%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG272^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n010.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 : Wed Sep 30 07:45:07 AM UTC 2026
% Result : Theorem 30.13s 6.92s
% Output : Refutation 30.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 25
% Syntax : Number of formulae : 112 ( 37 unt; 0 typ; 24 def)
% Number of atoms : 508 ( 488 equ; 0 cnn)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 1594 ( 180 ~; 154 |; 123 &;1137 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 14 con; 0-6 aty)
% Number of variables : 369 ( 59 ^; 231 !; 62 ?; 369 :)
% ( 0 !>; 0 ?*; 0 @-; 17 @+)
% Comments :
%------------------------------------------------------------------------------
thf(g_type,type,
g: $tType ).
thf(cGROUP1_decl,type,
cGROUP1: ( g > g > g ) > g > $o ).
thf(cGROUP2_decl,type,
cGROUP2: ( g > g > g ) > g > $o ).
thf(cGRP_ASSOC_decl,type,
cGRP_ASSOC: ( g > g > g ) > $o ).
thf(cGRP_INVERSE_decl,type,
cGRP_INVERSE: ( g > g > g ) > g > $o ).
thf(cGRP_LEFT_INVERSE_decl,type,
cGRP_LEFT_INVERSE: ( g > g > g ) > g > $o ).
thf(cGRP_LEFT_UNIT_decl,type,
cGRP_LEFT_UNIT: ( g > g > g ) > g > $o ).
thf(cGRP_UNIT_decl,type,
cGRP_UNIT: ( g > g > g ) > g > $o ).
thf(sk1_decl,type,
sk1: g > g > g ).
thf(sk2_decl,type,
sk2: g ).
thf(sk3_decl,type,
sk3: g ).
thf(sk4_decl,type,
sk4: g ).
thf(sk5_decl,type,
sk5: g ).
thf(sk6_decl,type,
sk6: g ).
thf(sk7_decl,type,
sk7: g ).
thf(sk8_decl,type,
sk8: g > g ).
thf(sk9_decl,type,
sk9: g > g ).
thf(sk10_decl,type,
sk10: g > g ).
thf(sk11_decl,type,
sk11: g > g ).
thf(sk12_decl,type,
sk12: g > g ).
thf(sk13_decl,type,
sk13: g > g ).
thf(sk14_decl,type,
sk14: g > g > g > g > g > g > g ).
thf(sk35_decl,type,
sk35: g ).
thf(sk61_decl,type,
sk61: g ).
thf(sk62_decl,type,
sk62: g ).
thf(sk63_decl,type,
sk63: g ).
thf(sk71_decl,type,
sk71: g ).
thf(sk72_decl,type,
sk72: g ).
thf(cGROUP1_def,definition,
( cGROUP1
= ( ^ [A: g > g > g,B: g] :
( ( cGRP_ASSOC @ A )
& ( cGRP_UNIT @ A @ B )
& ( cGRP_INVERSE @ A @ B ) ) ) ) ).
thf(cGROUP2_def,definition,
( cGROUP2
= ( ^ [A: g > g > g,B: g] :
( ( cGRP_ASSOC @ A )
& ( cGRP_LEFT_UNIT @ A @ B )
& ( cGRP_LEFT_INVERSE @ A @ B ) ) ) ) ).
thf(cGRP_ASSOC_def,definition,
( cGRP_ASSOC
= ( ^ [A: g > g > g] :
! [B: g,C: g,D: g] :
( ( A @ ( A @ B @ C ) @ D )
= ( A @ B @ ( A @ C @ D ) ) ) ) ) ).
thf(cGRP_INVERSE_def,definition,
( cGRP_INVERSE
= ( ^ [A: g > g > g,B: g] :
! [C: g] :
? [D: g] :
( ( ( A @ C @ D )
= B )
& ( ( A @ D @ C )
= B ) ) ) ) ).
thf(cGRP_LEFT_INVERSE_def,definition,
( cGRP_LEFT_INVERSE
= ( ^ [A: g > g > g,B: g] :
! [C: g] :
? [D: g] :
( ( A @ D @ C )
= B ) ) ) ).
thf(cGRP_LEFT_UNIT_def,definition,
( cGRP_LEFT_UNIT
= ( ^ [A: g > g > g,B: g] :
! [C: g] :
( ( A @ B @ C )
= C ) ) ) ).
thf(cGRP_UNIT_def,definition,
( cGRP_UNIT
= ( ^ [A: g > g > g,B: g] :
! [C: g] :
( ( ( A @ B @ C )
= C )
& ( ( A @ C @ B )
= C ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: g > g > g] :
~ ! [B: g] :
( ( ! [C: g,D: g,E: g] :
( ( A @ ( A @ C @ D ) @ E )
= ( A @ C @ ( A @ D @ E ) ) )
& ! [C: g] :
( ( ( A @ B @ C )
= C )
& ( ( A @ C @ B )
= C ) )
& ! [C: g] :
? [D: g] :
( ( ( A @ C @ D )
= B )
& ( ( A @ D @ C )
= B ) ) )
= ( ! [C: g,D: g,E: g] :
( ( A @ ( A @ C @ D ) @ E )
= ( A @ C @ ( A @ D @ E ) ) )
& ! [C: g] :
( ( A @ B @ C )
= C )
& ! [C: g] :
? [D: g] :
( ( A @ D @ C )
= B ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: g] :
( ( ! [B: g,C: g,D: g] :
( ( sk1 @ ( sk1 @ B @ C ) @ D )
= ( sk1 @ B @ ( sk1 @ C @ D ) ) )
& ! [B: g] :
( ( ( sk1 @ A @ B )
= B )
& ( ( sk1 @ B @ A )
= B ) )
& ! [B: g] :
? [C: g] :
( ( ( sk1 @ B @ C )
= A )
& ( ( sk1 @ C @ B )
= A ) ) )
!= ( ! [B: g,C: g,D: g] :
( ( sk1 @ ( sk1 @ B @ C ) @ D )
= ( sk1 @ B @ ( sk1 @ C @ D ) ) )
& ! [B: g] :
( ( sk1 @ A @ B )
= B )
& ! [B: g] :
? [C: g] :
( ( sk1 @ C @ B )
= A ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: g] :
~ ! [B: g,C: g] :
( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: g] :
~ ! [B: g] :
( ( sk1 @ ( sk1 @ sk3 @ A ) @ B )
= ( sk1 @ sk3 @ ( sk1 @ A @ B ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: g] :
( ( sk1 @ ( sk1 @ sk3 @ sk4 ) @ A )
!= ( sk1 @ sk3 @ ( sk1 @ sk4 @ A ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: g] :
~ ( ( ( sk1 @ sk2 @ A )
= A )
& ( ( sk1 @ A @ sk2 )
= A ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: g] :
~ ? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: g] :
@+[B: g] :
~ ! [C: g,D: g] :
( ( sk1 @ ( sk1 @ B @ C ) @ D )
= ( sk1 @ B @ ( sk1 @ C @ D ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: g] :
@+[B: g] :
~ ! [C: g] :
( ( sk1 @ ( sk1 @ ( sk8 @ A ) @ B ) @ C )
= ( sk1 @ ( sk8 @ A ) @ ( sk1 @ B @ C ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: g] :
@+[B: g] :
( ( sk1 @ ( sk1 @ ( sk8 @ A ) @ ( sk9 @ A ) ) @ B )
!= ( sk1 @ ( sk8 @ A ) @ ( sk1 @ ( sk9 @ A ) @ B ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: g] :
@+[B: g] :
( ( sk1 @ sk2 @ B )
!= B ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: g] :
@+[B: g] :
~ ? [C: g] :
( ( sk1 @ C @ B )
= sk2 ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: g] :
@+[B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: g,B: g,C: g,D: g,E: g,F: g] :
@+[G: g] :
( ( sk1 @ G @ A )
= sk2 ) ) ) ).
thf(sk35_def,definition,
( sk35
= ( @+[A: g] :
( ( sk1 @ A @ sk2 )
!= A ) ) ) ).
thf(sk71_def,definition,
( sk71
= ( @+[A: g] :
( ( ( sk1 @ sk61 @ A )
= sk2 )
& ( ( sk1 @ A @ sk61 )
= sk2 ) ) ) ) ).
thf(sk72_def,definition,
( sk72
= ( @+[A: g] :
( ( sk1 @ A @ sk61 )
= sk2 ) ) ) ).
thf(1,conjecture,
! [A: g > g > g,B: g] :
( ( cGROUP1 @ A @ B )
= ( cGROUP2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEQUIV_01_02) ).
thf(2,negated_conjecture,
~ ! [A: g > g > g,B: g] :
( ( cGROUP1 @ A @ B )
= ( cGROUP2 @ A @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: g > g > g,B: g] :
( ( ! [C: g,D: g,E: g] :
( ( A @ ( A @ C @ D ) @ E )
= ( A @ C @ ( A @ D @ E ) ) )
& ! [C: g] :
( ( ( A @ B @ C )
= C )
& ( ( A @ C @ B )
= C ) )
& ! [C: g] :
? [D: g] :
( ( ( A @ C @ D )
= B )
& ( ( A @ D @ C )
= B ) ) )
= ( ! [C: g,D: g,E: g] :
( ( A @ ( A @ C @ D ) @ E )
= ( A @ C @ ( A @ D @ E ) ) )
& ! [C: g] :
( ( A @ B @ C )
= C )
& ! [C: g] :
? [D: g] :
( ( A @ D @ C )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [A: g,B: g,C: g] :
( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) )
& ! [A: g] :
( ( ( sk1 @ sk2 @ A )
= A )
& ( ( sk1 @ A @ sk2 )
= A ) )
& ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ! [A: g,B: g,C: g] :
( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) )
& ! [A: g] :
( ( sk1 @ sk2 @ A )
= A )
& ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [A: g,B: g,C: g] :
( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) )
& ! [A: g] :
( ( ( sk1 @ sk2 @ A )
= A )
& ( ( sk1 @ A @ sk2 )
= A ) )
& ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ! [A: g,B: g,C: g] :
( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) )
& ! [A: g] :
( ( sk1 @ sk2 @ A )
= A )
& ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(8,plain,
( ( ! [A: g,B: g,C: g] :
( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) )
& ! [A: g] :
( ( ( sk1 @ sk2 @ A )
= A )
& ( ( sk1 @ A @ sk2 )
= A ) )
& ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
| ( ! [A: g,B: g,C: g] :
( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) )
& ! [A: g] :
( ( sk1 @ sk2 @ A )
= A )
& ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(12,plain,
! [J: g,I: g,H: g,G: g,F: g,E: g,D: g,C: g,B: g,A: g] :
( ( ( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) )
| ( ( sk1 @ ( sk1 @ F @ G ) @ H )
= ( sk1 @ F @ ( sk1 @ G @ H ) ) ) )
& ( ( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) )
| ( ( sk1 @ sk2 @ I )
= I ) )
& ( ( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) )
| ( ( sk1 @ ( sk14 @ J @ E @ D @ C @ B @ A ) @ J )
= sk2 ) )
& ( ( ( sk1 @ sk2 @ D )
= D )
| ( ( sk1 @ ( sk1 @ F @ G ) @ H )
= ( sk1 @ F @ ( sk1 @ G @ H ) ) ) )
& ( ( ( sk1 @ sk2 @ D )
= D )
| ( ( sk1 @ sk2 @ I )
= I ) )
& ( ( ( sk1 @ sk2 @ D )
= D )
| ( ( sk1 @ ( sk14 @ J @ E @ D @ C @ B @ A ) @ J )
= sk2 ) )
& ( ( ( sk1 @ D @ sk2 )
= D )
| ( ( sk1 @ ( sk1 @ F @ G ) @ H )
= ( sk1 @ F @ ( sk1 @ G @ H ) ) ) )
& ( ( ( sk1 @ D @ sk2 )
= D )
| ( ( sk1 @ sk2 @ I )
= I ) )
& ( ( ( sk1 @ D @ sk2 )
= D )
| ( ( sk1 @ ( sk14 @ J @ E @ D @ C @ B @ A ) @ J )
= sk2 ) )
& ( ( ( sk1 @ E @ ( sk13 @ E ) )
= sk2 )
| ( ( sk1 @ ( sk1 @ F @ G ) @ H )
= ( sk1 @ F @ ( sk1 @ G @ H ) ) ) )
& ( ( ( sk1 @ E @ ( sk13 @ E ) )
= sk2 )
| ( ( sk1 @ sk2 @ I )
= I ) )
& ( ( ( sk1 @ E @ ( sk13 @ E ) )
= sk2 )
| ( ( sk1 @ ( sk14 @ J @ E @ D @ C @ B @ A ) @ J )
= sk2 ) )
& ( ( ( sk1 @ ( sk13 @ E ) @ E )
= sk2 )
| ( ( sk1 @ ( sk1 @ F @ G ) @ H )
= ( sk1 @ F @ ( sk1 @ G @ H ) ) ) )
& ( ( ( sk1 @ ( sk13 @ E ) @ E )
= sk2 )
| ( ( sk1 @ sk2 @ I )
= I ) )
& ( ( ( sk1 @ ( sk13 @ E ) @ E )
= sk2 )
| ( ( sk1 @ ( sk14 @ J @ E @ D @ C @ B @ A ) @ J )
= sk2 ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(17,plain,
! [B: g,A: g] :
( ( ( sk1 @ sk2 @ A )
= A )
| ( ( sk1 @ sk2 @ B )
= B ) ),
inference(cnfConj,[status(thm)],[12]) ).
thf(36,plain,
! [B: g,A: g] :
( ( ( sk1 @ sk2 @ A )
= A )
| ( ( sk1 @ sk2 @ B )
= B ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(37,plain,
! [B: g,A: g] :
( ( ( sk1 @ sk2 @ A )
= A )
| ( ( sk1 @ sk2 @ B )
= B ) ),
inference(simp,[status(thm)],[36]) ).
thf(179,plain,
! [B: g,A: g] :
( ( ( sk1 @ sk2 @ A )
= A )
| ( ( sk1 @ sk2 @ B )
!= ( sk1 @ sk2 @ A ) )
| ( B != A ) ),
inference(eqfactor_ordered,[status(thm)],[37]) ).
thf(181,plain,
! [A: g] :
( ( sk1 @ sk2 @ A )
= A ),
inference(pattern_uni,[status(thm)],[179:[bind(A,$thf( B ))]]) ).
thf(183,plain,
! [A: g] :
( ( sk1 @ sk2 @ A )
= A ),
inference(simp,[status(thm)],[181]) ).
thf(6,plain,
( ( ( ! [A: g,B: g,C: g] :
( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) ) )
!= ( ! [A: g,B: g,C: g] :
( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) ) ) )
| ( ( ! [A: g] :
( ( ( sk1 @ sk2 @ A )
= A )
& ( ( sk1 @ A @ sk2 )
= A ) )
& ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ! [A: g] :
( ( sk1 @ sk2 @ A )
= A )
& ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ) ),
inference(simp,[status(thm)],[5]) ).
thf(9,plain,
( ( ! [A: g] :
( ( ( sk1 @ sk2 @ A )
= A )
& ( ( sk1 @ A @ sk2 )
= A ) )
& ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ! [A: g] :
( ( sk1 @ sk2 @ A )
= A )
& ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ),
inference(simp,[status(thm)],[6]) ).
thf(58,plain,
( ( ( ! [A: g] :
( ( ( sk1 @ sk2 @ A )
= A )
& ( ( sk1 @ A @ sk2 )
= A ) ) )
!= ( ! [A: g] :
( ( sk1 @ sk2 @ A )
= A ) ) )
| ( ( ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ) ),
inference(simp,[status(thm)],[9]) ).
thf(193,plain,
( ( ( ! [A: g] :
( ( A = A )
& ( ( sk1 @ A @ sk2 )
= A ) ) )
!= ( ! [A: g] : ( A = A ) ) )
| ( ( ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ) ),
inference(rewrite,[status(thm)],[58,183]) ).
thf(194,plain,
( ~ ! [A: g] :
( ( sk1 @ A @ sk2 )
= A )
| ( ( ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ) ),
inference(simp,[status(thm)],[193]) ).
thf(199,plain,
( ( ( sk1 @ sk35 @ sk2 )
!= sk35 )
| ( ( ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ) ),
inference(cnf,[status(esa)],[194]) ).
thf(200,plain,
( ( ( sk1 @ sk35 @ sk2 )
!= sk35 )
| ( ( ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ) ),
inference(lifteq,[status(thm)],[199]) ).
thf(386,plain,
! [A: g] :
( ( A != sk35 )
| ( ( ! [B: g] :
? [C: g] :
( ( ( sk1 @ B @ C )
= sk2 )
& ( ( sk1 @ C @ B )
= sk2 ) ) )
!= ( ! [B: g] :
? [C: g] :
( ( sk1 @ C @ B )
= sk2 ) ) )
| ( ( sk1 @ sk2 @ A )
!= ( sk1 @ sk35 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[183,200]) ).
thf(390,plain,
( ( ( ^ [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ^ [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) )
| ( sk35 != sk2 )
| ( sk35 != sk2 ) ),
inference(simp,[status(thm)],[386]) ).
thf(399,plain,
( ( ( ^ [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ^ [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) )
| ( sk35 != sk2 ) ),
inference(simp,[status(thm)],[390]) ).
thf(401,plain,
( ( ( ? [A: g] :
( ( ( sk1 @ sk61 @ A )
= sk2 )
& ( ( sk1 @ A @ sk61 )
= sk2 ) ) )
!= ( ? [A: g] :
( ( sk1 @ A @ sk61 )
= sk2 ) ) )
| ( sk35 != sk2 ) ),
inference(func_ext,[status(esa)],[399]) ).
thf(523,plain,
( ( ( ^ [A: g] :
( ( ( sk1 @ sk61 @ A )
= sk2 )
& ( ( sk1 @ A @ sk61 )
= sk2 ) ) )
!= ( ^ [A: g] :
( ( sk1 @ A @ sk61 )
= sk2 ) ) )
| ( sk35 != sk2 ) ),
inference(simp,[status(thm)],[401]) ).
thf(400,plain,
( ( ( ^ [A: g,B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ^ [A: g,B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) )
| ( sk35 != sk2 ) ),
inference(simp,[status(thm)],[399]) ).
thf(404,plain,
( ( ( ( ( sk1 @ sk62 @ sk63 )
= sk2 )
& ( ( sk1 @ sk63 @ sk62 )
= sk2 ) )
!= ( ( sk1 @ sk63 @ sk62 )
= sk2 ) )
| ( sk35 != sk2 ) ),
inference(func_ext,[status(esa)],[400]) ).
thf(107,plain,
( ( ( ^ [A: g] :
( ( ( sk1 @ sk2 @ A )
= A )
& ( ( sk1 @ A @ sk2 )
= A ) ) )
!= ( ^ [A: g] :
( ( sk1 @ sk2 @ A )
= A ) ) )
| ( ( ^ [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ^ [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ) ),
inference(simp,[status(thm)],[58]) ).
thf(195,plain,
( ( ( ^ [A: g] :
( ( A = A )
& ( ( sk1 @ A @ sk2 )
= A ) ) )
!= ( ^ [A: g] : ( A = A ) ) )
| ( ( ^ [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ^ [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ) ),
inference(rewrite,[status(thm)],[107,183]) ).
thf(196,plain,
( ( ( ^ [A: g] :
( ( sk1 @ A @ sk2 )
= A ) )
!= ( ^ [A: g] : $true ) )
| ( ( ^ [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ^ [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ) ),
inference(simp,[status(thm)],[195]) ).
thf(14,plain,
! [F: g,E: g,D: g,C: g,B: g,A: g] :
( ( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) )
| ( ( sk1 @ ( sk14 @ F @ E @ D @ C @ B @ A ) @ F )
= sk2 ) ),
inference(cnfConj,[status(thm)],[12]) ).
thf(28,plain,
! [F: g,E: g,D: g,C: g,B: g,A: g] :
( ( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) )
| ( ( sk1 @ ( sk14 @ F @ E @ D @ C @ B @ A ) @ F )
= sk2 ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(29,plain,
! [F: g,E: g,D: g,C: g,B: g,A: g] :
( ( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) )
| ( ( sk1 @ ( sk14 @ F @ E @ D @ C @ B @ A ) @ F )
= sk2 ) ),
inference(simp,[status(thm)],[28]) ).
thf(847,plain,
( ( sk35 != sk2 )
| ( ( ( sk1 @ sk62 @ sk63 )
= sk2 )
& ( ( sk1 @ sk63 @ sk62 )
= sk2 ) )
| ( ( sk1 @ sk63 @ sk62 )
= sk2 ) ),
inference(bool_ext,[status(thm)],[404]) ).
thf(867,plain,
( ( ( sk1 @ sk63 @ sk62 )
= sk2 )
| ( sk35 != sk2 )
| ( ( ( sk1 @ sk62 @ sk63 )
= sk2 )
& ( ( sk1 @ sk63 @ sk62 )
= sk2 ) ) ),
inference(lifteq,[status(thm)],[847]) ).
thf(889,plain,
( ( ( ( sk1 @ sk63 @ sk62 )
= sk2 )
| ( sk35 != sk2 )
| ( ( sk1 @ sk62 @ sk63 )
= sk2 ) )
& ( ( ( sk1 @ sk63 @ sk62 )
= sk2 )
| ( sk35 != sk2 )
| ( ( sk1 @ sk63 @ sk62 )
= sk2 ) ) ),
inference(cnf,[status(esa)],[867]) ).
thf(891,plain,
( ( ( sk1 @ sk63 @ sk62 )
= sk2 )
| ( sk35 != sk2 )
| ( ( sk1 @ sk63 @ sk62 )
= sk2 ) ),
inference(cnfConj,[status(thm)],[889]) ).
thf(893,plain,
( ( ( sk1 @ sk63 @ sk62 )
= sk2 )
| ( ( sk1 @ sk63 @ sk62 )
= sk2 )
| ( sk35 != sk2 ) ),
inference(lifteq,[status(thm)],[891]) ).
thf(894,plain,
( ( ( sk1 @ sk63 @ sk62 )
= sk2 )
| ( sk35 != sk2 ) ),
inference(simp,[status(thm)],[893]) ).
thf(912,plain,
( ( sk35 != sk2 )
| ( ( ( sk2 = sk2 )
& ( ( sk1 @ sk63 @ sk62 )
= sk2 ) )
!= ( ( sk1 @ sk63 @ sk62 )
= sk2 ) )
| ( sk35 != sk2 )
| ( ( sk1 @ sk63 @ sk62 )
!= ( sk1 @ sk62 @ sk63 ) ) ),
inference(paramod_ordered,[status(thm)],[894,404]) ).
thf(913,plain,
( ( sk35 != sk2 )
| ( ( sk1 @ sk63 @ sk62 )
!= ( sk1 @ sk62 @ sk63 ) ) ),
inference(simp,[status(thm)],[912]) ).
thf(967,plain,
( ( sk35 != sk2 )
| ( sk63 != sk62 )
| ( sk63 != sk62 ) ),
inference(simp,[status(thm)],[913]) ).
thf(1012,plain,
( ( sk35 != sk2 )
| ( sk63 != sk62 ) ),
inference(simp,[status(thm)],[967]) ).
thf(383,plain,
( ( ( sk1 @ sk35 @ sk2 )
!= sk35 )
| ( ( ^ [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ^ [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ) ),
inference(simp,[status(thm)],[200]) ).
thf(488,plain,
( ( ( sk1 @ sk35 @ sk2 )
!= sk35 )
| ( ( ^ [A: g,B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ^ [A: g,B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ) ),
inference(simp,[status(thm)],[383]) ).
thf(909,plain,
( ( sk35 != sk2 )
| ( ( ( ( sk1 @ sk62 @ sk63 )
= sk2 )
& ( sk2 = sk2 ) )
!= ( ( sk1 @ sk63 @ sk62 )
= sk2 ) )
| ( sk35 != sk2 )
| ( ( sk1 @ sk63 @ sk62 )
!= ( sk1 @ sk63 @ sk62 ) ) ),
inference(paramod_ordered,[status(thm)],[894,404]) ).
thf(910,plain,
( ( sk35 != sk2 )
| ( ( ( sk1 @ sk62 @ sk63 )
= sk2 )
!= ( ( sk1 @ sk63 @ sk62 )
= sk2 ) )
| ( ( sk1 @ sk63 @ sk62 )
!= ( sk1 @ sk63 @ sk62 ) ) ),
inference(simp,[status(thm)],[909]) ).
thf(911,plain,
( ( sk35 != sk2 )
| ( ( ( sk1 @ sk62 @ sk63 )
= sk2 )
!= ( ( sk1 @ sk63 @ sk62 )
= sk2 ) ) ),
inference(pattern_uni,[status(thm)],[910:[]]) ).
thf(389,plain,
( ( ( ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) )
| ( sk35 != sk2 )
| ( sk35 != sk2 ) ),
inference(simp,[status(thm)],[386]) ).
thf(398,plain,
( ( ( ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) )
| ( sk35 != sk2 ) ),
inference(simp,[status(thm)],[389]) ).
thf(7,plain,
( ~ ( ! [A: g,B: g,C: g] :
( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) )
& ! [A: g] :
( ( ( sk1 @ sk2 @ A )
= A )
& ( ( sk1 @ A @ sk2 )
= A ) )
& ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
| ~ ( ! [A: g,B: g,C: g] :
( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) )
& ! [A: g] :
( ( sk1 @ sk2 @ A )
= A )
& ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(10,plain,
! [B: g,A: g] :
( ( ( sk1 @ ( sk1 @ sk3 @ sk4 ) @ sk5 )
!= ( sk1 @ sk3 @ ( sk1 @ sk4 @ sk5 ) ) )
| ( ( sk1 @ sk2 @ sk6 )
!= sk6 )
| ( ( sk1 @ sk6 @ sk2 )
!= sk6 )
| ( ( sk1 @ sk7 @ A )
!= sk2 )
| ( ( sk1 @ A @ sk7 )
!= sk2 )
| ( ( sk1 @ ( sk1 @ ( sk8 @ A ) @ ( sk9 @ A ) ) @ ( sk10 @ A ) )
!= ( sk1 @ ( sk8 @ A ) @ ( sk1 @ ( sk9 @ A ) @ ( sk10 @ A ) ) ) )
| ( ( sk1 @ sk2 @ ( sk11 @ A ) )
!= ( sk11 @ A ) )
| ( ( sk1 @ B @ ( sk12 @ A ) )
!= sk2 ) ),
inference(cnf,[status(esa)],[7]) ).
thf(11,plain,
! [B: g,A: g] :
( ( ( sk1 @ ( sk1 @ sk3 @ sk4 ) @ sk5 )
!= ( sk1 @ sk3 @ ( sk1 @ sk4 @ sk5 ) ) )
| ( ( sk1 @ sk2 @ sk6 )
!= sk6 )
| ( ( sk1 @ sk6 @ sk2 )
!= sk6 )
| ( ( sk1 @ sk7 @ A )
!= sk2 )
| ( ( sk1 @ A @ sk7 )
!= sk2 )
| ( ( sk1 @ ( sk1 @ ( sk8 @ A ) @ ( sk9 @ A ) ) @ ( sk10 @ A ) )
!= ( sk1 @ ( sk8 @ A ) @ ( sk1 @ ( sk9 @ A ) @ ( sk10 @ A ) ) ) )
| ( ( sk1 @ sk2 @ ( sk11 @ A ) )
!= ( sk11 @ A ) )
| ( ( sk1 @ B @ ( sk12 @ A ) )
!= sk2 ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(203,plain,
! [B: g,A: g] :
( ( ( sk1 @ ( sk1 @ sk3 @ sk4 ) @ sk5 )
!= ( sk1 @ sk3 @ ( sk1 @ sk4 @ sk5 ) ) )
| ( sk6 != sk6 )
| ( ( sk1 @ sk6 @ sk2 )
!= sk6 )
| ( ( sk1 @ sk7 @ A )
!= sk2 )
| ( ( sk1 @ A @ sk7 )
!= sk2 )
| ( ( sk1 @ ( sk1 @ ( sk8 @ A ) @ ( sk9 @ A ) ) @ ( sk10 @ A ) )
!= ( sk1 @ ( sk8 @ A ) @ ( sk1 @ ( sk9 @ A ) @ ( sk10 @ A ) ) ) )
| ( ( sk11 @ A )
!= ( sk11 @ A ) )
| ( ( sk1 @ B @ ( sk12 @ A ) )
!= sk2 ) ),
inference(rewrite,[status(thm)],[11,183]) ).
thf(204,plain,
! [B: g,A: g] :
( ( ( sk1 @ ( sk1 @ sk3 @ sk4 ) @ sk5 )
!= ( sk1 @ sk3 @ ( sk1 @ sk4 @ sk5 ) ) )
| ( ( sk1 @ sk6 @ sk2 )
!= sk6 )
| ( ( sk1 @ sk7 @ A )
!= sk2 )
| ( ( sk1 @ A @ sk7 )
!= sk2 )
| ( ( sk1 @ ( sk1 @ ( sk8 @ A ) @ ( sk9 @ A ) ) @ ( sk10 @ A ) )
!= ( sk1 @ ( sk8 @ A ) @ ( sk1 @ ( sk9 @ A ) @ ( sk10 @ A ) ) ) )
| ( ( sk1 @ B @ ( sk12 @ A ) )
!= sk2 ) ),
inference(simp,[status(thm)],[203]) ).
thf(846,plain,
( ( sk35 != sk2 )
| ~ ( ( ( sk1 @ sk62 @ sk63 )
= sk2 )
& ( ( sk1 @ sk63 @ sk62 )
= sk2 ) )
| ( ( sk1 @ sk63 @ sk62 )
!= sk2 ) ),
inference(bool_ext,[status(thm)],[404]) ).
thf(866,plain,
( ( ( sk1 @ sk63 @ sk62 )
!= sk2 )
| ( sk35 != sk2 )
| ~ ( ( ( sk1 @ sk62 @ sk63 )
= sk2 )
& ( ( sk1 @ sk63 @ sk62 )
= sk2 ) ) ),
inference(lifteq,[status(thm)],[846]) ).
thf(886,plain,
( ( ( sk1 @ sk63 @ sk62 )
!= sk2 )
| ( sk35 != sk2 )
| ( ( sk1 @ sk62 @ sk63 )
!= sk2 )
| ( ( sk1 @ sk63 @ sk62 )
!= sk2 ) ),
inference(cnf,[status(esa)],[866]) ).
thf(887,plain,
( ( ( sk1 @ sk62 @ sk63 )
!= sk2 )
| ( ( sk1 @ sk63 @ sk62 )
!= sk2 )
| ( ( sk1 @ sk63 @ sk62 )
!= sk2 )
| ( sk35 != sk2 ) ),
inference(lifteq,[status(thm)],[886]) ).
thf(888,plain,
( ( ( sk1 @ sk62 @ sk63 )
!= sk2 )
| ( ( sk1 @ sk63 @ sk62 )
!= sk2 )
| ( sk35 != sk2 ) ),
inference(simp,[status(thm)],[887]) ).
thf(1032,plain,
( ( sk35 != sk2 )
| ( ( sk1 @ sk62 @ sk63 )
!= sk2 )
| ( sk2 != sk2 )
| ( sk35 != sk2 )
| ( ( sk1 @ sk63 @ sk62 )
!= ( sk1 @ sk63 @ sk62 ) ) ),
inference(paramod_ordered,[status(thm)],[894,888]) ).
thf(1033,plain,
( ( sk35 != sk2 )
| ( ( sk1 @ sk62 @ sk63 )
!= sk2 )
| ( ( sk1 @ sk63 @ sk62 )
!= ( sk1 @ sk63 @ sk62 ) ) ),
inference(simp,[status(thm)],[1032]) ).
thf(1034,plain,
( ( sk35 != sk2 )
| ( ( sk1 @ sk62 @ sk63 )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[1033:[]]) ).
thf(1361,plain,
! [A: g] :
( ( sk35 != sk2 )
| ( A != sk2 )
| ( ( sk1 @ sk2 @ A )
!= ( sk1 @ sk62 @ sk63 ) ) ),
inference(paramod_ordered,[status(thm)],[183,1034]) ).
thf(1368,plain,
( ( sk35 != sk2 )
| ( sk62 != sk2 )
| ( sk63 != sk2 ) ),
inference(simp,[status(thm)],[1361]) ).
thf(1379,plain,
( ( sk35 != sk2 )
| ( ( sk1 @ sk63 @ sk62 )
!= ( sk1 @ sk62 @ sk63 ) )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[911]) ).
thf(1449,plain,
( ( sk35 != sk2 )
| ( ( sk1 @ sk63 @ sk62 )
!= ( sk1 @ sk62 @ sk63 ) ) ),
inference(simp,[status(thm)],[1379]) ).
thf(21,plain,
! [F: g,E: g,D: g,C: g,B: g,A: g] :
( ( ( sk1 @ D @ sk2 )
= D )
| ( ( sk1 @ ( sk14 @ F @ E @ D @ C @ B @ A ) @ F )
= sk2 ) ),
inference(cnfConj,[status(thm)],[12]) ).
thf(32,plain,
! [F: g,E: g,D: g,C: g,B: g,A: g] :
( ( ( sk1 @ D @ sk2 )
= D )
| ( ( sk1 @ ( sk14 @ F @ E @ D @ C @ B @ A ) @ F )
= sk2 ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(33,plain,
! [F: g,E: g,D: g,C: g,B: g,A: g] :
( ( ( sk1 @ D @ sk2 )
= D )
| ( ( sk1 @ ( sk14 @ F @ E @ D @ C @ B @ A ) @ F )
= sk2 ) ),
inference(simp,[status(thm)],[32]) ).
thf(943,plain,
! [A: g] :
( ( sk35 != sk2 )
| ( sk2 = A )
| ( ( sk1 @ sk63 @ sk62 )
!= ( sk1 @ sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[894,183]) ).
thf(956,plain,
! [A: g] :
( ( sk2 = A )
| ( sk35 != sk2 )
| ( sk63 != sk2 )
| ( sk62 != A ) ),
inference(simp,[status(thm)],[943]) ).
thf(1011,plain,
( ( sk62 = sk2 )
| ( sk35 != sk2 )
| ( sk63 != sk2 ) ),
inference(simp,[status(thm)],[956]) ).
thf(18,plain,
! [D: g,C: g,B: g,A: g] :
( ( ( sk1 @ ( sk13 @ A ) @ A )
= sk2 )
| ( ( sk1 @ ( sk1 @ B @ C ) @ D )
= ( sk1 @ B @ ( sk1 @ C @ D ) ) ) ),
inference(cnfConj,[status(thm)],[12]) ).
thf(38,plain,
! [D: g,C: g,B: g,A: g] :
( ( ( sk1 @ ( sk13 @ A ) @ A )
= sk2 )
| ( ( sk1 @ ( sk1 @ B @ C ) @ D )
= ( sk1 @ B @ ( sk1 @ C @ D ) ) ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(39,plain,
! [D: g,C: g,B: g,A: g] :
( ( ( sk1 @ ( sk13 @ A ) @ A )
= sk2 )
| ( ( sk1 @ ( sk1 @ B @ C ) @ D )
= ( sk1 @ B @ ( sk1 @ C @ D ) ) ) ),
inference(simp,[status(thm)],[38]) ).
thf(525,plain,
( ( sk35 != sk2 )
| ? [A: g] :
( ( ( sk1 @ sk61 @ A )
= sk2 )
& ( ( sk1 @ A @ sk61 )
= sk2 ) )
| ? [A: g] :
( ( sk1 @ A @ sk61 )
= sk2 ) ),
inference(bool_ext,[status(thm)],[401]) ).
thf(528,plain,
( ( ( sk35 != sk2 )
| ( ( sk1 @ sk61 @ sk71 )
= sk2 )
| ( ( sk1 @ sk72 @ sk61 )
= sk2 ) )
& ( ( sk35 != sk2 )
| ( ( sk1 @ sk71 @ sk61 )
= sk2 )
| ( ( sk1 @ sk72 @ sk61 )
= sk2 ) ) ),
inference(cnf,[status(esa)],[525]) ).
thf(529,plain,
( ( sk35 != sk2 )
| ( ( sk1 @ sk61 @ sk71 )
= sk2 )
| ( ( sk1 @ sk72 @ sk61 )
= sk2 ) ),
inference(cnfConj,[status(thm)],[528]) ).
thf(531,plain,
( ( ( sk1 @ sk61 @ sk71 )
= sk2 )
| ( ( sk1 @ sk72 @ sk61 )
= sk2 )
| ( sk35 != sk2 ) ),
inference(lifteq,[status(thm)],[529]) ).
thf(185,plain,
( ( ! [A: g,B: g,C: g] :
( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) )
& ! [A: g] :
( ( A = A )
& ( ( sk1 @ A @ sk2 )
= A ) )
& ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ! [A: g,B: g,C: g] :
( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) )
& ! [A: g] : ( A = A )
& ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ),
inference(rewrite,[status(thm)],[5,183]) ).
thf(186,plain,
( ( ! [A: g,B: g,C: g] :
( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) )
& ! [A: g] :
( ( sk1 @ A @ sk2 )
= A )
& ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ! [A: g,B: g,C: g] :
( ( sk1 @ ( sk1 @ A @ B ) @ C )
= ( sk1 @ A @ ( sk1 @ B @ C ) ) )
& ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ),
inference(simp,[status(thm)],[185]) ).
thf(378,plain,
( ( ( ^ [A: g] :
( ( sk1 @ A @ sk2 )
= A ) )
!= ( ^ [A: g] : $true ) )
| ( ( ^ [A: g,B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ^ [A: g,B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ) ),
inference(simp,[status(thm)],[196]) ).
thf(189,plain,
( ( ! [A: g] :
( ( A = A )
& ( ( sk1 @ A @ sk2 )
= A ) )
& ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ! [A: g] : ( A = A )
& ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ),
inference(rewrite,[status(thm)],[9,183]) ).
thf(190,plain,
( ( ! [A: g] :
( ( sk1 @ A @ sk2 )
= A )
& ! [A: g] :
? [B: g] :
( ( ( sk1 @ A @ B )
= sk2 )
& ( ( sk1 @ B @ A )
= sk2 ) ) )
!= ( ! [A: g] :
? [B: g] :
( ( sk1 @ B @ A )
= sk2 ) ) ),
inference(simp,[status(thm)],[189]) ).
thf(530,plain,
( ( sk35 != sk2 )
| ( ( sk1 @ sk71 @ sk61 )
= sk2 )
| ( ( sk1 @ sk72 @ sk61 )
= sk2 ) ),
inference(cnfConj,[status(thm)],[528]) ).
thf(532,plain,
( ( ( sk1 @ sk71 @ sk61 )
= sk2 )
| ( ( sk1 @ sk72 @ sk61 )
= sk2 )
| ( sk35 != sk2 ) ),
inference(lifteq,[status(thm)],[530]) ).
thf(4850,plain,
$false,
inference(e,[status(thm)],[523,404,196,29,1012,488,911,398,204,1368,200,1449,894,33,1011,39,399,3,1034,531,186,401,378,383,190,183,400,532]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG272^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.11/0.22 % Computer : n010.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 17:36:18 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.99/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.16/0.99 % [INFO] Parsing done (187ms).
% 1.16/1.00 % [INFO] Running in sequential loop mode.
% 2.02/1.41 % [INFO] eprover registered as external prover.
% 2.02/1.41 % [INFO] Scanning for conjecture ...
% 2.21/1.53 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.21/1.56 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.21/1.57 % [INFO] Problem is higher-order (TPTP THF).
% 2.21/1.57 % [INFO] Type checking passed.
% 2.21/1.58 % [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 ...
% 30.13/6.92 % External prover 'e' found a proof!
% 30.13/6.92 % [INFO] Killing All external provers ...
% 30.13/6.92 % Time passed: 6546ms (effective reasoning time: 5910ms)
% 30.13/6.92 % 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)>
% 30.13/6.92 % Axioms used in derivation (0):
% 30.13/6.92 % No. of inferences in proof: 88
% 30.13/6.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6546 ms resp. 5910 ms w/o parsing
% 30.87/7.04 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 30.87/7.04 % [INFO] Killing All external provers ...
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