%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG210+1 : TPTP v9.3.1. Released v3.1.0.
% 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 : n002.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 06:46:18 AM UTC 2026
% Result : Theorem 14.36s 4.67s
% Output : Refutation 12.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 110 ( 45 unt; 0 typ; 3 def)
% Number of atoms : 242 ( 166 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 845 ( 112 ~; 78 |; 17 &; 628 @)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 104 ( 1 ^; 95 !; 5 ?; 104 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(element_decl,type,
element: $i > $o ).
thf(times_decl,type,
times: $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( B @ element )
& ( A @ element ) )
=> ( B @ ( A @ times ) @ element ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( ( A @ element )
& ( sk1 @ element ) )
=> ( A @ ( sk1 @ times ) @ element ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i] :
@+[B: $i] :
( ( ( A @ ( A @ times ) )
= B )
& ( ( B @ ( A @ times ) )
= A ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( B @ element )
& ( A @ element ) )
=> ( B @ ( A @ times ) @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( B @ element )
& ( A @ element ) )
=> ( B @ ( A @ times ) @ element ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: $i,B: $i] :
( ( ( B @ element )
& ( A @ element ) )
=> ( B @ ( A @ times ) @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ times ) @ times ) )
= ( A @ ( C @ times ) @ ( B @ times ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
thf(10,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ times ) @ times ) )
= ( A @ ( C @ times ) @ ( B @ times ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ element )
<=> ? [B: $i] :
( ( ( A @ ( A @ times ) )
= B )
& ( ( B @ ( A @ times ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
thf(13,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( ( A @ ( A @ times ) )
= B )
& ( ( B @ ( A @ times ) )
= A ) )
=> ( A @ element ) )
& ( ( A @ element )
=> ? [B: $i] :
( ( ( A @ ( A @ times ) )
= B )
& ( ( B @ ( A @ times ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,plain,
( ! [A: $i] :
( ? [B: $i] :
( ( ( A @ ( A @ times ) )
= B )
& ( ( B @ ( A @ times ) )
= A ) )
=> ( A @ element ) )
& ! [A: $i] :
( ( A @ element )
=> ? [B: $i] :
( ( ( A @ ( A @ times ) )
= B )
& ( ( B @ ( A @ times ) )
= A ) ) ) ),
inference(miniscope,[status(thm)],[13]) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ element )
| ( ( B @ ( B @ times ) )
!= C )
| ( ( C @ ( B @ times ) )
!= B ) )
& ( ( ( A @ ( A @ times ) )
= ( A @ sk3 ) )
| ~ ( A @ element ) )
& ( ( ( A @ sk3 @ ( A @ times ) )
= A )
| ~ ( A @ element ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(17,plain,
! [A: $i] :
( ( ( A @ ( A @ times ) )
= ( A @ sk3 ) )
| ~ ( A @ element ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(20,plain,
! [A: $i] :
( ~ ( A @ element )
| ( ( A @ ( A @ times ) )
= ( A @ sk3 ) ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(6,plain,
( ~ ( sk2 @ ( sk1 @ times ) @ element )
& ( sk2 @ element )
& ( sk1 @ element ) ),
inference(cnf,[status(esa)],[5]) ).
thf(8,plain,
sk2 @ element,
inference(cnfConj,[status(thm)],[6]) ).
thf(482,plain,
! [A: $i] :
( ( ( sk2 @ element )
!= ( A @ element ) )
| ~ $true
| ( ( A @ ( A @ times ) )
= ( A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[8,20]) ).
thf(483,plain,
! [A: $i] :
( ( ( sk2 @ element )
!= ( A @ element ) )
| ( ( A @ ( A @ times ) )
= ( A @ sk3 ) ) ),
inference(simp,[status(thm)],[482]) ).
thf(484,plain,
( ( sk2 @ ( sk2 @ times ) )
= ( sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[483:[bind(A,$thf( sk2 ))]]) ).
thf(7,plain,
sk1 @ element,
inference(cnfConj,[status(thm)],[6]) ).
thf(465,plain,
! [A: $i] :
( ( ( sk1 @ element )
!= ( A @ element ) )
| ~ $true
| ( ( A @ ( A @ times ) )
= ( A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[7,20]) ).
thf(466,plain,
! [A: $i] :
( ( ( sk1 @ element )
!= ( A @ element ) )
| ( ( A @ ( A @ times ) )
= ( A @ sk3 ) ) ),
inference(simp,[status(thm)],[465]) ).
thf(467,plain,
( ( sk1 @ ( sk1 @ times ) )
= ( sk1 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[466:[bind(A,$thf( sk1 ))]]) ).
thf(630,plain,
( ( ( sk2 @ ( sk2 @ times ) )
!= ( sk1 @ ( sk1 @ times ) ) )
| ( ( sk2 @ sk3 )
= ( sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[484,467]) ).
thf(646,plain,
( ( sk2 != sk1 )
| ( sk2 != sk1 )
| ( ( sk2 @ sk3 )
= ( sk1 @ sk3 ) ) ),
inference(simp,[status(thm)],[630]) ).
thf(669,plain,
( ( sk2 != sk1 )
| ( ( sk2 @ sk3 )
= ( sk1 @ sk3 ) ) ),
inference(simp,[status(thm)],[646]) ).
thf(11,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ times ) @ times ) )
= ( A @ ( C @ times ) @ ( B @ times ) ) ),
inference(cnf,[status(esa)],[10]) ).
thf(12,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ times ) @ times ) )
= ( A @ ( C @ times ) @ ( B @ times ) ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(16,plain,
! [A: $i] :
( ( ( A @ sk3 @ ( A @ times ) )
= A )
| ~ ( A @ element ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(19,plain,
! [A: $i] :
( ~ ( A @ element )
| ( ( A @ sk3 @ ( A @ times ) )
= A ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(33,plain,
! [A: $i] :
( ( ( sk1 @ element )
!= ( A @ element ) )
| ~ $true
| ( ( A @ sk3 @ ( A @ times ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[7,19]) ).
thf(34,plain,
! [A: $i] :
( ( ( sk1 @ element )
!= ( A @ element ) )
| ( ( A @ sk3 @ ( A @ times ) )
= A ) ),
inference(simp,[status(thm)],[33]) ).
thf(35,plain,
( ( sk1 @ sk3 @ ( sk1 @ times ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[34:[bind(A,$thf( sk1 ))]]) ).
thf(9,plain,
~ ( sk2 @ ( sk1 @ times ) @ element ),
inference(cnfConj,[status(thm)],[6]) ).
thf(632,plain,
( ( ( sk2 @ ( sk2 @ times ) )
!= ( sk2 @ ( sk1 @ times ) ) )
| ~ ( sk2 @ sk3 @ element ) ),
inference(paramod_ordered,[status(thm)],[484,9]) ).
thf(653,plain,
( ( sk2 != sk2 )
| ( sk2 != sk1 )
| ~ ( sk2 @ sk3 @ element ) ),
inference(simp,[status(thm)],[632]) ).
thf(675,plain,
( ( sk2 != sk1 )
| ~ ( sk2 @ sk3 @ element ) ),
inference(simp,[status(thm)],[653]) ).
thf(90,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ sk3 @ ( sk1 @ times ) )
!= ( B @ ( A @ times ) ) )
| ( ( C @ ( sk1 @ times ) )
= ( A @ ( C @ times ) @ ( B @ times ) ) ) ),
inference(paramod_ordered,[status(thm)],[35,12]) ).
thf(91,plain,
! [A: $i] :
( ( sk1 @ ( A @ times ) @ ( sk1 @ sk3 @ times ) )
= ( A @ ( sk1 @ times ) ) ),
inference(pattern_uni,[status(thm)],[90:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 @ sk3 )),bind(C,$thf( C ))]]) ).
thf(140,plain,
! [A: $i] :
( ( sk1 @ ( A @ times ) @ ( sk1 @ sk3 @ times ) )
= ( A @ ( sk1 @ times ) ) ),
inference(simp,[status(thm)],[91]) ).
thf(546,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ times ) )
!= ( sk1 @ ( A @ times ) ) )
| ( ( sk1 @ sk3 @ ( sk1 @ sk3 @ times ) )
= ( A @ ( sk1 @ times ) ) ) ),
inference(paramod_ordered,[status(thm)],[467,140]) ).
thf(547,plain,
( ( sk1 @ sk3 @ ( sk1 @ sk3 @ times ) )
= ( sk1 @ ( sk1 @ times ) ) ),
inference(pattern_uni,[status(thm)],[546:[bind(A,$thf( sk1 ))]]) ).
thf(688,plain,
( ( sk1 @ sk3 @ ( sk1 @ sk3 @ times ) )
= ( sk1 @ sk3 ) ),
inference(rewrite,[status(thm)],[547,467]) ).
thf(555,plain,
( ( ( sk2 @ ( sk1 @ times ) )
!= ( sk1 @ ( sk1 @ times ) ) )
| ~ ( sk1 @ sk3 @ element ) ),
inference(paramod_ordered,[status(thm)],[467,9]) ).
thf(564,plain,
( ( sk2 != sk1 )
| ( sk1 != sk1 )
| ~ ( sk1 @ sk3 @ element ) ),
inference(simp,[status(thm)],[555]) ).
thf(596,plain,
( ( sk2 != sk1 )
| ~ ( sk1 @ sk3 @ element ) ),
inference(simp,[status(thm)],[564]) ).
thf(36,plain,
! [A: $i] :
( ( ( sk2 @ element )
!= ( A @ element ) )
| ~ $true
| ( ( A @ sk3 @ ( A @ times ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[8,19]) ).
thf(37,plain,
! [A: $i] :
( ( ( sk2 @ element )
!= ( A @ element ) )
| ( ( A @ sk3 @ ( A @ times ) )
= A ) ),
inference(simp,[status(thm)],[36]) ).
thf(38,plain,
( ( sk2 @ sk3 @ ( sk2 @ times ) )
= sk2 ),
inference(pattern_uni,[status(thm)],[37:[bind(A,$thf( sk2 ))]]) ).
thf(113,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ sk3 @ ( sk2 @ times ) )
!= ( A @ ( C @ times ) ) )
| ( ( C @ ( B @ ( A @ times ) @ times ) )
= ( sk2 @ ( B @ times ) ) ) ),
inference(paramod_ordered,[status(thm)],[38,12]) ).
thf(114,plain,
! [A: $i] :
( ( sk2 @ ( A @ ( sk2 @ sk3 @ times ) @ times ) )
= ( sk2 @ ( A @ times ) ) ),
inference(pattern_uni,[status(thm)],[113:[bind(A,$thf( sk2 @ sk3 )),bind(B,$thf( B )),bind(C,$thf( sk2 ))]]) ).
thf(147,plain,
! [A: $i] :
( ( sk2 @ ( A @ ( sk2 @ sk3 @ times ) @ times ) )
= ( sk2 @ ( A @ times ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(538,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ times ) )
!= ( B @ ( A @ times ) ) )
| ( ( C @ ( sk1 @ sk3 @ times ) )
= ( A @ ( C @ times ) @ ( B @ times ) ) ) ),
inference(paramod_ordered,[status(thm)],[467,12]) ).
thf(539,plain,
! [A: $i] :
( ( A @ ( sk1 @ sk3 @ times ) )
= ( sk1 @ ( A @ times ) @ ( sk1 @ times ) ) ),
inference(pattern_uni,[status(thm)],[538:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(594,plain,
! [A: $i] :
( ( A @ ( sk1 @ sk3 @ times ) )
= ( sk1 @ ( A @ times ) @ ( sk1 @ times ) ) ),
inference(simp,[status(thm)],[539]) ).
thf(1041,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ times ) )
!= ( sk1 @ ( A @ times ) ) )
| ( ( A @ ( sk1 @ sk3 @ times ) )
= ( sk1 @ sk3 @ ( sk1 @ times ) ) ) ),
inference(paramod_ordered,[status(thm)],[467,594]) ).
thf(1042,plain,
( ( sk1 @ ( sk1 @ sk3 @ times ) )
= ( sk1 @ sk3 @ ( sk1 @ times ) ) ),
inference(pattern_uni,[status(thm)],[1041:[bind(A,$thf( sk1 ))]]) ).
thf(1377,plain,
( ( sk1 @ ( sk1 @ sk3 @ times ) )
= sk1 ),
inference(rewrite,[status(thm)],[1042,35]) ).
thf(108,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ times ) @ times ) )
!= ( sk2 @ sk3 @ ( sk2 @ times ) ) )
| ( ( A @ ( C @ times ) @ ( B @ times ) )
= sk2 ) ),
inference(paramod_ordered,[status(thm)],[12,38]) ).
thf(129,plain,
! [C: $i,B: $i,A: $i] :
( ( C
!= ( sk2 @ sk3 ) )
| ( ( B @ ( A @ times ) )
!= sk2 )
| ( ( A @ ( C @ times ) @ ( B @ times ) )
= sk2 ) ),
inference(simp,[status(thm)],[108]) ).
thf(133,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ times ) )
!= sk2 )
| ( ( A @ ( sk2 @ sk3 @ times ) @ ( B @ times ) )
= sk2 ) ),
inference(simp,[status(thm)],[129]) ).
thf(110,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ sk3 @ ( sk2 @ times ) )
!= ( B @ ( A @ times ) ) )
| ( ( C @ ( sk2 @ times ) )
= ( A @ ( C @ times ) @ ( B @ times ) ) ) ),
inference(paramod_ordered,[status(thm)],[38,12]) ).
thf(111,plain,
! [A: $i] :
( ( sk2 @ ( A @ times ) @ ( sk2 @ sk3 @ times ) )
= ( A @ ( sk2 @ times ) ) ),
inference(pattern_uni,[status(thm)],[110:[bind(A,$thf( sk2 )),bind(B,$thf( sk2 @ sk3 )),bind(C,$thf( C ))]]) ).
thf(146,plain,
! [A: $i] :
( ( sk2 @ ( A @ times ) @ ( sk2 @ sk3 @ times ) )
= ( A @ ( sk2 @ times ) ) ),
inference(simp,[status(thm)],[111]) ).
thf(636,plain,
! [A: $i] :
( ( ( sk2 @ ( sk2 @ times ) )
!= ( sk2 @ ( A @ times ) ) )
| ( ( sk2 @ sk3 @ ( sk2 @ sk3 @ times ) )
= ( A @ ( sk2 @ times ) ) ) ),
inference(paramod_ordered,[status(thm)],[484,146]) ).
thf(637,plain,
( ( sk2 @ sk3 @ ( sk2 @ sk3 @ times ) )
= ( sk2 @ ( sk2 @ times ) ) ),
inference(pattern_uni,[status(thm)],[636:[bind(A,$thf( sk2 ))]]) ).
thf(774,plain,
( ( sk2 @ sk3 @ ( sk2 @ sk3 @ times ) )
= ( sk2 @ sk3 ) ),
inference(rewrite,[status(thm)],[637,484]) ).
thf(25,plain,
( ( ( sk2 @ ( sk1 @ times ) @ element )
!= ( sk2 @ element ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8,9]) ).
thf(26,plain,
( ( sk2 @ ( sk1 @ times ) @ element )
!= ( sk2 @ element ) ),
inference(simp,[status(thm)],[25]) ).
thf(28,plain,
( ( sk2 @ ( sk1 @ times ) )
!= sk2 ),
inference(simp,[status(thm)],[26]) ).
thf(799,plain,
( ( ( sk2 @ sk3 @ ( sk2 @ sk3 @ times ) )
!= ( sk2 @ ( sk1 @ times ) ) )
| ( ( sk2 @ sk3 )
!= sk2 ) ),
inference(paramod_ordered,[status(thm)],[774,28]) ).
thf(840,plain,
( ( ( sk2 @ sk3 )
!= sk2 )
| ( ( sk2 @ sk3 )
!= sk1 )
| ( ( sk2 @ sk3 )
!= sk2 ) ),
inference(simp,[status(thm)],[799]) ).
thf(849,plain,
( ( ( sk2 @ sk3 )
!= sk1 )
| ( ( sk2 @ sk3 )
!= sk2 ) ),
inference(simp,[status(thm)],[840]) ).
thf(98,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ times ) @ ( B @ times ) )
!= ( D @ sk3 @ ( D @ times ) ) )
| ~ ( D @ element )
| ( ( C @ ( B @ ( A @ times ) @ times ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[12,19]) ).
thf(128,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ times ) )
!= ( D @ sk3 ) )
| ( B != D )
| ~ ( D @ element )
| ( ( C @ ( B @ ( A @ times ) @ times ) )
= D ) ),
inference(simp,[status(thm)],[98]) ).
thf(132,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ times ) )
!= ( C @ sk3 ) )
| ~ ( C @ element )
| ( ( B @ ( C @ ( A @ times ) @ times ) )
= C ) ),
inference(simp,[status(thm)],[128]) ).
thf(68,plain,
( ( ( sk2 @ sk3 @ ( sk2 @ times ) )
!= ( sk2 @ ( sk1 @ times ) ) )
| ( sk2 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[38,28]) ).
thf(69,plain,
( ( sk2 @ sk3 @ ( sk2 @ times ) )
!= ( sk2 @ ( sk1 @ times ) ) ),
inference(simp,[status(thm)],[68]) ).
thf(70,plain,
( ( ( sk2 @ sk3 )
!= sk2 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[69]) ).
thf(1011,plain,
! [A: $i] :
( ( ( A @ ( sk1 @ sk3 @ times ) )
!= ( sk1 @ sk3 @ ( sk1 @ sk3 @ times ) ) )
| ( ( sk1 @ ( A @ times ) @ ( sk1 @ times ) )
= ( sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[594,688]) ).
thf(1012,plain,
( ( sk1 @ ( sk1 @ sk3 @ times ) @ ( sk1 @ times ) )
= ( sk1 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[1011:[bind(A,$thf( sk1 @ sk3 ))]]) ).
thf(1279,plain,
! [A: $i] :
( ( ( A @ ( sk1 @ sk3 @ times ) )
!= ( sk1 @ ( sk1 @ sk3 @ times ) ) )
| ( ( sk1 @ ( A @ times ) @ ( sk1 @ times ) @ ( sk1 @ times ) )
= ( sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[594,1012]) ).
thf(1280,plain,
( ( sk1 @ ( sk1 @ times ) @ ( sk1 @ times ) @ ( sk1 @ times ) )
= ( sk1 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[1279:[bind(A,$thf( sk1 ))]]) ).
thf(1555,plain,
( ( sk1 @ sk3 @ ( sk1 @ times ) @ ( sk1 @ times ) )
= ( sk1 @ sk3 ) ),
inference(rewrite,[status(thm)],[1280,467]) ).
thf(93,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ sk3 @ ( sk1 @ times ) )
!= ( A @ ( C @ times ) ) )
| ( ( C @ ( B @ ( A @ times ) @ times ) )
= ( sk1 @ ( B @ times ) ) ) ),
inference(paramod_ordered,[status(thm)],[35,12]) ).
thf(94,plain,
! [A: $i] :
( ( sk1 @ ( A @ ( sk1 @ sk3 @ times ) @ times ) )
= ( sk1 @ ( A @ times ) ) ),
inference(pattern_uni,[status(thm)],[93:[bind(A,$thf( sk1 @ sk3 )),bind(B,$thf( B )),bind(C,$thf( sk1 ))]]) ).
thf(141,plain,
! [A: $i] :
( ( sk1 @ ( A @ ( sk1 @ sk3 @ times ) @ times ) )
= ( sk1 @ ( A @ times ) ) ),
inference(simp,[status(thm)],[94]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( A @ element )
| ( ( A @ ( A @ times ) )
!= B )
| ( ( B @ ( A @ times ) )
!= A ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( A @ element )
| ( ( A @ ( A @ times ) )
!= B )
| ( ( B @ ( A @ times ) )
!= A ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(22,plain,
! [A: $i] :
( ( A @ element )
| ( ( A @ ( A @ times ) @ ( A @ times ) )
!= A ) ),
inference(simp,[status(thm)],[21]) ).
thf(23,plain,
( ( ( sk2 @ ( sk1 @ times ) @ element )
!= ( sk1 @ element ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7,9]) ).
thf(24,plain,
( ( sk2 @ ( sk1 @ times ) @ element )
!= ( sk1 @ element ) ),
inference(simp,[status(thm)],[23]) ).
thf(27,plain,
( ( sk2 @ ( sk1 @ times ) )
!= sk1 ),
inference(simp,[status(thm)],[24]) ).
thf(1070,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk1 @ sk3 @ times ) )
!= ( sk1 @ ( B @ times ) ) )
| ( ( sk1 @ ( A @ times ) @ ( sk1 @ times ) @ ( sk1 @ sk3 @ times ) )
= ( B @ ( sk1 @ times ) ) ) ),
inference(paramod_ordered,[status(thm)],[594,140]) ).
thf(1071,plain,
( ( sk1 @ ( sk1 @ times ) @ ( sk1 @ times ) @ ( sk1 @ sk3 @ times ) )
= ( sk1 @ sk3 @ ( sk1 @ times ) ) ),
inference(pattern_uni,[status(thm)],[1070:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 @ sk3 ))]]) ).
thf(1721,plain,
( ( sk1 @ sk3 @ ( sk1 @ times ) @ ( sk1 @ sk3 @ times ) )
= sk1 ),
inference(rewrite,[status(thm)],[1071,35,467]) ).
thf(1783,plain,
! [A: $i] :
( ( ( sk1 @ sk3 @ ( sk1 @ times ) @ ( sk1 @ sk3 @ times ) )
!= ( A @ ( sk1 @ sk3 @ times ) ) )
| ( ( sk1 @ ( A @ times ) @ ( sk1 @ times ) )
= sk1 ) ),
inference(paramod_ordered,[status(thm)],[1721,594]) ).
thf(1784,plain,
( ( sk1 @ ( sk1 @ sk3 @ ( sk1 @ times ) @ times ) @ ( sk1 @ times ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[1783:[bind(A,$thf( sk1 @ sk3 @ ( sk1 @ times ) ))]]) ).
thf(2180,plain,
( ( sk1 @ ( sk1 @ times ) @ ( sk1 @ times ) )
= sk1 ),
inference(rewrite,[status(thm)],[1784,35]) ).
thf(537,plain,
( ( ( sk2 @ ( sk1 @ times ) )
!= ( sk1 @ ( sk1 @ times ) ) )
| ( ( sk1 @ sk3 )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[467,27]) ).
thf(576,plain,
( ( sk2 != sk1 )
| ( sk1 != sk1 )
| ( ( sk1 @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[537]) ).
thf(588,plain,
( ( sk2 != sk1 )
| ( ( sk1 @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[576]) ).
thf(48,plain,
( ( ( sk1 @ sk3 @ ( sk1 @ times ) )
!= ( sk2 @ ( sk1 @ times ) ) )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[35,27]) ).
thf(49,plain,
( ( sk1 @ sk3 @ ( sk1 @ times ) )
!= ( sk2 @ ( sk1 @ times ) ) ),
inference(simp,[status(thm)],[48]) ).
thf(55,plain,
( ( ( sk1 @ sk3 )
!= sk2 )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[49]) ).
thf(58,plain,
( ( sk1 @ sk3 )
!= sk2 ),
inference(simp,[status(thm)],[55]) ).
thf(613,plain,
( ( ( sk2 @ ( sk2 @ times ) )
!= ( sk2 @ ( sk1 @ times ) ) )
| ( ( sk2 @ sk3 )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[484,27]) ).
thf(666,plain,
( ( sk2 != sk2 )
| ( sk2 != sk1 )
| ( ( sk2 @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[613]) ).
thf(684,plain,
( ( sk2 != sk1 )
| ( ( sk2 @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[666]) ).
thf(3225,plain,
$false,
inference(e,[status(thm)],[5,10,20,669,13,12,7,35,675,688,596,147,1377,133,849,132,774,70,28,38,467,484,1555,9,141,22,27,2180,594,140,588,1721,8,58,684,146,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG210+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.08 % 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
% 0.15/0.40 % Computer : n002.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sat Sep 26 21:28:38 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 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
% 0.83/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.18/1.16 % [INFO] Parsing done (175ms).
% 1.18/1.18 % [INFO] Running in sequential loop mode.
% 1.68/1.58 % [INFO] eprover registered as external prover.
% 1.68/1.59 % [INFO] Scanning for conjecture ...
% 1.87/1.68 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.01/1.71 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.01/1.72 % [INFO] Problem is first-order (TPTP FOF).
% 2.01/1.73 % [INFO] Type checking passed.
% 2.01/1.73 % [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 ...
% 14.36/4.66 % External prover 'e' found a proof!
% 14.36/4.66 % [INFO] Killing All external provers ...
% 14.36/4.66 % Time passed: 4115ms (effective reasoning time: 3478ms)
% 14.36/4.66 % 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)>
% 14.36/4.67 % Axioms used in derivation (2): axiom_1, axiom_2
% 14.36/4.67 % No. of inferences in proof: 107
% 14.36/4.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4115 ms resp. 3478 ms w/o parsing
% 12.41/4.74 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.41/4.74 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------