TSTP Solution File: SWV401+1 by Leo-III-SAT---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : SWV401+1 : TPTP v8.2.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n026.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 17:28:53 EDT 2024
% Result : Theorem 135.05s 25.34s
% Output : Refutation 135.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 6
% Syntax : Number of formulae : 89 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 241 ( 78 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1082 ( 91 ~; 81 |; 20 &; 867 @)
% ( 2 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 8 con; 0-3 aty)
% Number of variables : 214 ( 0 ^ 214 !; 0 ?; 214 :)
% Comments :
%------------------------------------------------------------------------------
thf(pair_in_list_type,type,
pair_in_list: $i > $i > $i > $o ).
thf(less_than_type,type,
less_than: $i > $i > $o ).
thf(update_slb_type,type,
update_slb: $i > $i > $i ).
thf(insert_slb_type,type,
insert_slb: $i > $i > $i ).
thf(pair_type,type,
pair: $i > $i > $i ).
thf(strictly_less_than_type,type,
strictly_less_than: $i > $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i ).
thf(1,conjecture,
! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( pair_in_list @ A @ B @ C )
& ( less_than @ D @ C ) )
=> ( pair_in_list @ ( update_slb @ A @ D ) @ B @ C ) )
=> ! [B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( pair_in_list @ ( insert_slb @ A @ ( pair @ E @ F ) ) @ B @ C )
& ( less_than @ D @ C ) )
=> ( pair_in_list @ ( update_slb @ ( insert_slb @ A @ ( pair @ E @ F ) ) @ D ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l37_co) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( pair_in_list @ A @ B @ C )
& ( less_than @ D @ C ) )
=> ( pair_in_list @ ( update_slb @ A @ D ) @ B @ C ) )
=> ! [B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( pair_in_list @ ( insert_slb @ A @ ( pair @ E @ F ) ) @ B @ C )
& ( less_than @ D @ C ) )
=> ( pair_in_list @ ( update_slb @ ( insert_slb @ A @ ( pair @ E @ F ) ) @ D ) @ B @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( pair_in_list @ A @ B @ C )
& ( less_than @ D @ C ) )
=> ( pair_in_list @ ( update_slb @ A @ D ) @ B @ C ) )
=> ! [B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( pair_in_list @ ( insert_slb @ A @ ( pair @ E @ F ) ) @ B @ C )
& ( less_than @ D @ C ) )
=> ( pair_in_list @ ( update_slb @ ( insert_slb @ A @ ( pair @ E @ F ) ) @ D ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,plain,
~ ( pair_in_list @ ( update_slb @ ( insert_slb @ sk1 @ ( pair @ sk5 @ sk6 ) ) @ sk4 ) @ sk2 @ sk3 ),
inference(cnf,[status(esa)],[21]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( less_than @ A @ B )
| ( less_than @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).
thf(70,plain,
! [A: $i,B: $i] :
( ( less_than @ A @ B )
| ( less_than @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ( less_than @ A @ B )
| ( less_than @ B @ A ) ),
inference(cnf,[status(esa)],[70]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( strictly_less_than @ A @ B )
<=> ( ( less_than @ A @ B )
& ~ ( less_than @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricly_smaller_definition) ).
thf(56,plain,
! [A: $i,B: $i] :
( ( ( strictly_less_than @ A @ B )
=> ( ( less_than @ A @ B )
& ~ ( less_than @ B @ A ) ) )
& ( ( ( less_than @ A @ B )
& ~ ( less_than @ B @ A ) )
=> ( strictly_less_than @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(57,plain,
( ! [A: $i,B: $i] :
( ( strictly_less_than @ A @ B )
=> ( ( less_than @ A @ B )
& ~ ( less_than @ B @ A ) ) )
& ! [A: $i,B: $i] :
( ( ( less_than @ A @ B )
& ~ ( less_than @ B @ A ) )
=> ( strictly_less_than @ A @ B ) ) ),
inference(miniscope,[status(thm)],[56]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ~ ( less_than @ A @ B )
| ( less_than @ B @ A )
| ( strictly_less_than @ A @ B ) ),
inference(cnf,[status(esa)],[57]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ~ ( less_than @ A @ B )
| ( less_than @ B @ A )
| ( strictly_less_than @ A @ B ) ),
inference(simp,[status(thm)],[58]) ).
thf(24,plain,
pair_in_list @ ( insert_slb @ sk1 @ ( pair @ sk5 @ sk6 ) ) @ sk2 @ sk3,
inference(cnf,[status(esa)],[21]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
<=> ( ( pair_in_list @ A @ C @ E )
| ( ( B = C )
& ( D = E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).
thf(72,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
=> ( ( pair_in_list @ A @ C @ E )
| ( ( B = C )
& ( D = E ) ) ) )
& ( ( ( pair_in_list @ A @ C @ E )
| ( ( B = C )
& ( D = E ) ) )
=> ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(73,plain,
( ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
=> ( ( pair_in_list @ A @ C @ E )
| ( ( B = C )
& ( D = E ) ) ) )
& ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( pair_in_list @ A @ C @ E )
| ( ( B = C )
& ( D = E ) ) )
=> ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E ) ) ),
inference(miniscope,[status(thm)],[72]) ).
thf(76,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
| ( pair_in_list @ A @ C @ E )
| ( D = E ) ),
inference(cnf,[status(esa)],[73]) ).
thf(81,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
| ( pair_in_list @ A @ C @ E ) ),
inference(lifteq,[status(thm)],[76]) ).
thf(4403,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ( pair_in_list @ A @ C @ E )
| ( ( pair_in_list @ ( insert_slb @ sk1 @ ( pair @ sk5 @ sk6 ) ) @ sk2 @ sk3 )
!= ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E ) ) ),
inference(paramod_ordered,[status(thm)],[24,81]) ).
thf(4404,plain,
( ( sk6 = sk3 )
| ( pair_in_list @ sk1 @ sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[4403:[bind(A,$thf( sk1 )),bind(B,$thf( sk5 )),bind(C,$thf( sk2 )),bind(D,$thf( sk6 )),bind(E,$thf( sk3 ))]]) ).
thf(23,plain,
less_than @ sk4 @ sk3,
inference(cnf,[status(esa)],[21]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( pair_in_list @ sk1 @ A @ B )
| ~ ( less_than @ C @ B )
| ( pair_in_list @ ( update_slb @ sk1 @ C ) @ A @ B ) ),
inference(cnf,[status(esa)],[21]) ).
thf(103,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( pair_in_list @ sk1 @ A @ B )
| ( pair_in_list @ ( update_slb @ sk1 @ C ) @ A @ B )
| ( ( less_than @ sk4 @ sk3 )
!= ( less_than @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[23,25]) ).
thf(104,plain,
! [A: $i] :
( ~ ( pair_in_list @ sk1 @ A @ sk3 )
| ( pair_in_list @ ( update_slb @ sk1 @ sk4 ) @ A @ sk3 ) ),
inference(pattern_uni,[status(thm)],[103:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 ))]]) ).
thf(74,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( pair_in_list @ A @ C @ E )
| ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E ) ),
inference(cnf,[status(esa)],[73]) ).
thf(78,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( pair_in_list @ A @ C @ E )
| ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E ) ),
inference(simp,[status(thm)],[74]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( strictly_less_than @ D @ C )
=> ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax29) ).
thf(49,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( strictly_less_than @ D @ C )
=> ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(50,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( strictly_less_than @ D @ C )
| ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ C ) ) ) ),
inference(cnf,[status(esa)],[49]) ).
thf(51,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ C ) ) )
| ~ ( strictly_less_than @ D @ C ) ),
inference(lifteq,[status(thm)],[50]) ).
thf(1692,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( strictly_less_than @ D @ C )
| ~ ( pair_in_list @ ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ C ) ) @ sk2 @ sk3 )
| ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
!= ( update_slb @ ( insert_slb @ sk1 @ ( pair @ sk5 @ sk6 ) ) @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[51,22]) ).
thf(1693,plain,
( ~ ( strictly_less_than @ sk6 @ sk4 )
| ~ ( pair_in_list @ ( insert_slb @ ( update_slb @ sk1 @ sk4 ) @ ( pair @ sk5 @ sk4 ) ) @ sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[1692:[bind(A,$thf( sk1 )),bind(B,$thf( sk5 )),bind(C,$thf( sk4 )),bind(D,$thf( sk6 ))]]) ).
thf(3495,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( pair_in_list @ A @ C @ E )
| ~ ( strictly_less_than @ sk6 @ sk4 )
| ( ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
!= ( pair_in_list @ ( insert_slb @ ( update_slb @ sk1 @ sk4 ) @ ( pair @ sk5 @ sk4 ) ) @ sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[78,1693]) ).
thf(3496,plain,
( ~ ( pair_in_list @ ( update_slb @ sk1 @ sk4 ) @ sk2 @ sk3 )
| ~ ( strictly_less_than @ sk6 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[3495:[bind(A,$thf( update_slb @ sk1 @ sk4 )),bind(B,$thf( sk5 )),bind(C,$thf( sk2 )),bind(D,$thf( sk4 )),bind(E,$thf( sk3 ))]]) ).
thf(3959,plain,
! [A: $i] :
( ~ ( pair_in_list @ sk1 @ A @ sk3 )
| ~ ( strictly_less_than @ sk6 @ sk4 )
| ( ( pair_in_list @ ( update_slb @ sk1 @ sk4 ) @ A @ sk3 )
!= ( pair_in_list @ ( update_slb @ sk1 @ sk4 ) @ sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[104,3496]) ).
thf(3960,plain,
( ~ ( pair_in_list @ sk1 @ sk2 @ sk3 )
| ~ ( strictly_less_than @ sk6 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[3959:[bind(A,$thf( sk2 ))]]) ).
thf(6165,plain,
( ( sk6 = sk3 )
| ~ ( strictly_less_than @ sk6 @ sk4 )
| ( ( pair_in_list @ sk1 @ sk2 @ sk3 )
!= ( pair_in_list @ sk1 @ sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[4404,3960]) ).
thf(6166,plain,
( ( sk6 = sk3 )
| ~ ( strictly_less_than @ sk6 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[6165:[]]) ).
thf(77,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
| ( pair_in_list @ A @ C @ E )
| ( B = C ) ),
inference(cnf,[status(esa)],[73]) ).
thf(82,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
| ( pair_in_list @ A @ C @ E ) ),
inference(lifteq,[status(thm)],[77]) ).
thf(6452,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( pair_in_list @ A @ C @ E )
| ( ( pair_in_list @ ( insert_slb @ sk1 @ ( pair @ sk5 @ sk6 ) ) @ sk2 @ sk3 )
!= ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E ) ) ),
inference(paramod_ordered,[status(thm)],[24,82]) ).
thf(6453,plain,
( ( sk5 = sk2 )
| ( pair_in_list @ sk1 @ sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[6452:[bind(A,$thf( sk1 )),bind(B,$thf( sk5 )),bind(C,$thf( sk2 )),bind(D,$thf( sk6 )),bind(E,$thf( sk3 ))]]) ).
thf(8796,plain,
( ( sk5 = sk2 )
| ~ ( strictly_less_than @ sk6 @ sk4 )
| ( ( pair_in_list @ sk1 @ sk2 @ sk3 )
!= ( pair_in_list @ sk1 @ sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[6453,3960]) ).
thf(8797,plain,
( ( sk5 = sk2 )
| ~ ( strictly_less_than @ sk6 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[8796:[]]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( less_than @ C @ D )
=> ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax30) ).
thf(83,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( less_than @ C @ D )
=> ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(84,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( less_than @ C @ D )
| ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ D ) ) ) ),
inference(cnf,[status(esa)],[83]) ).
thf(85,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ D ) )
= ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C ) )
| ~ ( less_than @ C @ D ) ),
inference(lifteq,[status(thm)],[84]) ).
thf(9054,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ D ) )
= ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C ) )
| ( ( less_than @ sk4 @ sk3 )
!= ( less_than @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[23,85]) ).
thf(9055,plain,
! [B: $i,A: $i] :
( ( insert_slb @ ( update_slb @ A @ sk4 ) @ ( pair @ B @ sk3 ) )
= ( update_slb @ ( insert_slb @ A @ ( pair @ B @ sk3 ) ) @ sk4 ) ),
inference(pattern_uni,[status(thm)],[9054:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk4 )),bind(D,$thf( sk3 ))]]) ).
thf(75,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B != C )
| ( D != E )
| ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E ) ),
inference(cnf,[status(esa)],[73]) ).
thf(79,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B != C )
| ( D != E )
| ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E ) ),
inference(lifteq,[status(thm)],[75]) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] : ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B @ C ),
inference(simp,[status(thm)],[79]) ).
thf(744,plain,
! [C: $i,B: $i,A: $i] :
( ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B @ C )
!= ( pair_in_list @ ( update_slb @ ( insert_slb @ sk1 @ ( pair @ sk5 @ sk6 ) ) @ sk4 ) @ sk2 @ sk3 ) ),
inference(paramod_ordered,[status(thm)],[80,22]) ).
thf(752,plain,
! [C: $i,B: $i,A: $i] :
( ( ( insert_slb @ A @ ( pair @ B @ C ) )
!= ( update_slb @ ( insert_slb @ sk1 @ ( pair @ sk5 @ sk6 ) ) @ sk4 ) )
| ( B != sk2 )
| ( C != sk3 ) ),
inference(simp,[status(thm)],[744]) ).
thf(755,plain,
! [A: $i] :
( ( insert_slb @ A @ ( pair @ sk2 @ sk3 ) )
!= ( update_slb @ ( insert_slb @ sk1 @ ( pair @ sk5 @ sk6 ) ) @ sk4 ) ),
inference(simp,[status(thm)],[752]) ).
thf(9716,plain,
! [C: $i,B: $i,A: $i] :
( ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ sk3 ) ) @ sk4 )
!= ( update_slb @ ( insert_slb @ sk1 @ ( pair @ sk5 @ sk6 ) ) @ sk4 ) )
| ( ( insert_slb @ ( update_slb @ A @ sk4 ) @ ( pair @ B @ sk3 ) )
!= ( insert_slb @ C @ ( pair @ sk2 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[9055,755]) ).
thf(9717,plain,
! [A: $i] :
( ( update_slb @ ( insert_slb @ A @ ( pair @ sk2 @ sk3 ) ) @ sk4 )
!= ( update_slb @ ( insert_slb @ sk1 @ ( pair @ sk5 @ sk6 ) ) @ sk4 ) ),
inference(pattern_uni,[status(thm)],[9716:[bind(A,$thf( D )),bind(B,$thf( sk2 )),bind(C,$thf( update_slb @ D @ sk4 ))]]) ).
thf(9839,plain,
! [A: $i] :
( ( update_slb @ ( insert_slb @ A @ ( pair @ sk2 @ sk3 ) ) @ sk4 )
!= ( update_slb @ ( insert_slb @ sk1 @ ( pair @ sk5 @ sk6 ) ) @ sk4 ) ),
inference(simp,[status(thm)],[9717]) ).
thf(13207,plain,
! [A: $i] :
( ( ( insert_slb @ A @ ( pair @ sk2 @ sk3 ) )
!= ( insert_slb @ sk1 @ ( pair @ sk5 @ sk6 ) ) )
| ( sk4 != sk4 ) ),
inference(simp,[status(thm)],[9839]) ).
thf(13532,plain,
! [A: $i] :
( ( insert_slb @ A @ ( pair @ sk2 @ sk3 ) )
!= ( insert_slb @ sk1 @ ( pair @ sk5 @ sk6 ) ) ),
inference(simp,[status(thm)],[13207]) ).
thf(14694,plain,
! [A: $i] :
( ( A != sk1 )
| ( ( pair @ sk5 @ sk6 )
!= ( pair @ sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[13532]) ).
thf(14926,plain,
( ( pair @ sk5 @ sk6 )
!= ( pair @ sk2 @ sk3 ) ),
inference(simp,[status(thm)],[14694]) ).
thf(14947,plain,
( ( sk5 != sk2 )
| ( sk6 != sk3 ) ),
inference(simp,[status(thm)],[14926]) ).
thf(15357,plain,
( ~ ( strictly_less_than @ sk6 @ sk4 )
| ( sk6 != sk3 )
| ( sk5 != sk5 ) ),
inference(paramod_ordered,[status(thm)],[8797,14947]) ).
thf(15358,plain,
( ~ ( strictly_less_than @ sk6 @ sk4 )
| ( sk6 != sk3 ) ),
inference(pattern_uni,[status(thm)],[15357:[]]) ).
thf(16324,plain,
( ~ ( strictly_less_than @ sk6 @ sk4 )
| ( sk6 != sk6 ) ),
inference(paramod_ordered,[status(thm)],[6166,15358]) ).
thf(16325,plain,
~ ( strictly_less_than @ sk6 @ sk4 ),
inference(pattern_uni,[status(thm)],[16324:[]]) ).
thf(16364,plain,
! [B: $i,A: $i] :
( ~ ( less_than @ A @ B )
| ( less_than @ B @ A )
| ( ( strictly_less_than @ A @ B )
!= ( strictly_less_than @ sk6 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[61,16325]) ).
thf(16365,plain,
( ~ ( less_than @ sk6 @ sk4 )
| ( less_than @ sk4 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[16364:[bind(A,$thf( sk6 )),bind(B,$thf( sk4 ))]]) ).
thf(19552,plain,
! [B: $i,A: $i] :
( ( less_than @ B @ A )
| ( less_than @ sk4 @ sk6 )
| ( ( less_than @ A @ B )
!= ( less_than @ sk6 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[71,16365]) ).
thf(19553,plain,
( ( less_than @ sk4 @ sk6 )
| ( less_than @ sk4 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[19552:[bind(A,$thf( sk6 )),bind(B,$thf( sk4 ))]]) ).
thf(19616,plain,
less_than @ sk4 @ sk6,
inference(simp,[status(thm)],[19553]) ).
thf(19634,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ D ) )
= ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C ) )
| ( ( less_than @ sk4 @ sk6 )
!= ( less_than @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[19616,85]) ).
thf(19635,plain,
! [B: $i,A: $i] :
( ( insert_slb @ ( update_slb @ A @ sk4 ) @ ( pair @ B @ sk6 ) )
= ( update_slb @ ( insert_slb @ A @ ( pair @ B @ sk6 ) ) @ sk4 ) ),
inference(pattern_uni,[status(thm)],[19634:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk4 )),bind(D,$thf( sk6 ))]]) ).
thf(15391,plain,
( ( pair_in_list @ sk1 @ sk2 @ sk3 )
| ( sk6 != sk3 )
| ( sk5 != sk5 ) ),
inference(paramod_ordered,[status(thm)],[6453,14947]) ).
thf(15392,plain,
( ( pair_in_list @ sk1 @ sk2 @ sk3 )
| ( sk6 != sk3 ) ),
inference(pattern_uni,[status(thm)],[15391:[]]) ).
thf(17955,plain,
( ( pair_in_list @ sk1 @ sk2 @ sk3 )
| ( sk6 != sk6 ) ),
inference(paramod_ordered,[status(thm)],[4404,15392]) ).
thf(17956,plain,
pair_in_list @ sk1 @ sk2 @ sk3,
inference(pattern_uni,[status(thm)],[17955:[]]) ).
thf(18066,plain,
! [A: $i] :
( ( pair_in_list @ ( update_slb @ sk1 @ sk4 ) @ A @ sk3 )
| ( ( pair_in_list @ sk1 @ sk2 @ sk3 )
!= ( pair_in_list @ sk1 @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[17956,104]) ).
thf(18067,plain,
pair_in_list @ ( update_slb @ sk1 @ sk4 ) @ sk2 @ sk3,
inference(pattern_uni,[status(thm)],[18066:[bind(A,$thf( sk2 ))]]) ).
thf(18667,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
| ( ( pair_in_list @ ( update_slb @ sk1 @ sk4 ) @ sk2 @ sk3 )
!= ( pair_in_list @ A @ C @ E ) ) ),
inference(paramod_ordered,[status(thm)],[18067,78]) ).
thf(18668,plain,
! [B: $i,A: $i] : ( pair_in_list @ ( insert_slb @ ( update_slb @ sk1 @ sk4 ) @ ( pair @ A @ B ) ) @ sk2 @ sk3 ),
inference(pattern_uni,[status(thm)],[18667:[bind(A,$thf( update_slb @ sk1 @ sk4 )),bind(B,$thf( B )),bind(C,$thf( sk2 )),bind(D,$thf( D )),bind(E,$thf( sk3 ))]]) ).
thf(18808,plain,
! [B: $i,A: $i] : ( pair_in_list @ ( insert_slb @ ( update_slb @ sk1 @ sk4 ) @ ( pair @ A @ B ) ) @ sk2 @ sk3 ),
inference(simp,[status(thm)],[18668]) ).
thf(56447,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( pair_in_list @ ( update_slb @ ( insert_slb @ A @ ( pair @ B @ sk6 ) ) @ sk4 ) @ sk2 @ sk3 )
| ( ( insert_slb @ ( update_slb @ A @ sk4 ) @ ( pair @ B @ sk6 ) )
!= ( insert_slb @ ( update_slb @ sk1 @ sk4 ) @ ( pair @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[19635,18808]) ).
thf(56448,plain,
! [A: $i] : ( pair_in_list @ ( update_slb @ ( insert_slb @ sk1 @ ( pair @ A @ sk6 ) ) @ sk4 ) @ sk2 @ sk3 ),
inference(pattern_uni,[status(thm)],[56447:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( sk6 ))]]) ).
thf(56772,plain,
! [A: $i] : ( pair_in_list @ ( update_slb @ ( insert_slb @ sk1 @ ( pair @ A @ sk6 ) ) @ sk4 ) @ sk2 @ sk3 ),
inference(simp,[status(thm)],[56448]) ).
thf(57243,plain,
~ $true,
inference(rewrite,[status(thm)],[22,56772]) ).
thf(57244,plain,
$false,
inference(simp,[status(thm)],[57243]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV401+1 : TPTP v8.2.0. Released v3.3.0.
% 0.11/0.12 % Command : run_Leo-III %s %d SAT
% 0.12/0.33 % Computer : n026.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
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 20 14:17:25 EDT 2024
% 0.12/0.33 % CPUTime :
% 1.04/0.92 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/1.06 % [INFO] Parsing done (138ms).
% 1.24/1.07 % [INFO] Running in sequential loop mode.
% 1.75/1.29 % [INFO] nitpick registered as external prover.
% 1.75/1.29 % [INFO] Scanning for conjecture ...
% 2.00/1.36 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 2.16/1.41 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 2.16/1.43 % [INFO] Problem is first-order (TPTP FOF).
% 2.16/1.44 % [INFO] Type checking passed.
% 2.16/1.44 % [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 ...
% 135.05/25.33 % [INFO] Killing All external provers ...
% 135.05/25.34 % Time passed: 24808ms (effective reasoning time: 24259ms)
% 135.05/25.34 % 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)>
% 135.05/25.34 % Axioms used in derivation (5): stricly_smaller_definition, totality, ax23, ax30, ax29
% 135.05/25.34 % No. of inferences in proof: 89
% 135.05/25.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 24808 ms resp. 24259 ms w/o parsing
% 135.13/25.42 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 135.13/25.42 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------