TSTP Solution File: COM003_1 by Leo-III-SAT---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : COM003_1 : TPTP v8.2.0. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n019.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 : Mon Jun 24 04:56:54 EDT 2024
% Result : Theorem 11.11s 3.05s
% Output : Refutation 11.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 26
% Syntax : Number of formulae : 100 ( 12 unt; 21 typ; 0 def)
% Number of atoms : 304 ( 18 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 958 ( 89 ~; 106 |; 42 &; 680 @)
% ( 0 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 8 con; 0-3 aty)
% Number of variables : 188 ( 0 ^ 166 !; 22 ?; 188 :)
% Comments :
%------------------------------------------------------------------------------
thf(program_type,type,
program: $tType ).
thf(algorithm_type,type,
algorithm: $tType ).
thf(input_type,type,
input: $tType ).
thf(output_type,type,
output: $tType ).
thf(bad_type,type,
bad: output ).
thf(good_type,type,
good: output ).
thf(decides_type,type,
decides: algorithm > program > input > $o ).
thf(halts2_type,type,
halts2: program > input > $o ).
thf(halts3_type,type,
halts3: program > program > input > $o ).
thf(outputs_type,type,
outputs: program > output > $o ).
thf(algorithm_of_type,type,
algorithm_of: program > algorithm ).
thf(as_input_type,type,
as_input: program > input ).
thf(sk1_type,type,
sk1: algorithm ).
thf(sk2_type,type,
sk2: algorithm > program ).
thf(sk3_type,type,
sk3: algorithm > input ).
thf(sk4_type,type,
sk4: program ).
thf(sk5_type,type,
sk5: $o ).
thf(sk6_type,type,
sk6: program > $o ).
thf(sk7_type,type,
sk7: program > program ).
thf(sk8_type,type,
sk8: program > program ).
thf(sk10_type,type,
sk10: program ).
thf(6,axiom,
( ? [A: program] :
! [B: program] :
( ( ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts2 @ A @ ( as_input @ B ) )
& ( outputs @ A @ good ) ) )
& ( ~ ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts2 @ A @ ( as_input @ B ) )
& ( outputs @ A @ bad ) ) ) )
=> ? [A: program] :
! [B: program] :
( ( ( halts2 @ B @ ( as_input @ B ) )
=> ~ ( halts2 @ A @ ( as_input @ B ) ) )
& ( ~ ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts2 @ A @ ( as_input @ B ) )
& ( outputs @ A @ bad ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
thf(34,plain,
( ? [A: program] :
! [B: program] :
( ( ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts2 @ A @ ( as_input @ B ) )
& ( outputs @ A @ good ) ) )
& ( ~ ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts2 @ A @ ( as_input @ B ) )
& ( outputs @ A @ bad ) ) ) )
=> ? [A: program] :
! [B: program] :
( ( ( halts2 @ B @ ( as_input @ B ) )
=> ~ ( halts2 @ A @ ( as_input @ B ) ) )
& ( ~ ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts2 @ A @ ( as_input @ B ) )
& ( outputs @ A @ bad ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(35,plain,
( ? [A: program] :
( ! [B: program] :
( ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts2 @ A @ ( as_input @ B ) )
& ( outputs @ A @ good ) ) )
& ! [B: program] :
( ~ ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts2 @ A @ ( as_input @ B ) )
& ( outputs @ A @ bad ) ) ) )
=> ? [A: program] :
( ! [B: program] :
( ( halts2 @ B @ ( as_input @ B ) )
=> ~ ( halts2 @ A @ ( as_input @ B ) ) )
& ! [B: program] :
( ~ ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts2 @ A @ ( as_input @ B ) )
& ( outputs @ A @ bad ) ) ) ) ),
inference(miniscope,[status(thm)],[34]) ).
thf(42,plain,
! [A: program] :
( ~ sk5
| ( halts2 @ A @ ( as_input @ A ) )
| ( halts2 @ sk10 @ ( as_input @ A ) ) ),
inference(cnf,[status(esa)],[35]) ).
thf(47,plain,
! [A: program] :
( ~ sk5
| ( halts2 @ A @ ( as_input @ A ) )
| ( halts2 @ sk10 @ ( as_input @ A ) ) ),
inference(simp,[status(thm)],[42]) ).
thf(1,conjecture,
~ ? [A: algorithm] :
! [B: program,C: input] : ( decides @ A @ B @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
thf(2,negated_conjecture,
~ ~ ? [A: algorithm] :
! [B: program,C: input] : ( decides @ A @ B @ C ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ~ ? [A: algorithm] :
! [B: program,C: input] : ( decides @ A @ B @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
? [A: algorithm] :
! [B: program,C: input] : ( decides @ A @ B @ C ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
! [B: input,A: program] : ( decides @ sk1 @ A @ B ),
inference(cnf,[status(esa)],[8]) ).
thf(3,axiom,
( ? [A: algorithm] :
! [B: program,C: input] : ( decides @ A @ B @ C )
=> ? [A: program] :
! [B: program,C: input] : ( decides @ ( algorithm_of @ A ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
thf(10,plain,
( ? [A: algorithm] :
! [B: program,C: input] : ( decides @ A @ B @ C )
=> ? [A: program] :
! [B: program,C: input] : ( decides @ ( algorithm_of @ A ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,plain,
! [C: input,B: program,A: algorithm] :
( ~ ( decides @ A @ ( sk2 @ A ) @ ( sk3 @ A ) )
| ( decides @ ( algorithm_of @ sk4 ) @ B @ C ) ),
inference(cnf,[status(esa)],[10]) ).
thf(49,plain,
! [E: input,D: program,C: algorithm,B: input,A: program] :
( ( decides @ ( algorithm_of @ sk4 ) @ D @ E )
| ( ( decides @ sk1 @ A @ B )
!= ( decides @ C @ ( sk2 @ C ) @ ( sk3 @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,11]) ).
thf(50,plain,
! [B: input,A: program] : ( decides @ ( algorithm_of @ sk4 ) @ A @ B ),
inference(pattern_uni,[status(thm)],[49:[bind(A,$thf( sk2 @ sk1 )),bind(B,$thf( sk3 @ sk1 )),bind(C,$thf( sk1 )),bind(D,$thf( D )),bind(E,$thf( E ))]]) ).
thf(53,plain,
! [B: input,A: program] : ( decides @ ( algorithm_of @ sk4 ) @ A @ B ),
inference(simp,[status(thm)],[50]) ).
thf(4,axiom,
! [A: program,B: program,C: input] :
( ( decides @ ( algorithm_of @ A ) @ B @ C )
=> ! [D: program,E: input] :
( ( ( halts2 @ D @ E )
=> ( ( halts3 @ A @ D @ E )
& ( outputs @ A @ good ) ) )
& ( ~ ( halts2 @ D @ E )
=> ( ( halts3 @ A @ D @ E )
& ( outputs @ A @ bad ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
thf(12,plain,
! [A: program,B: program,C: input] :
( ( decides @ ( algorithm_of @ A ) @ B @ C )
=> ! [D: program,E: input] :
( ( ( halts2 @ D @ E )
=> ( ( halts3 @ A @ D @ E )
& ( outputs @ A @ good ) ) )
& ( ~ ( halts2 @ D @ E )
=> ( ( halts3 @ A @ D @ E )
& ( outputs @ A @ bad ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,plain,
! [A: program] :
( ? [B: program,C: input] : ( decides @ ( algorithm_of @ A ) @ B @ C )
=> ( ! [B: program,C: input] :
( ( halts2 @ B @ C )
=> ( ( halts3 @ A @ B @ C )
& ( outputs @ A @ good ) ) )
& ! [B: program,C: input] :
( ~ ( halts2 @ B @ C )
=> ( ( halts3 @ A @ B @ C )
& ( outputs @ A @ bad ) ) ) ) ),
inference(miniscope,[status(thm)],[12]) ).
thf(16,plain,
! [E: input,D: program,C: input,B: program,A: program] :
( ~ ( decides @ ( algorithm_of @ A ) @ B @ C )
| ( halts2 @ D @ E )
| ( outputs @ A @ bad ) ),
inference(cnf,[status(esa)],[13]) ).
thf(18,plain,
! [E: input,D: program,C: input,B: program,A: program] :
( ~ ( decides @ ( algorithm_of @ A ) @ B @ C )
| ( halts2 @ D @ E )
| ( outputs @ A @ bad ) ),
inference(simp,[status(thm)],[16]) ).
thf(210,plain,
! [G: input,F: program,E: input,D: program,C: program,B: input,A: program] :
( ( halts2 @ F @ G )
| ( outputs @ C @ bad )
| ( ( decides @ ( algorithm_of @ sk4 ) @ A @ B )
!= ( decides @ ( algorithm_of @ C ) @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[53,18]) ).
thf(211,plain,
! [B: input,A: program] :
( ( halts2 @ A @ B )
| ( outputs @ sk4 @ bad ) ),
inference(pattern_uni,[status(thm)],[210:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk4 )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(227,plain,
! [B: input,A: program] :
( ( halts2 @ A @ B )
| ( outputs @ sk4 @ bad ) ),
inference(simp,[status(thm)],[211]) ).
thf(17,plain,
! [E: input,D: program,C: input,B: program,A: program] :
( ~ ( decides @ ( algorithm_of @ A ) @ B @ C )
| ( halts2 @ D @ E )
| ( halts3 @ A @ D @ E ) ),
inference(cnf,[status(esa)],[13]) ).
thf(19,plain,
! [E: input,D: program,C: input,B: program,A: program] :
( ~ ( decides @ ( algorithm_of @ A ) @ B @ C )
| ( halts2 @ D @ E )
| ( halts3 @ A @ D @ E ) ),
inference(simp,[status(thm)],[17]) ).
thf(363,plain,
! [G: input,F: program,E: input,D: program,C: program,B: input,A: program] :
( ( halts2 @ F @ G )
| ( halts3 @ C @ F @ G )
| ( ( decides @ ( algorithm_of @ sk4 ) @ A @ B )
!= ( decides @ ( algorithm_of @ C ) @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[53,19]) ).
thf(364,plain,
! [B: input,A: program] :
( ( halts2 @ A @ B )
| ( halts3 @ sk4 @ A @ B ) ),
inference(pattern_uni,[status(thm)],[363:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk4 )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(366,plain,
! [B: input,A: program] :
( ( halts2 @ A @ B )
| ( halts3 @ sk4 @ A @ B ) ),
inference(simp,[status(thm)],[364]) ).
thf(5,axiom,
( ? [A: program] :
! [B: program] :
( ( ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts3 @ A @ B @ ( as_input @ B ) )
& ( outputs @ A @ good ) ) )
& ( ~ ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts3 @ A @ B @ ( as_input @ B ) )
& ( outputs @ A @ bad ) ) ) )
=> ? [A: program] :
! [B: program] :
( ( ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts2 @ A @ ( as_input @ B ) )
& ( outputs @ A @ good ) ) )
& ( ~ ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts2 @ A @ ( as_input @ B ) )
& ( outputs @ A @ bad ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
thf(20,plain,
( ? [A: program] :
! [B: program] :
( ( ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts3 @ A @ B @ ( as_input @ B ) )
& ( outputs @ A @ good ) ) )
& ( ~ ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts3 @ A @ B @ ( as_input @ B ) )
& ( outputs @ A @ bad ) ) ) )
=> ? [A: program] :
! [B: program] :
( ( ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts2 @ A @ ( as_input @ B ) )
& ( outputs @ A @ good ) ) )
& ( ~ ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts2 @ A @ ( as_input @ B ) )
& ( outputs @ A @ bad ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,plain,
( ? [A: program] :
( ! [B: program] :
( ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts3 @ A @ B @ ( as_input @ B ) )
& ( outputs @ A @ good ) ) )
& ! [B: program] :
( ~ ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts3 @ A @ B @ ( as_input @ B ) )
& ( outputs @ A @ bad ) ) ) )
=> ? [A: program] :
( ! [B: program] :
( ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts2 @ A @ ( as_input @ B ) )
& ( outputs @ A @ good ) ) )
& ! [B: program] :
( ~ ( halts2 @ B @ ( as_input @ B ) )
=> ( ( halts2 @ A @ ( as_input @ B ) )
& ( outputs @ A @ bad ) ) ) ) ),
inference(miniscope,[status(thm)],[20]) ).
thf(24,plain,
! [A: program] :
( ( sk6 @ A )
| ~ ( halts3 @ A @ ( sk8 @ A ) @ ( as_input @ ( sk8 @ A ) ) )
| ~ ( outputs @ A @ bad )
| sk5 ),
inference(cnf,[status(esa)],[21]) ).
thf(467,plain,
! [C: program,B: input,A: program] :
( ( halts2 @ A @ B )
| ( sk6 @ C )
| ~ ( outputs @ C @ bad )
| sk5
| ( ( halts3 @ sk4 @ A @ B )
!= ( halts3 @ C @ ( sk8 @ C ) @ ( as_input @ ( sk8 @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[366,24]) ).
thf(468,plain,
( ( halts2 @ ( sk8 @ sk4 ) @ ( as_input @ ( sk8 @ sk4 ) ) )
| ( sk6 @ sk4 )
| ~ ( outputs @ sk4 @ bad )
| sk5 ),
inference(pattern_uni,[status(thm)],[467:[bind(A,$thf( sk8 @ sk4 )),bind(B,$thf( as_input @ ( sk8 @ sk4 ) )),bind(C,$thf( sk4 ))]]) ).
thf(639,plain,
! [B: input,A: program] :
( ( halts2 @ A @ B )
| ( halts2 @ ( sk8 @ sk4 ) @ ( as_input @ ( sk8 @ sk4 ) ) )
| ( sk6 @ sk4 )
| sk5
| ( ( outputs @ sk4 @ bad )
!= ( outputs @ sk4 @ bad ) ) ),
inference(paramod_ordered,[status(thm)],[227,468]) ).
thf(640,plain,
! [B: input,A: program] :
( ( halts2 @ A @ B )
| ( halts2 @ ( sk8 @ sk4 ) @ ( as_input @ ( sk8 @ sk4 ) ) )
| ( sk6 @ sk4 )
| sk5 ),
inference(pattern_uni,[status(thm)],[639:[]]) ).
thf(775,plain,
! [B: input,A: program] :
( ( halts2 @ A @ B )
| ( sk6 @ sk4 )
| sk5
| ( ( halts2 @ ( sk8 @ sk4 ) @ ( as_input @ ( sk8 @ sk4 ) ) )
!= ( halts2 @ A @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[640]) ).
thf(778,plain,
( ( halts2 @ ( sk8 @ sk4 ) @ ( as_input @ ( sk8 @ sk4 ) ) )
| ( sk6 @ sk4 )
| sk5 ),
inference(pattern_uni,[status(thm)],[775:[bind(A,$thf( sk8 @ sk4 )),bind(B,$thf( as_input @ ( sk8 @ sk4 ) ))]]) ).
thf(29,plain,
! [A: program] :
( ( sk6 @ A )
| ~ ( halts2 @ ( sk8 @ A ) @ ( as_input @ ( sk8 @ A ) ) )
| sk5 ),
inference(cnf,[status(esa)],[21]) ).
thf(985,plain,
! [A: program] :
( ( sk6 @ sk4 )
| sk5
| ( sk6 @ A )
| ( ( halts2 @ ( sk8 @ sk4 ) @ ( as_input @ ( sk8 @ sk4 ) ) )
!= ( halts2 @ ( sk8 @ A ) @ ( as_input @ ( sk8 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[778,29]) ).
thf(986,plain,
( ( sk6 @ sk4 )
| sk5
| ( sk6 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[985:[bind(A,$thf( sk4 ))]]) ).
thf(999,plain,
( ( sk6 @ sk4 )
| sk5 ),
inference(simp,[status(thm)],[986]) ).
thf(26,plain,
! [A: program] :
( ( halts2 @ ( sk7 @ A ) @ ( as_input @ ( sk7 @ A ) ) )
| ~ ( sk6 @ A )
| sk5 ),
inference(cnf,[status(esa)],[21]) ).
thf(14,plain,
! [E: input,D: program,C: input,B: program,A: program] :
( ~ ( decides @ ( algorithm_of @ A ) @ B @ C )
| ~ ( halts2 @ D @ E )
| ( outputs @ A @ good ) ),
inference(cnf,[status(esa)],[13]) ).
thf(70,plain,
! [G: input,F: program,E: input,D: program,C: program,B: input,A: program] :
( ~ ( halts2 @ F @ G )
| ( outputs @ C @ good )
| ( ( decides @ ( algorithm_of @ sk4 ) @ A @ B )
!= ( decides @ ( algorithm_of @ C ) @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[53,14]) ).
thf(71,plain,
! [B: input,A: program] :
( ~ ( halts2 @ A @ B )
| ( outputs @ sk4 @ good ) ),
inference(pattern_uni,[status(thm)],[70:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk4 )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(74,plain,
! [B: input,A: program] :
( ~ ( halts2 @ A @ B )
| ( outputs @ sk4 @ good ) ),
inference(simp,[status(thm)],[71]) ).
thf(679,plain,
! [C: input,B: program,A: program] :
( ~ ( sk6 @ A )
| sk5
| ( outputs @ sk4 @ good )
| ( ( halts2 @ ( sk7 @ A ) @ ( as_input @ ( sk7 @ A ) ) )
!= ( halts2 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[26,74]) ).
thf(680,plain,
! [A: program] :
( ~ ( sk6 @ A )
| sk5
| ( outputs @ sk4 @ good ) ),
inference(pattern_uni,[status(thm)],[679:[bind(A,$thf( F )),bind(B,$thf( sk7 @ F )),bind(C,$thf( as_input @ ( sk7 @ F ) ))]]) ).
thf(701,plain,
! [A: program] :
( ~ ( sk6 @ A )
| sk5
| ( outputs @ sk4 @ good ) ),
inference(simp,[status(thm)],[680]) ).
thf(1001,plain,
! [A: program] :
( sk5
| ( outputs @ sk4 @ good )
| ( ( sk6 @ sk4 )
!= ( sk6 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[999,701]) ).
thf(1002,plain,
( sk5
| ( outputs @ sk4 @ good ) ),
inference(pattern_uni,[status(thm)],[1001:[bind(A,$thf( sk4 ))]]) ).
thf(1009,plain,
! [A: program] :
( sk5
| ( halts2 @ ( sk7 @ A ) @ ( as_input @ ( sk7 @ A ) ) )
| ( ( sk6 @ sk4 )
!= ( sk6 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[999,26]) ).
thf(1010,plain,
( sk5
| ( halts2 @ ( sk7 @ sk4 ) @ ( as_input @ ( sk7 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[1009:[bind(A,$thf( sk4 ))]]) ).
thf(15,plain,
! [E: input,D: program,C: input,B: program,A: program] :
( ~ ( decides @ ( algorithm_of @ A ) @ B @ C )
| ~ ( halts2 @ D @ E )
| ( halts3 @ A @ D @ E ) ),
inference(cnf,[status(esa)],[13]) ).
thf(134,plain,
! [G: input,F: program,E: input,D: program,C: program,B: input,A: program] :
( ~ ( halts2 @ F @ G )
| ( halts3 @ C @ F @ G )
| ( ( decides @ ( algorithm_of @ sk4 ) @ A @ B )
!= ( decides @ ( algorithm_of @ C ) @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[53,15]) ).
thf(135,plain,
! [B: input,A: program] :
( ~ ( halts2 @ A @ B )
| ( halts3 @ sk4 @ A @ B ) ),
inference(pattern_uni,[status(thm)],[134:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk4 )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(139,plain,
! [B: input,A: program] :
( ~ ( halts2 @ A @ B )
| ( halts3 @ sk4 @ A @ B ) ),
inference(simp,[status(thm)],[135]) ).
thf(1038,plain,
! [B: input,A: program] :
( sk5
| ( halts3 @ sk4 @ A @ B )
| ( ( halts2 @ ( sk7 @ sk4 ) @ ( as_input @ ( sk7 @ sk4 ) ) )
!= ( halts2 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1010,139]) ).
thf(1039,plain,
( sk5
| ( halts3 @ sk4 @ ( sk7 @ sk4 ) @ ( as_input @ ( sk7 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[1038:[bind(A,$thf( sk7 @ sk4 )),bind(B,$thf( as_input @ ( sk7 @ sk4 ) ))]]) ).
thf(28,plain,
! [A: program] :
( ~ ( halts3 @ A @ ( sk7 @ A ) @ ( as_input @ ( sk7 @ A ) ) )
| ~ ( outputs @ A @ good )
| ~ ( sk6 @ A )
| sk5 ),
inference(cnf,[status(esa)],[21]) ).
thf(1053,plain,
! [A: program] :
( sk5
| ~ ( outputs @ A @ good )
| ~ ( sk6 @ A )
| ( ( halts3 @ sk4 @ ( sk7 @ sk4 ) @ ( as_input @ ( sk7 @ sk4 ) ) )
!= ( halts3 @ A @ ( sk7 @ A ) @ ( as_input @ ( sk7 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1039,28]) ).
thf(1054,plain,
( sk5
| ~ ( outputs @ sk4 @ good )
| ~ ( sk6 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[1053:[bind(A,$thf( sk4 ))]]) ).
thf(1114,plain,
( sk5
| ~ ( sk6 @ sk4 )
| ( ( outputs @ sk4 @ good )
!= ( outputs @ sk4 @ good ) ) ),
inference(paramod_ordered,[status(thm)],[1002,1054]) ).
thf(1115,plain,
( sk5
| ~ ( sk6 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[1114:[]]) ).
thf(1196,plain,
( sk5
| ( ( sk6 @ sk4 )
!= ( sk6 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[999,1115]) ).
thf(1197,plain,
sk5,
inference(pattern_uni,[status(thm)],[1196:[]]) ).
thf(1411,plain,
! [A: program] :
( ~ $true
| ( halts2 @ A @ ( as_input @ A ) )
| ( halts2 @ sk10 @ ( as_input @ A ) ) ),
inference(rewrite,[status(thm)],[47,1197]) ).
thf(1412,plain,
! [A: program] :
( ( halts2 @ A @ ( as_input @ A ) )
| ( halts2 @ sk10 @ ( as_input @ A ) ) ),
inference(simp,[status(thm)],[1411]) ).
thf(40,plain,
! [A: program] :
( ~ sk5
| ~ ( halts2 @ A @ ( as_input @ A ) )
| ~ ( halts2 @ sk10 @ ( as_input @ A ) ) ),
inference(cnf,[status(esa)],[35]) ).
thf(55,plain,
! [A: program] :
( ~ sk5
| ~ ( halts2 @ A @ ( as_input @ A ) )
| ( ( halts2 @ sk10 @ ( as_input @ A ) )
!= ( halts2 @ A @ ( as_input @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[40]) ).
thf(56,plain,
( ~ sk5
| ~ ( halts2 @ sk10 @ ( as_input @ sk10 ) ) ),
inference(pattern_uni,[status(thm)],[55:[bind(A,$thf( sk10 ))]]) ).
thf(1210,plain,
( ~ $true
| ~ ( halts2 @ sk10 @ ( as_input @ sk10 ) ) ),
inference(rewrite,[status(thm)],[56,1197]) ).
thf(1211,plain,
~ ( halts2 @ sk10 @ ( as_input @ sk10 ) ),
inference(simp,[status(thm)],[1210]) ).
thf(1413,plain,
! [A: program] :
( ( halts2 @ sk10 @ ( as_input @ A ) )
| ( ( halts2 @ A @ ( as_input @ A ) )
!= ( halts2 @ sk10 @ ( as_input @ sk10 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1412,1211]) ).
thf(1414,plain,
halts2 @ sk10 @ ( as_input @ sk10 ),
inference(pattern_uni,[status(thm)],[1413:[bind(A,$thf( sk10 ))]]) ).
thf(1456,plain,
$false,
inference(rewrite,[status(thm)],[1414,1211]) ).
thf(1457,plain,
$false,
inference(simp,[status(thm)],[1456]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COM003_1 : TPTP v8.2.0. Released v5.0.0.
% 0.11/0.12 % Command : run_Leo-III %s %d SAT
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.18/0.33 % WCLimit : 300
% 0.18/0.33 % DateTime : Fri Jun 21 00:14:40 EDT 2024
% 0.18/0.33 % CPUTime :
% 0.98/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.36/1.03 % [INFO] Parsing done (123ms).
% 1.36/1.04 % [INFO] Running in sequential loop mode.
% 1.72/1.25 % [INFO] nitpick registered as external prover.
% 1.72/1.25 % [INFO] Scanning for conjecture ...
% 1.94/1.32 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 1.94/1.34 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.94/1.36 % [INFO] Problem is typed first-order (TPTP TFF).
% 1.94/1.36 % [INFO] Type checking passed.
% 1.94/1.36 % [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 ...
% 11.11/3.04 % [INFO] Killing All external provers ...
% 11.11/3.04 % Time passed: 2507ms (effective reasoning time: 1994ms)
% 11.11/3.04 % 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)>
% 11.11/3.04 % Axioms used in derivation (4): p4, p1, p2, p3
% 11.11/3.04 % No. of inferences in proof: 79
% 11.11/3.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2507 ms resp. 1994 ms w/o parsing
% 11.11/3.08 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.11/3.09 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------