%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG071+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:46:03 AM UTC 2026
% Result : Theorem 28.05s 6.42s
% Output : Refutation 24.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 7
% Syntax : Number of formulae : 107 ( 30 unt; 0 typ; 2 def)
% Number of atoms : 366 ( 102 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1120 ( 128 ~; 106 |; 34 &; 811 @)
% ( 0 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 129 ( 1 ^; 120 !; 6 ?; 129 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(sorti1_decl,type,
sorti1: $i > $o ).
thf(sorti2_decl,type,
sorti2: $i > $o ).
thf(h_decl,type,
h: $i > $i ).
thf(j_decl,type,
j: $i > $i ).
thf(op1_decl,type,
op1: $i > $i > $i ).
thf(op2_decl,type,
op2: $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i > $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i] :
@+[B: $i] :
( ( ( A @ ( B @ op1 ) @ ( A @ op1 ) )
= B )
& ( ( A @ ( B @ op1 ) @ ( B @ op1 ) )
!= A )
& ( B @ sorti1 ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( A @ sorti2 )
=> ? [B: $i] :
( ( ( A @ ( B @ op2 ) @ ( A @ op2 ) )
= B )
& ( ( A @ ( B @ op2 ) @ ( B @ op2 ) )
!= A )
& ( B @ sorti2 ) ) ) ) ) ).
thf(6,axiom,
~ ! [A: $i] :
( ( A @ sorti2 )
=> ? [B: $i] :
( ( ( A @ ( B @ op2 ) @ ( A @ op2 ) )
= B )
& ( ( A @ ( B @ op2 ) @ ( B @ op2 ) )
!= A )
& ( B @ sorti2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
thf(35,plain,
~ ! [A: $i] :
( ( A @ sorti2 )
=> ? [B: $i] :
( ( ( A @ ( B @ op2 ) @ ( A @ op2 ) )
= B )
& ( ( A @ ( B @ op2 ) @ ( B @ op2 ) )
!= A )
& ( B @ sorti2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(36,plain,
~ ! [A: $i] :
( ( A @ sorti2 )
=> ? [B: $i] :
( ( ( A @ ( B @ op2 ) @ ( A @ op2 ) )
= B )
& ( ( A @ ( B @ op2 ) @ ( B @ op2 ) )
!= A )
& ( B @ sorti2 ) ) ),
inference(polarity_switch,[status(thm)],[35]) ).
thf(37,plain,
! [A: $i] :
( ( ( ( sk2 @ ( A @ op2 ) @ ( sk2 @ op2 ) )
!= A )
| ( ( sk2 @ ( A @ op2 ) @ ( A @ op2 ) )
= sk2 )
| ~ ( A @ sorti2 ) )
& ( sk2 @ sorti2 ) ),
inference(cnf,[status(esa)],[36]) ).
thf(38,plain,
sk2 @ sorti2,
inference(cnfConj,[status(thm)],[37]) ).
thf(1,conjecture,
( ( ! [A: $i] :
( ( A @ sorti2 )
=> ( A @ j @ sorti1 ) )
& ! [A: $i] :
( ( A @ sorti1 )
=> ( A @ h @ sorti2 ) ) )
=> ~ ( ! [A: $i] :
( ( A @ sorti1 )
=> ( ( A @ h @ j )
= A ) )
& ! [A: $i] :
( ( A @ sorti2 )
=> ( ( A @ j @ h )
= A ) )
& ! [A: $i] :
( ( A @ sorti2 )
=> ! [B: $i] :
( ( B @ sorti2 )
=> ( ( B @ ( A @ op2 ) @ j )
= ( B @ j @ ( A @ j @ op1 ) ) ) ) )
& ! [A: $i] :
( ( A @ sorti1 )
=> ! [B: $i] :
( ( B @ sorti1 )
=> ( ( B @ ( A @ op1 ) @ h )
= ( B @ h @ ( A @ h @ op2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i] :
( ( A @ sorti2 )
=> ( A @ j @ sorti1 ) )
& ! [A: $i] :
( ( A @ sorti1 )
=> ( A @ h @ sorti2 ) ) )
=> ~ ( ! [A: $i] :
( ( A @ sorti1 )
=> ( ( A @ h @ j )
= A ) )
& ! [A: $i] :
( ( A @ sorti2 )
=> ( ( A @ j @ h )
= A ) )
& ! [A: $i] :
( ( A @ sorti2 )
=> ! [B: $i] :
( ( B @ sorti2 )
=> ( ( B @ ( A @ op2 ) @ j )
= ( B @ j @ ( A @ j @ op1 ) ) ) ) )
& ! [A: $i] :
( ( A @ sorti1 )
=> ! [B: $i] :
( ( B @ sorti1 )
=> ( ( B @ ( A @ op1 ) @ h )
= ( B @ h @ ( A @ h @ op2 ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ( ( ! [A: $i] :
( ( A @ sorti2 )
=> ( A @ j @ sorti1 ) )
& ! [A: $i] :
( ( A @ sorti1 )
=> ( A @ h @ sorti2 ) ) )
=> ~ ( ! [A: $i] :
( ( A @ sorti1 )
=> ( ( A @ h @ j )
= A ) )
& ! [A: $i] :
( ( A @ sorti2 )
=> ( ( A @ j @ h )
= A ) )
& ! [A: $i] :
( ( A @ sorti2 )
=> ! [B: $i] :
( ( B @ sorti2 )
=> ( ( B @ ( A @ op2 ) @ j )
= ( B @ j @ ( A @ j @ op1 ) ) ) ) )
& ! [A: $i] :
( ( A @ sorti1 )
=> ! [B: $i] :
( ( B @ sorti1 )
=> ( ( B @ ( A @ op1 ) @ h )
= ( B @ h @ ( A @ h @ op2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ( H @ h @ j )
= H )
| ~ ( H @ sorti1 ) )
& ( ( ( G @ j @ h )
= G )
| ~ ( G @ sorti2 ) )
& ( ( ( F @ ( E @ op2 ) @ j )
= ( F @ j @ ( E @ j @ op1 ) ) )
| ~ ( F @ sorti2 )
| ~ ( E @ sorti2 ) )
& ( ( ( D @ ( C @ op1 ) @ h )
= ( D @ h @ ( C @ h @ op2 ) ) )
| ~ ( D @ sorti1 )
| ~ ( C @ sorti1 ) )
& ( ( B @ j @ sorti1 )
| ~ ( B @ sorti2 ) )
& ( ( A @ h @ sorti2 )
| ~ ( A @ sorti1 ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(14,plain,
! [A: $i] :
( ( A @ j @ sorti1 )
| ~ ( A @ sorti2 ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(17,plain,
! [A: $i] :
( ( A @ j @ sorti1 )
| ~ ( A @ sorti2 ) ),
inference(simp,[status(thm)],[14]) ).
thf(41,plain,
! [A: $i] :
( ( ( sk2 @ sorti2 )
!= ( A @ sorti2 ) )
| ( A @ j @ sorti1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[38,17]) ).
thf(42,plain,
! [A: $i] :
( ( ( sk2 @ sorti2 )
!= ( A @ sorti2 ) )
| ( A @ j @ sorti1 ) ),
inference(simp,[status(thm)],[41]) ).
thf(43,plain,
sk2 @ j @ sorti1,
inference(pattern_uni,[status(thm)],[42:[bind(A,$thf( sk2 ))]]) ).
thf(11,plain,
! [A: $i] :
( ( A @ h @ sorti2 )
| ~ ( A @ sorti1 ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(52,plain,
! [A: $i] :
( ( ( sk2 @ j @ sorti1 )
!= ( A @ sorti1 ) )
| ( A @ h @ sorti2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,11]) ).
thf(53,plain,
! [A: $i] :
( ( ( sk2 @ j @ sorti1 )
!= ( A @ sorti1 ) )
| ( A @ h @ sorti2 ) ),
inference(simp,[status(thm)],[52]) ).
thf(54,plain,
sk2 @ j @ h @ sorti2,
inference(pattern_uni,[status(thm)],[53:[bind(A,$thf( sk2 @ j ))]]) ).
thf(62,plain,
! [A: $i] :
( ( ( sk2 @ j @ h @ sorti2 )
!= ( A @ sorti2 ) )
| ( A @ j @ sorti1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[54,17]) ).
thf(63,plain,
! [A: $i] :
( ( ( sk2 @ j @ h @ sorti2 )
!= ( A @ sorti2 ) )
| ( A @ j @ sorti1 ) ),
inference(simp,[status(thm)],[62]) ).
thf(64,plain,
sk2 @ j @ h @ j @ sorti1,
inference(pattern_uni,[status(thm)],[63:[bind(A,$thf( sk2 @ j @ h ))]]) ).
thf(68,plain,
! [A: $i] :
( ( ( sk2 @ j @ h @ j @ sorti1 )
!= ( A @ sorti1 ) )
| ( A @ h @ sorti2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[64,11]) ).
thf(69,plain,
! [A: $i] :
( ( ( sk2 @ j @ h @ j @ sorti1 )
!= ( A @ sorti1 ) )
| ( A @ h @ sorti2 ) ),
inference(simp,[status(thm)],[68]) ).
thf(70,plain,
sk2 @ j @ h @ j @ h @ sorti2,
inference(pattern_uni,[status(thm)],[69:[bind(A,$thf( sk2 @ j @ h @ j ))]]) ).
thf(71,plain,
! [A: $i] :
( ( ( sk2 @ j @ h @ j @ h @ sorti2 )
!= ( A @ sorti2 ) )
| ( A @ j @ sorti1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[70,17]) ).
thf(72,plain,
! [A: $i] :
( ( ( sk2 @ j @ h @ j @ h @ sorti2 )
!= ( A @ sorti2 ) )
| ( A @ j @ sorti1 ) ),
inference(simp,[status(thm)],[71]) ).
thf(73,plain,
sk2 @ j @ h @ j @ h @ j @ sorti1,
inference(pattern_uni,[status(thm)],[72:[bind(A,$thf( sk2 @ j @ h @ j @ h ))]]) ).
thf(148,plain,
! [A: $i] :
( ( ( sk2 @ j @ h @ j @ h @ j @ sorti1 )
!= ( A @ sorti1 ) )
| ( A @ h @ sorti2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[73,11]) ).
thf(149,plain,
! [A: $i] :
( ( ( sk2 @ j @ h @ j @ h @ j @ sorti1 )
!= ( A @ sorti1 ) )
| ( A @ h @ sorti2 ) ),
inference(simp,[status(thm)],[148]) ).
thf(150,plain,
sk2 @ j @ h @ j @ h @ j @ h @ sorti2,
inference(pattern_uni,[status(thm)],[149:[bind(A,$thf( sk2 @ j @ h @ j @ h @ j ))]]) ).
thf(163,plain,
! [A: $i] :
( ( ( sk2 @ j @ h @ j @ h @ j @ h @ sorti2 )
!= ( A @ sorti2 ) )
| ( A @ j @ sorti1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[150,17]) ).
thf(164,plain,
! [A: $i] :
( ( ( sk2 @ j @ h @ j @ h @ j @ h @ sorti2 )
!= ( A @ sorti2 ) )
| ( A @ j @ sorti1 ) ),
inference(simp,[status(thm)],[163]) ).
thf(165,plain,
sk2 @ j @ h @ j @ h @ j @ h @ j @ sorti1,
inference(pattern_uni,[status(thm)],[164:[bind(A,$thf( sk2 @ j @ h @ j @ h @ j @ h ))]]) ).
thf(177,plain,
! [A: $i] :
( ( ( sk2 @ j @ h @ j @ h @ j @ h @ j @ sorti1 )
!= ( A @ sorti1 ) )
| ( A @ h @ sorti2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[165,11]) ).
thf(178,plain,
! [A: $i] :
( ( ( sk2 @ j @ h @ j @ h @ j @ h @ j @ sorti1 )
!= ( A @ sorti1 ) )
| ( A @ h @ sorti2 ) ),
inference(simp,[status(thm)],[177]) ).
thf(179,plain,
sk2 @ j @ h @ j @ h @ j @ h @ j @ h @ sorti2,
inference(pattern_uni,[status(thm)],[178:[bind(A,$thf( sk2 @ j @ h @ j @ h @ j @ h @ j ))]]) ).
thf(194,plain,
! [A: $i] :
( ( ( sk2 @ j @ h @ j @ h @ j @ h @ j @ h @ sorti2 )
!= ( A @ sorti2 ) )
| ( A @ j @ sorti1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[179,17]) ).
thf(195,plain,
! [A: $i] :
( ( ( sk2 @ j @ h @ j @ h @ j @ h @ j @ h @ sorti2 )
!= ( A @ sorti2 ) )
| ( A @ j @ sorti1 ) ),
inference(simp,[status(thm)],[194]) ).
thf(196,plain,
sk2 @ j @ h @ j @ h @ j @ h @ j @ h @ j @ sorti1,
inference(pattern_uni,[status(thm)],[195:[bind(A,$thf( sk2 @ j @ h @ j @ h @ j @ h @ j @ h ))]]) ).
thf(252,plain,
! [A: $i] :
( ( ( sk2 @ j @ h @ j @ h @ j @ h @ j @ h @ j @ sorti1 )
!= ( A @ sorti1 ) )
| ( A @ h @ sorti2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[196,11]) ).
thf(253,plain,
! [A: $i] :
( ( ( sk2 @ j @ h @ j @ h @ j @ h @ j @ h @ j @ sorti1 )
!= ( A @ sorti1 ) )
| ( A @ h @ sorti2 ) ),
inference(simp,[status(thm)],[252]) ).
thf(254,plain,
sk2 @ j @ h @ j @ h @ j @ h @ j @ h @ j @ h @ sorti2,
inference(pattern_uni,[status(thm)],[253:[bind(A,$thf( sk2 @ j @ h @ j @ h @ j @ h @ j @ h @ j ))]]) ).
thf(9,plain,
! [A: $i] :
( ( ( A @ h @ j )
= A )
| ~ ( A @ sorti1 ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(18,plain,
! [A: $i] :
( ~ ( A @ sorti1 )
| ( ( A @ h @ j )
= A ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(19,plain,
! [A: $i] :
( ~ ( A @ sorti1 )
| ( ( A @ h @ j )
= A ) ),
inference(simp,[status(thm)],[18]) ).
thf(398,plain,
! [A: $i] :
( ( ( sk2 @ j @ h @ j @ sorti1 )
!= ( A @ sorti1 ) )
| ~ $true
| ( ( A @ h @ j )
= A ) ),
inference(paramod_ordered,[status(thm)],[64,19]) ).
thf(399,plain,
! [A: $i] :
( ( ( sk2 @ j @ h @ j @ sorti1 )
!= ( A @ sorti1 ) )
| ( ( A @ h @ j )
= A ) ),
inference(simp,[status(thm)],[398]) ).
thf(400,plain,
( ( sk2 @ j @ h @ j @ h @ j )
= ( sk2 @ j @ h @ j ) ),
inference(pattern_uni,[status(thm)],[399:[bind(A,$thf( sk2 @ j @ h @ j ))]]) ).
thf(13,plain,
! [A: $i] :
( ( ( A @ j @ h )
= A )
| ~ ( A @ sorti2 ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(20,plain,
! [A: $i] :
( ~ ( A @ sorti2 )
| ( ( A @ j @ h )
= A ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(21,plain,
! [A: $i] :
( ~ ( A @ sorti2 )
| ( ( A @ j @ h )
= A ) ),
inference(simp,[status(thm)],[20]) ).
thf(536,plain,
! [A: $i] :
( ( ( sk2 @ sorti2 )
!= ( A @ sorti2 ) )
| ~ $true
| ( ( A @ j @ h )
= A ) ),
inference(paramod_ordered,[status(thm)],[38,21]) ).
thf(537,plain,
! [A: $i] :
( ( ( sk2 @ sorti2 )
!= ( A @ sorti2 ) )
| ( ( A @ j @ h )
= A ) ),
inference(simp,[status(thm)],[536]) ).
thf(538,plain,
( ( sk2 @ j @ h )
= sk2 ),
inference(pattern_uni,[status(thm)],[537:[bind(A,$thf( sk2 ))]]) ).
thf(844,plain,
( ( sk2 @ j @ h @ j )
= ( sk2 @ j ) ),
inference(rewrite,[status(thm)],[400,538]) ).
thf(962,plain,
sk2 @ j @ h @ j @ h @ j @ h @ j @ h @ sorti2,
inference(rewrite,[status(thm)],[254,844]) ).
thf(965,plain,
( ( ( sk2 @ j @ h )
!= ( sk2 @ j @ h ) )
| ( sk2 @ j @ h @ j @ h @ j @ h @ sorti2 ) ),
inference(paramod_ordered,[status(thm)],[538,962]) ).
thf(966,plain,
sk2 @ j @ h @ j @ h @ j @ h @ sorti2,
inference(pattern_uni,[status(thm)],[965:[]]) ).
thf(1026,plain,
sk2 @ j @ h @ j @ h @ sorti2,
inference(rewrite,[status(thm)],[966,844]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ sorti2 )
=> ! [B: $i] :
( ( B @ sorti2 )
=> ( B @ ( A @ op2 ) @ sorti2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(26,plain,
! [A: $i] :
( ( A @ sorti2 )
=> ! [B: $i] :
( ( B @ sorti2 )
=> ( B @ ( A @ op2 ) @ sorti2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ op2 ) @ sorti2 )
| ~ ( B @ sorti2 )
| ~ ( A @ sorti2 ) ),
inference(cnf,[status(esa)],[26]) ).
thf(427,plain,
! [A: $i] :
( ( ( sk2 @ j @ sorti1 )
!= ( A @ sorti1 ) )
| ~ $true
| ( ( A @ h @ j )
= A ) ),
inference(paramod_ordered,[status(thm)],[43,19]) ).
thf(428,plain,
! [A: $i] :
( ( ( sk2 @ j @ sorti1 )
!= ( A @ sorti1 ) )
| ( ( A @ h @ j )
= A ) ),
inference(simp,[status(thm)],[427]) ).
thf(429,plain,
( ( sk2 @ j @ h @ j )
= ( sk2 @ j ) ),
inference(pattern_uni,[status(thm)],[428:[bind(A,$thf( sk2 @ j ))]]) ).
thf(461,plain,
sk2 @ j @ h @ j @ h @ j @ sorti1,
inference(rewrite,[status(thm)],[165,429]) ).
thf(499,plain,
sk2 @ j @ h @ j @ sorti1,
inference(rewrite,[status(thm)],[461,429]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( ( A @ h @ sorti2 )
!= ( B @ sorti2 ) )
| ( B @ j @ sorti1 )
| ~ $true
| ~ ( A @ sorti1 ) ),
inference(paramod_ordered,[status(thm)],[11,17]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( ( A @ h @ sorti2 )
!= ( B @ sorti2 ) )
| ( B @ j @ sorti1 )
| ~ ( A @ sorti1 ) ),
inference(simp,[status(thm)],[47]) ).
thf(49,plain,
! [A: $i] :
( ( A @ h @ j @ sorti1 )
| ~ ( A @ sorti1 ) ),
inference(pattern_uni,[status(thm)],[48:[bind(A,$thf( C )),bind(B,$thf( C @ h ))]]) ).
thf(50,plain,
! [A: $i] :
( ( A @ h @ j @ sorti1 )
| ~ ( A @ sorti1 ) ),
inference(simp,[status(thm)],[49]) ).
thf(506,plain,
! [A: $i] :
( ( ( sk2 @ j @ h @ j @ sorti1 )
!= ( A @ sorti1 ) )
| ( A @ h @ j @ sorti1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[499,50]) ).
thf(507,plain,
! [A: $i] :
( ( ( sk2 @ j @ h @ j @ sorti1 )
!= ( A @ sorti1 ) )
| ( A @ h @ j @ sorti1 ) ),
inference(simp,[status(thm)],[506]) ).
thf(508,plain,
sk2 @ j @ h @ j @ h @ j @ sorti1,
inference(pattern_uni,[status(thm)],[507:[bind(A,$thf( sk2 @ j @ h @ j ))]]) ).
thf(584,plain,
sk2 @ j @ h @ j @ sorti1,
inference(rewrite,[status(thm)],[508,538]) ).
thf(597,plain,
! [A: $i] :
( ( ( sk2 @ j @ h @ j @ sorti1 )
!= ( A @ sorti1 ) )
| ( A @ h @ sorti2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[584,11]) ).
thf(598,plain,
! [A: $i] :
( ( ( sk2 @ j @ h @ j @ sorti1 )
!= ( A @ sorti1 ) )
| ( A @ h @ sorti2 ) ),
inference(simp,[status(thm)],[597]) ).
thf(599,plain,
sk2 @ j @ h @ j @ h @ sorti2,
inference(pattern_uni,[status(thm)],[598:[bind(A,$thf( sk2 @ j @ h @ j ))]]) ).
thf(609,plain,
sk2 @ j @ h @ sorti2,
inference(rewrite,[status(thm)],[599,538]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ sorti1 )
=> ! [B: $i] :
( ( B @ sorti1 )
=> ( B @ ( A @ op1 ) @ sorti1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(24,plain,
! [A: $i] :
( ( A @ sorti1 )
=> ! [B: $i] :
( ( B @ sorti1 )
=> ( B @ ( A @ op1 ) @ sorti1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ op1 ) @ sorti1 )
| ~ ( B @ sorti1 )
| ~ ( A @ sorti1 ) ),
inference(cnf,[status(esa)],[24]) ).
thf(1030,plain,
! [A: $i] :
( ( ( sk2 @ j @ h @ j @ h @ sorti2 )
!= ( A @ sorti2 ) )
| ( A @ j @ sorti1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1026,17]) ).
thf(1031,plain,
! [A: $i] :
( ( ( sk2 @ j @ h @ j @ h @ sorti2 )
!= ( A @ sorti2 ) )
| ( A @ j @ sorti1 ) ),
inference(simp,[status(thm)],[1030]) ).
thf(1032,plain,
sk2 @ j @ h @ j @ h @ j @ sorti1,
inference(pattern_uni,[status(thm)],[1031:[bind(A,$thf( sk2 @ j @ h @ j @ h ))]]) ).
thf(1074,plain,
sk2 @ j @ h @ j @ sorti1,
inference(rewrite,[status(thm)],[1032,844]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ sorti1 )
=> ? [B: $i] :
( ( ( A @ ( B @ op1 ) @ ( A @ op1 ) )
= B )
& ( ( A @ ( B @ op1 ) @ ( B @ op1 ) )
!= A )
& ( B @ sorti1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(28,plain,
! [A: $i] :
( ( A @ sorti1 )
=> ? [B: $i] :
( ( ( A @ ( B @ op1 ) @ ( A @ op1 ) )
= B )
& ( ( A @ ( B @ op1 ) @ ( B @ op1 ) )
!= A )
& ( B @ sorti1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(29,plain,
! [A: $i] :
( ( ( ( A @ ( A @ sk1 @ op1 ) @ ( A @ op1 ) )
= ( A @ sk1 ) )
| ~ ( A @ sorti1 ) )
& ( ( ( A @ ( A @ sk1 @ op1 ) @ ( A @ sk1 @ op1 ) )
!= A )
| ~ ( A @ sorti1 ) )
& ( ( A @ sk1 @ sorti1 )
| ~ ( A @ sorti1 ) ) ),
inference(cnf,[status(esa)],[28]) ).
thf(31,plain,
! [A: $i] :
( ( ( A @ ( A @ sk1 @ op1 ) @ ( A @ sk1 @ op1 ) )
!= A )
| ~ ( A @ sorti1 ) ),
inference(cnfConj,[status(thm)],[29]) ).
thf(33,plain,
! [A: $i] :
( ~ ( A @ sorti1 )
| ( ( A @ ( A @ sk1 @ op1 ) @ ( A @ sk1 @ op1 ) )
!= A ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(58,plain,
! [A: $i] :
( ( ( sk2 @ j @ sorti1 )
!= ( A @ sorti1 ) )
| ~ $true
| ( ( A @ ( A @ sk1 @ op1 ) @ ( A @ sk1 @ op1 ) )
!= A ) ),
inference(paramod_ordered,[status(thm)],[43,33]) ).
thf(59,plain,
! [A: $i] :
( ( ( sk2 @ j @ sorti1 )
!= ( A @ sorti1 ) )
| ( ( A @ ( A @ sk1 @ op1 ) @ ( A @ sk1 @ op1 ) )
!= A ) ),
inference(simp,[status(thm)],[58]) ).
thf(60,plain,
( ( sk2 @ j @ ( sk2 @ j @ sk1 @ op1 ) @ ( sk2 @ j @ sk1 @ op1 ) )
!= ( sk2 @ j ) ),
inference(pattern_uni,[status(thm)],[59:[bind(A,$thf( sk2 @ j ))]]) ).
thf(10,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ op2 ) @ j )
= ( B @ j @ ( A @ j @ op1 ) ) )
| ~ ( B @ sorti2 )
| ~ ( A @ sorti2 ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ~ ( B @ sorti2 )
| ~ ( A @ sorti2 )
| ( ( B @ ( A @ op2 ) @ j )
= ( B @ j @ ( A @ j @ op1 ) ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ~ ( B @ sorti2 )
| ~ ( A @ sorti2 )
| ( ( B @ ( A @ op2 ) @ j )
= ( B @ j @ ( A @ j @ op1 ) ) ) ),
inference(simp,[status(thm)],[15]) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ op1 ) @ h )
= ( B @ h @ ( A @ h @ op2 ) ) )
| ~ ( B @ sorti1 )
| ~ ( A @ sorti1 ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ~ ( B @ sorti1 )
| ~ ( A @ sorti1 )
| ( ( B @ h @ ( A @ h @ op2 ) )
= ( B @ ( A @ op1 ) @ h ) ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ~ ( B @ sorti1 )
| ~ ( A @ sorti1 )
| ( ( B @ h @ ( A @ h @ op2 ) )
= ( B @ ( A @ op1 ) @ h ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( ( A @ j @ sorti1 )
!= ( B @ sorti1 ) )
| ( B @ h @ sorti2 )
| ~ $true
| ~ ( A @ sorti2 ) ),
inference(paramod_ordered,[status(thm)],[17,11]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( ( A @ j @ sorti1 )
!= ( B @ sorti1 ) )
| ( B @ h @ sorti2 )
| ~ ( A @ sorti2 ) ),
inference(simp,[status(thm)],[44]) ).
thf(46,plain,
! [A: $i] :
( ( A @ j @ h @ sorti2 )
| ~ ( A @ sorti2 ) ),
inference(pattern_uni,[status(thm)],[45:[bind(A,$thf( C )),bind(B,$thf( C @ j ))]]) ).
thf(51,plain,
! [A: $i] :
( ( A @ j @ h @ sorti2 )
| ~ ( A @ sorti2 ) ),
inference(simp,[status(thm)],[46]) ).
thf(6266,plain,
$false,
inference(e,[status(thm)],[962,538,1026,17,27,7,609,35,844,24,25,1074,60,21,33,28,38,50,16,11,43,26,23,51,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ALG071+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sat Sep 26 21:05:39 UTC 2026
% 0.04/0.32 % CPUTime :
% 0.04/0.32 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.61/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.94/0.94 % [INFO] Parsing done (152ms).
% 0.94/0.95 % [INFO] Running in sequential loop mode.
% 1.45/1.29 % [INFO] eprover registered as external prover.
% 1.45/1.30 % [INFO] Scanning for conjecture ...
% 1.64/1.38 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 1.84/1.42 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.84/1.43 % [INFO] Problem is first-order (TPTP FOF).
% 1.84/1.44 % [INFO] Type checking passed.
% 1.84/1.44 % [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 ...
% 28.05/6.41 % External prover 'e' found a proof!
% 28.05/6.41 % [INFO] Killing All external provers ...
% 28.05/6.41 % Time passed: 5974ms (effective reasoning time: 5457ms)
% 28.05/6.41 % 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)>
% 28.05/6.42 % Axioms used in derivation (4): ax4, ax2, ax1, ax3
% 28.05/6.42 % No. of inferences in proof: 105
% 28.05/6.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5974 ms resp. 5457 ms w/o parsing
% 24.08/6.51 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 24.08/6.51 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------