TSTP Solution File: COM003-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : COM003-1 : TPTP v8.1.2. Bugfixed v1.0.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.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 : Fri May 19 10:13:51 EDT 2023
% Result : Unsatisfiable 17.19s 3.86s
% Output : Refutation 17.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 68
% Syntax : Number of formulae : 176 ( 3 unt; 18 typ; 0 def)
% Number of atoms : 836 ( 40 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 2727 ( 505 ~; 624 |; 0 &;1598 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 8 con; 0-3 aty)
% Number of variables : 229 ( 0 ^; 229 !; 0 ?; 229 :)
% Comments :
%------------------------------------------------------------------------------
thf(algorithm_type,type,
algorithm: $i > $o ).
thf(c4_type,type,
c4: $i ).
thf(program_type,type,
program: $i > $o ).
thf(decides_type,type,
decides: $i > $i > $i > $o ).
thf(halts3_type,type,
halts3: $i > $i > $i > $o ).
thf(f5_type,type,
f5: $i > $i ).
thf(outputs_type,type,
outputs: $i > $i > $o ).
thf(good_type,type,
good: $i ).
thf(halts2_type,type,
halts2: $i > $i > $o ).
thf(c2_type,type,
c2: $i ).
thf(f6_type,type,
f6: $i > $i ).
thf(bad_type,type,
bad: $i ).
thf(c3_type,type,
c3: $i ).
thf(f2_type,type,
f2: $i > $i ).
thf(f1_type,type,
f1: $i > $i ).
thf(c1_type,type,
c1: $i ).
thf(f4_type,type,
f4: $i > $i ).
thf(f3_type,type,
f3: $i > $i ).
thf(47,axiom,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ~ ( halts2 @ B @ B )
| ~ ( halts2 @ c3 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_4_14) ).
thf(142,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ~ ( halts2 @ B @ B )
| ~ ( halts2 @ c3 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(143,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ~ ( halts2 @ B @ B )
| ~ ( halts2 @ c3 @ B ) ),
inference(cnf,[status(esa)],[142]) ).
thf(174,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ~ ( halts2 @ B @ B )
| ( ( halts2 @ c3 @ B )
!= ( halts2 @ B @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[143]) ).
thf(175,plain,
! [A: $i] :
( ~ ( program @ A )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( outputs @ A @ bad )
| ~ ( program @ c3 )
| ~ ( halts2 @ c3 @ c3 ) ),
inference(pattern_uni,[status(thm)],[174:[bind(A,$thf( A )),bind(B,$thf( c3 ))]]) ).
thf(551,plain,
! [A: $i] :
( ~ ( program @ A )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( outputs @ A @ bad )
| ~ ( program @ c3 )
| ( ( halts2 @ c3 @ c3 )
!= ( halts2 @ A @ ( f6 @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[175]) ).
thf(553,plain,
! [A: $i] :
( ~ ( program @ A )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( outputs @ A @ bad )
| ~ ( program @ c3 )
| ( c3 != A )
| ( ( f6 @ A )
!= c3 ) ),
inference(simp,[status(thm)],[551]) ).
thf(561,plain,
( ~ ( program @ c3 )
| ~ ( halts2 @ c3 @ ( f6 @ c3 ) )
| ~ ( outputs @ c3 @ good )
| ~ ( outputs @ c3 @ bad )
| ~ ( program @ c3 )
| ( ( f6 @ c3 )
!= c3 ) ),
inference(simp,[status(thm)],[553]) ).
thf(565,plain,
( ~ ( program @ c3 )
| ~ ( halts2 @ c3 @ ( f6 @ c3 ) )
| ~ ( outputs @ c3 @ good )
| ~ ( outputs @ c3 @ bad )
| ( ( f6 @ c3 )
!= c3 ) ),
inference(simp,[status(thm)],[561]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( program @ ( f6 @ A ) )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( outputs @ c3 @ bad ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_4_4) ).
thf(70,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( program @ ( f6 @ A ) )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( outputs @ c3 @ bad ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( halts2 @ ( f6 @ A ) @ ( f6 @ A ) )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( halts2 @ c3 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_4_11) ).
thf(92,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( halts2 @ ( f6 @ A ) @ ( f6 @ A ) )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( halts2 @ c3 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(2,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( decides @ c4 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_the_algorithm_doesnt_exist) ).
thf(52,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( decides @ c4 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( decides @ c4 @ A @ B ) ),
inference(cnf,[status(esa)],[52]) ).
thf(1,negated_conjecture,
algorithm @ c4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_deciding_algorithm) ).
thf(51,plain,
algorithm @ c4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(32,axiom,
! [A: $i] :
( ~ ( algorithm @ A )
| ( program @ ( f2 @ A ) )
| ( program @ c1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_1_1) ).
thf(112,plain,
! [A: $i] :
( ~ ( algorithm @ A )
| ( program @ ( f2 @ A ) )
| ( program @ c1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(113,plain,
! [A: $i] :
( ~ ( algorithm @ A )
| ( program @ ( f2 @ A ) )
| ( program @ c1 ) ),
inference(cnf,[status(esa)],[112]) ).
thf(150,plain,
! [A: $i] :
( ( program @ ( f2 @ A ) )
| ( program @ c1 )
| ( ( algorithm @ c4 )
!= ( algorithm @ A ) ) ),
inference(paramod_ordered,[status(thm)],[51,113]) ).
thf(151,plain,
( ( program @ ( f2 @ c4 ) )
| ( program @ c1 ) ),
inference(pattern_uni,[status(thm)],[150:[bind(A,$thf( c4 ))]]) ).
thf(42,axiom,
! [A: $i] :
( ~ ( program @ A )
| ( program @ ( f5 @ A ) )
| ( program @ c2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_1) ).
thf(132,plain,
! [A: $i] :
( ~ ( program @ A )
| ( program @ ( f5 @ A ) )
| ( program @ c2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(133,plain,
! [A: $i] :
( ~ ( program @ A )
| ( program @ ( f5 @ A ) )
| ( program @ c2 ) ),
inference(cnf,[status(esa)],[132]) ).
thf(234,plain,
! [A: $i] :
( ( program @ c1 )
| ( program @ ( f5 @ A ) )
| ( program @ c2 )
| ( ( program @ ( f2 @ c4 ) )
!= ( program @ A ) ) ),
inference(paramod_ordered,[status(thm)],[151,133]) ).
thf(235,plain,
( ( program @ c1 )
| ( program @ ( f5 @ ( f2 @ c4 ) ) )
| ( program @ c2 ) ),
inference(pattern_uni,[status(thm)],[234:[bind(A,$thf( f2 @ c4 ))]]) ).
thf(248,plain,
! [A: $i] :
( ( program @ c1 )
| ( program @ c2 )
| ( program @ ( f5 @ A ) )
| ( ( program @ ( f5 @ ( f2 @ c4 ) ) )
!= ( program @ A ) ) ),
inference(paramod_ordered,[status(thm)],[235,133]) ).
thf(249,plain,
( ( program @ c1 )
| ( program @ c2 )
| ( program @ ( f5 @ ( f5 @ ( f2 @ c4 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[248:[bind(A,$thf( f5 @ ( f2 @ c4 ) ))]]) ).
thf(362,plain,
( ( program @ c1 )
| ( program @ c2 )
| ( ( program @ ( f5 @ ( f5 @ ( f2 @ c4 ) ) ) )
!= ( program @ c1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[249]) ).
thf(371,plain,
( ( program @ c1 )
| ( program @ c2 )
| ( ( program @ ( f5 @ ( f5 @ ( f2 @ c4 ) ) ) )
!= ( program @ c1 ) ) ),
inference(simp,[status(thm)],[362]) ).
thf(28,axiom,
! [A: $i] :
( ~ ( program @ A )
| ( halts2 @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ bad )
| ( program @ c2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_6) ).
thf(104,plain,
! [A: $i] :
( ~ ( program @ A )
| ( halts2 @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ bad )
| ( program @ c2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( program @ ( f5 @ A ) )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( outputs @ c2 @ bad ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_5) ).
thf(138,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( program @ ( f5 @ A ) )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( outputs @ c2 @ bad ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(20,axiom,
! [A: $i] :
( ~ ( program @ A )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( halts2 @ ( f5 @ A ) @ ( f5 @ A ) )
| ( program @ c2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_11) ).
thf(88,plain,
! [A: $i] :
( ~ ( program @ A )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( halts2 @ ( f5 @ A ) @ ( f5 @ A ) )
| ( program @ c2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( outputs @ c2 @ bad ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_20) ).
thf(120,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( outputs @ c2 @ bad ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(263,plain,
( ( program @ c1 )
| ( program @ c2 )
| ( ( program @ ( f5 @ ( f2 @ c4 ) ) )
!= ( program @ c1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[235]) ).
thf(269,plain,
( ( program @ c1 )
| ( program @ c2 )
| ( ( f5 @ ( f2 @ c4 ) )
!= c1 ) ),
inference(simp,[status(thm)],[263]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( program @ ( f5 @ A ) )
| ~ ( program @ B )
| ~ ( halts2 @ B @ B )
| ( outputs @ c2 @ good ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_3) ).
thf(56,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( program @ ( f5 @ A ) )
| ~ ( program @ B )
| ~ ( halts2 @ B @ B )
| ( outputs @ c2 @ good ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(372,plain,
( ( program @ c1 )
| ( program @ c2 )
| ( ( f5 @ ( f5 @ ( f2 @ c4 ) ) )
!= c1 ) ),
inference(simp,[status(thm)],[362]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( halts2 @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( halts2 @ c2 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_14) ).
thf(110,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( halts2 @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( halts2 @ c2 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(343,plain,
! [A: $i] :
( ( program @ c1 )
| ( program @ c2 )
| ( program @ ( f5 @ A ) )
| ( ( program @ ( f5 @ ( f5 @ ( f2 @ c4 ) ) ) )
!= ( program @ A ) ) ),
inference(paramod_ordered,[status(thm)],[249,133]) ).
thf(344,plain,
( ( program @ c1 )
| ( program @ c2 )
| ( program @ ( f5 @ ( f5 @ ( f5 @ ( f2 @ c4 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[343:[bind(A,$thf( f5 @ ( f5 @ ( f2 @ c4 ) ) ))]]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( program @ ( f5 @ A ) )
| ~ ( program @ B )
| ~ ( halts2 @ B @ B )
| ( outputs @ c2 @ good ) ),
inference(cnf,[status(esa)],[56]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( program @ ( f6 @ A ) )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( halts2 @ c3 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_4_3) ).
thf(78,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( program @ ( f6 @ A ) )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( halts2 @ c3 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( halts2 @ ( f6 @ A ) @ ( f6 @ A ) )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( halts2 @ c3 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_4_7) ).
thf(106,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( halts2 @ ( f6 @ A ) @ ( f6 @ A ) )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( halts2 @ c3 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( halts2 @ ( f6 @ A ) @ ( f6 @ A ) )
| ~ ( program @ B )
| ~ ( halts2 @ B @ B )
| ~ ( halts2 @ c3 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_4_10) ).
thf(84,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( halts2 @ ( f6 @ A ) @ ( f6 @ A ) )
| ~ ( program @ B )
| ~ ( halts2 @ B @ B )
| ~ ( halts2 @ c3 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(34,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( decides @ A @ ( f4 @ A ) @ ( f3 @ A ) )
| ~ ( program @ B )
| ( halts2 @ B @ C )
| ( halts3 @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_2_7) ).
thf(116,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( decides @ A @ ( f4 @ A ) @ ( f3 @ A ) )
| ~ ( program @ B )
| ( halts2 @ B @ C )
| ( halts3 @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(13,axiom,
! [A: $i] :
( ~ ( program @ A )
| ( halts2 @ ( f6 @ A ) @ ( f6 @ A ) )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ bad )
| ( program @ c3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_4_5) ).
thf(74,plain,
! [A: $i] :
( ~ ( program @ A )
| ( halts2 @ ( f6 @ A ) @ ( f6 @ A ) )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ bad )
| ( program @ c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( algorithm @ A )
| ~ ( decides @ A @ ( f2 @ A ) @ ( f1 @ A ) )
| ( program @ c1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_1_3) ).
thf(60,plain,
! [A: $i] :
( ~ ( algorithm @ A )
| ~ ( decides @ A @ ( f2 @ A ) @ ( f1 @ A ) )
| ( program @ c1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(507,plain,
( ( program @ c1 )
| ( program @ c2 )
| ( ( program @ ( f5 @ ( f5 @ ( f5 @ ( f2 @ c4 ) ) ) ) )
!= ( program @ c2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[344]) ).
thf(512,plain,
( ( program @ c1 )
| ( program @ c2 )
| ( ( f5 @ ( f5 @ ( f5 @ ( f2 @ c4 ) ) ) )
!= c2 ) ),
inference(simp,[status(thm)],[507]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( program @ A )
| ( program @ ( f4 @ A ) )
| ~ ( program @ B )
| ( halts2 @ B @ C )
| ( halts3 @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_2_3) ).
thf(102,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( program @ A )
| ( program @ ( f4 @ A ) )
| ~ ( program @ B )
| ( halts2 @ B @ C )
| ( halts3 @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( decides @ A @ ( f4 @ A ) @ ( f3 @ A ) )
| ~ ( program @ B )
| ( halts2 @ B @ C )
| ( outputs @ A @ bad ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_2_8) ).
thf(124,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( decides @ A @ ( f4 @ A ) @ ( f3 @ A ) )
| ~ ( program @ B )
| ( halts2 @ B @ C )
| ( outputs @ A @ bad ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( algorithm @ A )
| ( program @ ( f2 @ A ) )
| ~ ( program @ B )
| ( decides @ c1 @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_1_2) ).
thf(96,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( algorithm @ A )
| ( program @ ( f2 @ A ) )
| ~ ( program @ B )
| ( decides @ c1 @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(43,axiom,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( program @ ( f5 @ A ) )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( halts2 @ c2 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_4) ).
thf(134,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( program @ ( f5 @ A ) )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( halts2 @ c2 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(40,axiom,
! [A: $i] :
( ~ ( program @ A )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( outputs @ A @ bad )
| ( program @ c2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_16) ).
thf(128,plain,
! [A: $i] :
( ~ ( program @ A )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( outputs @ A @ bad )
| ( program @ c2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(264,plain,
( ( program @ c1 )
| ( program @ c2 )
| ( ( program @ ( f5 @ ( f2 @ c4 ) ) )
!= ( program @ c2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[235]) ).
thf(266,plain,
( ( program @ c1 )
| ( program @ c2 )
| ( ( program @ ( f5 @ ( f2 @ c4 ) ) )
!= ( program @ c2 ) ) ),
inference(simp,[status(thm)],[264]) ).
thf(485,plain,
! [A: $i] :
( ( program @ c1 )
| ( program @ c2 )
| ( program @ ( f5 @ A ) )
| ( ( program @ ( f5 @ ( f5 @ ( f5 @ ( f2 @ c4 ) ) ) ) )
!= ( program @ A ) ) ),
inference(paramod_ordered,[status(thm)],[344,133]) ).
thf(486,plain,
( ( program @ c1 )
| ( program @ c2 )
| ( program @ ( f5 @ ( f5 @ ( f5 @ ( f5 @ ( f2 @ c4 ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[485:[bind(A,$thf( f5 @ ( f5 @ ( f5 @ ( f2 @ c4 ) ) ) ))]]) ).
thf(608,plain,
( ( program @ c1 )
| ( program @ c2 )
| ( ( program @ ( f5 @ ( f5 @ ( f5 @ ( f5 @ ( f2 @ c4 ) ) ) ) ) )
!= ( program @ c2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[486]) ).
thf(618,plain,
( ( program @ c1 )
| ( program @ c2 )
| ( ( f5 @ ( f5 @ ( f5 @ ( f5 @ ( f2 @ c4 ) ) ) ) )
!= c2 ) ),
inference(simp,[status(thm)],[608]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ~ ( halts2 @ B @ B )
| ( halts2 @ c2 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_17) ).
thf(148,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ~ ( halts2 @ B @ B )
| ( halts2 @ c2 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(160,plain,
( ( program @ c1 )
| ( ( program @ ( f2 @ c4 ) )
!= ( program @ c1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[151]) ).
thf(161,plain,
( ( program @ c1 )
| ( ( program @ ( f2 @ c4 ) )
!= ( program @ c1 ) ) ),
inference(simp,[status(thm)],[160]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( halts2 @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( program @ B )
| ~ ( halts2 @ B @ B )
| ( halts2 @ c2 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_12) ).
thf(64,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( halts2 @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( program @ B )
| ~ ( halts2 @ B @ B )
| ( halts2 @ c2 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(363,plain,
( ( program @ c1 )
| ( program @ c2 )
| ( ( program @ ( f5 @ ( f5 @ ( f2 @ c4 ) ) ) )
!= ( program @ c2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[249]) ).
thf(375,plain,
( ( program @ c1 )
| ( program @ c2 )
| ( ( f5 @ ( f5 @ ( f2 @ c4 ) ) )
!= c2 ) ),
inference(simp,[status(thm)],[363]) ).
thf(173,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ~ ( halts2 @ B @ B )
| ( ( halts2 @ c3 @ B )
!= ( halts2 @ A @ ( f6 @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[143]) ).
thf(176,plain,
( ~ ( program @ c3 )
| ~ ( halts2 @ c3 @ ( f6 @ c3 ) )
| ~ ( outputs @ c3 @ good )
| ~ ( outputs @ c3 @ bad )
| ~ ( program @ ( f6 @ c3 ) )
| ~ ( halts2 @ ( f6 @ c3 ) @ ( f6 @ c3 ) ) ),
inference(pattern_uni,[status(thm)],[173:[bind(A,$thf( c3 )),bind(B,$thf( f6 @ c3 ))]]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( halts2 @ c3 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_4_15) ).
thf(58,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( halts2 @ c3 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( halts2 @ c3 @ B ) ),
inference(cnf,[status(esa)],[58]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( program @ A )
| ( program @ ( f4 @ A ) )
| ~ ( program @ B )
| ~ ( halts2 @ B @ C )
| ( halts3 @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_2_1) ).
thf(118,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( program @ A )
| ( program @ ( f4 @ A ) )
| ~ ( program @ B )
| ~ ( halts2 @ B @ C )
| ( halts3 @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( halts2 @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( program @ B )
| ~ ( halts2 @ B @ B )
| ( outputs @ c2 @ good ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_13) ).
thf(54,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( halts2 @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( program @ B )
| ~ ( halts2 @ B @ B )
| ( outputs @ c2 @ good ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(48,axiom,
! [A: $i] :
( ~ ( program @ A )
| ( program @ ( f6 @ A ) )
| ( program @ c3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_4_1) ).
thf(144,plain,
! [A: $i] :
( ~ ( program @ A )
| ( program @ ( f6 @ A ) )
| ( program @ c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( halts2 @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( outputs @ c2 @ bad ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_10) ).
thf(86,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( halts2 @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( outputs @ c2 @ bad ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( halts2 @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( halts2 @ c2 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_9) ).
thf(76,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( halts2 @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( halts2 @ c2 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( halts2 @ ( f6 @ A ) @ ( f6 @ A ) )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( outputs @ c3 @ bad ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_4_8) ).
thf(98,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( halts2 @ ( f6 @ A ) @ ( f6 @ A ) )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( outputs @ c3 @ bad ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(552,plain,
! [A: $i] :
( ~ ( program @ A )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( outputs @ A @ bad )
| ~ ( program @ c3 )
| ( ( halts2 @ c3 @ c3 )
!= ( halts2 @ A @ ( f6 @ A ) ) ) ),
inference(simp,[status(thm)],[551]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ~ ( halts2 @ B @ B )
| ( outputs @ c2 @ good ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_18) ).
thf(140,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ~ ( halts2 @ B @ B )
| ( outputs @ c2 @ good ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(607,plain,
( ( program @ c1 )
| ( program @ c2 )
| ( ( program @ ( f5 @ ( f5 @ ( f5 @ ( f5 @ ( f2 @ c4 ) ) ) ) ) )
!= ( program @ c1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[486]) ).
thf(621,plain,
( ( program @ c1 )
| ( program @ c2 )
| ( ( f5 @ ( f5 @ ( f5 @ ( f5 @ ( f2 @ c4 ) ) ) ) )
!= c1 ) ),
inference(simp,[status(thm)],[607]) ).
thf(30,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( program @ A )
| ( program @ ( f4 @ A ) )
| ~ ( program @ B )
| ( halts2 @ B @ C )
| ( outputs @ A @ bad ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_2_4) ).
thf(108,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( program @ A )
| ( program @ ( f4 @ A ) )
| ~ ( program @ B )
| ( halts2 @ B @ C )
| ( outputs @ A @ bad ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(506,plain,
( ( program @ c1 )
| ( program @ c2 )
| ( ( program @ ( f5 @ ( f5 @ ( f5 @ ( f2 @ c4 ) ) ) ) )
!= ( program @ c1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[344]) ).
thf(520,plain,
( ( program @ c1 )
| ( program @ c2 )
| ( ( f5 @ ( f5 @ ( f5 @ ( f2 @ c4 ) ) ) )
!= c1 ) ),
inference(simp,[status(thm)],[506]) ).
thf(9,axiom,
! [A: $i] :
( ~ ( program @ A )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( halts2 @ ( f6 @ A ) @ ( f6 @ A ) )
| ( program @ c3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_4_9) ).
thf(66,plain,
! [A: $i] :
( ~ ( program @ A )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( halts2 @ ( f6 @ A ) @ ( f6 @ A ) )
| ( program @ c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( halts2 @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ~ ( halts2 @ B @ B )
| ( halts2 @ c2 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_7) ).
thf(130,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( halts2 @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ~ ( halts2 @ B @ B )
| ( halts2 @ c2 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(267,plain,
( ( program @ c1 )
| ( program @ c2 )
| ( ( f5 @ ( f2 @ c4 ) )
!= c2 ) ),
inference(simp,[status(thm)],[264]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( decides @ A @ ( f4 @ A ) @ ( f3 @ A ) )
| ~ ( program @ B )
| ~ ( halts2 @ B @ C )
| ( outputs @ A @ good ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_2_6) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( decides @ A @ ( f4 @ A ) @ ( f3 @ A ) )
| ~ ( program @ B )
| ~ ( halts2 @ B @ C )
| ( outputs @ A @ good ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(162,plain,
( ( program @ c1 )
| ( ( f2 @ c4 )
!= c1 ) ),
inference(simp,[status(thm)],[160]) ).
thf(374,plain,
( ( program @ c1 )
| ( program @ c2 )
| ( ( program @ ( f5 @ ( f5 @ ( f2 @ c4 ) ) ) )
!= ( program @ c2 ) ) ),
inference(simp,[status(thm)],[363]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( halts2 @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( outputs @ c2 @ bad ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_15) ).
thf(72,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( halts2 @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( outputs @ c2 @ bad ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( halts2 @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( program @ B )
| ~ ( halts2 @ B @ B )
| ( outputs @ c2 @ good ) ),
inference(cnf,[status(esa)],[54]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( algorithm @ A )
| ~ ( decides @ A @ ( f2 @ A ) @ ( f1 @ A ) )
| ~ ( program @ B )
| ( decides @ c1 @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_1_4) ).
thf(114,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( algorithm @ A )
| ~ ( decides @ A @ ( f2 @ A ) @ ( f1 @ A ) )
| ~ ( program @ B )
| ( decides @ c1 @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( outputs @ c3 @ bad ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_4_17) ).
thf(82,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( outputs @ c3 @ bad ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(49,axiom,
! [A: $i] :
( ~ ( program @ A )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( outputs @ A @ bad )
| ( program @ c3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_4_13) ).
thf(146,plain,
! [A: $i] :
( ~ ( program @ A )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( outputs @ A @ bad )
| ( program @ c3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(187,plain,
( ~ ( program @ c3 )
| ~ ( halts2 @ c3 @ ( f6 @ c3 ) )
| ~ ( outputs @ c3 @ good )
| ~ ( outputs @ c3 @ bad )
| ~ ( program @ ( f6 @ c3 ) )
| ( ( halts2 @ ( f6 @ c3 ) @ ( f6 @ c3 ) )
!= ( halts2 @ c3 @ ( f6 @ c3 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[176]) ).
thf(190,plain,
( ~ ( program @ c3 )
| ~ ( halts2 @ c3 @ ( f6 @ c3 ) )
| ~ ( outputs @ c3 @ good )
| ~ ( outputs @ c3 @ bad )
| ~ ( program @ ( f6 @ c3 ) )
| ( ( halts2 @ ( f6 @ c3 ) @ ( f6 @ c3 ) )
!= ( halts2 @ c3 @ ( f6 @ c3 ) ) ) ),
inference(simp,[status(thm)],[187]) ).
thf(250,plain,
! [B: $i,A: $i] :
( ( program @ c1 )
| ( program @ c2 )
| ( decides @ c4 @ A @ B )
| ( ( program @ ( f5 @ ( f2 @ c4 ) ) )
!= ( program @ A ) ) ),
inference(paramod_ordered,[status(thm)],[235,53]) ).
thf(251,plain,
! [A: $i] :
( ( program @ c1 )
| ( program @ c2 )
| ( decides @ c4 @ ( f5 @ ( f2 @ c4 ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[250:[bind(A,$thf( f5 @ ( f2 @ c4 ) )),bind(B,$thf( B ))]]) ).
thf(273,plain,
! [A: $i] :
( ( program @ c1 )
| ( program @ c2 )
| ( decides @ c4 @ ( f5 @ ( f2 @ c4 ) ) @ A ) ),
inference(simp,[status(thm)],[251]) ).
thf(268,plain,
( ( program @ c1 )
| ( program @ c2 )
| ( ( program @ ( f5 @ ( f2 @ c4 ) ) )
!= ( program @ c1 ) ) ),
inference(simp,[status(thm)],[263]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( halts2 @ ( f6 @ A ) @ ( f6 @ A ) )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ~ ( halts2 @ B @ B )
| ~ ( halts2 @ c3 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_4_6) ).
thf(94,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( halts2 @ ( f6 @ A ) @ ( f6 @ A ) )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ~ ( halts2 @ B @ B )
| ~ ( halts2 @ c3 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( decides @ A @ ( f4 @ A ) @ ( f3 @ A ) )
| ~ ( program @ B )
| ~ ( halts2 @ B @ C )
| ( halts3 @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_2_5) ).
thf(126,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( decides @ A @ ( f4 @ A ) @ ( f3 @ A ) )
| ~ ( program @ B )
| ~ ( halts2 @ B @ C )
| ( halts3 @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( halts2 @ ( f6 @ A ) @ ( f6 @ A ) )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( outputs @ c3 @ bad ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_4_12) ).
thf(136,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts2 @ A @ ( f6 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( halts2 @ ( f6 @ A ) @ ( f6 @ A ) )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( outputs @ c3 @ bad ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(158,plain,
! [B: $i,A: $i] :
( ( program @ c1 )
| ( decides @ c4 @ A @ B )
| ( ( program @ ( f2 @ c4 ) )
!= ( program @ A ) ) ),
inference(paramod_ordered,[status(thm)],[151,53]) ).
thf(159,plain,
! [A: $i] :
( ( program @ c1 )
| ( decides @ c4 @ ( f2 @ c4 ) @ A ) ),
inference(pattern_uni,[status(thm)],[158:[bind(A,$thf( f2 @ c4 )),bind(B,$thf( B ))]]) ).
thf(163,plain,
! [A: $i] :
( ( program @ c1 )
| ( decides @ c4 @ ( f2 @ c4 ) @ A ) ),
inference(simp,[status(thm)],[159]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( halts2 @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ~ ( halts2 @ B @ B )
| ( outputs @ c2 @ good ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_8) ).
thf(68,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( halts2 @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ~ ( halts2 @ B @ B )
| ( outputs @ c2 @ good ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( program @ ( f5 @ A ) )
| ~ ( program @ B )
| ~ ( halts2 @ B @ B )
| ( halts2 @ c2 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_2) ).
thf(62,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( program @ ( f5 @ A ) )
| ~ ( program @ B )
| ~ ( halts2 @ B @ B )
| ( halts2 @ c2 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( halts2 @ c2 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_3_19) ).
thf(90,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ~ ( halts3 @ A @ ( f5 @ A ) @ ( f5 @ A ) )
| ~ ( outputs @ A @ good )
| ~ ( outputs @ A @ bad )
| ~ ( program @ B )
| ( halts2 @ B @ B )
| ( halts2 @ c2 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(37,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( program @ A )
| ( program @ ( f4 @ A ) )
| ~ ( program @ B )
| ~ ( halts2 @ B @ C )
| ( outputs @ A @ good ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_2_2) ).
thf(122,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( program @ A )
| ( program @ ( f4 @ A ) )
| ~ ( program @ B )
| ~ ( halts2 @ B @ C )
| ( outputs @ A @ good ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(26,axiom,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( program @ ( f6 @ A ) )
| ~ ( program @ B )
| ~ ( halts2 @ B @ B )
| ~ ( halts2 @ c3 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis_4_2) ).
thf(100,plain,
! [B: $i,A: $i] :
( ~ ( program @ A )
| ( program @ ( f6 @ A ) )
| ~ ( program @ B )
| ~ ( halts2 @ B @ B )
| ~ ( halts2 @ c3 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(2899,plain,
$false,
inference(cvc4,[status(thm)],[565,70,92,53,371,104,138,249,88,120,269,56,142,52,372,110,344,57,78,106,84,132,133,116,74,60,512,102,124,96,134,128,266,618,148,161,64,375,176,59,118,54,144,86,113,76,98,552,140,621,108,520,66,130,267,80,162,374,112,72,175,143,55,114,58,235,82,151,146,51,190,273,268,94,126,136,163,68,62,90,486,122,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COM003-1 : TPTP v8.1.2. Bugfixed v1.0.1.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n002.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 19 03:29:51 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.84/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.14/0.99 % [INFO] Parsing done (129ms).
% 1.44/1.00 % [INFO] Running in sequential loop mode.
% 1.87/1.25 % [INFO] eprover registered as external prover.
% 1.87/1.25 % [INFO] cvc4 registered as external prover.
% 1.87/1.26 % [INFO] Scanning for conjecture ...
% 2.08/1.33 % [INFO] Found a conjecture and 48 axioms. Running axiom selection ...
% 2.29/1.39 % [INFO] Axiom selection finished. Selected 48 axioms (removed 0 axioms).
% 2.29/1.46 % [INFO] Problem is propositional (TPTP CNF).
% 2.29/1.46 % [INFO] Type checking passed.
% 2.29/1.46 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 17.19/3.85 % External prover 'cvc4' found a proof!
% 17.19/3.85 % [INFO] Killing All external provers ...
% 17.19/3.85 % Time passed: 3334ms (effective reasoning time: 2851ms)
% 17.19/3.86 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 17.19/3.86 % Axioms used in derivation (48): hypothesis_4_7, hypothesis_3_3, hypothesis_4_8, hypothesis_3_19, hypothesis_2_4, hypothesis_4_2, hypothesis_4_12, hypothesis_1_2, hypothesis_4_11, hypothesis_4_1, hypothesis_3_8, hypothesis_4_10, hypothesis_2_6, hypothesis_4_5, hypothesis_3_18, hypothesis_3_13, hypothesis_4_14, hypothesis_3_9, hypothesis_4_4, hypothesis_1_4, hypothesis_3_14, hypothesis_3_2, hypothesis_3_12, hypothesis_2_5, hypothesis_4_13, hypothesis_2_1, hypothesis_3_6, hypothesis_4_3, hypothesis_4_15, hypothesis_3_20, hypothesis_2_8, hypothesis_3_11, hypothesis_3_1, hypothesis_3_15, hypothesis_4_9, hypothesis_3_5, hypothesis_4_6, hypothesis_3_10, hypothesis_2_7, hypothesis_3_16, hypothesis_1_1, hypothesis_3_17, hypothesis_2_2, hypothesis_1_3, hypothesis_4_17, hypothesis_3_4, hypothesis_2_3, hypothesis_3_7
% 17.19/3.86 % No. of inferences in proof: 158
% 17.19/3.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3334 ms resp. 2851 ms w/o parsing
% 17.35/3.91 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 17.35/3.91 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------