%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG072+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 : n016.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 37.61s 13.49s
% Output : Refutation 32.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of formulae : 91 ( 25 unt; 0 typ; 3 def)
% Number of atoms : 340 ( 133 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 795 ( 124 ~; 100 |; 49 &; 473 @)
% ( 0 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 124 ( 0 ^; 113 !; 8 ?; 124 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% 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(unit1_decl,type,
unit1: $i ).
thf(unit2_decl,type,
unit2: $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
( ( unit1 = A )
& ( A @ sorti1 ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
( ( unit2 = A )
& ( A @ sorti2 ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
( ! [B: $i] :
( ( B @ sorti1 )
=> ! [C: $i] :
( ( C @ sorti1 )
=> ( ( ( A != unit1 )
& ( ( A @ ( B @ op1 ) )
= C ) )
| ( ( C @ ( B @ op1 ) )
!= A ) ) ) )
& ( A @ sorti1 ) ) ) ) ).
thf(5,axiom,
unit2 @ sorti2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(38,plain,
unit2 @ sorti2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
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(11,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(12,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)],[11]) ).
thf(18,plain,
! [A: $i] :
( ( A @ j @ sorti1 )
| ~ ( A @ sorti2 ) ),
inference(cnfConj,[status(thm)],[12]) ).
thf(25,plain,
! [A: $i] :
( ( A @ j @ sorti1 )
| ~ ( A @ sorti2 ) ),
inference(simp,[status(thm)],[18]) ).
thf(168,plain,
! [A: $i] :
( ( ( unit2 @ sorti2 )
!= ( A @ sorti2 ) )
| ( A @ j @ sorti1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[38,25]) ).
thf(169,plain,
! [A: $i] :
( ( ( unit2 @ sorti2 )
!= ( A @ sorti2 ) )
| ( A @ j @ sorti1 ) ),
inference(simp,[status(thm)],[168]) ).
thf(170,plain,
unit2 @ j @ sorti1,
inference(pattern_uni,[status(thm)],[169:[bind(A,$thf( unit2 ))]]) ).
thf(9,axiom,
? [A: $i] :
( ! [B: $i] :
( ( B @ sorti1 )
=> ! [C: $i] :
( ( C @ sorti1 )
=> ( ( ( A != unit1 )
& ( ( A @ ( B @ op1 ) )
= C ) )
| ( ( C @ ( B @ op1 ) )
!= A ) ) ) )
& ( A @ sorti1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
thf(52,plain,
? [A: $i] :
( ! [B: $i] :
( ( B @ sorti1 )
=> ! [C: $i] :
( ( C @ sorti1 )
=> ( ( ( A != unit1 )
& ( ( A @ ( B @ op1 ) )
= C ) )
| ( ( C @ ( B @ op1 ) )
!= A ) ) ) )
& ( A @ sorti1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(17,plain,
! [A: $i] :
( ( ( A @ j @ h )
= A )
| ~ ( A @ sorti2 ) ),
inference(cnfConj,[status(thm)],[12]) ).
thf(23,plain,
! [A: $i] :
( ~ ( A @ sorti2 )
| ( ( A @ j @ h )
= A ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(24,plain,
! [A: $i] :
( ~ ( A @ sorti2 )
| ( ( A @ j @ h )
= A ) ),
inference(simp,[status(thm)],[23]) ).
thf(401,plain,
! [A: $i] :
( ( ( unit2 @ sorti2 )
!= ( A @ sorti2 ) )
| ~ $true
| ( ( A @ j @ h )
= A ) ),
inference(paramod_ordered,[status(thm)],[38,24]) ).
thf(402,plain,
! [A: $i] :
( ( ( unit2 @ sorti2 )
!= ( A @ sorti2 ) )
| ( ( A @ j @ h )
= A ) ),
inference(simp,[status(thm)],[401]) ).
thf(403,plain,
( ( unit2 @ j @ h )
= unit2 ),
inference(pattern_uni,[status(thm)],[402:[bind(A,$thf( unit2 ))]]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( ( sk3 != unit1 )
| ( ( B @ ( A @ op1 ) )
!= sk3 )
| ~ ( B @ sorti1 )
| ~ ( A @ sorti1 ) )
& ( ( ( sk3 @ ( A @ op1 ) )
= B )
| ( ( B @ ( A @ op1 ) )
!= sk3 )
| ~ ( B @ sorti1 )
| ~ ( A @ sorti1 ) )
& ( sk3 @ sorti1 ) ),
inference(cnf,[status(esa)],[52]) ).
thf(54,plain,
sk3 @ sorti1,
inference(cnfConj,[status(thm)],[53]) ).
thf(3,axiom,
unit1 @ sorti1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(28,plain,
unit1 @ sorti1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( sk3 != unit1 )
| ( ( B @ ( A @ op1 ) )
!= sk3 )
| ~ ( B @ sorti1 )
| ~ ( A @ sorti1 ) ),
inference(cnfConj,[status(thm)],[53]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ~ ( B @ sorti1 )
| ~ ( A @ sorti1 )
| ( sk3 != unit1 )
| ( ( B @ ( A @ op1 ) )
!= sk3 ) ),
inference(lifteq,[status(thm)],[56]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ( ( unit1 @ sorti1 )
!= ( A @ sorti1 ) )
| ~ ( B @ sorti1 )
| ~ $true
| ( sk3 != unit1 )
| ( ( B @ ( A @ op1 ) )
!= sk3 ) ),
inference(paramod_ordered,[status(thm)],[28,58]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ( ( unit1 @ sorti1 )
!= ( A @ sorti1 ) )
| ~ ( B @ sorti1 )
| ( sk3 != unit1 )
| ( ( B @ ( A @ op1 ) )
!= sk3 ) ),
inference(simp,[status(thm)],[69]) ).
thf(71,plain,
! [A: $i] :
( ~ ( A @ sorti1 )
| ( sk3 != unit1 )
| ( ( A @ ( unit1 @ op1 ) )
!= sk3 ) ),
inference(pattern_uni,[status(thm)],[70:[bind(A,$thf( unit1 ))]]) ).
thf(75,plain,
! [A: $i] :
( ~ ( A @ sorti1 )
| ( sk3 != unit1 )
| ( ( A @ ( unit1 @ op1 ) )
!= sk3 ) ),
inference(simp,[status(thm)],[71]) ).
thf(148,plain,
! [A: $i] :
( ( ( sk3 @ sorti1 )
!= ( A @ sorti1 ) )
| ~ $true
| ( sk3 != unit1 )
| ( ( A @ ( unit1 @ op1 ) )
!= sk3 ) ),
inference(paramod_ordered,[status(thm)],[54,75]) ).
thf(149,plain,
! [A: $i] :
( ( ( sk3 @ sorti1 )
!= ( A @ sorti1 ) )
| ( sk3 != unit1 )
| ( ( A @ ( unit1 @ op1 ) )
!= sk3 ) ),
inference(simp,[status(thm)],[148]) ).
thf(150,plain,
( ( sk3 != unit1 )
| ( ( sk3 @ ( unit1 @ op1 ) )
!= sk3 ) ),
inference(pattern_uni,[status(thm)],[149:[bind(A,$thf( sk3 ))]]) ).
thf(4,axiom,
( ? [A: $i] :
( ( unit1 = A )
& ( A @ sorti1 ) )
& ! [A: $i] :
( ( A @ sorti1 )
=> ( ( ( unit1 @ ( A @ op1 ) )
= A )
& ( ( A @ ( unit1 @ op1 ) )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(29,plain,
( ? [A: $i] :
( ( unit1 = A )
& ( A @ sorti1 ) )
& ! [A: $i] :
( ( A @ sorti1 )
=> ( ( ( unit1 @ ( A @ op1 ) )
= A )
& ( ( A @ ( unit1 @ op1 ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(30,plain,
! [A: $i] :
( ( unit1 = sk1 )
& ( sk1 @ sorti1 )
& ( ( ( unit1 @ ( A @ op1 ) )
= A )
| ~ ( A @ sorti1 ) )
& ( ( ( A @ ( unit1 @ op1 ) )
= A )
| ~ ( A @ sorti1 ) ) ),
inference(cnf,[status(esa)],[29]) ).
thf(31,plain,
! [A: $i] :
( ( ( A @ ( unit1 @ op1 ) )
= A )
| ~ ( A @ sorti1 ) ),
inference(cnfConj,[status(thm)],[30]) ).
thf(35,plain,
! [A: $i] :
( ~ ( A @ sorti1 )
| ( ( A @ ( unit1 @ op1 ) )
= A ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(561,plain,
! [A: $i] :
( ( ( sk3 @ sorti1 )
!= ( A @ sorti1 ) )
| ~ $true
| ( ( A @ ( unit1 @ op1 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[54,35]) ).
thf(562,plain,
! [A: $i] :
( ( ( sk3 @ sorti1 )
!= ( A @ sorti1 ) )
| ( ( A @ ( unit1 @ op1 ) )
= A ) ),
inference(simp,[status(thm)],[561]) ).
thf(563,plain,
( ( sk3 @ ( unit1 @ op1 ) )
= sk3 ),
inference(pattern_uni,[status(thm)],[562:[bind(A,$thf( sk3 ))]]) ).
thf(600,plain,
( ( sk3 != unit1 )
| ( sk3 != sk3 ) ),
inference(rewrite,[status(thm)],[150,563]) ).
thf(601,plain,
sk3 != unit1,
inference(simp,[status(thm)],[600]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ sorti1 )
=> ! [B: $i] :
( ( B @ sorti1 )
=> ( B @ ( A @ op1 ) @ sorti1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
thf(48,plain,
! [A: $i] :
( ( A @ sorti1 )
=> ! [B: $i] :
( ( B @ sorti1 )
=> ( B @ ( A @ op1 ) @ sorti1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ sorti2 )
=> ! [B: $i] :
( ( B @ sorti2 )
=> ( B @ ( A @ op2 ) @ sorti2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
thf(50,plain,
! [A: $i] :
( ( A @ sorti2 )
=> ! [B: $i] :
( ( B @ sorti2 )
=> ( B @ ( A @ op2 ) @ sorti2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,plain,
! [A: $i] :
( ( ( A @ h @ j )
= A )
| ~ ( A @ sorti1 ) ),
inference(cnfConj,[status(thm)],[12]) ).
thf(21,plain,
! [A: $i] :
( ~ ( A @ sorti1 )
| ( ( A @ h @ j )
= A ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(22,plain,
! [A: $i] :
( ~ ( A @ sorti1 )
| ( ( A @ h @ j )
= A ) ),
inference(simp,[status(thm)],[21]) ).
thf(233,plain,
! [A: $i] :
( ( ( sk3 @ sorti1 )
!= ( A @ sorti1 ) )
| ~ $true
| ( ( A @ h @ j )
= A ) ),
inference(paramod_ordered,[status(thm)],[54,22]) ).
thf(234,plain,
! [A: $i] :
( ( ( sk3 @ sorti1 )
!= ( A @ sorti1 ) )
| ( ( A @ h @ j )
= A ) ),
inference(simp,[status(thm)],[233]) ).
thf(235,plain,
( ( sk3 @ h @ j )
= sk3 ),
inference(pattern_uni,[status(thm)],[234:[bind(A,$thf( sk3 ))]]) ).
thf(252,plain,
! [A: $i] :
( ( ( unit1 @ sorti1 )
!= ( A @ sorti1 ) )
| ~ $true
| ( ( A @ h @ j )
= A ) ),
inference(paramod_ordered,[status(thm)],[28,22]) ).
thf(253,plain,
! [A: $i] :
( ( ( unit1 @ sorti1 )
!= ( A @ sorti1 ) )
| ( ( A @ h @ j )
= A ) ),
inference(simp,[status(thm)],[252]) ).
thf(254,plain,
( ( unit1 @ h @ j )
= unit1 ),
inference(pattern_uni,[status(thm)],[253:[bind(A,$thf( unit1 ))]]) ).
thf(34,plain,
unit1 = sk1,
inference(cnfConj,[status(thm)],[30]) ).
thf(37,plain,
sk1 = unit1,
inference(lifteq,[status(thm)],[34]) ).
thf(14,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ op2 ) @ j )
= ( B @ j @ ( A @ j @ op1 ) ) )
| ~ ( B @ sorti2 )
| ~ ( A @ sorti2 ) ),
inference(cnfConj,[status(thm)],[12]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ~ ( B @ sorti2 )
| ~ ( A @ sorti2 )
| ( ( B @ ( A @ op2 ) @ j )
= ( B @ j @ ( A @ j @ op1 ) ) ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ~ ( B @ sorti2 )
| ~ ( A @ sorti2 )
| ( ( B @ ( A @ op2 ) @ j )
= ( B @ j @ ( A @ j @ op1 ) ) ) ),
inference(simp,[status(thm)],[19]) ).
thf(10,axiom,
~ ? [A: $i] :
( ! [B: $i] :
( ( B @ sorti2 )
=> ! [C: $i] :
( ( C @ sorti2 )
=> ( ( ( A != unit2 )
& ( ( A @ ( B @ op2 ) )
= C ) )
| ( ( C @ ( B @ op2 ) )
!= A ) ) ) )
& ( A @ sorti2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax8) ).
thf(59,plain,
~ ? [A: $i] :
( ! [B: $i] :
( ( B @ sorti2 )
=> ! [C: $i] :
( ( C @ sorti2 )
=> ( ( ( A != unit2 )
& ( ( A @ ( B @ op2 ) )
= C ) )
| ( ( C @ ( B @ op2 ) )
!= A ) ) ) )
& ( A @ sorti2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ op1 ) @ h )
= ( B @ h @ ( A @ h @ op2 ) ) )
| ~ ( B @ sorti1 )
| ~ ( A @ sorti1 ) ),
inference(cnfConj,[status(thm)],[12]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ~ ( B @ sorti1 )
| ~ ( A @ sorti1 )
| ( ( B @ h @ ( A @ h @ op2 ) )
= ( B @ ( A @ op1 ) @ h ) ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ~ ( B @ sorti1 )
| ~ ( A @ sorti1 )
| ( ( B @ h @ ( A @ h @ op2 ) )
= ( B @ ( A @ op1 ) @ h ) ) ),
inference(simp,[status(thm)],[26]) ).
thf(15,plain,
! [A: $i] :
( ( A @ h @ sorti2 )
| ~ ( A @ sorti1 ) ),
inference(cnfConj,[status(thm)],[12]) ).
thf(79,plain,
! [A: $i] :
( ( ( unit1 @ sorti1 )
!= ( A @ sorti1 ) )
| ( A @ h @ sorti2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28,15]) ).
thf(80,plain,
! [A: $i] :
( ( ( unit1 @ sorti1 )
!= ( A @ sorti1 ) )
| ( A @ h @ sorti2 ) ),
inference(simp,[status(thm)],[79]) ).
thf(81,plain,
unit1 @ h @ sorti2,
inference(pattern_uni,[status(thm)],[80:[bind(A,$thf( unit1 ))]]) ).
thf(6,axiom,
( ? [A: $i] :
( ( unit2 = A )
& ( A @ sorti2 ) )
& ! [A: $i] :
( ( A @ sorti2 )
=> ( ( ( unit2 @ ( A @ op2 ) )
= A )
& ( ( A @ ( unit2 @ op2 ) )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
thf(39,plain,
( ? [A: $i] :
( ( unit2 = A )
& ( A @ sorti2 ) )
& ! [A: $i] :
( ( A @ sorti2 )
=> ( ( ( unit2 @ ( A @ op2 ) )
= A )
& ( ( A @ ( unit2 @ op2 ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(133,plain,
! [A: $i] :
( ( ( sk3 @ sorti1 )
!= ( A @ sorti1 ) )
| ( A @ h @ sorti2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[54,15]) ).
thf(134,plain,
! [A: $i] :
( ( ( sk3 @ sorti1 )
!= ( A @ sorti1 ) )
| ( A @ h @ sorti2 ) ),
inference(simp,[status(thm)],[133]) ).
thf(135,plain,
sk3 @ h @ sorti2,
inference(pattern_uni,[status(thm)],[134:[bind(A,$thf( sk3 ))]]) ).
thf(206,plain,
! [A: $i] :
( ( ( unit2 @ j @ sorti1 )
!= ( A @ sorti1 ) )
| ( A @ h @ sorti2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[170,15]) ).
thf(207,plain,
! [A: $i] :
( ( ( unit2 @ j @ sorti1 )
!= ( A @ sorti1 ) )
| ( A @ h @ sorti2 ) ),
inference(simp,[status(thm)],[206]) ).
thf(208,plain,
unit2 @ j @ h @ sorti2,
inference(pattern_uni,[status(thm)],[207:[bind(A,$thf( unit2 @ j ))]]) ).
thf(284,plain,
! [A: $i] :
( ( ( unit2 @ j @ h @ sorti2 )
!= ( A @ sorti2 ) )
| ( A @ j @ sorti1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[208,25]) ).
thf(285,plain,
! [A: $i] :
( ( ( unit2 @ j @ h @ sorti2 )
!= ( A @ sorti2 ) )
| ( A @ j @ sorti1 ) ),
inference(simp,[status(thm)],[284]) ).
thf(286,plain,
unit2 @ j @ h @ j @ sorti1,
inference(pattern_uni,[status(thm)],[285:[bind(A,$thf( unit2 @ j @ h ))]]) ).
thf(381,plain,
! [A: $i] :
( ( ( unit2 @ j @ h @ j @ sorti1 )
!= ( A @ sorti1 ) )
| ( A @ h @ sorti2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[286,15]) ).
thf(382,plain,
! [A: $i] :
( ( ( unit2 @ j @ h @ j @ sorti1 )
!= ( A @ sorti1 ) )
| ( A @ h @ sorti2 ) ),
inference(simp,[status(thm)],[381]) ).
thf(383,plain,
unit2 @ j @ h @ j @ h @ sorti2,
inference(pattern_uni,[status(thm)],[382:[bind(A,$thf( unit2 @ j @ h @ j ))]]) ).
thf(459,plain,
unit2 @ j @ h @ sorti2,
inference(rewrite,[status(thm)],[383,403]) ).
thf(40,plain,
! [A: $i] :
( ( unit2 = sk2 )
& ( sk2 @ sorti2 )
& ( ( ( unit2 @ ( A @ op2 ) )
= A )
| ~ ( A @ sorti2 ) )
& ( ( ( A @ ( unit2 @ op2 ) )
= A )
| ~ ( A @ sorti2 ) ) ),
inference(cnf,[status(esa)],[39]) ).
thf(44,plain,
unit2 = sk2,
inference(cnfConj,[status(thm)],[40]) ).
thf(47,plain,
sk2 = unit2,
inference(lifteq,[status(thm)],[44]) ).
thf(13428,plain,
$false,
inference(e,[status(thm)],[170,52,403,601,54,48,50,11,235,254,24,37,25,20,29,28,38,22,59,27,81,39,35,135,563,459,47,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG072+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.06 % 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
% 0.14/5.40 % Computer : n016.cluster.edu
% 0.14/5.40 % Model : x86_64 x86_64
% 0.14/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.40 % Memory : 8046.5625MB
% 0.14/5.40 % OS : Linux 6.8.0-71-generic
% 0.06/5.40 % CPULimit : 300
% 0.06/5.40 % WCLimit : 300
% 0.06/5.40 % DateTime : Sat Sep 26 21:10:51 UTC 2026
% 0.06/5.40 % CPUTime :
% 0.06/5.40 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
% 0.16/5.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.36/6.27 % [INFO] Parsing done (277ms).
% 1.36/6.29 % [INFO] Running in sequential loop mode.
% 2.16/6.77 % [INFO] eprover registered as external prover.
% 2.16/6.79 % [INFO] Scanning for conjecture ...
% 2.56/6.95 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.56/7.02 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.56/7.05 % [INFO] Problem is first-order (TPTP FOF).
% 2.85/7.07 % [INFO] Type checking passed.
% 2.85/7.08 % [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 ...
% 37.61/13.48 % External prover 'e' found a proof!
% 37.61/13.48 % [INFO] Killing All external provers ...
% 37.61/13.49 % Time passed: 7941ms (effective reasoning time: 7184ms)
% 37.61/13.49 % 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)>
% 37.61/13.49 % Axioms used in derivation (8): ax4, ax6, ax8, ax2, ax1, ax7, ax3, ax5
% 37.61/13.49 % No. of inferences in proof: 88
% 37.61/13.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7941 ms resp. 7184 ms w/o parsing
% 32.32/13.56 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 32.32/13.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------