(c3) | program(f6(V)))) | program(c3) | (~program(c2)) | program(f6(c2))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.51 tff(84,plain,
% 0.20/0.51 (program(f6(c2))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[83, 77, 67, 66])).
% 0.20/0.51 tff(85,plain,
% 0.20/0.51 (^[W: $i, Y: $i] : refl(((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | program(f5(W))) <=> ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | program(f5(W))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(86,plain,
% 0.20/0.51 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | program(f5(W))) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | program(f5(W)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[85])).
% 0.20/0.51 tff(87,plain,
% 0.20/0.51 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | program(f5(W))) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | program(f5(W)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(88,plain,
% 0.20/0.51 (^[W: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~program(W)) | program(f5(W))) | (~program(Y))) <=> ((~program(W)) | (~program(Y)) | program(f5(W)))), (((((~program(W)) | program(f5(W))) | (~program(Y))) | halts2(Y, Y)) <=> (((~program(W)) | (~program(Y)) | program(f5(W))) | halts2(Y, Y)))), rewrite((((~program(W)) | (~program(Y)) | program(f5(W))) | halts2(Y, Y)) <=> ((~program(W)) | (~program(Y)) | halts2(Y, Y) | program(f5(W)))), (((((~program(W)) | program(f5(W))) | (~program(Y))) | halts2(Y, Y)) <=> ((~program(W)) | (~program(Y)) | halts2(Y, Y) | program(f5(W))))), ((((((~program(W)) | program(f5(W))) | (~program(Y))) | halts2(Y, Y)) | halts2(c2, Y)) <=> (((~program(W)) | (~program(Y)) | halts2(Y, Y) | program(f5(W))) | halts2(c2, Y)))), rewrite((((~program(W)) | (~program(Y)) | halts2(Y, Y) | program(f5(W))) | halts2(c2, Y)) <=> ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | program(f5(W)))), ((((((~program(W)) | program(f5(W))) | (~program(Y))) | halts2(Y, Y)) | halts2(c2, Y)) <=> ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | program(f5(W)))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(89,plain,
% 0.20/0.52 (![W: $i, Y: $i] : (((((~program(W)) | program(f5(W))) | (~program(Y))) | halts2(Y, Y)) | halts2(c2, Y)) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | program(f5(W)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[88])).
% 0.20/0.52 tff(90,axiom,(![W: $i, Y: $i] : (((((~program(W)) | program(f5(W))) | (~program(Y))) | halts2(Y, Y)) | halts2(c2, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_3_4')).
% 0.20/0.52 tff(91,plain,
% 0.20/0.52 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | program(f5(W)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.20/0.52 tff(92,plain,
% 0.20/0.52 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | program(f5(W)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.20/0.52 tff(93,plain,(
% 0.20/0.52 ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | program(f5(W)))),
% 0.20/0.52 inference(skolemize,[status(sab)],[92])).
% 0.20/0.52 tff(94,plain,
% 0.20/0.52 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | program(f5(W)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.20/0.52 tff(95,plain,
% 0.20/0.52 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | program(f5(W)))) | ((~program(c1)) | program(f5(c1)) | (~program(c2)) | halts2(c2, c2))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | program(f5(W)))) | (~program(c1)) | program(f5(c1)) | (~program(c2)) | halts2(c2, c2))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(96,plain,
% 0.20/0.52 (((~program(c1)) | (~program(c2)) | halts2(c2, c2) | halts2(c2, c2) | program(f5(c1))) <=> ((~program(c1)) | program(f5(c1)) | (~program(c2)) | halts2(c2, c2))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(97,plain,
% 0.20/0.52 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | program(f5(W)))) | ((~program(c1)) | (~program(c2)) | halts2(c2, c2) | halts2(c2, c2) | program(f5(c1)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | program(f5(W)))) | ((~program(c1)) | program(f5(c1)) | (~program(c2)) | halts2(c2, c2)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[96])).
% 0.20/0.52 tff(98,plain,
% 0.20/0.52 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | program(f5(W)))) | ((~program(c1)) | (~program(c2)) | halts2(c2, c2) | halts2(c2, c2) | program(f5(c1)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | program(f5(W)))) | (~program(c1)) | program(f5(c1)) | (~program(c2)) | halts2(c2, c2))),
% 0.20/0.52 inference(transitivity,[status(thm)],[97, 95])).
% 0.20/0.52 tff(99,plain,
% 0.20/0.52 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | program(f5(W)))) | ((~program(c1)) | (~program(c2)) | halts2(c2, c2) | halts2(c2, c2) | program(f5(c1)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(100,plain,
% 0.20/0.52 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | program(f5(W)))) | (~program(c1)) | program(f5(c1)) | (~program(c2)) | halts2(c2, c2)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.52 tff(101,plain,
% 0.20/0.52 (halts2(c2, c2)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[100, 94, 48, 66, 2])).
% 0.20/0.52 tff(102,plain,
% 0.20/0.52 (^[W: $i, Y: $i] : refl(((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | program(f5(W))) <=> ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | program(f5(W))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(103,plain,
% 0.20/0.52 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | program(f5(W))) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | program(f5(W)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[102])).
% 0.20/0.52 tff(104,plain,
% 0.20/0.52 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | program(f5(W))) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | program(f5(W)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(105,plain,
% 0.20/0.52 (^[W: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~program(W)) | program(f5(W))) | (~program(Y))) <=> ((~program(W)) | (~program(Y)) | program(f5(W)))), (((((~program(W)) | program(f5(W))) | (~program(Y))) | (~halts2(Y, Y))) <=> (((~program(W)) | (~program(Y)) | program(f5(W))) | (~halts2(Y, Y))))), rewrite((((~program(W)) | (~program(Y)) | program(f5(W))) | (~halts2(Y, Y))) <=> ((~program(W)) | (~program(Y)) | (~halts2(Y, Y)) | program(f5(W)))), (((((~program(W)) | program(f5(W))) | (~program(Y))) | (~halts2(Y, Y))) <=> ((~program(W)) | (~program(Y)) | (~halts2(Y, Y)) | program(f5(W))))), ((((((~program(W)) | program(f5(W))) | (~program(Y))) | (~halts2(Y, Y))) | outputs(c2, good)) <=> (((~program(W)) | (~program(Y)) | (~halts2(Y, Y)) | program(f5(W))) | outputs(c2, good)))), rewrite((((~program(W)) | (~program(Y)) | (~halts2(Y, Y)) | program(f5(W))) | outputs(c2, good)) <=> ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | program(f5(W)))), ((((((~program(W)) | program(f5(W))) | (~program(Y))) | (~halts2(Y, Y))) | outputs(c2, good)) <=> ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | program(f5(W)))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(106,plain,
% 0.20/0.52 (![W: $i, Y: $i] : (((((~program(W)) | program(f5(W))) | (~program(Y))) | (~halts2(Y, Y))) | outputs(c2, good)) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | program(f5(W)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[105])).
% 0.20/0.52 tff(107,axiom,(![W: $i, Y: $i] : (((((~program(W)) | program(f5(W))) | (~program(Y))) | (~halts2(Y, Y))) | outputs(c2, good))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_3_3')).
% 0.20/0.52 tff(108,plain,
% 0.20/0.52 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | program(f5(W)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.20/0.52 tff(109,plain,
% 0.20/0.52 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | program(f5(W)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.20/0.52 tff(110,plain,(
% 0.20/0.52 ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | program(f5(W)))),
% 0.20/0.52 inference(skolemize,[status(sab)],[109])).
% 0.20/0.52 tff(111,plain,
% 0.20/0.52 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | program(f5(W)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.20/0.52 tff(112,plain,
% 0.20/0.52 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | program(f5(W)))) | (outputs(c2, good) | (~program(c1)) | program(f5(c1)) | (~program(c2)) | (~halts2(c2, c2)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | program(f5(W)))) | outputs(c2, good) | (~program(c1)) | program(f5(c1)) | (~program(c2)) | (~halts2(c2, c2)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(113,plain,
% 0.20/0.52 (((~program(c1)) | (~program(c2)) | outputs(c2, good) | (~halts2(c2, c2)) | program(f5(c1))) <=> (outputs(c2, good) | (~program(c1)) | program(f5(c1)) | (~program(c2)) | (~halts2(c2, c2)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(114,plain,
% 0.20/0.52 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | program(f5(W)))) | ((~program(c1)) | (~program(c2)) | outputs(c2, good) | (~halts2(c2, c2)) | program(f5(c1)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | program(f5(W)))) | (outputs(c2, good) | (~program(c1)) | program(f5(c1)) | (~program(c2)) | (~halts2(c2, c2))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[113])).
% 0.20/0.52 tff(115,plain,
% 0.20/0.52 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | program(f5(W)))) | ((~program(c1)) | (~program(c2)) | outputs(c2, good) | (~halts2(c2, c2)) | program(f5(c1)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | program(f5(W)))) | outputs(c2, good) | (~program(c1)) | program(f5(c1)) | (~program(c2)) | (~halts2(c2, c2)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[114, 112])).
% 0.20/0.52 tff(116,plain,
% 0.20/0.52 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | program(f5(W)))) | ((~program(c1)) | (~program(c2)) | outputs(c2, good) | (~halts2(c2, c2)) | program(f5(c1)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(117,plain,
% 0.20/0.52 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | program(f5(W)))) | outputs(c2, good) | (~program(c1)) | program(f5(c1)) | (~program(c2)) | (~halts2(c2, c2))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.20/0.52 tff(118,plain,
% 0.20/0.52 (outputs(c2, good)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[117, 111, 48, 66, 2, 101])).
% 0.20/0.52 tff(119,assumption,(~halts2(c2, f6(c2))), introduced(assumption)).
% 0.20/0.52 tff(120,assumption,(program(f6(c2))), introduced(assumption)).
% 0.20/0.52 tff(121,assumption,(~halts2(f6(c2), f6(c2))), introduced(assumption)).
% 0.20/0.52 tff(122,plain,
% 0.20/0.52 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | program(f5(W)))) | ((~program(c1)) | program(f5(c1)) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2))))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | program(f5(W)))) | (~program(c1)) | program(f5(c1)) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(123,plain,
% 0.20/0.52 (((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | program(f5(c1))) <=> ((~program(c1)) | program(f5(c1)) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(124,plain,
% 0.20/0.52 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | program(f5(W)))) | ((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | program(f5(c1)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | program(f5(W)))) | ((~program(c1)) | program(f5(c1)) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2)))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[123])).
% 0.20/0.52 tff(125,plain,
% 0.20/0.52 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | program(f5(W)))) | ((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | program(f5(c1)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | program(f5(W)))) | (~program(c1)) | program(f5(c1)) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[124, 122])).
% 0.20/0.52 tff(126,plain,
% 0.20/0.52 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | program(f5(W)))) | ((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | program(f5(c1)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(127,plain,
% 0.20/0.52 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | program(f5(W)))) | (~program(c1)) | program(f5(c1)) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.20/0.52 tff(128,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[127, 94, 48, 2, 119, 121, 120])).
% 0.20/0.52 tff(129,plain,((~program(f6(c2))) | program(f5(c1)) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(130,plain,
% 0.20/0.52 (halts2(f6(c2), f6(c2))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[129, 84, 119, 2])).
% 0.20/0.52 tff(131,plain,
% 0.20/0.53 (^[W: $i, Y: $i] : refl(((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | program(f5(W))) <=> ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | program(f5(W))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(132,plain,
% 0.20/0.53 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | program(f5(W))) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | program(f5(W)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[131])).
% 0.20/0.53 tff(133,plain,
% 0.20/0.53 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | program(f5(W))) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | program(f5(W)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(134,plain,
% 0.20/0.53 (^[W: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~program(W)) | program(f5(W))) | (~program(Y))) <=> ((~program(W)) | (~program(Y)) | program(f5(W)))), (((((~program(W)) | program(f5(W))) | (~program(Y))) | (~halts2(Y, Y))) <=> (((~program(W)) | (~program(Y)) | program(f5(W))) | (~halts2(Y, Y))))), rewrite((((~program(W)) | (~program(Y)) | program(f5(W))) | (~halts2(Y, Y))) <=> ((~program(W)) | (~program(Y)) | (~halts2(Y, Y)) | program(f5(W)))), (((((~program(W)) | program(f5(W))) | (~program(Y))) | (~halts2(Y, Y))) <=> ((~program(W)) | (~program(Y)) | (~halts2(Y, Y)) | program(f5(W))))), ((((((~program(W)) | program(f5(W))) | (~program(Y))) | (~halts2(Y, Y))) | halts2(c2, Y)) <=> (((~program(W)) | (~program(Y)) | (~halts2(Y, Y)) | program(f5(W))) | halts2(c2, Y)))), rewrite((((~program(W)) | (~program(Y)) | (~halts2(Y, Y)) | program(f5(W))) | halts2(c2, Y)) <=> ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | program(f5(W)))), ((((((~program(W)) | program(f5(W))) | (~program(Y))) | (~halts2(Y, Y))) | halts2(c2, Y)) <=> ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | program(f5(W)))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(135,plain,
% 0.20/0.53 (![W: $i, Y: $i] : (((((~program(W)) | program(f5(W))) | (~program(Y))) | (~halts2(Y, Y))) | halts2(c2, Y)) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | program(f5(W)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[134])).
% 0.20/0.53 tff(136,axiom,(![W: $i, Y: $i] : (((((~program(W)) | program(f5(W))) | (~program(Y))) | (~halts2(Y, Y))) | halts2(c2, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_3_2')).
% 0.20/0.53 tff(137,plain,
% 0.20/0.53 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | program(f5(W)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.20/0.53 tff(138,plain,
% 0.20/0.53 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | program(f5(W)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.20/0.53 tff(139,plain,(
% 0.20/0.53 ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | program(f5(W)))),
% 0.20/0.53 inference(skolemize,[status(sab)],[138])).
% 0.20/0.53 tff(140,plain,
% 0.20/0.53 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | program(f5(W)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[139, 132])).
% 0.20/0.53 tff(141,plain,
% 0.20/0.53 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | program(f5(W)))) | ((~program(c1)) | program(f5(c1)) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~program(f6(c2))))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | program(f5(W)))) | (~program(c1)) | program(f5(c1)) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~program(f6(c2))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(142,plain,
% 0.20/0.53 (((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | program(f5(c1))) <=> ((~program(c1)) | program(f5(c1)) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~program(f6(c2))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(143,plain,
% 0.20/0.53 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | program(f5(W)))) | ((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | program(f5(c1)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | program(f5(W)))) | ((~program(c1)) | program(f5(c1)) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~program(f6(c2)))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[142])).
% 0.20/0.53 tff(144,plain,
% 0.20/0.53 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | program(f5(W)))) | ((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | program(f5(c1)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | program(f5(W)))) | (~program(c1)) | program(f5(c1)) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~program(f6(c2))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[143, 141])).
% 0.20/0.53 tff(145,plain,
% 0.20/0.53 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | program(f5(W)))) | ((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | program(f5(c1)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(146,plain,
% 0.20/0.53 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | program(f5(W)))) | (~program(c1)) | program(f5(c1)) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~program(f6(c2)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.20/0.53 tff(147,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[146, 140, 48, 2, 119, 130, 84])).
% 0.20/0.53 tff(148,plain,(halts2(c2, f6(c2)) | program(f5(c1)) | program(c3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(149,plain,
% 0.20/0.53 (halts2(c2, f6(c2))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[148, 67, 2])).
% 0.20/0.53 tff(150,plain,
% 0.20/0.53 (^[V: $i] : refl(((~program(V)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V)))) <=> ((~program(V)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V)))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(151,plain,
% 0.20/0.53 (![V: $i] : ((~program(V)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V)))) <=> ![V: $i] : ((~program(V)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[150])).
% 0.20/0.53 tff(152,plain,
% 0.20/0.53 (![V: $i] : ((~program(V)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V)))) <=> ![V: $i] : ((~program(V)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(153,plain,
% 0.20/0.53 (^[V: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) <=> ((~program(V)) | (~outputs(V, good)) | (~halts2(V, f6(V))))), (((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~halts2(f6(V), f6(V)))) <=> (((~program(V)) | (~outputs(V, good)) | (~halts2(V, f6(V)))) | (~halts2(f6(V), f6(V)))))), rewrite((((~program(V)) | (~outputs(V, good)) | (~halts2(V, f6(V)))) | (~halts2(f6(V), f6(V)))) <=> ((~program(V)) | (~outputs(V, good)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))), (((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~halts2(f6(V), f6(V)))) <=> ((~program(V)) | (~outputs(V, good)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V)))))), ((((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~halts2(f6(V), f6(V)))) | program(c3)) <=> (((~program(V)) | (~outputs(V, good)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V)))) | program(c3)))), rewrite((((~program(V)) | (~outputs(V, good)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V)))) | program(c3)) <=> ((~program(V)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))), ((((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~halts2(f6(V), f6(V)))) | program(c3)) <=> ((~program(V)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(154,plain,
% 0.20/0.53 (![V: $i] : (((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~halts2(f6(V), f6(V)))) | program(c3)) <=> ![V: $i] : ((~program(V)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[153])).
% 0.20/0.53 tff(155,axiom,(![V: $i] : (((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~halts2(f6(V), f6(V)))) | program(c3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_4_9')).
% 0.20/0.53 tff(156,plain,
% 0.20/0.53 (![V: $i] : ((~program(V)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.20/0.53 tff(157,plain,
% 0.20/0.53 (![V: $i] : ((~program(V)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[156, 152])).
% 0.20/0.53 tff(158,plain,(
% 0.20/0.53 ![V: $i] : ((~program(V)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))),
% 0.20/0.53 inference(skolemize,[status(sab)],[157])).
% 0.20/0.53 tff(159,plain,
% 0.20/0.53 (![V: $i] : ((~program(V)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[158, 151])).
% 0.20/0.53 tff(160,plain,
% 0.20/0.53 (((~![V: $i] : ((~program(V)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))) | (program(c3) | (~program(c2)) | (~outputs(c2, good)) | (~halts2(c2, f6(c2))) | (~halts2(f6(c2), f6(c2))))) <=> ((~![V: $i] : ((~program(V)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))) | program(c3) | (~program(c2)) | (~outputs(c2, good)) | (~halts2(c2, f6(c2))) | (~halts2(f6(c2), f6(c2))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(161,plain,
% 0.20/0.53 (((~program(c2)) | (~outputs(c2, good)) | program(c3) | (~halts2(c2, f6(c2))) | (~halts2(f6(c2), f6(c2)))) <=> (program(c3) | (~program(c2)) | (~outputs(c2, good)) | (~halts2(c2, f6(c2))) | (~halts2(f6(c2), f6(c2))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(162,plain,
% 0.20/0.53 (((~![V: $i] : ((~program(V)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))) | ((~program(c2)) | (~outputs(c2, good)) | program(c3) | (~halts2(c2, f6(c2))) | (~halts2(f6(c2), f6(c2))))) <=> ((~![V: $i] : ((~program(V)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))) | (program(c3) | (~program(c2)) | (~outputs(c2, good)) | (~halts2(c2, f6(c2))) | (~halts2(f6(c2), f6(c2)))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[161])).
% 0.20/0.53 tff(163,plain,
% 0.20/0.53 (((~![V: $i] : ((~program(V)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))) | ((~program(c2)) | (~outputs(c2, good)) | program(c3) | (~halts2(c2, f6(c2))) | (~halts2(f6(c2), f6(c2))))) <=> ((~![V: $i] : ((~program(V)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))) | program(c3) | (~program(c2)) | (~outputs(c2, good)) | (~halts2(c2, f6(c2))) | (~halts2(f6(c2), f6(c2))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[162, 160])).
% 0.20/0.53 tff(164,plain,
% 0.20/0.53 ((~![V: $i] : ((~program(V)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))) | ((~program(c2)) | (~outputs(c2, good)) | program(c3) | (~halts2(c2, f6(c2))) | (~halts2(f6(c2), f6(c2))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(165,plain,
% 0.20/0.53 ((~![V: $i] : ((~program(V)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))) | program(c3) | (~program(c2)) | (~outputs(c2, good)) | (~halts2(c2, f6(c2))) | (~halts2(f6(c2), f6(c2)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.20/0.53 tff(166,plain,
% 0.20/0.53 (program(c3) | (~outputs(c2, good)) | (~halts2(c2, f6(c2))) | (~halts2(f6(c2), f6(c2)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[165, 159, 66])).
% 0.20/0.53 tff(167,plain,
% 0.20/0.53 (~halts2(f6(c2), f6(c2))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[166, 149, 118, 67])).
% 0.20/0.53 tff(168,plain,
% 0.20/0.53 (^[V: $i] : refl(((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V)))) <=> ((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V)))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(169,plain,
% 0.20/0.54 (![V: $i] : ((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V)))) <=> ![V: $i] : ((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[168])).
% 0.20/0.54 tff(170,plain,
% 0.20/0.54 (![V: $i] : ((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V)))) <=> ![V: $i] : ((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(171,plain,
% 0.20/0.54 (^[V: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) <=> ((~program(V)) | (~outputs(V, good)) | (~halts2(V, f6(V))))), (((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~outputs(V, bad))) <=> (((~program(V)) | (~outputs(V, good)) | (~halts2(V, f6(V)))) | (~outputs(V, bad))))), rewrite((((~program(V)) | (~outputs(V, good)) | (~halts2(V, f6(V)))) | (~outputs(V, bad))) <=> ((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(V, f6(V))))), (((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~outputs(V, bad))) <=> ((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(V, f6(V)))))), ((((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~outputs(V, bad))) | program(c3)) <=> (((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(V, f6(V)))) | program(c3)))), rewrite((((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(V, f6(V)))) | program(c3)) <=> ((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))))), ((((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~outputs(V, bad))) | program(c3)) <=> ((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(172,plain,
% 0.20/0.54 (![V: $i] : (((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~outputs(V, bad))) | program(c3)) <=> ![V: $i] : ((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[171])).
% 0.20/0.54 tff(173,axiom,(![V: $i] : (((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~outputs(V, bad))) | program(c3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_4_13')).
% 0.20/0.54 tff(174,plain,
% 0.20/0.54 (![V: $i] : ((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.20/0.54 tff(175,plain,
% 0.20/0.54 (![V: $i] : ((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[174, 170])).
% 0.20/0.54 tff(176,plain,(
% 0.20/0.54 ![V: $i] : ((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))))),
% 0.20/0.54 inference(skolemize,[status(sab)],[175])).
% 0.20/0.54 tff(177,plain,
% 0.20/0.54 (![V: $i] : ((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[176, 169])).
% 0.20/0.54 tff(178,plain,
% 0.20/0.54 (((~![V: $i] : ((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))))) | (program(c3) | (~program(c2)) | (~outputs(c2, good)) | (~outputs(c2, bad)) | (~halts2(c2, f6(c2))))) <=> ((~![V: $i] : ((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))))) | program(c3) | (~program(c2)) | (~outputs(c2, good)) | (~outputs(c2, bad)) | (~halts2(c2, f6(c2))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(179,plain,
% 0.20/0.54 (((~program(c2)) | (~outputs(c2, bad)) | (~outputs(c2, good)) | program(c3) | (~halts2(c2, f6(c2)))) <=> (program(c3) | (~program(c2)) | (~outputs(c2, good)) | (~outputs(c2, bad)) | (~halts2(c2, f6(c2))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(180,plain,
% 0.20/0.54 (((~![V: $i] : ((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))))) | ((~program(c2)) | (~outputs(c2, bad)) | (~outputs(c2, good)) | program(c3) | (~halts2(c2, f6(c2))))) <=> ((~![V: $i] : ((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))))) | (program(c3) | (~program(c2)) | (~outputs(c2, good)) | (~outputs(c2, bad)) | (~halts2(c2, f6(c2)))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[179])).
% 0.20/0.54 tff(181,plain,
% 0.20/0.54 (((~![V: $i] : ((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))))) | ((~program(c2)) | (~outputs(c2, bad)) | (~outputs(c2, good)) | program(c3) | (~halts2(c2, f6(c2))))) <=> ((~![V: $i] : ((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))))) | program(c3) | (~program(c2)) | (~outputs(c2, good)) | (~outputs(c2, bad)) | (~halts2(c2, f6(c2))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[180, 178])).
% 0.20/0.54 tff(182,plain,
% 0.20/0.54 ((~![V: $i] : ((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))))) | ((~program(c2)) | (~outputs(c2, bad)) | (~outputs(c2, good)) | program(c3) | (~halts2(c2, f6(c2))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(183,plain,
% 0.20/0.54 ((~![V: $i] : ((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | program(c3) | (~halts2(V, f6(V))))) | program(c3) | (~program(c2)) | (~outputs(c2, good)) | (~outputs(c2, bad)) | (~halts2(c2, f6(c2)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.20/0.54 tff(184,plain,
% 0.20/0.54 (program(c3) | (~outputs(c2, good)) | (~outputs(c2, bad)) | (~halts2(c2, f6(c2)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[183, 177, 66])).
% 0.20/0.54 tff(185,plain,
% 0.20/0.54 (~outputs(c2, bad)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[184, 149, 118, 67])).
% 0.20/0.54 tff(186,plain,
% 0.20/0.54 (^[W: $i, Y: $i] : refl(((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | program(f5(W))) <=> ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | program(f5(W))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(187,plain,
% 0.20/0.54 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | program(f5(W))) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | program(f5(W)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[186])).
% 0.20/0.54 tff(188,plain,
% 0.20/0.54 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | program(f5(W))) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | program(f5(W)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(189,plain,
% 0.20/0.54 (^[W: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~program(W)) | program(f5(W))) | (~program(Y))) <=> ((~program(W)) | (~program(Y)) | program(f5(W)))), (((((~program(W)) | program(f5(W))) | (~program(Y))) | halts2(Y, Y)) <=> (((~program(W)) | (~program(Y)) | program(f5(W))) | halts2(Y, Y)))), rewrite((((~program(W)) | (~program(Y)) | program(f5(W))) | halts2(Y, Y)) <=> ((~program(W)) | (~program(Y)) | halts2(Y, Y) | program(f5(W)))), (((((~program(W)) | program(f5(W))) | (~program(Y))) | halts2(Y, Y)) <=> ((~program(W)) | (~program(Y)) | halts2(Y, Y) | program(f5(W))))), ((((((~program(W)) | program(f5(W))) | (~program(Y))) | halts2(Y, Y)) | outputs(c2, bad)) <=> (((~program(W)) | (~program(Y)) | halts2(Y, Y) | program(f5(W))) | outputs(c2, bad)))), rewrite((((~program(W)) | (~program(Y)) | halts2(Y, Y) | program(f5(W))) | outputs(c2, bad)) <=> ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | program(f5(W)))), ((((((~program(W)) | program(f5(W))) | (~program(Y))) | halts2(Y, Y)) | outputs(c2, bad)) <=> ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | program(f5(W)))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(190,plain,
% 0.20/0.54 (![W: $i, Y: $i] : (((((~program(W)) | program(f5(W))) | (~program(Y))) | halts2(Y, Y)) | outputs(c2, bad)) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | program(f5(W)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[189])).
% 0.20/0.54 tff(191,axiom,(![W: $i, Y: $i] : (((((~program(W)) | program(f5(W))) | (~program(Y))) | halts2(Y, Y)) | outputs(c2, bad))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_3_5')).
% 0.20/0.54 tff(192,plain,
% 0.20/0.54 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | program(f5(W)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.20/0.54 tff(193,plain,
% 0.20/0.54 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | program(f5(W)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[192, 188])).
% 0.20/0.54 tff(194,plain,(
% 0.20/0.54 ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | program(f5(W)))),
% 0.20/0.54 inference(skolemize,[status(sab)],[193])).
% 0.20/0.54 tff(195,plain,
% 0.20/0.54 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | program(f5(W)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[194, 187])).
% 0.20/0.54 tff(196,plain,
% 0.20/0.54 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | program(f5(W)))) | (outputs(c2, bad) | (~program(c1)) | program(f5(c1)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2))))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | program(f5(W)))) | outputs(c2, bad) | (~program(c1)) | program(f5(c1)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(197,plain,
% 0.20/0.54 (((~program(c1)) | (~program(f6(c2))) | outputs(c2, bad) | halts2(f6(c2), f6(c2)) | program(f5(c1))) <=> (outputs(c2, bad) | (~program(c1)) | program(f5(c1)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(198,plain,
% 0.20/0.54 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | program(f5(W)))) | ((~program(c1)) | (~program(f6(c2))) | outputs(c2, bad) | halts2(f6(c2), f6(c2)) | program(f5(c1)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | program(f5(W)))) | (outputs(c2, bad) | (~program(c1)) | program(f5(c1)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2)))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[197])).
% 0.20/0.54 tff(199,plain,
% 0.20/0.54 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | program(f5(W)))) | ((~program(c1)) | (~program(f6(c2))) | outputs(c2, bad) | halts2(f6(c2), f6(c2)) | program(f5(c1)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | program(f5(W)))) | outputs(c2, bad) | (~program(c1)) | program(f5(c1)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[198, 196])).
% 0.20/0.54 tff(200,plain,
% 0.20/0.54 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | program(f5(W)))) | ((~program(c1)) | (~program(f6(c2))) | outputs(c2, bad) | halts2(f6(c2), f6(c2)) | program(f5(c1)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(201,plain,
% 0.20/0.54 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | program(f5(W)))) | outputs(c2, bad) | (~program(c1)) | program(f5(c1)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.20/0.54 tff(202,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[201, 195, 48, 185, 2, 167, 84])).
% 0.20/0.54 tff(203,plain,(program(c3) | program(f5(c1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(204,plain,
% 0.20/0.54 (program(c3)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[203, 2])).
% 0.20/0.54 tff(205,assumption,(~program(f6(c2))), introduced(assumption)).
% 0.20/0.54 tff(206,assumption,(program(c2)), introduced(assumption)).
% 0.20/0.54 tff(207,assumption,(program(c3)), introduced(assumption)).
% 0.20/0.54 tff(208,plain,
% 0.20/0.54 (^[V: $i, Y: $i] : refl(((~program(V)) | (~program(Y)) | halts2(Y, Y) | halts2(c3, Y) | program(f6(V))) <=> ((~program(V)) | (~program(Y)) | halts2(Y, Y) | halts2(c3, Y) | program(f6(V))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(209,plain,
% 0.20/0.54 (![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | halts2(c3, Y) | program(f6(V))) <=> ![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | halts2(c3, Y) | program(f6(V)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[208])).
% 0.20/0.54 tff(210,plain,
% 0.20/0.54 (![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | halts2(c3, Y) | program(f6(V))) <=> ![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | halts2(c3, Y) | program(f6(V)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(211,plain,
% 0.20/0.54 (^[V: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~program(V)) | program(f6(V))) | (~program(Y))) <=> ((~program(V)) | (~program(Y)) | program(f6(V)))), (((((~program(V)) | program(f6(V))) | (~program(Y))) | halts2(Y, Y)) <=> (((~program(V)) | (~program(Y)) | program(f6(V))) | halts2(Y, Y)))), rewrite((((~program(V)) | (~program(Y)) | program(f6(V))) | halts2(Y, Y)) <=> ((~program(V)) | (~program(Y)) | halts2(Y, Y) | program(f6(V)))), (((((~program(V)) | program(f6(V))) | (~program(Y))) | halts2(Y, Y)) <=> ((~program(V)) | (~program(Y)) | halts2(Y, Y) | program(f6(V))))), ((((((~program(V)) | program(f6(V))) | (~program(Y))) | halts2(Y, Y)) | halts2(c3, Y)) <=> (((~program(V)) | (~program(Y)) | halts2(Y, Y) | program(f6(V))) | halts2(c3, Y)))), rewrite((((~program(V)) | (~program(Y)) | halts2(Y, Y) | program(f6(V))) | halts2(c3, Y)) <=> ((~program(V)) | (~program(Y)) | halts2(Y, Y) | halts2(c3, Y) | program(f6(V)))), ((((((~program(V)) | program(f6(V))) | (~program(Y))) | halts2(Y, Y)) | halts2(c3, Y)) <=> ((~program(V)) | (~program(Y)) | halts2(Y, Y) | halts2(c3, Y) | program(f6(V)))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(212,plain,
% 0.20/0.54 (![V: $i, Y: $i] : (((((~program(V)) | program(f6(V))) | (~program(Y))) | halts2(Y, Y)) | halts2(c3, Y)) <=> ![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | halts2(c3, Y) | program(f6(V)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[211])).
% 0.20/0.54 tff(213,axiom,(![V: $i, Y: $i] : (((((~program(V)) | program(f6(V))) | (~program(Y))) | halts2(Y, Y)) | halts2(c3, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_4_3')).
% 0.20/0.54 tff(214,plain,
% 0.20/0.54 (![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | halts2(c3, Y) | program(f6(V)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.20/0.54 tff(215,plain,
% 0.20/0.54 (![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | halts2(c3, Y) | program(f6(V)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[214, 210])).
% 0.20/0.54 tff(216,plain,(
% 0.20/0.54 ![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | halts2(c3, Y) | program(f6(V)))),
% 0.20/0.54 inference(skolemize,[status(sab)],[215])).
% 0.20/0.54 tff(217,plain,
% 0.20/0.54 (![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | halts2(c3, Y) | program(f6(V)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[216, 209])).
% 0.20/0.54 tff(218,plain,
% 0.20/0.54 (((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | halts2(c3, Y) | program(f6(V)))) | ((~program(c2)) | halts2(c3, c3) | program(f6(c2)) | (~program(c3)))) <=> ((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | halts2(c3, Y) | program(f6(V)))) | (~program(c2)) | halts2(c3, c3) | program(f6(c2)) | (~program(c3)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(219,plain,
% 0.20/0.54 (((~program(c2)) | (~program(c3)) | halts2(c3, c3) | halts2(c3, c3) | program(f6(c2))) <=> ((~program(c2)) | halts2(c3, c3) | program(f6(c2)) | (~program(c3)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(220,plain,
% 0.20/0.54 (((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | halts2(c3, Y) | program(f6(V)))) | ((~program(c2)) | (~program(c3)) | halts2(c3, c3) | halts2(c3, c3) | program(f6(c2)))) <=> ((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | halts2(c3, Y) | program(f6(V)))) | ((~program(c2)) | halts2(c3, c3) | program(f6(c2)) | (~program(c3))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[219])).
% 0.20/0.54 tff(221,plain,
% 0.20/0.54 (((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | halts2(c3, Y) | program(f6(V)))) | ((~program(c2)) | (~program(c3)) | halts2(c3, c3) | halts2(c3, c3) | program(f6(c2)))) <=> ((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | halts2(c3, Y) | program(f6(V)))) | (~program(c2)) | halts2(c3, c3) | program(f6(c2)) | (~program(c3)))),
% 0.20/0.55 inference(transitivity,[status(thm)],[220, 218])).
% 0.20/0.55 tff(222,plain,
% 0.20/0.55 ((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | halts2(c3, Y) | program(f6(V)))) | ((~program(c2)) | (~program(c3)) | halts2(c3, c3) | halts2(c3, c3) | program(f6(c2)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(223,plain,
% 0.20/0.55 ((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | halts2(c3, Y) | program(f6(V)))) | (~program(c2)) | halts2(c3, c3) | program(f6(c2)) | (~program(c3))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.20/0.55 tff(224,plain,
% 0.20/0.55 (halts2(c3, c3) | program(f6(c2))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[223, 217, 207, 206])).
% 0.20/0.55 tff(225,plain,
% 0.20/0.55 (halts2(c3, c3)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[224, 205])).
% 0.20/0.55 tff(226,plain,
% 0.20/0.55 (^[V: $i, Y: $i] : refl(((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~halts2(c3, Y)) | program(f6(V))) <=> ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~halts2(c3, Y)) | program(f6(V))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(227,plain,
% 0.20/0.55 (![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~halts2(c3, Y)) | program(f6(V))) <=> ![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~halts2(c3, Y)) | program(f6(V)))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[226])).
% 0.20/0.55 tff(228,plain,
% 0.20/0.55 (![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~halts2(c3, Y)) | program(f6(V))) <=> ![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~halts2(c3, Y)) | program(f6(V)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(229,plain,
% 0.20/0.55 (^[V: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~program(V)) | program(f6(V))) | (~program(Y))) <=> ((~program(V)) | (~program(Y)) | program(f6(V)))), (((((~program(V)) | program(f6(V))) | (~program(Y))) | (~halts2(Y, Y))) <=> (((~program(V)) | (~program(Y)) | program(f6(V))) | (~halts2(Y, Y))))), rewrite((((~program(V)) | (~program(Y)) | program(f6(V))) | (~halts2(Y, Y))) <=> ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | program(f6(V)))), (((((~program(V)) | program(f6(V))) | (~program(Y))) | (~halts2(Y, Y))) <=> ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | program(f6(V))))), ((((((~program(V)) | program(f6(V))) | (~program(Y))) | (~halts2(Y, Y))) | (~halts2(c3, Y))) <=> (((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | program(f6(V))) | (~halts2(c3, Y))))), rewrite((((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | program(f6(V))) | (~halts2(c3, Y))) <=> ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~halts2(c3, Y)) | program(f6(V)))), ((((((~program(V)) | program(f6(V))) | (~program(Y))) | (~halts2(Y, Y))) | (~halts2(c3, Y))) <=> ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~halts2(c3, Y)) | program(f6(V)))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(230,plain,
% 0.20/0.55 (![V: $i, Y: $i] : (((((~program(V)) | program(f6(V))) | (~program(Y))) | (~halts2(Y, Y))) | (~halts2(c3, Y))) <=> ![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~halts2(c3, Y)) | program(f6(V)))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[229])).
% 0.20/0.55 tff(231,axiom,(![V: $i, Y: $i] : (((((~program(V)) | program(f6(V))) | (~program(Y))) | (~halts2(Y, Y))) | (~halts2(c3, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_4_2')).
% 0.20/0.55 tff(232,plain,
% 0.20/0.55 (![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~halts2(c3, Y)) | program(f6(V)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.20/0.55 tff(233,plain,
% 0.20/0.55 (![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~halts2(c3, Y)) | program(f6(V)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[232, 228])).
% 0.20/0.55 tff(234,plain,(
% 0.20/0.55 ![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~halts2(c3, Y)) | program(f6(V)))),
% 0.20/0.55 inference(skolemize,[status(sab)],[233])).
% 0.20/0.55 tff(235,plain,
% 0.20/0.55 (![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~halts2(c3, Y)) | program(f6(V)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[234, 227])).
% 0.20/0.55 tff(236,plain,
% 0.20/0.55 (((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~halts2(c3, Y)) | program(f6(V)))) | ((~program(c2)) | (~halts2(c3, c3)) | program(f6(c2)) | (~program(c3)))) <=> ((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~halts2(c3, Y)) | program(f6(V)))) | (~program(c2)) | (~halts2(c3, c3)) | program(f6(c2)) | (~program(c3)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(237,plain,
% 0.20/0.55 (((~program(c2)) | (~program(c3)) | (~halts2(c3, c3)) | (~halts2(c3, c3)) | program(f6(c2))) <=> ((~program(c2)) | (~halts2(c3, c3)) | program(f6(c2)) | (~program(c3)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(238,plain,
% 0.20/0.55 (((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~halts2(c3, Y)) | program(f6(V)))) | ((~program(c2)) | (~program(c3)) | (~halts2(c3, c3)) | (~halts2(c3, c3)) | program(f6(c2)))) <=> ((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~halts2(c3, Y)) | program(f6(V)))) | ((~program(c2)) | (~halts2(c3, c3)) | program(f6(c2)) | (~program(c3))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[237])).
% 0.20/0.55 tff(239,plain,
% 0.20/0.55 (((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~halts2(c3, Y)) | program(f6(V)))) | ((~program(c2)) | (~program(c3)) | (~halts2(c3, c3)) | (~halts2(c3, c3)) | program(f6(c2)))) <=> ((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~halts2(c3, Y)) | program(f6(V)))) | (~program(c2)) | (~halts2(c3, c3)) | program(f6(c2)) | (~program(c3)))),
% 0.20/0.55 inference(transitivity,[status(thm)],[238, 236])).
% 0.20/0.55 tff(240,plain,
% 0.20/0.55 ((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~halts2(c3, Y)) | program(f6(V)))) | ((~program(c2)) | (~program(c3)) | (~halts2(c3, c3)) | (~halts2(c3, c3)) | program(f6(c2)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(241,plain,
% 0.20/0.55 ((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~halts2(c3, Y)) | program(f6(V)))) | (~program(c2)) | (~halts2(c3, c3)) | program(f6(c2)) | (~program(c3))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.20/0.55 tff(242,plain,
% 0.20/0.55 ((~halts2(c3, c3)) | program(f6(c2))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[241, 235, 207, 206])).
% 0.20/0.55 tff(243,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[242, 225, 205])).
% 0.20/0.55 tff(244,plain,(program(f6(c2)) | (~program(c3)) | (~program(c2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(245,plain,
% 0.20/0.55 (program(f6(c2))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[244, 204, 66])).
% 0.20/0.55 tff(246,plain,
% 0.20/0.55 (halts2(f6(c2), f6(c2))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[129, 119, 245, 2])).
% 0.20/0.55 tff(247,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[146, 140, 48, 2, 119, 246, 245])).
% 0.20/0.55 tff(248,plain,(halts2(c2, f6(c2)) | program(f5(c1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(249,plain,
% 0.20/0.55 (halts2(c2, f6(c2))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[248, 2])).
% 0.20/0.55 tff(250,assumption,(outputs(c2, bad)), introduced(assumption)).
% 0.20/0.55 tff(251,assumption,(halts2(c2, f6(c2))), introduced(assumption)).
% 0.20/0.55 tff(252,assumption,(outputs(c2, good)), introduced(assumption)).
% 0.20/0.55 tff(253,plain,
% 0.20/0.55 (^[V: $i, Y: $i] : refl(((~program(V)) | (~program(Y)) | halts2(Y, Y) | (~outputs(V, bad)) | (~outputs(V, good)) | halts2(c3, Y) | (~halts2(V, f6(V)))) <=> ((~program(V)) | (~program(Y)) | halts2(Y, Y) | (~outputs(V, bad)) | (~outputs(V, good)) | halts2(c3, Y) | (~halts2(V, f6(V)))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(254,plain,
% 0.20/0.55 (![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | (~outputs(V, bad)) | (~outputs(V, good)) | halts2(c3, Y) | (~halts2(V, f6(V)))) <=> ![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | (~outputs(V, bad)) | (~outputs(V, good)) | halts2(c3, Y) | (~halts2(V, f6(V))))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[253])).
% 0.20/0.55 tff(255,plain,
% 0.20/0.55 (![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | (~outputs(V, bad)) | (~outputs(V, good)) | halts2(c3, Y) | (~halts2(V, f6(V)))) <=> ![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | (~outputs(V, bad)) | (~outputs(V, good)) | halts2(c3, Y) | (~halts2(V, f6(V))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(256,plain,
% 0.20/0.55 (^[V: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) <=> ((~program(V)) | (~outputs(V, good)) | (~halts2(V, f6(V))))), (((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~outputs(V, bad))) <=> (((~program(V)) | (~outputs(V, good)) | (~halts2(V, f6(V)))) | (~outputs(V, bad))))), rewrite((((~program(V)) | (~outputs(V, good)) | (~halts2(V, f6(V)))) | (~outputs(V, bad))) <=> ((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(V, f6(V))))), (((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~outputs(V, bad))) <=> ((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(V, f6(V)))))), ((((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~outputs(V, bad))) | (~program(Y))) <=> (((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(V, f6(V)))) | (~program(Y))))), rewrite((((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(V, f6(V)))) | (~program(Y))) <=> ((~program(V)) | (~program(Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(V, f6(V))))), ((((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~outputs(V, bad))) | (~program(Y))) <=> ((~program(V)) | (~program(Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(V, f6(V)))))), (((((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~outputs(V, bad))) | (~program(Y))) | halts2(Y, Y)) <=> (((~program(V)) | (~program(Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(V, f6(V)))) | halts2(Y, Y)))), rewrite((((~program(V)) | (~program(Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(V, f6(V)))) | halts2(Y, Y)) <=> ((~program(V)) | (~program(Y)) | halts2(Y, Y) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(V, f6(V))))), (((((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~outputs(V, bad))) | (~program(Y))) | halts2(Y, Y)) <=> ((~program(V)) | (~program(Y)) | halts2(Y, Y) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(V, f6(V)))))), ((((((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~outputs(V, bad))) | (~program(Y))) | halts2(Y, Y)) | halts2(c3, Y)) <=> (((~program(V)) | (~program(Y)) | halts2(Y, Y) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(V, f6(V)))) | halts2(c3, Y)))), rewrite((((~program(V)) | (~program(Y)) | halts2(Y, Y) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(V, f6(V)))) | halts2(c3, Y)) <=> ((~program(V)) | (~program(Y)) | halts2(Y, Y) | (~outputs(V, bad)) | (~outputs(V, good)) | halts2(c3, Y) | (~halts2(V, f6(V))))), ((((((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~outputs(V, bad))) | (~program(Y))) | halts2(Y, Y)) | halts2(c3, Y)) <=> ((~program(V)) | (~program(Y)) | halts2(Y, Y) | (~outputs(V, bad)) | (~outputs(V, good)) | halts2(c3, Y) | (~halts2(V, f6(V))))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(257,plain,
% 0.20/0.55 (![V: $i, Y: $i] : (((((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~outputs(V, bad))) | (~program(Y))) | halts2(Y, Y)) | halts2(c3, Y)) <=> ![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | (~outputs(V, bad)) | (~outputs(V, good)) | halts2(c3, Y) | (~halts2(V, f6(V))))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[256])).
% 0.20/0.55 tff(258,axiom,(![V: $i, Y: $i] : (((((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~outputs(V, bad))) | (~program(Y))) | halts2(Y, Y)) | halts2(c3, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_4_15')).
% 0.20/0.55 tff(259,plain,
% 0.20/0.55 (![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | (~outputs(V, bad)) | (~outputs(V, good)) | halts2(c3, Y) | (~halts2(V, f6(V))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.20/0.55 tff(260,plain,
% 0.20/0.55 (![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | (~outputs(V, bad)) | (~outputs(V, good)) | halts2(c3, Y) | (~halts2(V, f6(V))))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[259, 255])).
% 0.20/0.56 tff(261,plain,(
% 0.20/0.56 ![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | (~outputs(V, bad)) | (~outputs(V, good)) | halts2(c3, Y) | (~halts2(V, f6(V))))),
% 0.20/0.56 inference(skolemize,[status(sab)],[260])).
% 0.20/0.56 tff(262,plain,
% 0.20/0.56 (![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | (~outputs(V, bad)) | (~outputs(V, good)) | halts2(c3, Y) | (~halts2(V, f6(V))))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[261, 254])).
% 0.20/0.56 tff(263,plain,
% 0.20/0.56 (((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | (~outputs(V, bad)) | (~outputs(V, good)) | halts2(c3, Y) | (~halts2(V, f6(V))))) | ((~program(c2)) | (~outputs(c2, good)) | (~outputs(c2, bad)) | (~halts2(c2, f6(c2))) | halts2(c3, c3) | (~program(c3)))) <=> ((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | (~outputs(V, bad)) | (~outputs(V, good)) | halts2(c3, Y) | (~halts2(V, f6(V))))) | (~program(c2)) | (~outputs(c2, good)) | (~outputs(c2, bad)) | (~halts2(c2, f6(c2))) | halts2(c3, c3) | (~program(c3)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(264,plain,
% 0.20/0.56 (((~program(c2)) | (~program(c3)) | halts2(c3, c3) | (~outputs(c2, bad)) | (~outputs(c2, good)) | halts2(c3, c3) | (~halts2(c2, f6(c2)))) <=> ((~program(c2)) | (~outputs(c2, good)) | (~outputs(c2, bad)) | (~halts2(c2, f6(c2))) | halts2(c3, c3) | (~program(c3)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(265,plain,
% 0.20/0.56 (((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | (~outputs(V, bad)) | (~outputs(V, good)) | halts2(c3, Y) | (~halts2(V, f6(V))))) | ((~program(c2)) | (~program(c3)) | halts2(c3, c3) | (~outputs(c2, bad)) | (~outputs(c2, good)) | halts2(c3, c3) | (~halts2(c2, f6(c2))))) <=> ((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | (~outputs(V, bad)) | (~outputs(V, good)) | halts2(c3, Y) | (~halts2(V, f6(V))))) | ((~program(c2)) | (~outputs(c2, good)) | (~outputs(c2, bad)) | (~halts2(c2, f6(c2))) | halts2(c3, c3) | (~program(c3))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[264])).
% 0.20/0.56 tff(266,plain,
% 0.20/0.56 (((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | (~outputs(V, bad)) | (~outputs(V, good)) | halts2(c3, Y) | (~halts2(V, f6(V))))) | ((~program(c2)) | (~program(c3)) | halts2(c3, c3) | (~outputs(c2, bad)) | (~outputs(c2, good)) | halts2(c3, c3) | (~halts2(c2, f6(c2))))) <=> ((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | (~outputs(V, bad)) | (~outputs(V, good)) | halts2(c3, Y) | (~halts2(V, f6(V))))) | (~program(c2)) | (~outputs(c2, good)) | (~outputs(c2, bad)) | (~halts2(c2, f6(c2))) | halts2(c3, c3) | (~program(c3)))),
% 0.20/0.56 inference(transitivity,[status(thm)],[265, 263])).
% 0.20/0.56 tff(267,plain,
% 0.20/0.56 ((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | (~outputs(V, bad)) | (~outputs(V, good)) | halts2(c3, Y) | (~halts2(V, f6(V))))) | ((~program(c2)) | (~program(c3)) | halts2(c3, c3) | (~outputs(c2, bad)) | (~outputs(c2, good)) | halts2(c3, c3) | (~halts2(c2, f6(c2))))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(268,plain,
% 0.20/0.56 ((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | halts2(Y, Y) | (~outputs(V, bad)) | (~outputs(V, good)) | halts2(c3, Y) | (~halts2(V, f6(V))))) | (~program(c2)) | (~outputs(c2, good)) | (~outputs(c2, bad)) | (~halts2(c2, f6(c2))) | halts2(c3, c3) | (~program(c3))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.20/0.56 tff(269,plain,
% 0.20/0.56 ((~outputs(c2, bad)) | (~halts2(c2, f6(c2))) | halts2(c3, c3)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[268, 262, 207, 252, 206])).
% 0.20/0.56 tff(270,plain,
% 0.20/0.56 (halts2(c3, c3)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[269, 251, 250])).
% 0.20/0.56 tff(271,plain,
% 0.20/0.56 (^[V: $i, Y: $i] : refl(((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V)))) <=> ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V)))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(272,plain,
% 0.20/0.56 (![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V)))) <=> ![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[271])).
% 0.20/0.56 tff(273,plain,
% 0.20/0.56 (![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V)))) <=> ![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(274,plain,
% 0.20/0.56 (^[V: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) <=> ((~program(V)) | (~outputs(V, good)) | (~halts2(V, f6(V))))), (((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~outputs(V, bad))) <=> (((~program(V)) | (~outputs(V, good)) | (~halts2(V, f6(V)))) | (~outputs(V, bad))))), rewrite((((~program(V)) | (~outputs(V, good)) | (~halts2(V, f6(V)))) | (~outputs(V, bad))) <=> ((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(V, f6(V))))), (((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~outputs(V, bad))) <=> ((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(V, f6(V)))))), ((((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~outputs(V, bad))) | (~program(Y))) <=> (((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(V, f6(V)))) | (~program(Y))))), rewrite((((~program(V)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(V, f6(V)))) | (~program(Y))) <=> ((~program(V)) | (~program(Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(V, f6(V))))), ((((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~outputs(V, bad))) | (~program(Y))) <=> ((~program(V)) | (~program(Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(V, f6(V)))))), (((((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~outputs(V, bad))) | (~program(Y))) | (~halts2(Y, Y))) <=> (((~program(V)) | (~program(Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(V, f6(V)))) | (~halts2(Y, Y))))), rewrite((((~program(V)) | (~program(Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(V, f6(V)))) | (~halts2(Y, Y))) <=> ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(V, f6(V))))), (((((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~outputs(V, bad))) | (~program(Y))) | (~halts2(Y, Y))) <=> ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(V, f6(V)))))), ((((((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~outputs(V, bad))) | (~program(Y))) | (~halts2(Y, Y))) | (~halts2(c3, Y))) <=> (((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(V, f6(V)))) | (~halts2(c3, Y))))), rewrite((((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(V, f6(V)))) | (~halts2(c3, Y))) <=> ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))))), ((((((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~outputs(V, bad))) | (~program(Y))) | (~halts2(Y, Y))) | (~halts2(c3, Y))) <=> ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(275,plain,
% 0.20/0.56 (![V: $i, Y: $i] : (((((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~outputs(V, bad))) | (~program(Y))) | (~halts2(Y, Y))) | (~halts2(c3, Y))) <=> ![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[274])).
% 0.20/0.56 tff(276,axiom,(![V: $i, Y: $i] : (((((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~outputs(V, bad))) | (~program(Y))) | (~halts2(Y, Y))) | (~halts2(c3, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_4_14')).
% 0.20/0.56 tff(277,plain,
% 0.20/0.56 (![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.20/0.56 tff(278,plain,
% 0.20/0.56 (![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[277, 273])).
% 0.20/0.56 tff(279,plain,(
% 0.20/0.56 ![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))))),
% 0.20/0.56 inference(skolemize,[status(sab)],[278])).
% 0.20/0.56 tff(280,plain,
% 0.20/0.56 (![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[279, 272])).
% 0.20/0.56 tff(281,plain,
% 0.20/0.56 (((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))))) | ((~program(c2)) | (~outputs(c2, good)) | (~outputs(c2, bad)) | (~halts2(c2, f6(c2))) | (~halts2(c3, c3)) | (~program(c3)))) <=> ((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))))) | (~program(c2)) | (~outputs(c2, good)) | (~outputs(c2, bad)) | (~halts2(c2, f6(c2))) | (~halts2(c3, c3)) | (~program(c3)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(282,plain,
% 0.20/0.56 (((~program(c2)) | (~program(c3)) | (~halts2(c3, c3)) | (~outputs(c2, bad)) | (~outputs(c2, good)) | (~halts2(c3, c3)) | (~halts2(c2, f6(c2)))) <=> ((~program(c2)) | (~outputs(c2, good)) | (~outputs(c2, bad)) | (~halts2(c2, f6(c2))) | (~halts2(c3, c3)) | (~program(c3)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(283,plain,
% 0.20/0.56 (((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))))) | ((~program(c2)) | (~program(c3)) | (~halts2(c3, c3)) | (~outputs(c2, bad)) | (~outputs(c2, good)) | (~halts2(c3, c3)) | (~halts2(c2, f6(c2))))) <=> ((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))))) | ((~program(c2)) | (~outputs(c2, good)) | (~outputs(c2, bad)) | (~halts2(c2, f6(c2))) | (~halts2(c3, c3)) | (~program(c3))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[282])).
% 0.20/0.56 tff(284,plain,
% 0.20/0.56 (((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))))) | ((~program(c2)) | (~program(c3)) | (~halts2(c3, c3)) | (~outputs(c2, bad)) | (~outputs(c2, good)) | (~halts2(c3, c3)) | (~halts2(c2, f6(c2))))) <=> ((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))))) | (~program(c2)) | (~outputs(c2, good)) | (~outputs(c2, bad)) | (~halts2(c2, f6(c2))) | (~halts2(c3, c3)) | (~program(c3)))),
% 0.20/0.56 inference(transitivity,[status(thm)],[283, 281])).
% 0.20/0.56 tff(285,plain,
% 0.20/0.56 ((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))))) | ((~program(c2)) | (~program(c3)) | (~halts2(c3, c3)) | (~outputs(c2, bad)) | (~outputs(c2, good)) | (~halts2(c3, c3)) | (~halts2(c2, f6(c2))))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(286,plain,
% 0.20/0.56 ((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, bad)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))))) | (~program(c2)) | (~outputs(c2, good)) | (~outputs(c2, bad)) | (~halts2(c2, f6(c2))) | (~halts2(c3, c3)) | (~program(c3))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.20/0.57 tff(287,plain,
% 0.20/0.57 ((~outputs(c2, bad)) | (~halts2(c2, f6(c2))) | (~halts2(c3, c3))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[286, 280, 207, 252, 206])).
% 0.20/0.57 tff(288,plain,
% 0.20/0.57 ($false),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[287, 270, 251, 250])).
% 0.20/0.57 tff(289,plain,((~halts2(c2, f6(c2))) | (~outputs(c2, bad)) | (~program(c3)) | (~outputs(c2, good)) | (~program(c2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.57 tff(290,plain,
% 0.20/0.57 (~outputs(c2, bad)),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[289, 249, 204, 118, 66])).
% 0.20/0.57 tff(291,plain,
% 0.20/0.57 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | program(f5(W)))) | (outputs(c2, bad) | (~program(c1)) | program(f5(c1)) | halts2(c3, c3) | (~program(c3)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | program(f5(W)))) | outputs(c2, bad) | (~program(c1)) | program(f5(c1)) | halts2(c3, c3) | (~program(c3)))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(292,plain,
% 0.20/0.57 (((~program(c1)) | (~program(c3)) | outputs(c2, bad) | halts2(c3, c3) | program(f5(c1))) <=> (outputs(c2, bad) | (~program(c1)) | program(f5(c1)) | halts2(c3, c3) | (~program(c3)))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(293,plain,
% 0.20/0.57 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | program(f5(W)))) | ((~program(c1)) | (~program(c3)) | outputs(c2, bad) | halts2(c3, c3) | program(f5(c1)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | program(f5(W)))) | (outputs(c2, bad) | (~program(c1)) | program(f5(c1)) | halts2(c3, c3) | (~program(c3))))),
% 0.20/0.57 inference(monotonicity,[status(thm)],[292])).
% 0.20/0.57 tff(294,plain,
% 0.20/0.57 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | program(f5(W)))) | ((~program(c1)) | (~program(c3)) | outputs(c2, bad) | halts2(c3, c3) | program(f5(c1)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | program(f5(W)))) | outputs(c2, bad) | (~program(c1)) | program(f5(c1)) | halts2(c3, c3) | (~program(c3)))),
% 0.20/0.57 inference(transitivity,[status(thm)],[293, 291])).
% 0.20/0.57 tff(295,plain,
% 0.20/0.57 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | program(f5(W)))) | ((~program(c1)) | (~program(c3)) | outputs(c2, bad) | halts2(c3, c3) | program(f5(c1)))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(296,plain,
% 0.20/0.57 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | program(f5(W)))) | outputs(c2, bad) | (~program(c1)) | program(f5(c1)) | halts2(c3, c3) | (~program(c3))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.20/0.57 tff(297,plain,
% 0.20/0.57 (outputs(c2, bad) | halts2(c3, c3)),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[296, 195, 48, 204, 2])).
% 0.20/0.57 tff(298,plain,
% 0.20/0.57 (halts2(c3, c3)),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[297, 290])).
% 0.20/0.57 tff(299,plain,
% 0.20/0.57 (^[V: $i, Y: $i] : refl(((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V)))) <=> ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V)))))),
% 0.20/0.57 inference(bind,[status(th)],[])).
% 0.20/0.57 tff(300,plain,
% 0.20/0.57 (![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V)))) <=> ![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))),
% 0.20/0.57 inference(quant_intro,[status(thm)],[299])).
% 0.20/0.57 tff(301,plain,
% 0.20/0.57 (![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V)))) <=> ![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(302,plain,
% 0.20/0.57 (^[V: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) <=> ((~program(V)) | (~outputs(V, good)) | (~halts2(V, f6(V))))), (((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~halts2(f6(V), f6(V)))) <=> (((~program(V)) | (~outputs(V, good)) | (~halts2(V, f6(V)))) | (~halts2(f6(V), f6(V)))))), rewrite((((~program(V)) | (~outputs(V, good)) | (~halts2(V, f6(V)))) | (~halts2(f6(V), f6(V)))) <=> ((~program(V)) | (~outputs(V, good)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))), (((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~halts2(f6(V), f6(V)))) <=> ((~program(V)) | (~outputs(V, good)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V)))))), ((((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~halts2(f6(V), f6(V)))) | (~program(Y))) <=> (((~program(V)) | (~outputs(V, good)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V)))) | (~program(Y))))), rewrite((((~program(V)) | (~outputs(V, good)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V)))) | (~program(Y))) <=> ((~program(V)) | (~program(Y)) | (~outputs(V, good)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))), ((((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~halts2(f6(V), f6(V)))) | (~program(Y))) <=> ((~program(V)) | (~program(Y)) | (~outputs(V, good)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V)))))), (((((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~halts2(f6(V), f6(V)))) | (~program(Y))) | (~halts2(Y, Y))) <=> (((~program(V)) | (~program(Y)) | (~outputs(V, good)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V)))) | (~halts2(Y, Y))))), rewrite((((~program(V)) | (~program(Y)) | (~outputs(V, good)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V)))) | (~halts2(Y, Y))) <=> ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, good)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))), (((((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~halts2(f6(V), f6(V)))) | (~program(Y))) | (~halts2(Y, Y))) <=> ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, good)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V)))))), ((((((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~halts2(f6(V), f6(V)))) | (~program(Y))) | (~halts2(Y, Y))) | (~halts2(c3, Y))) <=> (((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, good)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V)))) | (~halts2(c3, Y))))), rewrite((((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, good)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V)))) | (~halts2(c3, Y))) <=> ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))), ((((((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~halts2(f6(V), f6(V)))) | (~program(Y))) | (~halts2(Y, Y))) | (~halts2(c3, Y))) <=> ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))))),
% 0.20/0.57 inference(bind,[status(th)],[])).
% 0.20/0.57 tff(303,plain,
% 0.20/0.57 (![V: $i, Y: $i] : (((((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~halts2(f6(V), f6(V)))) | (~program(Y))) | (~halts2(Y, Y))) | (~halts2(c3, Y))) <=> ![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))),
% 0.20/0.57 inference(quant_intro,[status(thm)],[302])).
% 0.20/0.57 tff(304,axiom,(![V: $i, Y: $i] : (((((((~program(V)) | (~halts2(V, f6(V)))) | (~outputs(V, good))) | (~halts2(f6(V), f6(V)))) | (~program(Y))) | (~halts2(Y, Y))) | (~halts2(c3, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_4_10')).
% 0.20/0.57 tff(305,plain,
% 0.20/0.57 (![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.20/0.57 tff(306,plain,
% 0.20/0.57 (![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[305, 301])).
% 0.20/0.57 tff(307,plain,(
% 0.20/0.57 ![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))),
% 0.20/0.57 inference(skolemize,[status(sab)],[306])).
% 0.20/0.57 tff(308,plain,
% 0.20/0.57 (![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[307, 300])).
% 0.20/0.57 tff(309,plain,
% 0.20/0.57 (((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))) | ((~program(c2)) | (~outputs(c2, good)) | (~halts2(c2, f6(c2))) | (~halts2(f6(c2), f6(c2))) | (~halts2(c3, c3)) | (~program(c3)))) <=> ((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))) | (~program(c2)) | (~outputs(c2, good)) | (~halts2(c2, f6(c2))) | (~halts2(f6(c2), f6(c2))) | (~halts2(c3, c3)) | (~program(c3)))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(310,plain,
% 0.20/0.57 (((~program(c2)) | (~program(c3)) | (~halts2(c3, c3)) | (~outputs(c2, good)) | (~halts2(c3, c3)) | (~halts2(c2, f6(c2))) | (~halts2(f6(c2), f6(c2)))) <=> ((~program(c2)) | (~outputs(c2, good)) | (~halts2(c2, f6(c2))) | (~halts2(f6(c2), f6(c2))) | (~halts2(c3, c3)) | (~program(c3)))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(311,plain,
% 0.20/0.57 (((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))) | ((~program(c2)) | (~program(c3)) | (~halts2(c3, c3)) | (~outputs(c2, good)) | (~halts2(c3, c3)) | (~halts2(c2, f6(c2))) | (~halts2(f6(c2), f6(c2))))) <=> ((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))) | ((~program(c2)) | (~outputs(c2, good)) | (~halts2(c2, f6(c2))) | (~halts2(f6(c2), f6(c2))) | (~halts2(c3, c3)) | (~program(c3))))),
% 0.20/0.57 inference(monotonicity,[status(thm)],[310])).
% 0.20/0.57 tff(312,plain,
% 0.20/0.57 (((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))) | ((~program(c2)) | (~program(c3)) | (~halts2(c3, c3)) | (~outputs(c2, good)) | (~halts2(c3, c3)) | (~halts2(c2, f6(c2))) | (~halts2(f6(c2), f6(c2))))) <=> ((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))) | (~program(c2)) | (~outputs(c2, good)) | (~halts2(c2, f6(c2))) | (~halts2(f6(c2), f6(c2))) | (~halts2(c3, c3)) | (~program(c3)))),
% 0.20/0.57 inference(transitivity,[status(thm)],[311, 309])).
% 0.20/0.57 tff(313,plain,
% 0.20/0.57 ((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))) | ((~program(c2)) | (~program(c3)) | (~halts2(c3, c3)) | (~outputs(c2, good)) | (~halts2(c3, c3)) | (~halts2(c2, f6(c2))) | (~halts2(f6(c2), f6(c2))))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(314,plain,
% 0.20/0.57 ((~![V: $i, Y: $i] : ((~program(V)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(V, good)) | (~halts2(c3, Y)) | (~halts2(V, f6(V))) | (~halts2(f6(V), f6(V))))) | (~program(c2)) | (~outputs(c2, good)) | (~halts2(c2, f6(c2))) | (~halts2(f6(c2), f6(c2))) | (~halts2(c3, c3)) | (~program(c3))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.20/0.57 tff(315,plain,
% 0.20/0.57 ((~halts2(c2, f6(c2))) | (~halts2(f6(c2), f6(c2))) | (~halts2(c3, c3))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[314, 308, 204, 118, 66])).
% 0.20/0.57 tff(316,plain,
% 0.20/0.57 (~halts2(f6(c2), f6(c2))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[315, 298, 249])).
% 0.20/0.57 tff(317,plain,
% 0.20/0.57 ($false),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[201, 195, 48, 290, 2, 316, 245])).
% 0.20/0.57 tff(318,plain,(program(f5(c1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.57 tff(319,assumption,(~halts2(f5(c1), f5(c1))), introduced(assumption)).
% 0.20/0.57 tff(320,assumption,(~program(c2)), introduced(assumption)).
% 0.20/0.57 tff(321,assumption,(~program(f2(c4))), introduced(assumption)).
% 0.20/0.57 tff(322,assumption,(halts2(f5(c1), f5(c1))), introduced(assumption)).
% 0.20/0.57 tff(323,assumption,(program(f5(c1))), introduced(assumption)).
% 0.20/0.57 tff(324,assumption,(~halts3(c1, f5(c1), f5(c1))), introduced(assumption)).
% 0.20/0.57 tff(325,plain,
% 0.20/0.57 (^[W: $i, Z: $i, Y: $i] : refl((halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W))) <=> (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W))))),
% 0.20/0.57 inference(bind,[status(th)],[])).
% 0.20/0.57 tff(326,plain,
% 0.20/0.57 (![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W))) <=> ![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)))),
% 0.20/0.57 inference(quant_intro,[status(thm)],[325])).
% 0.20/0.57 tff(327,plain,
% 0.20/0.57 (![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W))) <=> ![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(328,plain,
% 0.20/0.57 (^[W: $i, Z: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~program(W)) | program(f4(W))) | (~program(Y))) <=> ((~program(Y)) | program(f4(W)) | (~program(W)))), (((((~program(W)) | program(f4(W))) | (~program(Y))) | halts2(Y, Z)) <=> (((~program(Y)) | program(f4(W)) | (~program(W))) | halts2(Y, Z)))), rewrite((((~program(Y)) | program(f4(W)) | (~program(W))) | halts2(Y, Z)) <=> (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)))), (((((~program(W)) | program(f4(W))) | (~program(Y))) | halts2(Y, Z)) <=> (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W))))), ((((((~program(W)) | program(f4(W))) | (~program(Y))) | halts2(Y, Z)) | halts3(W, Y, Z)) <=> ((halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W))) | halts3(W, Y, Z)))), rewrite(((halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W))) | halts3(W, Y, Z)) <=> (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)))), ((((((~program(W)) | program(f4(W))) | (~program(Y))) | halts2(Y, Z)) | halts3(W, Y, Z)) <=> (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)))))),
% 0.20/0.57 inference(bind,[status(th)],[])).
% 0.20/0.57 tff(329,plain,
% 0.20/0.57 (![W: $i, Z: $i, Y: $i] : (((((~program(W)) | program(f4(W))) | (~program(Y))) | halts2(Y, Z)) | halts3(W, Y, Z)) <=> ![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)))),
% 0.20/0.57 inference(quant_intro,[status(thm)],[328])).
% 0.20/0.57 tff(330,axiom,(![W: $i, Z: $i, Y: $i] : (((((~program(W)) | program(f4(W))) | (~program(Y))) | halts2(Y, Z)) | halts3(W, Y, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_2_3')).
% 0.20/0.57 tff(331,plain,
% 0.20/0.57 (![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[330, 329])).
% 0.20/0.57 tff(332,plain,
% 0.20/0.57 (![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[331, 327])).
% 0.20/0.57 tff(333,plain,(
% 0.20/0.57 ![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)))),
% 0.20/0.57 inference(skolemize,[status(sab)],[332])).
% 0.20/0.57 tff(334,plain,
% 0.20/0.57 (![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[333, 326])).
% 0.20/0.57 tff(335,plain,
% 0.20/0.57 (((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)))) | (halts3(c1, f5(c1), f5(c1)) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(f5(c1))) | program(f4(c1)))) <=> ((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)))) | halts3(c1, f5(c1), f5(c1)) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(f5(c1))) | program(f4(c1)))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(336,plain,
% 0.20/0.58 ((halts3(c1, f5(c1), f5(c1)) | halts2(f5(c1), f5(c1)) | (~program(f5(c1))) | program(f4(c1)) | (~program(c1))) <=> (halts3(c1, f5(c1), f5(c1)) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(f5(c1))) | program(f4(c1)))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(337,plain,
% 0.20/0.58 (((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)))) | (halts3(c1, f5(c1), f5(c1)) | halts2(f5(c1), f5(c1)) | (~program(f5(c1))) | program(f4(c1)) | (~program(c1)))) <=> ((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)))) | (halts3(c1, f5(c1), f5(c1)) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(f5(c1))) | program(f4(c1))))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[336])).
% 0.20/0.58 tff(338,plain,
% 0.20/0.58 (((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)))) | (halts3(c1, f5(c1), f5(c1)) | halts2(f5(c1), f5(c1)) | (~program(f5(c1))) | program(f4(c1)) | (~program(c1)))) <=> ((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)))) | halts3(c1, f5(c1), f5(c1)) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(f5(c1))) | program(f4(c1)))),
% 0.20/0.58 inference(transitivity,[status(thm)],[337, 335])).
% 0.20/0.58 tff(339,plain,
% 0.20/0.58 ((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)))) | (halts3(c1, f5(c1), f5(c1)) | halts2(f5(c1), f5(c1)) | (~program(f5(c1))) | program(f4(c1)) | (~program(c1)))),
% 0.20/0.58 inference(quant_inst,[status(thm)],[])).
% 0.20/0.58 tff(340,plain,
% 0.20/0.58 ((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)))) | halts3(c1, f5(c1), f5(c1)) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(f5(c1))) | program(f4(c1))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.20/0.58 tff(341,plain,
% 0.20/0.58 (halts2(f5(c1), f5(c1)) | (~program(f5(c1))) | program(f4(c1))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[340, 334, 48, 324])).
% 0.20/0.58 tff(342,plain,
% 0.20/0.58 (program(f4(c1))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[341, 319, 323])).
% 0.20/0.58 tff(343,plain,
% 0.20/0.58 (^[W: $i, Z: $i, Y: $i] : refl((halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W)))) <=> (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W)))))),
% 0.20/0.58 inference(bind,[status(th)],[])).
% 0.20/0.58 tff(344,plain,
% 0.20/0.58 (![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W)))) <=> ![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))),
% 0.20/0.58 inference(quant_intro,[status(thm)],[343])).
% 0.20/0.58 tff(345,plain,
% 0.20/0.58 (![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W)))) <=> ![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(346,plain,
% 0.20/0.58 (^[W: $i, Z: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~program(W)) | (~decides(W, f4(W), f3(W)))) | (~program(Y))) <=> ((~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))), (((((~program(W)) | (~decides(W, f4(W), f3(W)))) | (~program(Y))) | halts2(Y, Z)) <=> (((~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W)))) | halts2(Y, Z)))), rewrite((((~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W)))) | halts2(Y, Z)) <=> (halts2(Y, Z) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))), (((((~program(W)) | (~decides(W, f4(W), f3(W)))) | (~program(Y))) | halts2(Y, Z)) <=> (halts2(Y, Z) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W)))))), ((((((~program(W)) | (~decides(W, f4(W), f3(W)))) | (~program(Y))) | halts2(Y, Z)) | halts3(W, Y, Z)) <=> ((halts2(Y, Z) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W)))) | halts3(W, Y, Z)))), rewrite(((halts2(Y, Z) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W)))) | halts3(W, Y, Z)) <=> (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))), ((((((~program(W)) | (~decides(W, f4(W), f3(W)))) | (~program(Y))) | halts2(Y, Z)) | halts3(W, Y, Z)) <=> (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))))),
% 0.20/0.58 inference(bind,[status(th)],[])).
% 0.20/0.58 tff(347,plain,
% 0.20/0.58 (![W: $i, Z: $i, Y: $i] : (((((~program(W)) | (~decides(W, f4(W), f3(W)))) | (~program(Y))) | halts2(Y, Z)) | halts3(W, Y, Z)) <=> ![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))),
% 0.20/0.58 inference(quant_intro,[status(thm)],[346])).
% 0.20/0.58 tff(348,axiom,(![W: $i, Z: $i, Y: $i] : (((((~program(W)) | (~decides(W, f4(W), f3(W)))) | (~program(Y))) | halts2(Y, Z)) | halts3(W, Y, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_2_7')).
% 0.20/0.58 tff(349,plain,
% 0.20/0.58 (![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.20/0.58 tff(350,plain,
% 0.20/0.58 (![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[349, 345])).
% 0.20/0.58 tff(351,plain,(
% 0.20/0.58 ![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))),
% 0.20/0.58 inference(skolemize,[status(sab)],[350])).
% 0.20/0.58 tff(352,plain,
% 0.20/0.58 (![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[351, 344])).
% 0.20/0.58 tff(353,plain,
% 0.20/0.58 (((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))) | (halts3(c1, f5(c1), f5(c1)) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(f5(c1))) | (~decides(c1, f4(c1), f3(c1))))) <=> ((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))) | halts3(c1, f5(c1), f5(c1)) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(f5(c1))) | (~decides(c1, f4(c1), f3(c1))))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(354,plain,
% 0.20/0.58 ((halts3(c1, f5(c1), f5(c1)) | halts2(f5(c1), f5(c1)) | (~program(f5(c1))) | (~program(c1)) | (~decides(c1, f4(c1), f3(c1)))) <=> (halts3(c1, f5(c1), f5(c1)) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(f5(c1))) | (~decides(c1, f4(c1), f3(c1))))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(355,plain,
% 0.20/0.58 (((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))) | (halts3(c1, f5(c1), f5(c1)) | halts2(f5(c1), f5(c1)) | (~program(f5(c1))) | (~program(c1)) | (~decides(c1, f4(c1), f3(c1))))) <=> ((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))) | (halts3(c1, f5(c1), f5(c1)) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(f5(c1))) | (~decides(c1, f4(c1), f3(c1)))))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[354])).
% 0.20/0.58 tff(356,plain,
% 0.20/0.58 (((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))) | (halts3(c1, f5(c1), f5(c1)) | halts2(f5(c1), f5(c1)) | (~program(f5(c1))) | (~program(c1)) | (~decides(c1, f4(c1), f3(c1))))) <=> ((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))) | halts3(c1, f5(c1), f5(c1)) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(f5(c1))) | (~decides(c1, f4(c1), f3(c1))))),
% 0.20/0.58 inference(transitivity,[status(thm)],[355, 353])).
% 0.20/0.58 tff(357,plain,
% 0.20/0.58 ((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))) | (halts3(c1, f5(c1), f5(c1)) | halts2(f5(c1), f5(c1)) | (~program(f5(c1))) | (~program(c1)) | (~decides(c1, f4(c1), f3(c1))))),
% 0.50/0.58 inference(quant_inst,[status(thm)],[])).
% 0.50/0.58 tff(358,plain,
% 0.50/0.58 ((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | halts2(Y, Z) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))) | halts3(c1, f5(c1), f5(c1)) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(f5(c1))) | (~decides(c1, f4(c1), f3(c1)))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[357, 356])).
% 0.50/0.58 tff(359,plain,
% 0.50/0.58 (halts2(f5(c1), f5(c1)) | (~program(f5(c1))) | (~decides(c1, f4(c1), f3(c1)))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[358, 352, 48, 324])).
% 0.50/0.58 tff(360,plain,
% 0.50/0.58 (~decides(c1, f4(c1), f3(c1))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[359, 319, 323])).
% 0.50/0.58 tff(361,plain,
% 0.50/0.58 (^[Z: $i, Y: $i, X: $i] : refl((program(f2(X)) | (~algorithm(X)) | decides(c1, Y, Z) | (~program(Y))) <=> (program(f2(X)) | (~algorithm(X)) | decides(c1, Y, Z) | (~program(Y))))),
% 0.50/0.58 inference(bind,[status(th)],[])).
% 0.50/0.58 tff(362,plain,
% 0.50/0.58 (![Z: $i, Y: $i, X: $i] : (program(f2(X)) | (~algorithm(X)) | decides(c1, Y, Z) | (~program(Y))) <=> ![Z: $i, Y: $i, X: $i] : (program(f2(X)) | (~algorithm(X)) | decides(c1, Y, Z) | (~program(Y)))),
% 0.50/0.58 inference(quant_intro,[status(thm)],[361])).
% 0.50/0.58 tff(363,plain,
% 0.50/0.58 (![Z: $i, Y: $i, X: $i] : (program(f2(X)) | (~algorithm(X)) | decides(c1, Y, Z) | (~program(Y))) <=> ![Z: $i, Y: $i, X: $i] : (program(f2(X)) | (~algorithm(X)) | decides(c1, Y, Z) | (~program(Y)))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(364,plain,
% 0.50/0.58 (^[Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite((((~algorithm(X)) | program(f2(X))) | (~program(Y))) <=> (program(f2(X)) | (~algorithm(X)) | (~program(Y)))), (((((~algorithm(X)) | program(f2(X))) | (~program(Y))) | decides(c1, Y, Z)) <=> ((program(f2(X)) | (~algorithm(X)) | (~program(Y))) | decides(c1, Y, Z)))), rewrite(((program(f2(X)) | (~algorithm(X)) | (~program(Y))) | decides(c1, Y, Z)) <=> (program(f2(X)) | (~algorithm(X)) | decides(c1, Y, Z) | (~program(Y)))), (((((~algorithm(X)) | program(f2(X))) | (~program(Y))) | decides(c1, Y, Z)) <=> (program(f2(X)) | (~algorithm(X)) | decides(c1, Y, Z) | (~program(Y)))))),
% 0.50/0.58 inference(bind,[status(th)],[])).
% 0.50/0.58 tff(365,plain,
% 0.50/0.58 (![Z: $i, Y: $i, X: $i] : ((((~algorithm(X)) | program(f2(X))) | (~program(Y))) | decides(c1, Y, Z)) <=> ![Z: $i, Y: $i, X: $i] : (program(f2(X)) | (~algorithm(X)) | decides(c1, Y, Z) | (~program(Y)))),
% 0.50/0.58 inference(quant_intro,[status(thm)],[364])).
% 0.50/0.58 tff(366,axiom,(![Z: $i, Y: $i, X: $i] : ((((~algorithm(X)) | program(f2(X))) | (~program(Y))) | decides(c1, Y, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_1_2')).
% 0.50/0.58 tff(367,plain,
% 0.50/0.58 (![Z: $i, Y: $i, X: $i] : (program(f2(X)) | (~algorithm(X)) | decides(c1, Y, Z) | (~program(Y)))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[366, 365])).
% 0.50/0.58 tff(368,plain,
% 0.50/0.58 (![Z: $i, Y: $i, X: $i] : (program(f2(X)) | (~algorithm(X)) | decides(c1, Y, Z) | (~program(Y)))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[367, 363])).
% 0.50/0.58 tff(369,plain,(
% 0.50/0.58 ![Z: $i, Y: $i, X: $i] : (program(f2(X)) | (~algorithm(X)) | decides(c1, Y, Z) | (~program(Y)))),
% 0.50/0.58 inference(skolemize,[status(sab)],[368])).
% 0.50/0.58 tff(370,plain,
% 0.50/0.58 (![Z: $i, Y: $i, X: $i] : (program(f2(X)) | (~algorithm(X)) | decides(c1, Y, Z) | (~program(Y)))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[369, 362])).
% 0.50/0.58 tff(371,plain,
% 0.50/0.58 (((~![Z: $i, Y: $i, X: $i] : (program(f2(X)) | (~algorithm(X)) | decides(c1, Y, Z) | (~program(Y)))) | (program(f2(c4)) | (~algorithm(c4)) | decides(c1, f4(c1), f3(c1)) | (~program(f4(c1))))) <=> ((~![Z: $i, Y: $i, X: $i] : (program(f2(X)) | (~algorithm(X)) | decides(c1, Y, Z) | (~program(Y)))) | program(f2(c4)) | (~algorithm(c4)) | decides(c1, f4(c1), f3(c1)) | (~program(f4(c1))))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(372,plain,
% 0.50/0.58 ((~![Z: $i, Y: $i, X: $i] : (program(f2(X)) | (~algorithm(X)) | decides(c1, Y, Z) | (~program(Y)))) | (program(f2(c4)) | (~algorithm(c4)) | decides(c1, f4(c1), f3(c1)) | (~program(f4(c1))))),
% 0.50/0.59 inference(quant_inst,[status(thm)],[])).
% 0.50/0.59 tff(373,plain,
% 0.50/0.59 ((~![Z: $i, Y: $i, X: $i] : (program(f2(X)) | (~algorithm(X)) | decides(c1, Y, Z) | (~program(Y)))) | program(f2(c4)) | (~algorithm(c4)) | decides(c1, f4(c1), f3(c1)) | (~program(f4(c1)))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[372, 371])).
% 0.50/0.59 tff(374,plain,
% 0.50/0.59 ($false),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[373, 370, 6, 321, 360, 342])).
% 0.50/0.59 tff(375,plain,(halts2(f5(c1), f5(c1)) | program(f2(c4)) | (~program(f5(c1))) | halts3(c1, f5(c1), f5(c1))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.59 tff(376,plain,
% 0.50/0.59 (halts2(f5(c1), f5(c1))),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[375, 323, 321, 324])).
% 0.50/0.59 tff(377,plain,
% 0.50/0.59 (^[W: $i, Z: $i, Y: $i] : refl((halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W))) <=> (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(378,plain,
% 0.50/0.59 (![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W))) <=> ![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[377])).
% 0.50/0.59 tff(379,plain,
% 0.50/0.59 (![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W))) <=> ![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(380,plain,
% 0.50/0.59 (^[W: $i, Z: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~program(W)) | program(f4(W))) | (~program(Y))) <=> ((~program(Y)) | program(f4(W)) | (~program(W)))), (((((~program(W)) | program(f4(W))) | (~program(Y))) | (~halts2(Y, Z))) <=> (((~program(Y)) | program(f4(W)) | (~program(W))) | (~halts2(Y, Z))))), rewrite((((~program(Y)) | program(f4(W)) | (~program(W))) | (~halts2(Y, Z))) <=> ((~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)))), (((((~program(W)) | program(f4(W))) | (~program(Y))) | (~halts2(Y, Z))) <=> ((~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W))))), ((((((~program(W)) | program(f4(W))) | (~program(Y))) | (~halts2(Y, Z))) | halts3(W, Y, Z)) <=> (((~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W))) | halts3(W, Y, Z)))), rewrite((((~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W))) | halts3(W, Y, Z)) <=> (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)))), ((((((~program(W)) | program(f4(W))) | (~program(Y))) | (~halts2(Y, Z))) | halts3(W, Y, Z)) <=> (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(381,plain,
% 0.50/0.59 (![W: $i, Z: $i, Y: $i] : (((((~program(W)) | program(f4(W))) | (~program(Y))) | (~halts2(Y, Z))) | halts3(W, Y, Z)) <=> ![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[380])).
% 0.50/0.59 tff(382,axiom,(![W: $i, Z: $i, Y: $i] : (((((~program(W)) | program(f4(W))) | (~program(Y))) | (~halts2(Y, Z))) | halts3(W, Y, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_2_1')).
% 0.50/0.59 tff(383,plain,
% 0.50/0.59 (![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[382, 381])).
% 0.50/0.59 tff(384,plain,
% 0.50/0.59 (![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[383, 379])).
% 0.50/0.59 tff(385,plain,(
% 0.50/0.59 ![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)))),
% 0.50/0.59 inference(skolemize,[status(sab)],[384])).
% 0.50/0.59 tff(386,plain,
% 0.50/0.59 (![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[385, 378])).
% 0.50/0.59 tff(387,plain,
% 0.50/0.59 (((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)))) | (halts3(c1, f5(c1), f5(c1)) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | (~program(f5(c1))) | program(f4(c1)))) <=> ((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)))) | halts3(c1, f5(c1), f5(c1)) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | (~program(f5(c1))) | program(f4(c1)))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(388,plain,
% 0.50/0.59 ((halts3(c1, f5(c1), f5(c1)) | (~halts2(f5(c1), f5(c1))) | (~program(f5(c1))) | program(f4(c1)) | (~program(c1))) <=> (halts3(c1, f5(c1), f5(c1)) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | (~program(f5(c1))) | program(f4(c1)))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(389,plain,
% 0.50/0.59 (((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)))) | (halts3(c1, f5(c1), f5(c1)) | (~halts2(f5(c1), f5(c1))) | (~program(f5(c1))) | program(f4(c1)) | (~program(c1)))) <=> ((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)))) | (halts3(c1, f5(c1), f5(c1)) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | (~program(f5(c1))) | program(f4(c1))))),
% 0.50/0.59 inference(monotonicity,[status(thm)],[388])).
% 0.50/0.59 tff(390,plain,
% 0.50/0.59 (((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)))) | (halts3(c1, f5(c1), f5(c1)) | (~halts2(f5(c1), f5(c1))) | (~program(f5(c1))) | program(f4(c1)) | (~program(c1)))) <=> ((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)))) | halts3(c1, f5(c1), f5(c1)) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | (~program(f5(c1))) | program(f4(c1)))),
% 0.50/0.59 inference(transitivity,[status(thm)],[389, 387])).
% 0.50/0.59 tff(391,plain,
% 0.50/0.59 ((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)))) | (halts3(c1, f5(c1), f5(c1)) | (~halts2(f5(c1), f5(c1))) | (~program(f5(c1))) | program(f4(c1)) | (~program(c1)))),
% 0.50/0.59 inference(quant_inst,[status(thm)],[])).
% 0.50/0.59 tff(392,plain,
% 0.50/0.59 ((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)))) | halts3(c1, f5(c1), f5(c1)) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | (~program(f5(c1))) | program(f4(c1))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[391, 390])).
% 0.50/0.59 tff(393,plain,
% 0.50/0.59 ((~halts2(f5(c1), f5(c1))) | (~program(f5(c1))) | program(f4(c1))),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[392, 386, 48, 324])).
% 0.50/0.59 tff(394,plain,
% 0.50/0.59 (program(f4(c1))),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[393, 376, 323])).
% 0.50/0.59 tff(395,plain,
% 0.50/0.59 (^[W: $i, Z: $i, Y: $i] : refl((halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W)))) <=> (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W)))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(396,plain,
% 0.50/0.59 (![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W)))) <=> ![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[395])).
% 0.50/0.59 tff(397,plain,
% 0.50/0.59 (![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W)))) <=> ![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(398,plain,
% 0.50/0.59 (^[W: $i, Z: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~program(W)) | (~decides(W, f4(W), f3(W)))) | (~program(Y))) <=> ((~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))), (((((~program(W)) | (~decides(W, f4(W), f3(W)))) | (~program(Y))) | (~halts2(Y, Z))) <=> (((~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W)))) | (~halts2(Y, Z))))), rewrite((((~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W)))) | (~halts2(Y, Z))) <=> ((~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))), (((((~program(W)) | (~decides(W, f4(W), f3(W)))) | (~program(Y))) | (~halts2(Y, Z))) <=> ((~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W)))))), ((((((~program(W)) | (~decides(W, f4(W), f3(W)))) | (~program(Y))) | (~halts2(Y, Z))) | halts3(W, Y, Z)) <=> (((~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W)))) | halts3(W, Y, Z)))), rewrite((((~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W)))) | halts3(W, Y, Z)) <=> (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))), ((((((~program(W)) | (~decides(W, f4(W), f3(W)))) | (~program(Y))) | (~halts2(Y, Z))) | halts3(W, Y, Z)) <=> (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(399,plain,
% 0.50/0.59 (![W: $i, Z: $i, Y: $i] : (((((~program(W)) | (~decides(W, f4(W), f3(W)))) | (~program(Y))) | (~halts2(Y, Z))) | halts3(W, Y, Z)) <=> ![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[398])).
% 0.50/0.59 tff(400,axiom,(![W: $i, Z: $i, Y: $i] : (((((~program(W)) | (~decides(W, f4(W), f3(W)))) | (~program(Y))) | (~halts2(Y, Z))) | halts3(W, Y, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_2_5')).
% 0.50/0.59 tff(401,plain,
% 0.50/0.59 (![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[400, 399])).
% 0.50/0.59 tff(402,plain,
% 0.50/0.59 (![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[401, 397])).
% 0.50/0.59 tff(403,plain,(
% 0.50/0.59 ![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))),
% 0.50/0.59 inference(skolemize,[status(sab)],[402])).
% 0.50/0.59 tff(404,plain,
% 0.50/0.59 (![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[403, 396])).
% 0.50/0.59 tff(405,plain,
% 0.50/0.59 (((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))) | (halts3(c1, f5(c1), f5(c1)) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | (~program(f5(c1))) | (~decides(c1, f4(c1), f3(c1))))) <=> ((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))) | halts3(c1, f5(c1), f5(c1)) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | (~program(f5(c1))) | (~decides(c1, f4(c1), f3(c1))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(406,plain,
% 0.50/0.59 ((halts3(c1, f5(c1), f5(c1)) | (~halts2(f5(c1), f5(c1))) | (~program(f5(c1))) | (~program(c1)) | (~decides(c1, f4(c1), f3(c1)))) <=> (halts3(c1, f5(c1), f5(c1)) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | (~program(f5(c1))) | (~decides(c1, f4(c1), f3(c1))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(407,plain,
% 0.50/0.59 (((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))) | (halts3(c1, f5(c1), f5(c1)) | (~halts2(f5(c1), f5(c1))) | (~program(f5(c1))) | (~program(c1)) | (~decides(c1, f4(c1), f3(c1))))) <=> ((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))) | (halts3(c1, f5(c1), f5(c1)) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | (~program(f5(c1))) | (~decides(c1, f4(c1), f3(c1)))))),
% 0.50/0.59 inference(monotonicity,[status(thm)],[406])).
% 0.50/0.59 tff(408,plain,
% 0.50/0.59 (((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))) | (halts3(c1, f5(c1), f5(c1)) | (~halts2(f5(c1), f5(c1))) | (~program(f5(c1))) | (~program(c1)) | (~decides(c1, f4(c1), f3(c1))))) <=> ((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))) | halts3(c1, f5(c1), f5(c1)) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | (~program(f5(c1))) | (~decides(c1, f4(c1), f3(c1))))),
% 0.50/0.60 inference(transitivity,[status(thm)],[407, 405])).
% 0.50/0.60 tff(409,plain,
% 0.50/0.60 ((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))) | (halts3(c1, f5(c1), f5(c1)) | (~halts2(f5(c1), f5(c1))) | (~program(f5(c1))) | (~program(c1)) | (~decides(c1, f4(c1), f3(c1))))),
% 0.50/0.60 inference(quant_inst,[status(thm)],[])).
% 0.50/0.60 tff(410,plain,
% 0.50/0.60 ((~![W: $i, Z: $i, Y: $i] : (halts3(W, Y, Z) | (~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))) | halts3(c1, f5(c1), f5(c1)) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | (~program(f5(c1))) | (~decides(c1, f4(c1), f3(c1)))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[409, 408])).
% 0.50/0.60 tff(411,plain,
% 0.50/0.60 ((~halts2(f5(c1), f5(c1))) | (~program(f5(c1))) | (~decides(c1, f4(c1), f3(c1)))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[410, 404, 48, 324])).
% 0.50/0.60 tff(412,plain,
% 0.50/0.60 (~decides(c1, f4(c1), f3(c1))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[411, 376, 323])).
% 0.50/0.60 tff(413,plain,
% 0.50/0.60 ($false),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[373, 370, 6, 321, 412, 394])).
% 0.50/0.60 tff(414,plain,((~program(f5(c1))) | program(f2(c4)) | halts3(c1, f5(c1), f5(c1))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.60 tff(415,plain,
% 0.50/0.60 (halts3(c1, f5(c1), f5(c1))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[414, 321, 318])).
% 0.50/0.60 tff(416,plain,
% 0.50/0.60 (^[W: $i] : refl((program(c2) | (~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)) | (~halts2(f5(W), f5(W)))) <=> (program(c2) | (~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)) | (~halts2(f5(W), f5(W)))))),
% 0.50/0.60 inference(bind,[status(th)],[])).
% 0.50/0.60 tff(417,plain,
% 0.50/0.60 (![W: $i] : (program(c2) | (~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)) | (~halts2(f5(W), f5(W)))) <=> ![W: $i] : (program(c2) | (~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)) | (~halts2(f5(W), f5(W))))),
% 0.50/0.60 inference(quant_intro,[status(thm)],[416])).
% 0.50/0.60 tff(418,plain,
% 0.50/0.60 (![W: $i] : (program(c2) | (~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)) | (~halts2(f5(W), f5(W)))) <=> ![W: $i] : (program(c2) | (~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)) | (~halts2(f5(W), f5(W))))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(419,plain,
% 0.50/0.60 (^[W: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) <=> ((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))), (((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) <=> (((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))))), rewrite((((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) <=> ((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)) | (~halts2(f5(W), f5(W))))), (((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) <=> ((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)) | (~halts2(f5(W), f5(W)))))), ((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | program(c2)) <=> (((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)) | (~halts2(f5(W), f5(W)))) | program(c2)))), rewrite((((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)) | (~halts2(f5(W), f5(W)))) | program(c2)) <=> (program(c2) | (~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)) | (~halts2(f5(W), f5(W))))), ((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | program(c2)) <=> (program(c2) | (~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)) | (~halts2(f5(W), f5(W))))))),
% 0.50/0.60 inference(bind,[status(th)],[])).
% 0.50/0.60 tff(420,plain,
% 0.50/0.60 (![W: $i] : (((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | program(c2)) <=> ![W: $i] : (program(c2) | (~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)) | (~halts2(f5(W), f5(W))))),
% 0.50/0.60 inference(quant_intro,[status(thm)],[419])).
% 0.50/0.60 tff(421,axiom,(![W: $i] : (((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | program(c2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_3_11')).
% 0.50/0.60 tff(422,plain,
% 0.50/0.60 (![W: $i] : (program(c2) | (~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)) | (~halts2(f5(W), f5(W))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[421, 420])).
% 0.50/0.60 tff(423,plain,
% 0.50/0.60 (![W: $i] : (program(c2) | (~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)) | (~halts2(f5(W), f5(W))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[422, 418])).
% 0.50/0.60 tff(424,plain,(
% 0.50/0.60 ![W: $i] : (program(c2) | (~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)) | (~halts2(f5(W), f5(W))))),
% 0.50/0.60 inference(skolemize,[status(sab)],[423])).
% 0.50/0.60 tff(425,plain,
% 0.50/0.60 (![W: $i] : (program(c2) | (~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)) | (~halts2(f5(W), f5(W))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[424, 417])).
% 0.50/0.60 tff(426,plain,
% 0.50/0.60 (((~![W: $i] : (program(c2) | (~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)) | (~halts2(f5(W), f5(W))))) | (program(c2) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)))) <=> ((~![W: $i] : (program(c2) | (~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)) | (~halts2(f5(W), f5(W))))) | program(c2) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(427,plain,
% 0.50/0.60 ((program(c2) | (~program(c1)) | (~halts3(c1, f5(c1), f5(c1))) | (~outputs(c1, good)) | (~halts2(f5(c1), f5(c1)))) <=> (program(c2) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(428,plain,
% 0.50/0.60 (((~![W: $i] : (program(c2) | (~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)) | (~halts2(f5(W), f5(W))))) | (program(c2) | (~program(c1)) | (~halts3(c1, f5(c1), f5(c1))) | (~outputs(c1, good)) | (~halts2(f5(c1), f5(c1))))) <=> ((~![W: $i] : (program(c2) | (~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)) | (~halts2(f5(W), f5(W))))) | (program(c2) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1))))),
% 0.50/0.60 inference(monotonicity,[status(thm)],[427])).
% 0.50/0.60 tff(429,plain,
% 0.50/0.60 (((~![W: $i] : (program(c2) | (~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)) | (~halts2(f5(W), f5(W))))) | (program(c2) | (~program(c1)) | (~halts3(c1, f5(c1), f5(c1))) | (~outputs(c1, good)) | (~halts2(f5(c1), f5(c1))))) <=> ((~![W: $i] : (program(c2) | (~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)) | (~halts2(f5(W), f5(W))))) | program(c2) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)))),
% 0.50/0.60 inference(transitivity,[status(thm)],[428, 426])).
% 0.50/0.60 tff(430,plain,
% 0.50/0.60 ((~![W: $i] : (program(c2) | (~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)) | (~halts2(f5(W), f5(W))))) | (program(c2) | (~program(c1)) | (~halts3(c1, f5(c1), f5(c1))) | (~outputs(c1, good)) | (~halts2(f5(c1), f5(c1))))),
% 0.50/0.60 inference(quant_inst,[status(thm)],[])).
% 0.50/0.60 tff(431,plain,
% 0.50/0.60 ((~![W: $i] : (program(c2) | (~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)) | (~halts2(f5(W), f5(W))))) | program(c2) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[430, 429])).
% 0.50/0.60 tff(432,plain,
% 0.50/0.60 (program(c2) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1)))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[431, 425, 48])).
% 0.50/0.60 tff(433,plain,
% 0.50/0.60 (~outputs(c1, good)),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[432, 322, 320, 415])).
% 0.50/0.60 tff(434,plain,
% 0.50/0.60 (^[W: $i, Z: $i, Y: $i] : refl(((~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | outputs(W, good) | (~decides(W, f4(W), f3(W)))) <=> ((~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | outputs(W, good) | (~decides(W, f4(W), f3(W)))))),
% 0.50/0.60 inference(bind,[status(th)],[])).
% 0.50/0.60 tff(435,plain,
% 0.50/0.60 (![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | outputs(W, good) | (~decides(W, f4(W), f3(W)))) <=> ![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | outputs(W, good) | (~decides(W, f4(W), f3(W))))),
% 0.50/0.60 inference(quant_intro,[status(thm)],[434])).
% 0.50/0.60 tff(436,plain,
% 0.50/0.60 (![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | outputs(W, good) | (~decides(W, f4(W), f3(W)))) <=> ![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | outputs(W, good) | (~decides(W, f4(W), f3(W))))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(437,plain,
% 0.50/0.60 (^[W: $i, Z: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~program(W)) | (~decides(W, f4(W), f3(W)))) | (~program(Y))) <=> ((~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))), (((((~program(W)) | (~decides(W, f4(W), f3(W)))) | (~program(Y))) | (~halts2(Y, Z))) <=> (((~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W)))) | (~halts2(Y, Z))))), rewrite((((~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W)))) | (~halts2(Y, Z))) <=> ((~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))), (((((~program(W)) | (~decides(W, f4(W), f3(W)))) | (~program(Y))) | (~halts2(Y, Z))) <=> ((~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W)))))), ((((((~program(W)) | (~decides(W, f4(W), f3(W)))) | (~program(Y))) | (~halts2(Y, Z))) | outputs(W, good)) <=> (((~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W)))) | outputs(W, good)))), rewrite((((~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W)))) | outputs(W, good)) <=> ((~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | outputs(W, good) | (~decides(W, f4(W), f3(W))))), ((((((~program(W)) | (~decides(W, f4(W), f3(W)))) | (~program(Y))) | (~halts2(Y, Z))) | outputs(W, good)) <=> ((~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | outputs(W, good) | (~decides(W, f4(W), f3(W))))))),
% 0.50/0.60 inference(bind,[status(th)],[])).
% 0.50/0.60 tff(438,plain,
% 0.50/0.60 (![W: $i, Z: $i, Y: $i] : (((((~program(W)) | (~decides(W, f4(W), f3(W)))) | (~program(Y))) | (~halts2(Y, Z))) | outputs(W, good)) <=> ![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | outputs(W, good) | (~decides(W, f4(W), f3(W))))),
% 0.50/0.60 inference(quant_intro,[status(thm)],[437])).
% 0.50/0.60 tff(439,axiom,(![W: $i, Z: $i, Y: $i] : (((((~program(W)) | (~decides(W, f4(W), f3(W)))) | (~program(Y))) | (~halts2(Y, Z))) | outputs(W, good))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_2_6')).
% 0.50/0.60 tff(440,plain,
% 0.50/0.60 (![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | outputs(W, good) | (~decides(W, f4(W), f3(W))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[439, 438])).
% 0.50/0.60 tff(441,plain,
% 0.50/0.60 (![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | outputs(W, good) | (~decides(W, f4(W), f3(W))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[440, 436])).
% 0.50/0.60 tff(442,plain,(
% 0.50/0.60 ![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | outputs(W, good) | (~decides(W, f4(W), f3(W))))),
% 0.50/0.60 inference(skolemize,[status(sab)],[441])).
% 0.50/0.60 tff(443,plain,
% 0.50/0.60 (![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | outputs(W, good) | (~decides(W, f4(W), f3(W))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[442, 435])).
% 0.50/0.60 tff(444,plain,
% 0.50/0.60 (((~![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | outputs(W, good) | (~decides(W, f4(W), f3(W))))) | (outputs(c1, good) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | (~program(f5(c1))) | (~decides(c1, f4(c1), f3(c1))))) <=> ((~![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | outputs(W, good) | (~decides(W, f4(W), f3(W))))) | outputs(c1, good) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | (~program(f5(c1))) | (~decides(c1, f4(c1), f3(c1))))),
% 0.53/0.60 inference(rewrite,[status(thm)],[])).
% 0.53/0.60 tff(445,plain,
% 0.53/0.60 (((~halts2(f5(c1), f5(c1))) | (~program(f5(c1))) | (~program(c1)) | outputs(c1, good) | (~decides(c1, f4(c1), f3(c1)))) <=> (outputs(c1, good) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | (~program(f5(c1))) | (~decides(c1, f4(c1), f3(c1))))),
% 0.53/0.60 inference(rewrite,[status(thm)],[])).
% 0.53/0.60 tff(446,plain,
% 0.53/0.60 (((~![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | outputs(W, good) | (~decides(W, f4(W), f3(W))))) | ((~halts2(f5(c1), f5(c1))) | (~program(f5(c1))) | (~program(c1)) | outputs(c1, good) | (~decides(c1, f4(c1), f3(c1))))) <=> ((~![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | outputs(W, good) | (~decides(W, f4(W), f3(W))))) | (outputs(c1, good) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | (~program(f5(c1))) | (~decides(c1, f4(c1), f3(c1)))))),
% 0.53/0.60 inference(monotonicity,[status(thm)],[445])).
% 0.53/0.60 tff(447,plain,
% 0.53/0.60 (((~![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | outputs(W, good) | (~decides(W, f4(W), f3(W))))) | ((~halts2(f5(c1), f5(c1))) | (~program(f5(c1))) | (~program(c1)) | outputs(c1, good) | (~decides(c1, f4(c1), f3(c1))))) <=> ((~![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | outputs(W, good) | (~decides(W, f4(W), f3(W))))) | outputs(c1, good) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | (~program(f5(c1))) | (~decides(c1, f4(c1), f3(c1))))),
% 0.53/0.60 inference(transitivity,[status(thm)],[446, 444])).
% 0.53/0.60 tff(448,plain,
% 0.53/0.60 ((~![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | outputs(W, good) | (~decides(W, f4(W), f3(W))))) | ((~halts2(f5(c1), f5(c1))) | (~program(f5(c1))) | (~program(c1)) | outputs(c1, good) | (~decides(c1, f4(c1), f3(c1))))),
% 0.53/0.60 inference(quant_inst,[status(thm)],[])).
% 0.53/0.60 tff(449,plain,
% 0.53/0.60 ((~![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | (~program(W)) | outputs(W, good) | (~decides(W, f4(W), f3(W))))) | outputs(c1, good) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | (~program(f5(c1))) | (~decides(c1, f4(c1), f3(c1)))),
% 0.53/0.60 inference(modus_ponens,[status(thm)],[448, 447])).
% 0.53/0.60 tff(450,plain,
% 0.53/0.60 (~decides(c1, f4(c1), f3(c1))),
% 0.53/0.60 inference(unit_resolution,[status(thm)],[449, 443, 48, 433, 322, 318])).
% 0.53/0.60 tff(451,plain,
% 0.53/0.60 (~program(f4(c1))),
% 0.53/0.60 inference(unit_resolution,[status(thm)],[373, 370, 6, 321, 450])).
% 0.53/0.60 tff(452,plain,
% 0.53/0.60 (^[W: $i, Z: $i, Y: $i] : refl(((~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, good)) <=> ((~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, good)))),
% 0.53/0.60 inference(bind,[status(th)],[])).
% 0.53/0.60 tff(453,plain,
% 0.53/0.60 (![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, good)) <=> ![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, good))),
% 0.53/0.60 inference(quant_intro,[status(thm)],[452])).
% 0.53/0.60 tff(454,plain,
% 0.53/0.60 (![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, good)) <=> ![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, good))),
% 0.53/0.60 inference(rewrite,[status(thm)],[])).
% 0.53/0.60 tff(455,plain,
% 0.53/0.60 (^[W: $i, Z: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~program(W)) | program(f4(W))) | (~program(Y))) <=> ((~program(Y)) | program(f4(W)) | (~program(W)))), (((((~program(W)) | program(f4(W))) | (~program(Y))) | (~halts2(Y, Z))) <=> (((~program(Y)) | program(f4(W)) | (~program(W))) | (~halts2(Y, Z))))), rewrite((((~program(Y)) | program(f4(W)) | (~program(W))) | (~halts2(Y, Z))) <=> ((~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)))), (((((~program(W)) | program(f4(W))) | (~program(Y))) | (~halts2(Y, Z))) <=> ((~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W))))), ((((((~program(W)) | program(f4(W))) | (~program(Y))) | (~halts2(Y, Z))) | outputs(W, good)) <=> (((~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W))) | outputs(W, good)))), rewrite((((~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W))) | outputs(W, good)) <=> ((~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, good))), ((((((~program(W)) | program(f4(W))) | (~program(Y))) | (~halts2(Y, Z))) | outputs(W, good)) <=> ((~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, good))))),
% 0.53/0.61 inference(bind,[status(th)],[])).
% 0.53/0.61 tff(456,plain,
% 0.53/0.61 (![W: $i, Z: $i, Y: $i] : (((((~program(W)) | program(f4(W))) | (~program(Y))) | (~halts2(Y, Z))) | outputs(W, good)) <=> ![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, good))),
% 0.53/0.61 inference(quant_intro,[status(thm)],[455])).
% 0.53/0.61 tff(457,axiom,(![W: $i, Z: $i, Y: $i] : (((((~program(W)) | program(f4(W))) | (~program(Y))) | (~halts2(Y, Z))) | outputs(W, good))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_2_2')).
% 0.53/0.61 tff(458,plain,
% 0.53/0.61 (![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, good))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[457, 456])).
% 0.53/0.61 tff(459,plain,
% 0.53/0.61 (![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, good))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[458, 454])).
% 0.53/0.61 tff(460,plain,(
% 0.53/0.61 ![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, good))),
% 0.53/0.61 inference(skolemize,[status(sab)],[459])).
% 0.53/0.61 tff(461,plain,
% 0.53/0.61 (![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, good))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[460, 453])).
% 0.53/0.61 tff(462,plain,
% 0.53/0.61 (((~![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, good))) | (outputs(c1, good) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | (~program(f5(c1))) | program(f4(c1)))) <=> ((~![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, good))) | outputs(c1, good) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | (~program(f5(c1))) | program(f4(c1)))),
% 0.53/0.61 inference(rewrite,[status(thm)],[])).
% 0.53/0.61 tff(463,plain,
% 0.53/0.61 (((~halts2(f5(c1), f5(c1))) | (~program(f5(c1))) | program(f4(c1)) | (~program(c1)) | outputs(c1, good)) <=> (outputs(c1, good) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | (~program(f5(c1))) | program(f4(c1)))),
% 0.53/0.61 inference(rewrite,[status(thm)],[])).
% 0.53/0.61 tff(464,plain,
% 0.53/0.61 (((~![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, good))) | ((~halts2(f5(c1), f5(c1))) | (~program(f5(c1))) | program(f4(c1)) | (~program(c1)) | outputs(c1, good))) <=> ((~![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, good))) | (outputs(c1, good) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | (~program(f5(c1))) | program(f4(c1))))),
% 0.53/0.61 inference(monotonicity,[status(thm)],[463])).
% 0.53/0.61 tff(465,plain,
% 0.53/0.61 (((~![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, good))) | ((~halts2(f5(c1), f5(c1))) | (~program(f5(c1))) | program(f4(c1)) | (~program(c1)) | outputs(c1, good))) <=> ((~![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, good))) | outputs(c1, good) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | (~program(f5(c1))) | program(f4(c1)))),
% 0.53/0.61 inference(transitivity,[status(thm)],[464, 462])).
% 0.53/0.61 tff(466,plain,
% 0.53/0.61 ((~![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, good))) | ((~halts2(f5(c1), f5(c1))) | (~program(f5(c1))) | program(f4(c1)) | (~program(c1)) | outputs(c1, good))),
% 0.53/0.61 inference(quant_inst,[status(thm)],[])).
% 0.53/0.61 tff(467,plain,
% 0.53/0.61 ((~![W: $i, Z: $i, Y: $i] : ((~halts2(Y, Z)) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, good))) | outputs(c1, good) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | (~program(f5(c1))) | program(f4(c1))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[466, 465])).
% 0.53/0.61 tff(468,plain,
% 0.53/0.61 ($false),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[467, 461, 48, 433, 322, 318, 451])).
% 0.53/0.61 tff(469,plain,((~halts2(f5(c1), f5(c1))) | program(f2(c4)) | program(c2)), inference(lemma,lemma(discharge,[]))).
% 0.53/0.61 tff(470,plain,
% 0.53/0.61 (~halts2(f5(c1), f5(c1))),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[469, 321, 320])).
% 0.53/0.61 tff(471,plain,
% 0.53/0.61 (^[W: $i] : refl((program(c2) | (~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) <=> (program(c2) | (~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))))),
% 0.53/0.61 inference(bind,[status(th)],[])).
% 0.53/0.61 tff(472,plain,
% 0.53/0.61 (![W: $i] : (program(c2) | (~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) <=> ![W: $i] : (program(c2) | (~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.53/0.61 inference(quant_intro,[status(thm)],[471])).
% 0.53/0.61 tff(473,plain,
% 0.53/0.61 (![W: $i] : (program(c2) | (~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) <=> ![W: $i] : (program(c2) | (~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.53/0.61 inference(rewrite,[status(thm)],[])).
% 0.53/0.61 tff(474,plain,
% 0.53/0.61 (^[W: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) <=> ((~program(W)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))), (((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) <=> (((~program(W)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | (~outputs(W, bad))))), rewrite((((~program(W)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | (~outputs(W, bad))) <=> ((~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))), (((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) <=> ((~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))))), ((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | program(c2)) <=> (((~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | program(c2)))), rewrite((((~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | program(c2)) <=> (program(c2) | (~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))), ((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | program(c2)) <=> (program(c2) | (~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))))),
% 0.53/0.61 inference(bind,[status(th)],[])).
% 0.53/0.61 tff(475,plain,
% 0.53/0.61 (![W: $i] : (((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | program(c2)) <=> ![W: $i] : (program(c2) | (~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.53/0.61 inference(quant_intro,[status(thm)],[474])).
% 0.53/0.61 tff(476,axiom,(![W: $i] : (((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | program(c2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_3_6')).
% 0.53/0.61 tff(477,plain,
% 0.53/0.61 (![W: $i] : (program(c2) | (~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[476, 475])).
% 0.53/0.61 tff(478,plain,
% 0.53/0.61 (![W: $i] : (program(c2) | (~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[477, 473])).
% 0.53/0.61 tff(479,plain,(
% 0.53/0.61 ![W: $i] : (program(c2) | (~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.53/0.61 inference(skolemize,[status(sab)],[478])).
% 0.53/0.61 tff(480,plain,
% 0.53/0.61 (![W: $i] : (program(c2) | (~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[479, 472])).
% 0.53/0.61 tff(481,plain,
% 0.53/0.61 (((~![W: $i] : (program(c2) | (~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | (program(c2) | (~program(c1)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)))) <=> ((~![W: $i] : (program(c2) | (~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | program(c2) | (~program(c1)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)))),
% 0.53/0.61 inference(rewrite,[status(thm)],[])).
% 0.53/0.61 tff(482,plain,
% 0.53/0.61 ((~![W: $i] : (program(c2) | (~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | (program(c2) | (~program(c1)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)))),
% 0.53/0.61 inference(quant_inst,[status(thm)],[])).
% 0.53/0.61 tff(483,plain,
% 0.53/0.61 ((~![W: $i] : (program(c2) | (~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | program(c2) | (~program(c1)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[482, 481])).
% 0.53/0.61 tff(484,plain,
% 0.53/0.61 (program(c2) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1))),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[483, 480, 48])).
% 0.53/0.61 tff(485,plain,
% 0.53/0.61 (~outputs(c1, bad)),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[484, 470, 320, 415])).
% 0.53/0.61 tff(486,plain,
% 0.53/0.61 (^[W: $i, Z: $i, Y: $i] : refl((halts2(Y, Z) | (~program(Y)) | (~program(W)) | outputs(W, bad) | (~decides(W, f4(W), f3(W)))) <=> (halts2(Y, Z) | (~program(Y)) | (~program(W)) | outputs(W, bad) | (~decides(W, f4(W), f3(W)))))),
% 0.53/0.61 inference(bind,[status(th)],[])).
% 0.53/0.61 tff(487,plain,
% 0.53/0.61 (![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | (~program(W)) | outputs(W, bad) | (~decides(W, f4(W), f3(W)))) <=> ![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | (~program(W)) | outputs(W, bad) | (~decides(W, f4(W), f3(W))))),
% 0.53/0.61 inference(quant_intro,[status(thm)],[486])).
% 0.53/0.61 tff(488,plain,
% 0.53/0.61 (![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | (~program(W)) | outputs(W, bad) | (~decides(W, f4(W), f3(W)))) <=> ![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | (~program(W)) | outputs(W, bad) | (~decides(W, f4(W), f3(W))))),
% 0.53/0.61 inference(rewrite,[status(thm)],[])).
% 0.53/0.61 tff(489,plain,
% 0.53/0.61 (^[W: $i, Z: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~program(W)) | (~decides(W, f4(W), f3(W)))) | (~program(Y))) <=> ((~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))), (((((~program(W)) | (~decides(W, f4(W), f3(W)))) | (~program(Y))) | halts2(Y, Z)) <=> (((~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W)))) | halts2(Y, Z)))), rewrite((((~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W)))) | halts2(Y, Z)) <=> (halts2(Y, Z) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W))))), (((((~program(W)) | (~decides(W, f4(W), f3(W)))) | (~program(Y))) | halts2(Y, Z)) <=> (halts2(Y, Z) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W)))))), ((((((~program(W)) | (~decides(W, f4(W), f3(W)))) | (~program(Y))) | halts2(Y, Z)) | outputs(W, bad)) <=> ((halts2(Y, Z) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W)))) | outputs(W, bad)))), rewrite(((halts2(Y, Z) | (~program(Y)) | (~program(W)) | (~decides(W, f4(W), f3(W)))) | outputs(W, bad)) <=> (halts2(Y, Z) | (~program(Y)) | (~program(W)) | outputs(W, bad) | (~decides(W, f4(W), f3(W))))), ((((((~program(W)) | (~decides(W, f4(W), f3(W)))) | (~program(Y))) | halts2(Y, Z)) | outputs(W, bad)) <=> (halts2(Y, Z) | (~program(Y)) | (~program(W)) | outputs(W, bad) | (~decides(W, f4(W), f3(W))))))),
% 0.53/0.61 inference(bind,[status(th)],[])).
% 0.53/0.61 tff(490,plain,
% 0.53/0.61 (![W: $i, Z: $i, Y: $i] : (((((~program(W)) | (~decides(W, f4(W), f3(W)))) | (~program(Y))) | halts2(Y, Z)) | outputs(W, bad)) <=> ![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | (~program(W)) | outputs(W, bad) | (~decides(W, f4(W), f3(W))))),
% 0.53/0.61 inference(quant_intro,[status(thm)],[489])).
% 0.53/0.61 tff(491,axiom,(![W: $i, Z: $i, Y: $i] : (((((~program(W)) | (~decides(W, f4(W), f3(W)))) | (~program(Y))) | halts2(Y, Z)) | outputs(W, bad))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_2_8')).
% 0.53/0.62 tff(492,plain,
% 0.53/0.62 (![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | (~program(W)) | outputs(W, bad) | (~decides(W, f4(W), f3(W))))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[491, 490])).
% 0.53/0.62 tff(493,plain,
% 0.53/0.62 (![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | (~program(W)) | outputs(W, bad) | (~decides(W, f4(W), f3(W))))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[492, 488])).
% 0.53/0.62 tff(494,plain,(
% 0.53/0.62 ![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | (~program(W)) | outputs(W, bad) | (~decides(W, f4(W), f3(W))))),
% 0.53/0.62 inference(skolemize,[status(sab)],[493])).
% 0.53/0.62 tff(495,plain,
% 0.53/0.62 (![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | (~program(W)) | outputs(W, bad) | (~decides(W, f4(W), f3(W))))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[494, 487])).
% 0.53/0.62 tff(496,plain,
% 0.53/0.62 (((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | (~program(W)) | outputs(W, bad) | (~decides(W, f4(W), f3(W))))) | (outputs(c1, bad) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(f5(c1))) | (~decides(c1, f4(c1), f3(c1))))) <=> ((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | (~program(W)) | outputs(W, bad) | (~decides(W, f4(W), f3(W))))) | outputs(c1, bad) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(f5(c1))) | (~decides(c1, f4(c1), f3(c1))))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(497,plain,
% 0.53/0.62 ((halts2(f5(c1), f5(c1)) | (~program(f5(c1))) | (~program(c1)) | outputs(c1, bad) | (~decides(c1, f4(c1), f3(c1)))) <=> (outputs(c1, bad) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(f5(c1))) | (~decides(c1, f4(c1), f3(c1))))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(498,plain,
% 0.53/0.62 (((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | (~program(W)) | outputs(W, bad) | (~decides(W, f4(W), f3(W))))) | (halts2(f5(c1), f5(c1)) | (~program(f5(c1))) | (~program(c1)) | outputs(c1, bad) | (~decides(c1, f4(c1), f3(c1))))) <=> ((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | (~program(W)) | outputs(W, bad) | (~decides(W, f4(W), f3(W))))) | (outputs(c1, bad) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(f5(c1))) | (~decides(c1, f4(c1), f3(c1)))))),
% 0.53/0.62 inference(monotonicity,[status(thm)],[497])).
% 0.53/0.62 tff(499,plain,
% 0.53/0.62 (((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | (~program(W)) | outputs(W, bad) | (~decides(W, f4(W), f3(W))))) | (halts2(f5(c1), f5(c1)) | (~program(f5(c1))) | (~program(c1)) | outputs(c1, bad) | (~decides(c1, f4(c1), f3(c1))))) <=> ((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | (~program(W)) | outputs(W, bad) | (~decides(W, f4(W), f3(W))))) | outputs(c1, bad) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(f5(c1))) | (~decides(c1, f4(c1), f3(c1))))),
% 0.53/0.62 inference(transitivity,[status(thm)],[498, 496])).
% 0.53/0.62 tff(500,plain,
% 0.53/0.62 ((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | (~program(W)) | outputs(W, bad) | (~decides(W, f4(W), f3(W))))) | (halts2(f5(c1), f5(c1)) | (~program(f5(c1))) | (~program(c1)) | outputs(c1, bad) | (~decides(c1, f4(c1), f3(c1))))),
% 0.53/0.62 inference(quant_inst,[status(thm)],[])).
% 0.53/0.62 tff(501,plain,
% 0.53/0.62 ((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | (~program(W)) | outputs(W, bad) | (~decides(W, f4(W), f3(W))))) | outputs(c1, bad) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(f5(c1))) | (~decides(c1, f4(c1), f3(c1)))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[500, 499])).
% 0.53/0.62 tff(502,plain,
% 0.53/0.62 (~decides(c1, f4(c1), f3(c1))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[501, 495, 48, 485, 470, 318])).
% 0.53/0.62 tff(503,plain,
% 0.53/0.62 (~program(f4(c1))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[373, 370, 6, 321, 502])).
% 0.53/0.62 tff(504,plain,
% 0.53/0.62 (^[W: $i, Z: $i, Y: $i] : refl((halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, bad)) <=> (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, bad)))),
% 0.53/0.62 inference(bind,[status(th)],[])).
% 0.53/0.62 tff(505,plain,
% 0.53/0.62 (![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, bad)) <=> ![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, bad))),
% 0.53/0.62 inference(quant_intro,[status(thm)],[504])).
% 0.53/0.62 tff(506,plain,
% 0.53/0.62 (![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, bad)) <=> ![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, bad))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(507,plain,
% 0.53/0.62 (^[W: $i, Z: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~program(W)) | program(f4(W))) | (~program(Y))) <=> ((~program(Y)) | program(f4(W)) | (~program(W)))), (((((~program(W)) | program(f4(W))) | (~program(Y))) | halts2(Y, Z)) <=> (((~program(Y)) | program(f4(W)) | (~program(W))) | halts2(Y, Z)))), rewrite((((~program(Y)) | program(f4(W)) | (~program(W))) | halts2(Y, Z)) <=> (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)))), (((((~program(W)) | program(f4(W))) | (~program(Y))) | halts2(Y, Z)) <=> (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W))))), ((((((~program(W)) | program(f4(W))) | (~program(Y))) | halts2(Y, Z)) | outputs(W, bad)) <=> ((halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W))) | outputs(W, bad)))), rewrite(((halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W))) | outputs(W, bad)) <=> (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, bad))), ((((((~program(W)) | program(f4(W))) | (~program(Y))) | halts2(Y, Z)) | outputs(W, bad)) <=> (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, bad))))),
% 0.53/0.62 inference(bind,[status(th)],[])).
% 0.53/0.62 tff(508,plain,
% 0.53/0.62 (![W: $i, Z: $i, Y: $i] : (((((~program(W)) | program(f4(W))) | (~program(Y))) | halts2(Y, Z)) | outputs(W, bad)) <=> ![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, bad))),
% 0.53/0.62 inference(quant_intro,[status(thm)],[507])).
% 0.53/0.62 tff(509,axiom,(![W: $i, Z: $i, Y: $i] : (((((~program(W)) | program(f4(W))) | (~program(Y))) | halts2(Y, Z)) | outputs(W, bad))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_2_4')).
% 0.53/0.62 tff(510,plain,
% 0.53/0.62 (![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, bad))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[509, 508])).
% 0.53/0.62 tff(511,plain,
% 0.53/0.62 (![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, bad))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[510, 506])).
% 0.53/0.62 tff(512,plain,(
% 0.53/0.62 ![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, bad))),
% 0.53/0.62 inference(skolemize,[status(sab)],[511])).
% 0.53/0.62 tff(513,plain,
% 0.53/0.62 (![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, bad))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[512, 505])).
% 0.53/0.62 tff(514,plain,
% 0.53/0.62 (((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, bad))) | (outputs(c1, bad) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(f5(c1))) | program(f4(c1)))) <=> ((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, bad))) | outputs(c1, bad) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(f5(c1))) | program(f4(c1)))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(515,plain,
% 0.53/0.62 ((halts2(f5(c1), f5(c1)) | (~program(f5(c1))) | program(f4(c1)) | (~program(c1)) | outputs(c1, bad)) <=> (outputs(c1, bad) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(f5(c1))) | program(f4(c1)))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(516,plain,
% 0.53/0.62 (((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, bad))) | (halts2(f5(c1), f5(c1)) | (~program(f5(c1))) | program(f4(c1)) | (~program(c1)) | outputs(c1, bad))) <=> ((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, bad))) | (outputs(c1, bad) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(f5(c1))) | program(f4(c1))))),
% 0.53/0.62 inference(monotonicity,[status(thm)],[515])).
% 0.53/0.62 tff(517,plain,
% 0.53/0.62 (((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, bad))) | (halts2(f5(c1), f5(c1)) | (~program(f5(c1))) | program(f4(c1)) | (~program(c1)) | outputs(c1, bad))) <=> ((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, bad))) | outputs(c1, bad) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(f5(c1))) | program(f4(c1)))),
% 0.53/0.62 inference(transitivity,[status(thm)],[516, 514])).
% 0.53/0.62 tff(518,plain,
% 0.53/0.62 ((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, bad))) | (halts2(f5(c1), f5(c1)) | (~program(f5(c1))) | program(f4(c1)) | (~program(c1)) | outputs(c1, bad))),
% 0.53/0.62 inference(quant_inst,[status(thm)],[])).
% 0.53/0.62 tff(519,plain,
% 0.53/0.62 ((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, bad))) | outputs(c1, bad) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(f5(c1))) | program(f4(c1))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[518, 517])).
% 0.53/0.62 tff(520,plain,
% 0.53/0.62 ($false),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[519, 513, 48, 485, 470, 318, 503])).
% 0.53/0.62 tff(521,plain,(program(f2(c4)) | program(c2)), inference(lemma,lemma(discharge,[]))).
% 0.53/0.62 tff(522,plain,
% 0.53/0.62 (program(f2(c4))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[521, 320])).
% 0.53/0.62 tff(523,assumption,(~decides(c4, f2(c4), f1(c4))), introduced(assumption)).
% 0.53/0.62 tff(524,assumption,(program(f2(c4))), introduced(assumption)).
% 0.53/0.62 tff(525,plain,
% 0.53/0.62 ($false),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[46, 43, 524, 523])).
% 0.53/0.62 tff(526,plain,(decides(c4, f2(c4), f1(c4)) | (~program(f2(c4)))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.62 tff(527,plain,
% 0.53/0.62 (decides(c4, f2(c4), f1(c4))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[526, 522])).
% 0.53/0.62 tff(528,assumption,(decides(c4, f2(c4), f1(c4))), introduced(assumption)).
% 0.53/0.62 tff(529,plain,
% 0.53/0.62 (halts2(f5(c1), f5(c1)) | program(f4(c1))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[340, 334, 48, 324, 318])).
% 0.53/0.62 tff(530,plain,
% 0.53/0.62 (program(f4(c1))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[529, 319])).
% 0.53/0.62 tff(531,plain,
% 0.53/0.62 (halts2(f5(c1), f5(c1)) | (~decides(c1, f4(c1), f3(c1)))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[358, 352, 48, 324, 318])).
% 0.53/0.62 tff(532,plain,
% 0.53/0.62 (~decides(c1, f4(c1), f3(c1))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[531, 319])).
% 0.53/0.62 tff(533,plain,
% 0.53/0.62 (^[Z: $i, Y: $i, X: $i] : refl(((~algorithm(X)) | (~decides(X, f2(X), f1(X))) | decides(c1, Y, Z) | (~program(Y))) <=> ((~algorithm(X)) | (~decides(X, f2(X), f1(X))) | decides(c1, Y, Z) | (~program(Y))))),
% 0.53/0.62 inference(bind,[status(th)],[])).
% 0.53/0.62 tff(534,plain,
% 0.53/0.62 (![Z: $i, Y: $i, X: $i] : ((~algorithm(X)) | (~decides(X, f2(X), f1(X))) | decides(c1, Y, Z) | (~program(Y))) <=> ![Z: $i, Y: $i, X: $i] : ((~algorithm(X)) | (~decides(X, f2(X), f1(X))) | decides(c1, Y, Z) | (~program(Y)))),
% 0.53/0.62 inference(quant_intro,[status(thm)],[533])).
% 0.53/0.62 tff(535,plain,
% 0.53/0.62 (![Z: $i, Y: $i, X: $i] : ((~algorithm(X)) | (~decides(X, f2(X), f1(X))) | decides(c1, Y, Z) | (~program(Y))) <=> ![Z: $i, Y: $i, X: $i] : ((~algorithm(X)) | (~decides(X, f2(X), f1(X))) | decides(c1, Y, Z) | (~program(Y)))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(536,plain,
% 0.53/0.62 (^[Z: $i, Y: $i, X: $i] : trans(monotonicity(rewrite((((~algorithm(X)) | (~decides(X, f2(X), f1(X)))) | (~program(Y))) <=> ((~algorithm(X)) | (~decides(X, f2(X), f1(X))) | (~program(Y)))), (((((~algorithm(X)) | (~decides(X, f2(X), f1(X)))) | (~program(Y))) | decides(c1, Y, Z)) <=> (((~algorithm(X)) | (~decides(X, f2(X), f1(X))) | (~program(Y))) | decides(c1, Y, Z)))), rewrite((((~algorithm(X)) | (~decides(X, f2(X), f1(X))) | (~program(Y))) | decides(c1, Y, Z)) <=> ((~algorithm(X)) | (~decides(X, f2(X), f1(X))) | decides(c1, Y, Z) | (~program(Y)))), (((((~algorithm(X)) | (~decides(X, f2(X), f1(X)))) | (~program(Y))) | decides(c1, Y, Z)) <=> ((~algorithm(X)) | (~decides(X, f2(X), f1(X))) | decides(c1, Y, Z) | (~program(Y)))))),
% 0.53/0.62 inference(bind,[status(th)],[])).
% 0.53/0.62 tff(537,plain,
% 0.53/0.62 (![Z: $i, Y: $i, X: $i] : ((((~algorithm(X)) | (~decides(X, f2(X), f1(X)))) | (~program(Y))) | decides(c1, Y, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~algorithm(X)) | (~decides(X, f2(X), f1(X))) | decides(c1, Y, Z) | (~program(Y)))),
% 0.53/0.63 inference(quant_intro,[status(thm)],[536])).
% 0.53/0.63 tff(538,axiom,(![Z: $i, Y: $i, X: $i] : ((((~algorithm(X)) | (~decides(X, f2(X), f1(X)))) | (~program(Y))) | decides(c1, Y, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_1_4')).
% 0.53/0.63 tff(539,plain,
% 0.53/0.63 (![Z: $i, Y: $i, X: $i] : ((~algorithm(X)) | (~decides(X, f2(X), f1(X))) | decides(c1, Y, Z) | (~program(Y)))),
% 0.53/0.63 inference(modus_ponens,[status(thm)],[538, 537])).
% 0.53/0.63 tff(540,plain,
% 0.53/0.63 (![Z: $i, Y: $i, X: $i] : ((~algorithm(X)) | (~decides(X, f2(X), f1(X))) | decides(c1, Y, Z) | (~program(Y)))),
% 0.53/0.63 inference(modus_ponens,[status(thm)],[539, 535])).
% 0.53/0.63 tff(541,plain,(
% 0.53/0.63 ![Z: $i, Y: $i, X: $i] : ((~algorithm(X)) | (~decides(X, f2(X), f1(X))) | decides(c1, Y, Z) | (~program(Y)))),
% 0.53/0.63 inference(skolemize,[status(sab)],[540])).
% 0.53/0.63 tff(542,plain,
% 0.53/0.63 (![Z: $i, Y: $i, X: $i] : ((~algorithm(X)) | (~decides(X, f2(X), f1(X))) | decides(c1, Y, Z) | (~program(Y)))),
% 0.53/0.63 inference(modus_ponens,[status(thm)],[541, 534])).
% 0.53/0.63 tff(543,plain,
% 0.53/0.63 (((~![Z: $i, Y: $i, X: $i] : ((~algorithm(X)) | (~decides(X, f2(X), f1(X))) | decides(c1, Y, Z) | (~program(Y)))) | ((~algorithm(c4)) | (~decides(c4, f2(c4), f1(c4))) | decides(c1, f4(c1), f3(c1)) | (~program(f4(c1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~algorithm(X)) | (~decides(X, f2(X), f1(X))) | decides(c1, Y, Z) | (~program(Y)))) | (~algorithm(c4)) | (~decides(c4, f2(c4), f1(c4))) | decides(c1, f4(c1), f3(c1)) | (~program(f4(c1))))),
% 0.53/0.63 inference(rewrite,[status(thm)],[])).
% 0.53/0.63 tff(544,plain,
% 0.53/0.63 ((~![Z: $i, Y: $i, X: $i] : ((~algorithm(X)) | (~decides(X, f2(X), f1(X))) | decides(c1, Y, Z) | (~program(Y)))) | ((~algorithm(c4)) | (~decides(c4, f2(c4), f1(c4))) | decides(c1, f4(c1), f3(c1)) | (~program(f4(c1))))),
% 0.53/0.63 inference(quant_inst,[status(thm)],[])).
% 0.53/0.63 tff(545,plain,
% 0.53/0.63 ((~![Z: $i, Y: $i, X: $i] : ((~algorithm(X)) | (~decides(X, f2(X), f1(X))) | decides(c1, Y, Z) | (~program(Y)))) | (~algorithm(c4)) | (~decides(c4, f2(c4), f1(c4))) | decides(c1, f4(c1), f3(c1)) | (~program(f4(c1)))),
% 0.53/0.63 inference(modus_ponens,[status(thm)],[544, 543])).
% 0.53/0.63 tff(546,plain,
% 0.53/0.63 ($false),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[545, 542, 6, 528, 532, 530])).
% 0.53/0.63 tff(547,plain,(halts2(f5(c1), f5(c1)) | (~decides(c4, f2(c4), f1(c4))) | halts3(c1, f5(c1), f5(c1))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.63 tff(548,plain,
% 0.53/0.63 (halts2(f5(c1), f5(c1))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[547, 324, 528])).
% 0.53/0.63 tff(549,plain,
% 0.53/0.63 ((~halts2(f5(c1), f5(c1))) | program(f4(c1))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[392, 386, 48, 324, 318])).
% 0.53/0.63 tff(550,plain,
% 0.53/0.63 (program(f4(c1))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[549, 548])).
% 0.53/0.63 tff(551,plain,
% 0.53/0.63 ((~halts2(f5(c1), f5(c1))) | (~decides(c1, f4(c1), f3(c1)))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[410, 404, 48, 324, 318])).
% 0.53/0.63 tff(552,plain,
% 0.53/0.63 (~decides(c1, f4(c1), f3(c1))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[551, 548])).
% 0.53/0.63 tff(553,plain,
% 0.53/0.63 ($false),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[545, 542, 6, 528, 552, 550])).
% 0.53/0.63 tff(554,plain,(halts3(c1, f5(c1), f5(c1)) | (~decides(c4, f2(c4), f1(c4)))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.63 tff(555,plain,
% 0.53/0.63 (halts3(c1, f5(c1), f5(c1))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[554, 527])).
% 0.53/0.63 tff(556,plain,
% 0.53/0.63 (~outputs(c1, bad)),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[484, 319, 320, 555])).
% 0.53/0.63 tff(557,plain,
% 0.53/0.63 (~decides(c1, f4(c1), f3(c1))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[501, 495, 48, 556, 319, 318])).
% 0.53/0.63 tff(558,plain,
% 0.53/0.63 (~program(f4(c1))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[545, 542, 6, 527, 557])).
% 0.53/0.63 tff(559,plain,
% 0.53/0.63 ($false),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[519, 513, 48, 556, 319, 318, 558])).
% 0.53/0.63 tff(560,plain,(halts2(f5(c1), f5(c1)) | program(c2)), inference(lemma,lemma(discharge,[]))).
% 0.53/0.63 tff(561,plain,
% 0.53/0.63 (halts2(f5(c1), f5(c1))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[560, 320])).
% 0.53/0.63 tff(562,plain,
% 0.53/0.63 (~outputs(c1, good)),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[432, 561, 320, 555])).
% 0.53/0.63 tff(563,plain,
% 0.53/0.63 (~decides(c1, f4(c1), f3(c1))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[449, 443, 48, 562, 561, 318])).
% 0.53/0.63 tff(564,plain,
% 0.53/0.63 (~program(f4(c1))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[545, 542, 6, 527, 563])).
% 0.53/0.63 tff(565,plain,
% 0.53/0.63 ($false),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[467, 461, 48, 562, 561, 318, 564])).
% 0.53/0.63 tff(566,plain,(program(c2)), inference(lemma,lemma(discharge,[]))).
% 0.53/0.63 tff(567,assumption,(outputs(c1, bad)), introduced(assumption)).
% 0.53/0.63 tff(568,plain,
% 0.53/0.63 (program(f6(c2))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[83, 77, 67, 566])).
% 0.53/0.63 tff(569,plain,
% 0.53/0.63 (program(f2(c4))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[414, 324, 318])).
% 0.53/0.63 tff(570,plain,
% 0.53/0.63 (~decides(c4, f2(c4), f1(c4))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[554, 324])).
% 0.53/0.63 tff(571,plain,
% 0.53/0.63 ($false),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[526, 570, 569])).
% 0.53/0.63 tff(572,plain,(halts3(c1, f5(c1), f5(c1))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.63 tff(573,plain,
% 0.53/0.63 (^[W: $i, Y: $i] : refl(((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) <=> ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))))),
% 0.53/0.63 inference(bind,[status(th)],[])).
% 0.53/0.63 tff(574,plain,
% 0.53/0.63 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.53/0.63 inference(quant_intro,[status(thm)],[573])).
% 0.53/0.63 tff(575,plain,
% 0.53/0.63 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.53/0.63 inference(rewrite,[status(thm)],[])).
% 0.53/0.63 tff(576,plain,
% 0.53/0.63 (^[W: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) <=> ((~program(W)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))), (((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) <=> (((~program(W)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | (~outputs(W, bad))))), rewrite((((~program(W)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | (~outputs(W, bad))) <=> ((~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))), (((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) <=> ((~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))))), ((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) <=> (((~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | (~program(Y))))), rewrite((((~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | (~program(Y))) <=> ((~program(W)) | (~program(Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))), ((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) <=> ((~program(W)) | (~program(Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))))), (((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) | halts2(Y, Y)) <=> (((~program(W)) | (~program(Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | halts2(Y, Y)))), rewrite((((~program(W)) | (~program(Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | halts2(Y, Y)) <=> ((~program(W)) | (~program(Y)) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))), (((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) | halts2(Y, Y)) <=> ((~program(W)) | (~program(Y)) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))))), ((((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) | halts2(Y, Y)) | halts2(c2, Y)) <=> (((~program(W)) | (~program(Y)) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | halts2(c2, Y)))), rewrite((((~program(W)) | (~program(Y)) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | halts2(c2, Y)) <=> ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))), ((((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) | halts2(Y, Y)) | halts2(c2, Y)) <=> ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))))),
% 0.53/0.63 inference(bind,[status(th)],[])).
% 0.53/0.63 tff(577,plain,
% 0.53/0.63 (![W: $i, Y: $i] : (((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) | halts2(Y, Y)) | halts2(c2, Y)) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.53/0.63 inference(quant_intro,[status(thm)],[576])).
% 0.53/0.63 tff(578,axiom,(![W: $i, Y: $i] : (((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) | halts2(Y, Y)) | halts2(c2, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_3_9')).
% 0.53/0.63 tff(579,plain,
% 0.53/0.63 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.53/0.63 inference(modus_ponens,[status(thm)],[578, 577])).
% 0.53/0.63 tff(580,plain,
% 0.53/0.63 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.53/0.63 inference(modus_ponens,[status(thm)],[579, 575])).
% 0.53/0.63 tff(581,plain,(
% 0.53/0.63 ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.53/0.63 inference(skolemize,[status(sab)],[580])).
% 0.53/0.63 tff(582,plain,
% 0.53/0.63 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.53/0.63 inference(modus_ponens,[status(thm)],[581, 574])).
% 0.53/0.63 tff(583,plain,
% 0.53/0.63 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | ((~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(c2)) | halts2(c2, c2))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(c2)) | halts2(c2, c2))),
% 0.53/0.63 inference(rewrite,[status(thm)],[])).
% 0.53/0.63 tff(584,plain,
% 0.53/0.63 (((~program(c1)) | (~program(c2)) | halts2(c2, c2) | halts2(c2, c2) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1))) <=> ((~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(c2)) | halts2(c2, c2))),
% 0.53/0.63 inference(rewrite,[status(thm)],[])).
% 0.53/0.63 tff(585,plain,
% 0.53/0.63 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | ((~program(c1)) | (~program(c2)) | halts2(c2, c2) | halts2(c2, c2) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | ((~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(c2)) | halts2(c2, c2)))),
% 0.56/0.63 inference(monotonicity,[status(thm)],[584])).
% 0.56/0.63 tff(586,plain,
% 0.56/0.63 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | ((~program(c1)) | (~program(c2)) | halts2(c2, c2) | halts2(c2, c2) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(c2)) | halts2(c2, c2))),
% 0.56/0.63 inference(transitivity,[status(thm)],[585, 583])).
% 0.56/0.63 tff(587,plain,
% 0.56/0.63 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | ((~program(c1)) | (~program(c2)) | halts2(c2, c2) | halts2(c2, c2) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)))),
% 0.56/0.63 inference(quant_inst,[status(thm)],[])).
% 0.56/0.63 tff(588,plain,
% 0.56/0.63 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(c2)) | halts2(c2, c2)),
% 0.56/0.63 inference(modus_ponens,[status(thm)],[587, 586])).
% 0.56/0.63 tff(589,plain,
% 0.56/0.63 ((~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | halts2(c2, c2)),
% 0.56/0.63 inference(unit_resolution,[status(thm)],[588, 582, 48, 566])).
% 0.56/0.63 tff(590,plain,
% 0.56/0.63 (halts2(c2, c2)),
% 0.56/0.63 inference(unit_resolution,[status(thm)],[589, 567, 572, 319])).
% 0.56/0.63 tff(591,plain,
% 0.56/0.63 (^[W: $i, Y: $i] : refl(((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) <=> ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))))),
% 0.56/0.63 inference(bind,[status(th)],[])).
% 0.56/0.63 tff(592,plain,
% 0.56/0.63 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.56/0.63 inference(quant_intro,[status(thm)],[591])).
% 0.56/0.63 tff(593,plain,
% 0.56/0.63 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.56/0.63 inference(rewrite,[status(thm)],[])).
% 0.56/0.63 tff(594,plain,
% 0.56/0.63 (^[W: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) <=> ((~program(W)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))), (((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) <=> (((~program(W)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | (~outputs(W, bad))))), rewrite((((~program(W)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | (~outputs(W, bad))) <=> ((~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))), (((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) <=> ((~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))))), ((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) <=> (((~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | (~program(Y))))), rewrite((((~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | (~program(Y))) <=> ((~program(W)) | (~program(Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))), ((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) <=> ((~program(W)) | (~program(Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))))), (((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) | (~halts2(Y, Y))) <=> (((~program(W)) | (~program(Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | (~halts2(Y, Y))))), rewrite((((~program(W)) | (~program(Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | (~halts2(Y, Y))) <=> ((~program(W)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))), (((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) | (~halts2(Y, Y))) <=> ((~program(W)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))))), ((((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) | (~halts2(Y, Y))) | outputs(c2, good)) <=> (((~program(W)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | outputs(c2, good)))), rewrite((((~program(W)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | outputs(c2, good)) <=> ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))), ((((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) | (~halts2(Y, Y))) | outputs(c2, good)) <=> ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))))),
% 0.56/0.64 inference(bind,[status(th)],[])).
% 0.56/0.64 tff(595,plain,
% 0.56/0.64 (![W: $i, Y: $i] : (((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) | (~halts2(Y, Y))) | outputs(c2, good)) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.56/0.64 inference(quant_intro,[status(thm)],[594])).
% 0.56/0.64 tff(596,axiom,(![W: $i, Y: $i] : (((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) | (~halts2(Y, Y))) | outputs(c2, good))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_3_8')).
% 0.56/0.64 tff(597,plain,
% 0.56/0.64 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.56/0.64 inference(modus_ponens,[status(thm)],[596, 595])).
% 0.56/0.64 tff(598,plain,
% 0.56/0.64 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.56/0.64 inference(modus_ponens,[status(thm)],[597, 593])).
% 0.56/0.64 tff(599,plain,(
% 0.56/0.64 ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.56/0.64 inference(skolemize,[status(sab)],[598])).
% 0.56/0.64 tff(600,plain,
% 0.56/0.64 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.56/0.64 inference(modus_ponens,[status(thm)],[599, 592])).
% 0.56/0.64 tff(601,plain,
% 0.56/0.64 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | (outputs(c2, good) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(c2)) | (~halts2(c2, c2)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | outputs(c2, good) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(c2)) | (~halts2(c2, c2)))),
% 0.56/0.64 inference(rewrite,[status(thm)],[])).
% 0.56/0.64 tff(602,plain,
% 0.56/0.64 (((~program(c1)) | (~program(c2)) | outputs(c2, good) | (~halts2(c2, c2)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1))) <=> (outputs(c2, good) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(c2)) | (~halts2(c2, c2)))),
% 0.56/0.64 inference(rewrite,[status(thm)],[])).
% 0.56/0.64 tff(603,plain,
% 0.56/0.64 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | ((~program(c1)) | (~program(c2)) | outputs(c2, good) | (~halts2(c2, c2)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | (outputs(c2, good) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(c2)) | (~halts2(c2, c2))))),
% 0.56/0.64 inference(monotonicity,[status(thm)],[602])).
% 0.56/0.64 tff(604,plain,
% 0.56/0.64 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | ((~program(c1)) | (~program(c2)) | outputs(c2, good) | (~halts2(c2, c2)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | outputs(c2, good) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(c2)) | (~halts2(c2, c2)))),
% 0.56/0.64 inference(transitivity,[status(thm)],[603, 601])).
% 0.56/0.64 tff(605,plain,
% 0.56/0.64 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | ((~program(c1)) | (~program(c2)) | outputs(c2, good) | (~halts2(c2, c2)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)))),
% 0.56/0.64 inference(quant_inst,[status(thm)],[])).
% 0.56/0.64 tff(606,plain,
% 0.56/0.64 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | outputs(c2, good) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(c2)) | (~halts2(c2, c2))),
% 0.56/0.64 inference(modus_ponens,[status(thm)],[605, 604])).
% 0.56/0.64 tff(607,plain,
% 0.56/0.64 (outputs(c2, good) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~halts2(c2, c2))),
% 0.56/0.64 inference(unit_resolution,[status(thm)],[606, 600, 48, 566])).
% 0.56/0.64 tff(608,plain,
% 0.56/0.64 (outputs(c2, good)),
% 0.56/0.64 inference(unit_resolution,[status(thm)],[607, 590, 572, 319, 567])).
% 0.56/0.64 tff(609,plain,
% 0.56/0.64 (^[W: $i, Y: $i] : refl(((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) <=> ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))))),
% 0.56/0.64 inference(bind,[status(th)],[])).
% 0.56/0.64 tff(610,plain,
% 0.56/0.64 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.56/0.64 inference(quant_intro,[status(thm)],[609])).
% 0.56/0.64 tff(611,plain,
% 0.56/0.64 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.56/0.64 inference(rewrite,[status(thm)],[])).
% 0.56/0.64 tff(612,plain,
% 0.56/0.64 (^[W: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) <=> ((~program(W)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))), (((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) <=> (((~program(W)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | (~outputs(W, bad))))), rewrite((((~program(W)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | (~outputs(W, bad))) <=> ((~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))), (((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) <=> ((~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))))), ((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) <=> (((~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | (~program(Y))))), rewrite((((~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | (~program(Y))) <=> ((~program(W)) | (~program(Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))), ((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) <=> ((~program(W)) | (~program(Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))))), (((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) | halts2(Y, Y)) <=> (((~program(W)) | (~program(Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | halts2(Y, Y)))), rewrite((((~program(W)) | (~program(Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | halts2(Y, Y)) <=> ((~program(W)) | (~program(Y)) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))), (((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) | halts2(Y, Y)) <=> ((~program(W)) | (~program(Y)) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))))), ((((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) | halts2(Y, Y)) | outputs(c2, bad)) <=> (((~program(W)) | (~program(Y)) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | outputs(c2, bad)))), rewrite((((~program(W)) | (~program(Y)) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | outputs(c2, bad)) <=> ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))), ((((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) | halts2(Y, Y)) | outputs(c2, bad)) <=> ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))))),
% 0.56/0.64 inference(bind,[status(th)],[])).
% 0.56/0.64 tff(613,plain,
% 0.56/0.64 (![W: $i, Y: $i] : (((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) | halts2(Y, Y)) | outputs(c2, bad)) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.56/0.65 inference(quant_intro,[status(thm)],[612])).
% 0.56/0.65 tff(614,axiom,(![W: $i, Y: $i] : (((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) | halts2(Y, Y)) | outputs(c2, bad))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_3_10')).
% 0.56/0.65 tff(615,plain,
% 0.56/0.65 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.56/0.65 inference(modus_ponens,[status(thm)],[614, 613])).
% 0.56/0.65 tff(616,plain,
% 0.56/0.65 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.56/0.65 inference(modus_ponens,[status(thm)],[615, 611])).
% 0.56/0.65 tff(617,plain,(
% 0.56/0.65 ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.56/0.65 inference(skolemize,[status(sab)],[616])).
% 0.56/0.65 tff(618,plain,
% 0.56/0.65 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.56/0.65 inference(modus_ponens,[status(thm)],[617, 610])).
% 0.56/0.65 tff(619,plain,
% 0.56/0.65 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | (outputs(c2, bad) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(f5(c1))))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | outputs(c2, bad) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(f5(c1))))),
% 0.56/0.65 inference(rewrite,[status(thm)],[])).
% 0.56/0.65 tff(620,plain,
% 0.56/0.65 (((~program(c1)) | (~program(f5(c1))) | outputs(c2, bad) | halts2(f5(c1), f5(c1)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1))) <=> (outputs(c2, bad) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(f5(c1))))),
% 0.56/0.65 inference(rewrite,[status(thm)],[])).
% 0.56/0.65 tff(621,plain,
% 0.56/0.65 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | ((~program(c1)) | (~program(f5(c1))) | outputs(c2, bad) | halts2(f5(c1), f5(c1)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | (outputs(c2, bad) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(f5(c1)))))),
% 0.56/0.65 inference(monotonicity,[status(thm)],[620])).
% 0.56/0.65 tff(622,plain,
% 0.56/0.65 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | ((~program(c1)) | (~program(f5(c1))) | outputs(c2, bad) | halts2(f5(c1), f5(c1)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | outputs(c2, bad) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(f5(c1))))),
% 0.56/0.65 inference(transitivity,[status(thm)],[621, 619])).
% 0.56/0.65 tff(623,plain,
% 0.56/0.65 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | ((~program(c1)) | (~program(f5(c1))) | outputs(c2, bad) | halts2(f5(c1), f5(c1)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)))),
% 0.56/0.65 inference(quant_inst,[status(thm)],[])).
% 0.56/0.65 tff(624,plain,
% 0.56/0.65 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | outputs(c2, bad) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~program(c1)) | (~program(f5(c1)))),
% 0.56/0.65 inference(modus_ponens,[status(thm)],[623, 622])).
% 0.56/0.65 tff(625,plain,
% 0.56/0.65 (outputs(c2, bad) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1))),
% 0.56/0.65 inference(unit_resolution,[status(thm)],[624, 618, 48, 318])).
% 0.56/0.65 tff(626,plain,
% 0.56/0.65 (outputs(c2, bad)),
% 0.56/0.65 inference(unit_resolution,[status(thm)],[625, 567, 319, 572])).
% 0.56/0.65 tff(627,plain,
% 0.56/0.65 (program(c3) | (~outputs(c2, good)) | (~outputs(c2, bad)) | (~halts2(c2, f6(c2)))),
% 0.56/0.65 inference(unit_resolution,[status(thm)],[183, 177, 566])).
% 0.56/0.65 tff(628,plain,
% 0.56/0.65 (~halts2(c2, f6(c2))),
% 0.56/0.65 inference(unit_resolution,[status(thm)],[627, 67, 626, 608])).
% 0.56/0.65 tff(629,plain,
% 0.56/0.65 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | ((~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~program(c1)) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2))))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~program(c1)) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2))))),
% 0.56/0.65 inference(rewrite,[status(thm)],[])).
% 0.56/0.65 tff(630,plain,
% 0.56/0.65 (((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1))) <=> ((~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~program(c1)) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2))))),
% 0.56/0.65 inference(rewrite,[status(thm)],[])).
% 0.56/0.65 tff(631,plain,
% 0.56/0.65 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | ((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | ((~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~program(c1)) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2)))))),
% 0.56/0.65 inference(monotonicity,[status(thm)],[630])).
% 0.56/0.65 tff(632,plain,
% 0.56/0.65 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | ((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~program(c1)) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2))))),
% 0.56/0.65 inference(transitivity,[status(thm)],[631, 629])).
% 0.56/0.65 tff(633,plain,
% 0.56/0.65 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | ((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)))),
% 0.56/0.65 inference(quant_inst,[status(thm)],[])).
% 0.56/0.65 tff(634,plain,
% 0.56/0.65 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~program(c1)) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2)))),
% 0.56/0.65 inference(modus_ponens,[status(thm)],[633, 632])).
% 0.56/0.65 tff(635,plain,
% 0.56/0.65 (halts2(f6(c2), f6(c2))),
% 0.56/0.65 inference(unit_resolution,[status(thm)],[634, 582, 48, 567, 572, 319, 628, 568])).
% 0.56/0.65 tff(636,plain,
% 0.56/0.65 (^[W: $i, Y: $i] : refl(((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) <=> ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))))),
% 0.56/0.65 inference(bind,[status(th)],[])).
% 0.56/0.65 tff(637,plain,
% 0.56/0.65 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.56/0.65 inference(quant_intro,[status(thm)],[636])).
% 0.56/0.65 tff(638,plain,
% 0.56/0.65 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.56/0.65 inference(rewrite,[status(thm)],[])).
% 0.56/0.65 tff(639,plain,
% 0.56/0.65 (^[W: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) <=> ((~program(W)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))), (((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) <=> (((~program(W)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | (~outputs(W, bad))))), rewrite((((~program(W)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | (~outputs(W, bad))) <=> ((~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))), (((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) <=> ((~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))))), ((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) <=> (((~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | (~program(Y))))), rewrite((((~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | (~program(Y))) <=> ((~program(W)) | (~program(Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))), ((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) <=> ((~program(W)) | (~program(Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))))), (((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) | (~halts2(Y, Y))) <=> (((~program(W)) | (~program(Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | (~halts2(Y, Y))))), rewrite((((~program(W)) | (~program(Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | (~halts2(Y, Y))) <=> ((~program(W)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))), (((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) | (~halts2(Y, Y))) <=> ((~program(W)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))))), ((((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) | (~halts2(Y, Y))) | halts2(c2, Y)) <=> (((~program(W)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | halts2(c2, Y)))), rewrite((((~program(W)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W))) | halts2(c2, Y)) <=> ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))), ((((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) | (~halts2(Y, Y))) | halts2(c2, Y)) <=> ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))))),
% 0.56/0.66 inference(bind,[status(th)],[])).
% 0.56/0.66 tff(640,plain,
% 0.56/0.66 (![W: $i, Y: $i] : (((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) | (~halts2(Y, Y))) | halts2(c2, Y)) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.56/0.66 inference(quant_intro,[status(thm)],[639])).
% 0.56/0.66 tff(641,axiom,(![W: $i, Y: $i] : (((((((~program(W)) | halts2(f5(W), f5(W))) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, bad))) | (~program(Y))) | (~halts2(Y, Y))) | halts2(c2, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_3_7')).
% 0.56/0.66 tff(642,plain,
% 0.56/0.66 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.56/0.66 inference(modus_ponens,[status(thm)],[641, 640])).
% 0.56/0.66 tff(643,plain,
% 0.56/0.66 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.56/0.66 inference(modus_ponens,[status(thm)],[642, 638])).
% 0.56/0.66 tff(644,plain,(
% 0.56/0.66 ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.56/0.66 inference(skolemize,[status(sab)],[643])).
% 0.56/0.66 tff(645,plain,
% 0.56/0.66 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))),
% 0.56/0.66 inference(modus_ponens,[status(thm)],[644, 637])).
% 0.56/0.66 tff(646,plain,
% 0.56/0.66 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | ((~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~program(c1)) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~program(f6(c2))))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~program(c1)) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~program(f6(c2))))),
% 0.56/0.66 inference(rewrite,[status(thm)],[])).
% 0.56/0.66 tff(647,plain,
% 0.56/0.66 (((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1))) <=> ((~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~program(c1)) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~program(f6(c2))))),
% 0.56/0.66 inference(rewrite,[status(thm)],[])).
% 0.56/0.66 tff(648,plain,
% 0.56/0.66 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | ((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | ((~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~program(c1)) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~program(f6(c2)))))),
% 0.56/0.66 inference(monotonicity,[status(thm)],[647])).
% 0.56/0.66 tff(649,plain,
% 0.56/0.66 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | ((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~program(c1)) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~program(f6(c2))))),
% 0.56/0.66 inference(transitivity,[status(thm)],[648, 646])).
% 0.56/0.66 tff(650,plain,
% 0.56/0.66 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | ((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)))),
% 0.56/0.66 inference(quant_inst,[status(thm)],[])).
% 0.56/0.66 tff(651,plain,
% 0.56/0.66 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | halts2(f5(W), f5(W)))) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | halts2(f5(c1), f5(c1)) | (~program(c1)) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~program(f6(c2)))),
% 0.56/0.66 inference(modus_ponens,[status(thm)],[650, 649])).
% 0.56/0.66 tff(652,plain,
% 0.56/0.66 ($false),
% 0.56/0.66 inference(unit_resolution,[status(thm)],[651, 645, 48, 567, 572, 319, 628, 568, 635])).
% 0.56/0.66 tff(653,plain,(program(c3) | (~outputs(c1, bad)) | halts2(f5(c1), f5(c1))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.66 tff(654,plain,
% 0.56/0.66 (program(c3)),
% 0.56/0.66 inference(unit_resolution,[status(thm)],[653, 567, 319])).
% 0.56/0.66 tff(655,plain,
% 0.56/0.66 (program(f6(c2))),
% 0.56/0.66 inference(unit_resolution,[status(thm)],[244, 654, 566])).
% 0.56/0.66 tff(656,plain,
% 0.56/0.66 (~halts2(c2, f6(c2))),
% 0.56/0.66 inference(unit_resolution,[status(thm)],[289, 654, 566, 608, 626])).
% 0.56/0.66 tff(657,plain,
% 0.56/0.66 (halts2(f6(c2), f6(c2))),
% 0.56/0.66 inference(unit_resolution,[status(thm)],[634, 582, 48, 567, 572, 319, 656, 655])).
% 0.56/0.66 tff(658,plain,
% 0.56/0.66 ($false),
% 0.56/0.66 inference(unit_resolution,[status(thm)],[651, 645, 48, 567, 572, 319, 656, 655, 657])).
% 0.56/0.66 tff(659,plain,((~outputs(c1, bad)) | halts2(f5(c1), f5(c1))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.66 tff(660,plain,
% 0.56/0.66 (~outputs(c1, bad)),
% 0.56/0.66 inference(unit_resolution,[status(thm)],[659, 319])).
% 0.56/0.66 tff(661,plain,
% 0.56/0.66 (outputs(c1, bad) | (~decides(c1, f4(c1), f3(c1)))),
% 0.56/0.66 inference(unit_resolution,[status(thm)],[501, 495, 48, 319, 318])).
% 0.56/0.66 tff(662,plain,
% 0.56/0.66 (~decides(c1, f4(c1), f3(c1))),
% 0.56/0.66 inference(unit_resolution,[status(thm)],[661, 660])).
% 0.56/0.66 tff(663,assumption,(~outputs(c1, bad)), introduced(assumption)).
% 0.56/0.66 tff(664,plain,
% 0.56/0.66 (program(f4(c1))),
% 0.56/0.66 inference(unit_resolution,[status(thm)],[519, 513, 48, 663, 319, 318])).
% 0.56/0.66 tff(665,plain,
% 0.56/0.66 (~decides(c1, f4(c1), f3(c1))),
% 0.56/0.66 inference(unit_resolution,[status(thm)],[661, 663])).
% 0.56/0.66 tff(666,plain,
% 0.56/0.66 ($false),
% 0.56/0.66 inference(unit_resolution,[status(thm)],[373, 370, 6, 321, 665, 664])).
% 0.56/0.66 tff(667,plain,(outputs(c1, bad) | program(f2(c4)) | halts2(f5(c1), f5(c1))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.66 tff(668,plain,
% 0.56/0.66 (program(f2(c4))),
% 0.56/0.66 inference(unit_resolution,[status(thm)],[667, 660, 319])).
% 0.56/0.66 tff(669,plain,
% 0.56/0.66 (decides(c4, f2(c4), f1(c4))),
% 0.56/0.66 inference(unit_resolution,[status(thm)],[526, 668])).
% 0.56/0.66 tff(670,plain,
% 0.56/0.66 (~program(f4(c1))),
% 0.56/0.66 inference(unit_resolution,[status(thm)],[545, 542, 6, 669, 662])).
% 0.56/0.66 tff(671,plain,
% 0.56/0.66 ($false),
% 0.56/0.66 inference(unit_resolution,[status(thm)],[519, 513, 48, 660, 319, 318, 670])).
% 0.56/0.66 tff(672,plain,(halts2(f5(c1), f5(c1))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.66 tff(673,plain,
% 0.56/0.66 (outputs(c1, good) | (~decides(c1, f4(c1), f3(c1)))),
% 0.56/0.66 inference(unit_resolution,[status(thm)],[449, 443, 48, 672, 318])).
% 0.56/0.66 tff(674,plain,
% 0.56/0.66 (~decides(c1, f4(c1), f3(c1))),
% 0.56/0.66 inference(unit_resolution,[status(thm)],[673, 1])).
% 0.56/0.66 tff(675,plain,
% 0.56/0.66 (program(f4(c1))),
% 0.56/0.66 inference(unit_resolution,[status(thm)],[467, 461, 48, 1, 672, 318])).
% 0.56/0.66 tff(676,plain,
% 0.56/0.66 ($false),
% 0.56/0.66 inference(unit_resolution,[status(thm)],[373, 370, 6, 321, 674, 675])).
% 0.56/0.66 tff(677,plain,(outputs(c1, good) | program(f2(c4))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.66 tff(678,plain,
% 0.56/0.66 (outputs(c1, good)),
% 0.56/0.66 inference(unit_resolution,[status(thm)],[677, 321])).
% 0.56/0.66 tff(679,assumption,(outputs(c1, good)), introduced(assumption)).
% 0.56/0.66 tff(680,plain,
% 0.56/0.66 (^[W: $i, Y: $i] : refl(((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) <=> ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))))),
% 0.56/0.66 inference(bind,[status(th)],[])).
% 0.56/0.66 tff(681,plain,
% 0.56/0.66 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.66 inference(quant_intro,[status(thm)],[680])).
% 0.56/0.66 tff(682,plain,
% 0.56/0.66 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.66 inference(rewrite,[status(thm)],[])).
% 0.56/0.66 tff(683,plain,
% 0.56/0.66 (^[W: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) <=> ((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))), (((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) <=> (((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))))), rewrite((((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) <=> ((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))), (((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) <=> ((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))))), ((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) <=> (((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) | (~program(Y))))), rewrite((((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) | (~program(Y))) <=> ((~program(W)) | (~program(Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))), ((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) <=> ((~program(W)) | (~program(Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))))), (((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) | (~halts2(Y, Y))) <=> (((~program(W)) | (~program(Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) | (~halts2(Y, Y))))), rewrite((((~program(W)) | (~program(Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) | (~halts2(Y, Y))) <=> ((~program(W)) | (~program(Y)) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))), (((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) | (~halts2(Y, Y))) <=> ((~program(W)) | (~program(Y)) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))))), ((((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) | (~halts2(Y, Y))) | outputs(c2, good)) <=> (((~program(W)) | (~program(Y)) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) | outputs(c2, good)))), rewrite((((~program(W)) | (~program(Y)) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) | outputs(c2, good)) <=> ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))), ((((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) | (~halts2(Y, Y))) | outputs(c2, good)) <=> ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))))),
% 0.56/0.67 inference(bind,[status(th)],[])).
% 0.56/0.67 tff(684,plain,
% 0.56/0.67 (![W: $i, Y: $i] : (((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) | (~halts2(Y, Y))) | outputs(c2, good)) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.67 inference(quant_intro,[status(thm)],[683])).
% 0.56/0.67 tff(685,axiom,(![W: $i, Y: $i] : (((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) | (~halts2(Y, Y))) | outputs(c2, good))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_3_13')).
% 0.56/0.67 tff(686,plain,
% 0.56/0.67 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.67 inference(modus_ponens,[status(thm)],[685, 684])).
% 0.56/0.67 tff(687,plain,
% 0.56/0.67 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.67 inference(modus_ponens,[status(thm)],[686, 682])).
% 0.56/0.67 tff(688,plain,(
% 0.56/0.67 ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.67 inference(skolemize,[status(sab)],[687])).
% 0.56/0.67 tff(689,plain,
% 0.56/0.67 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.67 inference(modus_ponens,[status(thm)],[688, 681])).
% 0.56/0.67 tff(690,plain,
% 0.56/0.67 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | (outputs(c2, good) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | (~program(f5(c1))))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | outputs(c2, good) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | (~program(f5(c1))))),
% 0.56/0.67 inference(rewrite,[status(thm)],[])).
% 0.56/0.67 tff(691,plain,
% 0.56/0.67 (((~program(c1)) | (~program(f5(c1))) | outputs(c2, good) | (~halts2(f5(c1), f5(c1))) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~outputs(c1, good))) <=> (outputs(c2, good) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | (~program(f5(c1))))),
% 0.56/0.67 inference(rewrite,[status(thm)],[])).
% 0.56/0.67 tff(692,plain,
% 0.56/0.67 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | ((~program(c1)) | (~program(f5(c1))) | outputs(c2, good) | (~halts2(f5(c1), f5(c1))) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~outputs(c1, good)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | (outputs(c2, good) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | (~program(f5(c1)))))),
% 0.56/0.67 inference(monotonicity,[status(thm)],[691])).
% 0.56/0.67 tff(693,plain,
% 0.56/0.67 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | ((~program(c1)) | (~program(f5(c1))) | outputs(c2, good) | (~halts2(f5(c1), f5(c1))) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~outputs(c1, good)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | outputs(c2, good) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | (~program(f5(c1))))),
% 0.56/0.67 inference(transitivity,[status(thm)],[692, 690])).
% 0.56/0.67 tff(694,plain,
% 0.56/0.67 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | ((~program(c1)) | (~program(f5(c1))) | outputs(c2, good) | (~halts2(f5(c1), f5(c1))) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~outputs(c1, good)))),
% 0.56/0.67 inference(quant_inst,[status(thm)],[])).
% 0.56/0.67 tff(695,plain,
% 0.56/0.67 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, good) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | outputs(c2, good) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | (~program(f5(c1)))),
% 0.56/0.67 inference(modus_ponens,[status(thm)],[694, 693])).
% 0.56/0.67 tff(696,plain,
% 0.56/0.67 (outputs(c2, good) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1)))),
% 0.56/0.67 inference(unit_resolution,[status(thm)],[695, 689, 48, 318])).
% 0.56/0.67 tff(697,plain,
% 0.56/0.67 (outputs(c2, good) | (~outputs(c1, good))),
% 0.56/0.67 inference(unit_resolution,[status(thm)],[696, 672, 572])).
% 0.56/0.67 tff(698,plain,
% 0.56/0.67 (outputs(c2, good)),
% 0.56/0.67 inference(unit_resolution,[status(thm)],[697, 679])).
% 0.56/0.67 tff(699,plain,
% 0.56/0.67 (program(c3) | (~outputs(c2, good)) | (~halts2(c2, f6(c2))) | (~halts2(f6(c2), f6(c2)))),
% 0.56/0.67 inference(unit_resolution,[status(thm)],[165, 159, 566])).
% 0.56/0.67 tff(700,plain,
% 0.56/0.67 (~halts2(f6(c2), f6(c2))),
% 0.56/0.67 inference(unit_resolution,[status(thm)],[699, 67, 698, 251])).
% 0.56/0.67 tff(701,plain,
% 0.56/0.67 ($false),
% 0.56/0.67 inference(unit_resolution,[status(thm)],[83, 77, 67, 566, 205])).
% 0.56/0.67 tff(702,plain,(program(f6(c2)) | program(c3)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.67 tff(703,plain,
% 0.56/0.67 (program(f6(c2))),
% 0.56/0.67 inference(unit_resolution,[status(thm)],[702, 67])).
% 0.56/0.67 tff(704,plain,
% 0.56/0.67 (^[V: $i] : refl(((~program(V)) | (~outputs(V, bad)) | program(c3) | (~halts2(V, f6(V))) | halts2(f6(V), f6(V))) <=> ((~program(V)) | (~outputs(V, bad)) | program(c3) | (~halts2(V, f6(V))) | halts2(f6(V), f6(V))))),
% 0.56/0.67 inference(bind,[status(th)],[])).
% 0.56/0.67 tff(705,plain,
% 0.56/0.67 (![V: $i] : ((~program(V)) | (~outputs(V, bad)) | program(c3) | (~halts2(V, f6(V))) | halts2(f6(V), f6(V))) <=> ![V: $i] : ((~program(V)) | (~outputs(V, bad)) | program(c3) | (~halts2(V, f6(V))) | halts2(f6(V), f6(V)))),
% 0.56/0.67 inference(quant_intro,[status(thm)],[704])).
% 0.56/0.67 tff(706,plain,
% 0.56/0.67 (![V: $i] : ((~program(V)) | (~outputs(V, bad)) | program(c3) | (~halts2(V, f6(V))) | halts2(f6(V), f6(V))) <=> ![V: $i] : ((~program(V)) | (~outputs(V, bad)) | program(c3) | (~halts2(V, f6(V))) | halts2(f6(V), f6(V)))),
% 0.56/0.67 inference(rewrite,[status(thm)],[])).
% 0.56/0.67 tff(707,plain,
% 0.56/0.67 (^[V: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~program(V)) | halts2(f6(V), f6(V))) | (~halts2(V, f6(V)))) <=> ((~program(V)) | (~halts2(V, f6(V))) | halts2(f6(V), f6(V)))), (((((~program(V)) | halts2(f6(V), f6(V))) | (~halts2(V, f6(V)))) | (~outputs(V, bad))) <=> (((~program(V)) | (~halts2(V, f6(V))) | halts2(f6(V), f6(V))) | (~outputs(V, bad))))), rewrite((((~program(V)) | (~halts2(V, f6(V))) | halts2(f6(V), f6(V))) | (~outputs(V, bad))) <=> ((~program(V)) | (~outputs(V, bad)) | (~halts2(V, f6(V))) | halts2(f6(V), f6(V)))), (((((~program(V)) | halts2(f6(V), f6(V))) | (~halts2(V, f6(V)))) | (~outputs(V, bad))) <=> ((~program(V)) | (~outputs(V, bad)) | (~halts2(V, f6(V))) | halts2(f6(V), f6(V))))), ((((((~program(V)) | halts2(f6(V), f6(V))) | (~halts2(V, f6(V)))) | (~outputs(V, bad))) | program(c3)) <=> (((~program(V)) | (~outputs(V, bad)) | (~halts2(V, f6(V))) | halts2(f6(V), f6(V))) | program(c3)))), rewrite((((~program(V)) | (~outputs(V, bad)) | (~halts2(V, f6(V))) | halts2(f6(V), f6(V))) | program(c3)) <=> ((~program(V)) | (~outputs(V, bad)) | program(c3) | (~halts2(V, f6(V))) | halts2(f6(V), f6(V)))), ((((((~program(V)) | halts2(f6(V), f6(V))) | (~halts2(V, f6(V)))) | (~outputs(V, bad))) | program(c3)) <=> ((~program(V)) | (~outputs(V, bad)) | program(c3) | (~halts2(V, f6(V))) | halts2(f6(V), f6(V)))))),
% 0.56/0.67 inference(bind,[status(th)],[])).
% 0.56/0.67 tff(708,plain,
% 0.56/0.67 (![V: $i] : (((((~program(V)) | halts2(f6(V), f6(V))) | (~halts2(V, f6(V)))) | (~outputs(V, bad))) | program(c3)) <=> ![V: $i] : ((~program(V)) | (~outputs(V, bad)) | program(c3) | (~halts2(V, f6(V))) | halts2(f6(V), f6(V)))),
% 0.56/0.67 inference(quant_intro,[status(thm)],[707])).
% 0.56/0.67 tff(709,axiom,(![V: $i] : (((((~program(V)) | halts2(f6(V), f6(V))) | (~halts2(V, f6(V)))) | (~outputs(V, bad))) | program(c3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_4_5')).
% 0.56/0.67 tff(710,plain,
% 0.56/0.67 (![V: $i] : ((~program(V)) | (~outputs(V, bad)) | program(c3) | (~halts2(V, f6(V))) | halts2(f6(V), f6(V)))),
% 0.56/0.67 inference(modus_ponens,[status(thm)],[709, 708])).
% 0.56/0.67 tff(711,plain,
% 0.56/0.67 (![V: $i] : ((~program(V)) | (~outputs(V, bad)) | program(c3) | (~halts2(V, f6(V))) | halts2(f6(V), f6(V)))),
% 0.56/0.67 inference(modus_ponens,[status(thm)],[710, 706])).
% 0.56/0.67 tff(712,plain,(
% 0.56/0.67 ![V: $i] : ((~program(V)) | (~outputs(V, bad)) | program(c3) | (~halts2(V, f6(V))) | halts2(f6(V), f6(V)))),
% 0.56/0.67 inference(skolemize,[status(sab)],[711])).
% 0.56/0.67 tff(713,plain,
% 0.56/0.67 (![V: $i] : ((~program(V)) | (~outputs(V, bad)) | program(c3) | (~halts2(V, f6(V))) | halts2(f6(V), f6(V)))),
% 0.56/0.67 inference(modus_ponens,[status(thm)],[712, 705])).
% 0.56/0.67 tff(714,plain,
% 0.56/0.67 (((~![V: $i] : ((~program(V)) | (~outputs(V, bad)) | program(c3) | (~halts2(V, f6(V))) | halts2(f6(V), f6(V)))) | (program(c3) | (~program(c2)) | (~outputs(c2, bad)) | (~halts2(c2, f6(c2))) | halts2(f6(c2), f6(c2)))) <=> ((~![V: $i] : ((~program(V)) | (~outputs(V, bad)) | program(c3) | (~halts2(V, f6(V))) | halts2(f6(V), f6(V)))) | program(c3) | (~program(c2)) | (~outputs(c2, bad)) | (~halts2(c2, f6(c2))) | halts2(f6(c2), f6(c2)))),
% 0.56/0.67 inference(rewrite,[status(thm)],[])).
% 0.56/0.67 tff(715,plain,
% 0.56/0.67 (((~program(c2)) | (~outputs(c2, bad)) | program(c3) | (~halts2(c2, f6(c2))) | halts2(f6(c2), f6(c2))) <=> (program(c3) | (~program(c2)) | (~outputs(c2, bad)) | (~halts2(c2, f6(c2))) | halts2(f6(c2), f6(c2)))),
% 0.56/0.67 inference(rewrite,[status(thm)],[])).
% 0.56/0.67 tff(716,plain,
% 0.56/0.67 (((~![V: $i] : ((~program(V)) | (~outputs(V, bad)) | program(c3) | (~halts2(V, f6(V))) | halts2(f6(V), f6(V)))) | ((~program(c2)) | (~outputs(c2, bad)) | program(c3) | (~halts2(c2, f6(c2))) | halts2(f6(c2), f6(c2)))) <=> ((~![V: $i] : ((~program(V)) | (~outputs(V, bad)) | program(c3) | (~halts2(V, f6(V))) | halts2(f6(V), f6(V)))) | (program(c3) | (~program(c2)) | (~outputs(c2, bad)) | (~halts2(c2, f6(c2))) | halts2(f6(c2), f6(c2))))),
% 0.56/0.67 inference(monotonicity,[status(thm)],[715])).
% 0.56/0.67 tff(717,plain,
% 0.56/0.67 (((~![V: $i] : ((~program(V)) | (~outputs(V, bad)) | program(c3) | (~halts2(V, f6(V))) | halts2(f6(V), f6(V)))) | ((~program(c2)) | (~outputs(c2, bad)) | program(c3) | (~halts2(c2, f6(c2))) | halts2(f6(c2), f6(c2)))) <=> ((~![V: $i] : ((~program(V)) | (~outputs(V, bad)) | program(c3) | (~halts2(V, f6(V))) | halts2(f6(V), f6(V)))) | program(c3) | (~program(c2)) | (~outputs(c2, bad)) | (~halts2(c2, f6(c2))) | halts2(f6(c2), f6(c2)))),
% 0.56/0.67 inference(transitivity,[status(thm)],[716, 714])).
% 0.56/0.67 tff(718,plain,
% 0.56/0.67 ((~![V: $i] : ((~program(V)) | (~outputs(V, bad)) | program(c3) | (~halts2(V, f6(V))) | halts2(f6(V), f6(V)))) | ((~program(c2)) | (~outputs(c2, bad)) | program(c3) | (~halts2(c2, f6(c2))) | halts2(f6(c2), f6(c2)))),
% 0.56/0.68 inference(quant_inst,[status(thm)],[])).
% 0.56/0.68 tff(719,plain,
% 0.56/0.68 ((~![V: $i] : ((~program(V)) | (~outputs(V, bad)) | program(c3) | (~halts2(V, f6(V))) | halts2(f6(V), f6(V)))) | program(c3) | (~program(c2)) | (~outputs(c2, bad)) | (~halts2(c2, f6(c2))) | halts2(f6(c2), f6(c2))),
% 0.56/0.68 inference(modus_ponens,[status(thm)],[718, 717])).
% 0.56/0.68 tff(720,plain,
% 0.56/0.68 (program(c3) | (~outputs(c2, bad)) | (~halts2(c2, f6(c2))) | halts2(f6(c2), f6(c2))),
% 0.56/0.68 inference(unit_resolution,[status(thm)],[719, 713, 566])).
% 0.56/0.68 tff(721,plain,
% 0.56/0.68 (~outputs(c2, bad)),
% 0.56/0.68 inference(unit_resolution,[status(thm)],[720, 67, 251, 700])).
% 0.56/0.68 tff(722,plain,
% 0.56/0.68 (^[W: $i, Y: $i] : refl(((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) <=> ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))))),
% 0.56/0.68 inference(bind,[status(th)],[])).
% 0.56/0.68 tff(723,plain,
% 0.56/0.68 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.68 inference(quant_intro,[status(thm)],[722])).
% 0.56/0.68 tff(724,plain,
% 0.56/0.68 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.68 inference(rewrite,[status(thm)],[])).
% 0.56/0.68 tff(725,plain,
% 0.56/0.68 (^[W: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) <=> ((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))), (((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) <=> (((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))))), rewrite((((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) <=> ((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))), (((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) <=> ((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))))), ((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) <=> (((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) | (~program(Y))))), rewrite((((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) | (~program(Y))) <=> ((~program(W)) | (~program(Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))), ((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) <=> ((~program(W)) | (~program(Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))))), (((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) | halts2(Y, Y)) <=> (((~program(W)) | (~program(Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) | halts2(Y, Y)))), rewrite((((~program(W)) | (~program(Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) | halts2(Y, Y)) <=> ((~program(W)) | (~program(Y)) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))), (((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) | halts2(Y, Y)) <=> ((~program(W)) | (~program(Y)) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))))), ((((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) | halts2(Y, Y)) | outputs(c2, bad)) <=> (((~program(W)) | (~program(Y)) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) | outputs(c2, bad)))), rewrite((((~program(W)) | (~program(Y)) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) | outputs(c2, bad)) <=> ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))), ((((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) | halts2(Y, Y)) | outputs(c2, bad)) <=> ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))))),
% 0.56/0.68 inference(bind,[status(th)],[])).
% 0.56/0.68 tff(726,plain,
% 0.56/0.68 (![W: $i, Y: $i] : (((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) | halts2(Y, Y)) | outputs(c2, bad)) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.68 inference(quant_intro,[status(thm)],[725])).
% 0.56/0.68 tff(727,axiom,(![W: $i, Y: $i] : (((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) | halts2(Y, Y)) | outputs(c2, bad))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_3_15')).
% 0.56/0.68 tff(728,plain,
% 0.56/0.68 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.68 inference(modus_ponens,[status(thm)],[727, 726])).
% 0.56/0.68 tff(729,plain,
% 0.56/0.68 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.68 inference(modus_ponens,[status(thm)],[728, 724])).
% 0.56/0.68 tff(730,plain,(
% 0.56/0.68 ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.68 inference(skolemize,[status(sab)],[729])).
% 0.56/0.68 tff(731,plain,
% 0.56/0.68 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.68 inference(modus_ponens,[status(thm)],[730, 723])).
% 0.56/0.68 tff(732,plain,
% 0.56/0.68 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | (outputs(c2, bad) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2))))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | outputs(c2, bad) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2))))),
% 0.56/0.68 inference(rewrite,[status(thm)],[])).
% 0.56/0.68 tff(733,plain,
% 0.56/0.68 (((~program(c1)) | (~program(f6(c2))) | outputs(c2, bad) | halts2(f6(c2), f6(c2)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~outputs(c1, good))) <=> (outputs(c2, bad) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2))))),
% 0.56/0.68 inference(rewrite,[status(thm)],[])).
% 0.56/0.68 tff(734,plain,
% 0.56/0.68 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | ((~program(c1)) | (~program(f6(c2))) | outputs(c2, bad) | halts2(f6(c2), f6(c2)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~outputs(c1, good)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | (outputs(c2, bad) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2)))))),
% 0.56/0.69 inference(monotonicity,[status(thm)],[733])).
% 0.56/0.69 tff(735,plain,
% 0.56/0.69 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | ((~program(c1)) | (~program(f6(c2))) | outputs(c2, bad) | halts2(f6(c2), f6(c2)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~outputs(c1, good)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | outputs(c2, bad) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2))))),
% 0.56/0.69 inference(transitivity,[status(thm)],[734, 732])).
% 0.56/0.69 tff(736,plain,
% 0.56/0.69 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | ((~program(c1)) | (~program(f6(c2))) | outputs(c2, bad) | halts2(f6(c2), f6(c2)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~outputs(c1, good)))),
% 0.56/0.69 inference(quant_inst,[status(thm)],[])).
% 0.56/0.69 tff(737,plain,
% 0.56/0.69 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | outputs(c2, bad) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2)))),
% 0.56/0.69 inference(modus_ponens,[status(thm)],[736, 735])).
% 0.56/0.69 tff(738,plain,
% 0.56/0.69 ($false),
% 0.56/0.69 inference(unit_resolution,[status(thm)],[737, 731, 48, 679, 721, 572, 672, 703, 700])).
% 0.56/0.69 tff(739,plain,(program(c3) | (~outputs(c1, good)) | (~halts2(c2, f6(c2)))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.69 tff(740,plain,
% 0.56/0.69 (program(c3)),
% 0.56/0.69 inference(unit_resolution,[status(thm)],[739, 251, 679])).
% 0.56/0.69 tff(741,plain,
% 0.56/0.69 ((~halts2(c2, f6(c2))) | (~outputs(c2, bad)) | (~program(c3)) | (~outputs(c2, good))),
% 0.56/0.69 inference(unit_resolution,[status(thm)],[289, 566])).
% 0.56/0.69 tff(742,plain,
% 0.56/0.69 (~outputs(c2, bad)),
% 0.56/0.69 inference(unit_resolution,[status(thm)],[741, 740, 698, 251])).
% 0.56/0.69 tff(743,plain,
% 0.56/0.69 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | (outputs(c2, bad) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | halts2(c3, c3) | (~program(c3)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | outputs(c2, bad) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | halts2(c3, c3) | (~program(c3)))),
% 0.56/0.69 inference(rewrite,[status(thm)],[])).
% 0.56/0.69 tff(744,plain,
% 0.56/0.69 (((~program(c1)) | (~program(c3)) | outputs(c2, bad) | halts2(c3, c3) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~outputs(c1, good))) <=> (outputs(c2, bad) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | halts2(c3, c3) | (~program(c3)))),
% 0.56/0.69 inference(rewrite,[status(thm)],[])).
% 0.56/0.69 tff(745,plain,
% 0.56/0.69 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | ((~program(c1)) | (~program(c3)) | outputs(c2, bad) | halts2(c3, c3) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~outputs(c1, good)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | (outputs(c2, bad) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | halts2(c3, c3) | (~program(c3))))),
% 0.56/0.69 inference(monotonicity,[status(thm)],[744])).
% 0.56/0.69 tff(746,plain,
% 0.56/0.69 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | ((~program(c1)) | (~program(c3)) | outputs(c2, bad) | halts2(c3, c3) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~outputs(c1, good)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | outputs(c2, bad) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | halts2(c3, c3) | (~program(c3)))),
% 0.56/0.69 inference(transitivity,[status(thm)],[745, 743])).
% 0.56/0.69 tff(747,plain,
% 0.56/0.69 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | ((~program(c1)) | (~program(c3)) | outputs(c2, bad) | halts2(c3, c3) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~outputs(c1, good)))),
% 0.56/0.69 inference(quant_inst,[status(thm)],[])).
% 0.56/0.69 tff(748,plain,
% 0.56/0.69 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | outputs(c2, bad) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | outputs(c2, bad) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | halts2(c3, c3) | (~program(c3))),
% 0.56/0.69 inference(modus_ponens,[status(thm)],[747, 746])).
% 0.56/0.69 tff(749,plain,
% 0.56/0.69 (halts2(c3, c3)),
% 0.56/0.69 inference(unit_resolution,[status(thm)],[748, 731, 48, 679, 740, 742, 572, 672])).
% 0.56/0.69 tff(750,plain,
% 0.56/0.69 (program(f6(c2)) | (~program(c3))),
% 0.56/0.69 inference(unit_resolution,[status(thm)],[244, 566])).
% 0.56/0.69 tff(751,plain,
% 0.56/0.69 (program(f6(c2))),
% 0.56/0.69 inference(unit_resolution,[status(thm)],[750, 740])).
% 0.56/0.69 tff(752,plain,
% 0.56/0.69 (halts2(f6(c2), f6(c2))),
% 0.56/0.69 inference(unit_resolution,[status(thm)],[737, 731, 48, 679, 742, 572, 672, 751])).
% 0.56/0.69 tff(753,plain,
% 0.56/0.69 ((~halts2(f6(c2), f6(c2))) | (~halts2(c3, c3))),
% 0.56/0.69 inference(unit_resolution,[status(thm)],[314, 308, 740, 698, 566, 251])).
% 0.56/0.69 tff(754,plain,
% 0.56/0.69 ($false),
% 0.56/0.69 inference(unit_resolution,[status(thm)],[753, 752, 749])).
% 0.56/0.69 tff(755,plain,((~halts2(c2, f6(c2))) | (~outputs(c1, good))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.69 tff(756,plain,
% 0.56/0.69 (~halts2(c2, f6(c2))),
% 0.56/0.69 inference(unit_resolution,[status(thm)],[755, 678])).
% 0.56/0.69 tff(757,plain,
% 0.56/0.69 (~program(c3)),
% 0.56/0.69 inference(unit_resolution,[status(thm)],[750, 205])).
% 0.56/0.69 tff(758,plain,
% 0.56/0.69 ($false),
% 0.56/0.69 inference(unit_resolution,[status(thm)],[702, 757, 205])).
% 0.56/0.69 tff(759,plain,(program(f6(c2))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.69 tff(760,plain,
% 0.56/0.69 (~halts2(c2, f6(c2))),
% 0.56/0.69 inference(unit_resolution,[status(thm)],[755, 679])).
% 0.56/0.69 tff(761,plain,
% 0.56/0.69 (^[W: $i, Y: $i] : refl(((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) <=> ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))))),
% 0.56/0.69 inference(bind,[status(th)],[])).
% 0.56/0.69 tff(762,plain,
% 0.56/0.69 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.69 inference(quant_intro,[status(thm)],[761])).
% 0.56/0.69 tff(763,plain,
% 0.56/0.69 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.69 inference(rewrite,[status(thm)],[])).
% 0.56/0.69 tff(764,plain,
% 0.56/0.69 (^[W: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) <=> ((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))), (((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~outputs(W, bad))) <=> (((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) | (~outputs(W, bad))))), rewrite((((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) | (~outputs(W, bad))) <=> ((~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))), (((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~outputs(W, bad))) <=> ((~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))))), ((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~outputs(W, bad))) | (~program(Y))) <=> (((~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) | (~program(Y))))), rewrite((((~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) | (~program(Y))) <=> ((~program(W)) | (~program(Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))), ((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~outputs(W, bad))) | (~program(Y))) <=> ((~program(W)) | (~program(Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))))), (((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~outputs(W, bad))) | (~program(Y))) | halts2(Y, Y)) <=> (((~program(W)) | (~program(Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) | halts2(Y, Y)))), rewrite((((~program(W)) | (~program(Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) | halts2(Y, Y)) <=> ((~program(W)) | (~program(Y)) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))), (((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~outputs(W, bad))) | (~program(Y))) | halts2(Y, Y)) <=> ((~program(W)) | (~program(Y)) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))))), ((((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~outputs(W, bad))) | (~program(Y))) | halts2(Y, Y)) | halts2(c2, Y)) <=> (((~program(W)) | (~program(Y)) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) | halts2(c2, Y)))), rewrite((((~program(W)) | (~program(Y)) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) | halts2(c2, Y)) <=> ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))), ((((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~outputs(W, bad))) | (~program(Y))) | halts2(Y, Y)) | halts2(c2, Y)) <=> ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))))),
% 0.56/0.69 inference(bind,[status(th)],[])).
% 0.56/0.69 tff(765,plain,
% 0.56/0.69 (![W: $i, Y: $i] : (((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~outputs(W, bad))) | (~program(Y))) | halts2(Y, Y)) | halts2(c2, Y)) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.69 inference(quant_intro,[status(thm)],[764])).
% 0.56/0.69 tff(766,axiom,(![W: $i, Y: $i] : (((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~outputs(W, bad))) | (~program(Y))) | halts2(Y, Y)) | halts2(c2, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_3_19')).
% 0.56/0.69 tff(767,plain,
% 0.56/0.69 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.70 inference(modus_ponens,[status(thm)],[766, 765])).
% 0.56/0.70 tff(768,plain,
% 0.56/0.70 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.70 inference(modus_ponens,[status(thm)],[767, 763])).
% 0.56/0.70 tff(769,plain,(
% 0.56/0.70 ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.70 inference(skolemize,[status(sab)],[768])).
% 0.56/0.70 tff(770,plain,
% 0.56/0.70 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.70 inference(modus_ponens,[status(thm)],[769, 762])).
% 0.56/0.70 tff(771,plain,
% 0.56/0.70 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))) | ((~outputs(c1, good)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | (~program(c1)) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2))))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))) | (~outputs(c1, good)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | (~program(c1)) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2))))),
% 0.56/0.70 inference(rewrite,[status(thm)],[])).
% 0.56/0.70 tff(772,plain,
% 0.56/0.70 (((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | (~outputs(c1, good))) <=> ((~outputs(c1, good)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | (~program(c1)) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2))))),
% 0.56/0.70 inference(rewrite,[status(thm)],[])).
% 0.56/0.70 tff(773,plain,
% 0.56/0.70 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))) | ((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | (~outputs(c1, good)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))) | ((~outputs(c1, good)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | (~program(c1)) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2)))))),
% 0.56/0.70 inference(monotonicity,[status(thm)],[772])).
% 0.56/0.70 tff(774,plain,
% 0.56/0.70 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))) | ((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | (~outputs(c1, good)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))) | (~outputs(c1, good)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | (~program(c1)) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2))))),
% 0.56/0.70 inference(transitivity,[status(thm)],[773, 771])).
% 0.56/0.70 tff(775,plain,
% 0.56/0.70 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))) | ((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | (~outputs(c1, good)))),
% 0.56/0.70 inference(quant_inst,[status(thm)],[])).
% 0.56/0.70 tff(776,plain,
% 0.56/0.70 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))) | (~outputs(c1, good)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | (~program(c1)) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2)))),
% 0.56/0.70 inference(modus_ponens,[status(thm)],[775, 774])).
% 0.56/0.70 tff(777,plain,
% 0.56/0.70 (halts2(f6(c2), f6(c2))),
% 0.56/0.70 inference(unit_resolution,[status(thm)],[776, 770, 48, 679, 567, 572, 760, 120])).
% 0.56/0.70 tff(778,plain,
% 0.56/0.70 (^[W: $i, Y: $i] : refl(((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) <=> ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))))),
% 0.56/0.70 inference(bind,[status(th)],[])).
% 0.56/0.70 tff(779,plain,
% 0.56/0.70 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.70 inference(quant_intro,[status(thm)],[778])).
% 0.56/0.70 tff(780,plain,
% 0.56/0.70 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.70 inference(rewrite,[status(thm)],[])).
% 0.56/0.70 tff(781,plain,
% 0.56/0.70 (^[W: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) <=> ((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))), (((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~outputs(W, bad))) <=> (((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) | (~outputs(W, bad))))), rewrite((((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) | (~outputs(W, bad))) <=> ((~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))), (((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~outputs(W, bad))) <=> ((~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))))), ((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~outputs(W, bad))) | (~program(Y))) <=> (((~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) | (~program(Y))))), rewrite((((~program(W)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) | (~program(Y))) <=> ((~program(W)) | (~program(Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))), ((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~outputs(W, bad))) | (~program(Y))) <=> ((~program(W)) | (~program(Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))))), (((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~outputs(W, bad))) | (~program(Y))) | (~halts2(Y, Y))) <=> (((~program(W)) | (~program(Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) | (~halts2(Y, Y))))), rewrite((((~program(W)) | (~program(Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) | (~halts2(Y, Y))) <=> ((~program(W)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))), (((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~outputs(W, bad))) | (~program(Y))) | (~halts2(Y, Y))) <=> ((~program(W)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))))), ((((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~outputs(W, bad))) | (~program(Y))) | (~halts2(Y, Y))) | halts2(c2, Y)) <=> (((~program(W)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) | halts2(c2, Y)))), rewrite((((~program(W)) | (~program(Y)) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) | halts2(c2, Y)) <=> ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))), ((((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~outputs(W, bad))) | (~program(Y))) | (~halts2(Y, Y))) | halts2(c2, Y)) <=> ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))))),
% 0.56/0.70 inference(bind,[status(th)],[])).
% 0.56/0.70 tff(782,plain,
% 0.56/0.70 (![W: $i, Y: $i] : (((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~outputs(W, bad))) | (~program(Y))) | (~halts2(Y, Y))) | halts2(c2, Y)) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.70 inference(quant_intro,[status(thm)],[781])).
% 0.56/0.70 tff(783,axiom,(![W: $i, Y: $i] : (((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~outputs(W, bad))) | (~program(Y))) | (~halts2(Y, Y))) | halts2(c2, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_3_17')).
% 0.56/0.70 tff(784,plain,
% 0.56/0.70 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.70 inference(modus_ponens,[status(thm)],[783, 782])).
% 0.56/0.70 tff(785,plain,
% 0.56/0.70 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.70 inference(modus_ponens,[status(thm)],[784, 780])).
% 0.56/0.70 tff(786,plain,(
% 0.56/0.70 ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.70 inference(skolemize,[status(sab)],[785])).
% 0.56/0.70 tff(787,plain,
% 0.56/0.70 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.70 inference(modus_ponens,[status(thm)],[786, 779])).
% 0.56/0.70 tff(788,plain,
% 0.56/0.70 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))) | ((~outputs(c1, good)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | (~program(c1)) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~program(f6(c2))))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))) | (~outputs(c1, good)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | (~program(c1)) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~program(f6(c2))))),
% 0.56/0.70 inference(rewrite,[status(thm)],[])).
% 0.56/0.70 tff(789,plain,
% 0.56/0.70 (((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | (~outputs(c1, good))) <=> ((~outputs(c1, good)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | (~program(c1)) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~program(f6(c2))))),
% 0.56/0.70 inference(rewrite,[status(thm)],[])).
% 0.56/0.70 tff(790,plain,
% 0.56/0.70 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))) | ((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | (~outputs(c1, good)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))) | ((~outputs(c1, good)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | (~program(c1)) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~program(f6(c2)))))),
% 0.56/0.70 inference(monotonicity,[status(thm)],[789])).
% 0.56/0.70 tff(791,plain,
% 0.56/0.70 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))) | ((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | (~outputs(c1, good)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))) | (~outputs(c1, good)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | (~program(c1)) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~program(f6(c2))))),
% 0.56/0.71 inference(transitivity,[status(thm)],[790, 788])).
% 0.56/0.71 tff(792,plain,
% 0.56/0.71 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))) | ((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | (~outputs(c1, good)))),
% 0.56/0.71 inference(quant_inst,[status(thm)],[])).
% 0.56/0.71 tff(793,plain,
% 0.56/0.71 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~outputs(W, bad)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))) | (~outputs(c1, good)) | (~outputs(c1, bad)) | (~halts3(c1, f5(c1), f5(c1))) | (~program(c1)) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~program(f6(c2)))),
% 0.56/0.71 inference(modus_ponens,[status(thm)],[792, 791])).
% 0.56/0.71 tff(794,plain,
% 0.56/0.71 ($false),
% 0.56/0.71 inference(unit_resolution,[status(thm)],[793, 787, 48, 679, 567, 572, 760, 120, 777])).
% 0.56/0.71 tff(795,plain,((~program(f6(c2))) | (~outputs(c1, good)) | (~outputs(c1, bad))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.71 tff(796,plain,
% 0.56/0.71 (~outputs(c1, bad)),
% 0.56/0.71 inference(unit_resolution,[status(thm)],[795, 678, 759])).
% 0.56/0.71 tff(797,plain,
% 0.56/0.71 (((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | (~program(W)) | outputs(W, bad) | (~decides(W, f4(W), f3(W))))) | (outputs(c1, bad) | (~program(c1)) | (~decides(c1, f4(c1), f3(c1))) | (~program(c2)) | halts2(c2, f6(c2)))) <=> ((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | (~program(W)) | outputs(W, bad) | (~decides(W, f4(W), f3(W))))) | outputs(c1, bad) | (~program(c1)) | (~decides(c1, f4(c1), f3(c1))) | (~program(c2)) | halts2(c2, f6(c2)))),
% 0.56/0.71 inference(rewrite,[status(thm)],[])).
% 0.56/0.71 tff(798,plain,
% 0.56/0.71 ((halts2(c2, f6(c2)) | (~program(c2)) | (~program(c1)) | outputs(c1, bad) | (~decides(c1, f4(c1), f3(c1)))) <=> (outputs(c1, bad) | (~program(c1)) | (~decides(c1, f4(c1), f3(c1))) | (~program(c2)) | halts2(c2, f6(c2)))),
% 0.56/0.71 inference(rewrite,[status(thm)],[])).
% 0.56/0.71 tff(799,plain,
% 0.56/0.71 (((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | (~program(W)) | outputs(W, bad) | (~decides(W, f4(W), f3(W))))) | (halts2(c2, f6(c2)) | (~program(c2)) | (~program(c1)) | outputs(c1, bad) | (~decides(c1, f4(c1), f3(c1))))) <=> ((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | (~program(W)) | outputs(W, bad) | (~decides(W, f4(W), f3(W))))) | (outputs(c1, bad) | (~program(c1)) | (~decides(c1, f4(c1), f3(c1))) | (~program(c2)) | halts2(c2, f6(c2))))),
% 0.56/0.71 inference(monotonicity,[status(thm)],[798])).
% 0.56/0.71 tff(800,plain,
% 0.56/0.71 (((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | (~program(W)) | outputs(W, bad) | (~decides(W, f4(W), f3(W))))) | (halts2(c2, f6(c2)) | (~program(c2)) | (~program(c1)) | outputs(c1, bad) | (~decides(c1, f4(c1), f3(c1))))) <=> ((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | (~program(W)) | outputs(W, bad) | (~decides(W, f4(W), f3(W))))) | outputs(c1, bad) | (~program(c1)) | (~decides(c1, f4(c1), f3(c1))) | (~program(c2)) | halts2(c2, f6(c2)))),
% 0.56/0.71 inference(transitivity,[status(thm)],[799, 797])).
% 0.56/0.71 tff(801,plain,
% 0.56/0.71 ((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | (~program(W)) | outputs(W, bad) | (~decides(W, f4(W), f3(W))))) | (halts2(c2, f6(c2)) | (~program(c2)) | (~program(c1)) | outputs(c1, bad) | (~decides(c1, f4(c1), f3(c1))))),
% 0.56/0.71 inference(quant_inst,[status(thm)],[])).
% 0.56/0.71 tff(802,plain,
% 0.56/0.71 ((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | (~program(W)) | outputs(W, bad) | (~decides(W, f4(W), f3(W))))) | outputs(c1, bad) | (~program(c1)) | (~decides(c1, f4(c1), f3(c1))) | (~program(c2)) | halts2(c2, f6(c2))),
% 0.56/0.71 inference(modus_ponens,[status(thm)],[801, 800])).
% 0.56/0.71 tff(803,plain,
% 0.56/0.71 (~decides(c1, f4(c1), f3(c1))),
% 0.56/0.71 inference(unit_resolution,[status(thm)],[802, 495, 48, 663, 566, 119])).
% 0.56/0.71 tff(804,plain,
% 0.56/0.71 (~program(f4(c1))),
% 0.56/0.71 inference(unit_resolution,[status(thm)],[373, 370, 6, 321, 803])).
% 0.56/0.71 tff(805,plain,
% 0.56/0.71 (((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, bad))) | (outputs(c1, bad) | (~program(c1)) | program(f4(c1)) | (~program(c2)) | halts2(c2, f6(c2)))) <=> ((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, bad))) | outputs(c1, bad) | (~program(c1)) | program(f4(c1)) | (~program(c2)) | halts2(c2, f6(c2)))),
% 0.56/0.71 inference(rewrite,[status(thm)],[])).
% 0.56/0.71 tff(806,plain,
% 0.56/0.71 ((halts2(c2, f6(c2)) | (~program(c2)) | program(f4(c1)) | (~program(c1)) | outputs(c1, bad)) <=> (outputs(c1, bad) | (~program(c1)) | program(f4(c1)) | (~program(c2)) | halts2(c2, f6(c2)))),
% 0.56/0.71 inference(rewrite,[status(thm)],[])).
% 0.56/0.71 tff(807,plain,
% 0.56/0.71 (((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, bad))) | (halts2(c2, f6(c2)) | (~program(c2)) | program(f4(c1)) | (~program(c1)) | outputs(c1, bad))) <=> ((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, bad))) | (outputs(c1, bad) | (~program(c1)) | program(f4(c1)) | (~program(c2)) | halts2(c2, f6(c2))))),
% 0.56/0.71 inference(monotonicity,[status(thm)],[806])).
% 0.56/0.71 tff(808,plain,
% 0.56/0.71 (((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, bad))) | (halts2(c2, f6(c2)) | (~program(c2)) | program(f4(c1)) | (~program(c1)) | outputs(c1, bad))) <=> ((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, bad))) | outputs(c1, bad) | (~program(c1)) | program(f4(c1)) | (~program(c2)) | halts2(c2, f6(c2)))),
% 0.56/0.71 inference(transitivity,[status(thm)],[807, 805])).
% 0.56/0.71 tff(809,plain,
% 0.56/0.71 ((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, bad))) | (halts2(c2, f6(c2)) | (~program(c2)) | program(f4(c1)) | (~program(c1)) | outputs(c1, bad))),
% 0.56/0.71 inference(quant_inst,[status(thm)],[])).
% 0.56/0.71 tff(810,plain,
% 0.56/0.71 ((~![W: $i, Z: $i, Y: $i] : (halts2(Y, Z) | (~program(Y)) | program(f4(W)) | (~program(W)) | outputs(W, bad))) | outputs(c1, bad) | (~program(c1)) | program(f4(c1)) | (~program(c2)) | halts2(c2, f6(c2))),
% 0.56/0.71 inference(modus_ponens,[status(thm)],[809, 808])).
% 0.56/0.71 tff(811,plain,
% 0.56/0.71 ($false),
% 0.56/0.71 inference(unit_resolution,[status(thm)],[810, 513, 48, 663, 566, 119, 804])).
% 0.56/0.71 tff(812,plain,(halts2(c2, f6(c2)) | outputs(c1, bad) | program(f2(c4))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.71 tff(813,plain,
% 0.56/0.71 ($false),
% 0.56/0.71 inference(unit_resolution,[status(thm)],[812, 796, 756, 321])).
% 0.56/0.71 tff(814,plain,(program(f2(c4))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.71 tff(815,plain,
% 0.56/0.71 (decides(c4, f2(c4), f1(c4))),
% 0.56/0.71 inference(unit_resolution,[status(thm)],[526, 814])).
% 0.56/0.71 tff(816,plain,
% 0.56/0.71 (~program(f4(c1))),
% 0.56/0.71 inference(unit_resolution,[status(thm)],[545, 542, 6, 815, 674])).
% 0.56/0.71 tff(817,plain,
% 0.56/0.71 ($false),
% 0.56/0.71 inference(unit_resolution,[status(thm)],[467, 461, 48, 1, 672, 318, 816])).
% 0.56/0.71 tff(818,plain,(outputs(c1, good)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.71 tff(819,plain,
% 0.56/0.71 (~halts2(c2, f6(c2))),
% 0.56/0.71 inference(unit_resolution,[status(thm)],[755, 818])).
% 0.56/0.71 tff(820,plain,
% 0.56/0.71 (^[W: $i, Y: $i] : refl(((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) <=> ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))))),
% 0.56/0.71 inference(bind,[status(th)],[])).
% 0.56/0.71 tff(821,plain,
% 0.56/0.71 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.71 inference(quant_intro,[status(thm)],[820])).
% 0.56/0.71 tff(822,plain,
% 0.56/0.71 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.71 inference(rewrite,[status(thm)],[])).
% 0.56/0.71 tff(823,plain,
% 0.56/0.71 (^[W: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) <=> ((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))), (((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) <=> (((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))))), rewrite((((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) <=> ((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))), (((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) <=> ((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))))), ((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) <=> (((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) | (~program(Y))))), rewrite((((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) | (~program(Y))) <=> ((~program(W)) | (~program(Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))), ((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) <=> ((~program(W)) | (~program(Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))))), (((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) | halts2(Y, Y)) <=> (((~program(W)) | (~program(Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) | halts2(Y, Y)))), rewrite((((~program(W)) | (~program(Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) | halts2(Y, Y)) <=> ((~program(W)) | (~program(Y)) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))), (((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) | halts2(Y, Y)) <=> ((~program(W)) | (~program(Y)) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))))), ((((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) | halts2(Y, Y)) | halts2(c2, Y)) <=> (((~program(W)) | (~program(Y)) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) | halts2(c2, Y)))), rewrite((((~program(W)) | (~program(Y)) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) | halts2(c2, Y)) <=> ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))), ((((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) | halts2(Y, Y)) | halts2(c2, Y)) <=> ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))))),
% 0.56/0.71 inference(bind,[status(th)],[])).
% 0.56/0.71 tff(824,plain,
% 0.56/0.71 (![W: $i, Y: $i] : (((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) | halts2(Y, Y)) | halts2(c2, Y)) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.71 inference(quant_intro,[status(thm)],[823])).
% 0.56/0.71 tff(825,axiom,(![W: $i, Y: $i] : (((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) | halts2(Y, Y)) | halts2(c2, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_3_14')).
% 0.56/0.72 tff(826,plain,
% 0.56/0.72 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[825, 824])).
% 0.56/0.72 tff(827,plain,
% 0.56/0.72 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[826, 822])).
% 0.56/0.72 tff(828,plain,(
% 0.56/0.72 ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.72 inference(skolemize,[status(sab)],[827])).
% 0.56/0.72 tff(829,plain,
% 0.56/0.72 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[828, 821])).
% 0.56/0.72 tff(830,plain,
% 0.56/0.72 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | ((~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2))))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2))))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(831,plain,
% 0.56/0.72 (((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~outputs(c1, good))) <=> ((~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2))))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(832,plain,
% 0.56/0.72 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | ((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~outputs(c1, good)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | ((~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2)))))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[831])).
% 0.56/0.72 tff(833,plain,
% 0.56/0.72 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | ((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~outputs(c1, good)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2))))),
% 0.56/0.72 inference(transitivity,[status(thm)],[832, 830])).
% 0.56/0.72 tff(834,plain,
% 0.56/0.72 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | ((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~outputs(c1, good)))),
% 0.56/0.72 inference(quant_inst,[status(thm)],[])).
% 0.56/0.72 tff(835,plain,
% 0.56/0.72 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | halts2(Y, Y) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2)) | (~program(f6(c2)))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[834, 833])).
% 0.56/0.72 tff(836,plain,
% 0.56/0.72 ((~outputs(c1, good)) | halts2(c2, f6(c2)) | halts2(f6(c2), f6(c2))),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[835, 829, 48, 572, 672, 759])).
% 0.56/0.72 tff(837,plain,
% 0.56/0.72 (halts2(f6(c2), f6(c2))),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[836, 818, 819])).
% 0.56/0.72 tff(838,plain,
% 0.56/0.72 (^[W: $i, Y: $i] : refl(((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) <=> ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))))),
% 0.56/0.72 inference(bind,[status(th)],[])).
% 0.56/0.72 tff(839,plain,
% 0.56/0.72 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.72 inference(quant_intro,[status(thm)],[838])).
% 0.56/0.72 tff(840,plain,
% 0.56/0.72 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(841,plain,
% 0.56/0.72 (^[W: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) <=> ((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good)))), (((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) <=> (((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))))), rewrite((((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) <=> ((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))), (((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) <=> ((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))))), ((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) <=> (((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) | (~program(Y))))), rewrite((((~program(W)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) | (~program(Y))) <=> ((~program(W)) | (~program(Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))), ((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) <=> ((~program(W)) | (~program(Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))))), (((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) | (~halts2(Y, Y))) <=> (((~program(W)) | (~program(Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) | (~halts2(Y, Y))))), rewrite((((~program(W)) | (~program(Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) | (~halts2(Y, Y))) <=> ((~program(W)) | (~program(Y)) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))), (((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) | (~halts2(Y, Y))) <=> ((~program(W)) | (~program(Y)) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))))), ((((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) | (~halts2(Y, Y))) | halts2(c2, Y)) <=> (((~program(W)) | (~program(Y)) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) | halts2(c2, Y)))), rewrite((((~program(W)) | (~program(Y)) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good))) | halts2(c2, Y)) <=> ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))), ((((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) | (~halts2(Y, Y))) | halts2(c2, Y)) <=> ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))))),
% 0.56/0.72 inference(bind,[status(th)],[])).
% 0.56/0.72 tff(842,plain,
% 0.56/0.72 (![W: $i, Y: $i] : (((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) | (~halts2(Y, Y))) | halts2(c2, Y)) <=> ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.72 inference(quant_intro,[status(thm)],[841])).
% 0.56/0.72 tff(843,axiom,(![W: $i, Y: $i] : (((((((~program(W)) | (~halts3(W, f5(W), f5(W)))) | (~outputs(W, good))) | (~halts2(f5(W), f5(W)))) | (~program(Y))) | (~halts2(Y, Y))) | halts2(c2, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_3_12')).
% 0.56/0.72 tff(844,plain,
% 0.56/0.72 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[843, 842])).
% 0.56/0.72 tff(845,plain,
% 0.56/0.72 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[844, 840])).
% 0.56/0.72 tff(846,plain,(
% 0.56/0.72 ![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.72 inference(skolemize,[status(sab)],[845])).
% 0.56/0.72 tff(847,plain,
% 0.56/0.72 (![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[846, 839])).
% 0.56/0.72 tff(848,plain,
% 0.56/0.72 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | ((~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~program(f6(c2))))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~program(f6(c2))))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(849,plain,
% 0.56/0.72 (((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~outputs(c1, good))) <=> ((~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~program(f6(c2))))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(850,plain,
% 0.56/0.72 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | ((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~outputs(c1, good)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | ((~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~program(f6(c2)))))),
% 0.65/0.73 inference(monotonicity,[status(thm)],[849])).
% 0.65/0.73 tff(851,plain,
% 0.65/0.73 (((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | ((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~outputs(c1, good)))) <=> ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~program(f6(c2))))),
% 0.65/0.73 inference(transitivity,[status(thm)],[850, 848])).
% 0.65/0.73 tff(852,plain,
% 0.65/0.73 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | ((~program(c1)) | (~program(f6(c2))) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~outputs(c1, good)))),
% 0.65/0.73 inference(quant_inst,[status(thm)],[])).
% 0.65/0.73 tff(853,plain,
% 0.65/0.73 ((~![W: $i, Y: $i] : ((~program(W)) | (~program(Y)) | halts2(c2, Y) | (~halts2(Y, Y)) | (~halts3(W, f5(W), f5(W))) | (~halts2(f5(W), f5(W))) | (~outputs(W, good)))) | (~outputs(c1, good)) | (~halts3(c1, f5(c1), f5(c1))) | (~halts2(f5(c1), f5(c1))) | (~program(c1)) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2))) | (~program(f6(c2)))),
% 0.65/0.73 inference(modus_ponens,[status(thm)],[852, 851])).
% 0.65/0.73 tff(854,plain,
% 0.65/0.73 ((~outputs(c1, good)) | halts2(c2, f6(c2)) | (~halts2(f6(c2), f6(c2)))),
% 0.65/0.73 inference(unit_resolution,[status(thm)],[853, 847, 48, 572, 672, 759])).
% 0.65/0.73 tff(855,plain,
% 0.65/0.73 ($false),
% 0.65/0.73 inference(unit_resolution,[status(thm)],[854, 837, 818, 819])).
% 0.65/0.73 % SZS output end Proof
%------------------------------------------------------------------------------