%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO309^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : 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 08:45:34 AM UTC 2026
% Result : Theorem 16.90s 4.73s
% Output : Refutation 14.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 6
% Syntax : Number of formulae : 56 ( 17 unt; 0 typ; 5 def)
% Number of atoms : 191 ( 44 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 755 ( 82 ~; 49 |; 1 &; 620 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 166 ( 32 ^; 88 !; 41 ?; 166 :)
% ( 0 !>; 0 ?*; 0 @-; 5 @+)
% Comments :
%------------------------------------------------------------------------------
thf(cS_decl,type,
cS: $i > $i ).
thf(cQ_decl,type,
cQ: $i > $i ).
thf(cR_decl,type,
cR: $i > $i > $o ).
thf(sk1_decl,type,
sk1: ( $i > $o ) > $i ).
thf(sk2_decl,type,
sk2: $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i > $o] :
@+[B: $i] :
( ( A @ B )
!= ( ~ ( A @ ( cS @ B ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i] :
@+[B: $i] : ( cR @ A @ ( cQ @ B ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i] :
@+[B: $i] : ( cR @ ( cS @ A ) @ ( cQ @ B ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i] :
@+[B: $i] : ( cR @ A @ ( cQ @ B ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i] :
@+[B: $i] : ( cR @ ( cS @ A ) @ ( cQ @ B ) ) ) ) ).
thf(1,conjecture,
( ! [A: $i] :
( ( ? [B: $i] : ( cR @ A @ ( cQ @ B ) ) )
= ( ~ ? [B: $i] : ( cR @ ( cS @ A ) @ ( cQ @ B ) ) ) )
=> ? [A: $i > $o] :
! [B: $i] :
( ( A @ B )
= ( ~ ( A @ ( cS @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEO1) ).
thf(2,negated_conjecture,
~ ( ! [A: $i] :
( ( ? [B: $i] : ( cR @ A @ ( cQ @ B ) ) )
= ( ~ ? [B: $i] : ( cR @ ( cS @ A ) @ ( cQ @ B ) ) ) )
=> ? [A: $i > $o] :
! [B: $i] :
( ( A @ B )
= ( ~ ( A @ ( cS @ B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i] :
( ( ? [B: $i] : ( cR @ A @ ( cQ @ B ) ) )
= ( ~ ? [B: $i] : ( cR @ ( cS @ A ) @ ( cQ @ B ) ) ) )
=> ? [A: $i > $o] :
! [B: $i] :
( ( A @ B )
= ( ~ ( A @ ( cS @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [B: $i > $o,A: $i] :
( ( ( ? [C: $i] : ( cR @ A @ ( cQ @ C ) ) )
= ( ~ ? [C: $i] : ( cR @ ( cS @ A ) @ ( cQ @ C ) ) ) )
& ( ( B @ ( sk1 @ B ) )
!= ( ~ ( B @ ( cS @ ( sk1 @ B ) ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
! [A: $i > $o] :
( ( A @ ( sk1 @ A ) )
!= ( ~ ( A @ ( cS @ ( sk1 @ A ) ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
! [A: $i > $o] :
( ( ~ ( A @ ( cS @ ( sk1 @ A ) ) ) )
!= ( A @ ( sk1 @ A ) ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(9,plain,
! [A: $i > $o] :
( ( ~ ( A @ ( cS @ ( sk1 @ A ) ) ) )
!= ( A @ ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[8]) ).
thf(69,plain,
! [A: $i > $o] :
( ~ ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ~ ( A @ ( sk1 @ A ) ) ),
inference(bool_ext,[status(thm)],[9]) ).
thf(92,plain,
! [A: $i > $o] :
( ( A @ ( cS @ ( sk1 @ A ) ) )
| ~ ( A @ ( sk1 @ A ) ) ),
inference(cnf,[status(esa)],[69]) ).
thf(5,plain,
! [A: $i] :
( ( ? [B: $i] : ( cR @ A @ ( cQ @ B ) ) )
= ( ~ ? [B: $i] : ( cR @ ( cS @ A ) @ ( cQ @ B ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
! [A: $i] :
( ( ? [B: $i] : ( cR @ A @ ( cQ @ B ) ) )
= ( ~ ? [B: $i] : ( cR @ ( cS @ A ) @ ( cQ @ B ) ) ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( ( ~ ~ ? [C: $i] : ( cR @ ( cS @ A ) @ ( cQ @ C ) ) )
= ( ? [C: $i] : ( cR @ B @ ( cQ @ C ) ) ) )
| ( ( ? [C: $i] : ( cR @ A @ ( cQ @ C ) ) )
!= ( ? [C: $i] : ( cR @ ( cS @ B ) @ ( cQ @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[7,7]) ).
thf(13,plain,
! [B: $i,A: $i] :
( ( ( ? [C: $i] : ( cR @ ( cS @ A ) @ ( cQ @ C ) ) )
= ( ? [C: $i] : ( cR @ B @ ( cQ @ C ) ) ) )
| ( ( ? [C: $i] : ( cR @ A @ ( cQ @ C ) ) )
!= ( ? [C: $i] : ( cR @ ( cS @ B ) @ ( cQ @ C ) ) ) ) ),
inference(simp,[status(thm)],[12]) ).
thf(14,plain,
! [A: $i] :
( ( ? [B: $i] : ( cR @ ( cS @ ( cS @ A ) ) @ ( cQ @ B ) ) )
= ( ? [B: $i] : ( cR @ A @ ( cQ @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[13:[bind(A,$thf( cS @ C )),bind(B,$thf( C ))]]) ).
thf(17,plain,
! [A: $i] :
( ( ? [B: $i] : ( cR @ ( cS @ ( cS @ A ) ) @ ( cQ @ B ) ) )
= ( ? [B: $i] : ( cR @ A @ ( cQ @ B ) ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( ( ~ ? [C: $i] : ( cR @ A @ ( cQ @ C ) ) )
= ( ? [C: $i] : ( cR @ B @ ( cQ @ C ) ) ) )
| ( ( ? [C: $i] : ( cR @ ( cS @ ( cS @ A ) ) @ ( cQ @ C ) ) )
!= ( ? [C: $i] : ( cR @ ( cS @ B ) @ ( cQ @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,7]) ).
thf(23,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( cR @ A @ ( cQ @ B ) ) )
= ( ? [B: $i] : ( cR @ ( cS @ A ) @ ( cQ @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[22:[bind(A,$thf( C )),bind(B,$thf( cS @ C ))]]) ).
thf(29,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( cR @ A @ ( cQ @ B ) ) )
= ( ? [B: $i] : ( cR @ ( cS @ A ) @ ( cQ @ B ) ) ) ),
inference(simp,[status(thm)],[23]) ).
thf(31,plain,
! [A: $i] :
( ~ ~ ? [B: $i] : ( cR @ A @ ( cQ @ B ) )
| ? [B: $i] : ( cR @ ( cS @ A ) @ ( cQ @ B ) ) ),
inference(bool_ext,[status(thm)],[29]) ).
thf(67,plain,
! [A: $i] :
( ( cR @ A @ ( cQ @ ( sk6 @ A ) ) )
| ( cR @ ( cS @ A ) @ ( cQ @ ( sk7 @ A ) ) ) ),
inference(cnf,[status(esa)],[31]) ).
thf(11,plain,
! [A: $i] :
( ? [B: $i] : ( cR @ A @ ( cQ @ B ) )
| ~ ~ ? [B: $i] : ( cR @ ( cS @ A ) @ ( cQ @ B ) ) ),
inference(bool_ext,[status(thm)],[7]) ).
thf(16,plain,
! [A: $i] :
( ( cR @ A @ ( cQ @ ( sk2 @ A ) ) )
| ( cR @ ( cS @ A ) @ ( cQ @ ( sk3 @ A ) ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(10,plain,
! [A: $i] :
( ~ ? [B: $i] : ( cR @ A @ ( cQ @ B ) )
| ~ ? [B: $i] : ( cR @ ( cS @ A ) @ ( cQ @ B ) ) ),
inference(bool_ext,[status(thm)],[7]) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( cR @ A @ ( cQ @ B ) )
| ~ ( cR @ ( cS @ A ) @ ( cQ @ C ) ) ),
inference(cnf,[status(esa)],[10]) ).
thf(286,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( cR @ A @ ( cQ @ ( sk2 @ A ) ) )
| ~ ( cR @ B @ ( cQ @ C ) )
| ~ $true
| ( ( cR @ ( cS @ A ) @ ( cQ @ ( sk3 @ A ) ) )
!= ( cR @ ( cS @ B ) @ ( cQ @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[16,15]) ).
thf(287,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( cR @ A @ ( cQ @ ( sk2 @ A ) ) )
| ~ ( cR @ B @ ( cQ @ C ) )
| ( ( cR @ ( cS @ A ) @ ( cQ @ ( sk3 @ A ) ) )
!= ( cR @ ( cS @ B ) @ ( cQ @ D ) ) ) ),
inference(simp,[status(thm)],[286]) ).
thf(288,plain,
! [B: $i,A: $i] :
( ( cR @ B @ ( cQ @ ( sk2 @ B ) ) )
| ~ ( cR @ B @ ( cQ @ A ) ) ),
inference(pattern_uni,[status(thm)],[287:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( C )),bind(D,$thf( sk3 @ E ))]]) ).
thf(298,plain,
! [B: $i,A: $i] :
( ( cR @ B @ ( cQ @ ( sk2 @ B ) ) )
| ~ ( cR @ B @ ( cQ @ A ) ) ),
inference(simp,[status(thm)],[288]) ).
thf(593,plain,
! [C: $i,B: $i,A: $i] :
( ( cR @ A @ ( cQ @ ( sk6 @ A ) ) )
| ( cR @ C @ ( cQ @ ( sk2 @ C ) ) )
| ~ $true
| ( ( cR @ ( cS @ A ) @ ( cQ @ ( sk7 @ A ) ) )
!= ( cR @ C @ ( cQ @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[67,298]) ).
thf(594,plain,
! [C: $i,B: $i,A: $i] :
( ( cR @ A @ ( cQ @ ( sk6 @ A ) ) )
| ( cR @ C @ ( cQ @ ( sk2 @ C ) ) )
| ( ( cR @ ( cS @ A ) @ ( cQ @ ( sk7 @ A ) ) )
!= ( cR @ C @ ( cQ @ B ) ) ) ),
inference(simp,[status(thm)],[593]) ).
thf(595,plain,
! [A: $i] :
( ( cR @ A @ ( cQ @ ( sk6 @ A ) ) )
| ( cR @ ( cS @ A ) @ ( cQ @ ( sk2 @ ( cS @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[594:[bind(A,$thf( E )),bind(B,$thf( sk7 @ E )),bind(C,$thf( cS @ E ))]]) ).
thf(626,plain,
! [A: $i] :
( ( cR @ A @ ( cQ @ ( sk6 @ A ) ) )
| ( cR @ ( cS @ A ) @ ( cQ @ ( sk2 @ ( cS @ A ) ) ) ) ),
inference(simp,[status(thm)],[595]) ).
thf(967,plain,
! [B: $i > $o,A: $i] :
( ( cR @ A @ ( cQ @ ( sk6 @ A ) ) )
| ( ( B @ ( sk1 @ B ) )
!= ( ~ $true ) )
| ( ( cR @ ( cS @ A ) @ ( cQ @ ( sk2 @ ( cS @ A ) ) ) )
!= ( B @ ( cS @ ( sk1 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[626,9]) ).
thf(968,plain,
! [B: $i > $o,A: $i] :
( ( cR @ A @ ( cQ @ ( sk6 @ A ) ) )
| ( B @ ( sk1 @ B ) )
| ( ( cR @ ( cS @ A ) @ ( cQ @ ( sk2 @ ( cS @ A ) ) ) )
!= ( B @ ( cS @ ( sk1 @ B ) ) ) ) ),
inference(simp,[status(thm)],[967]) ).
thf(1010,plain,
( ( cR
@ ( sk1
@ ^ [A: $i] : ( cR @ A @ ( cQ @ ( sk2 @ A ) ) ) )
@ ( cQ
@ ( sk6
@ ( sk1
@ ^ [A: $i] : ( cR @ A @ ( cQ @ ( sk2 @ A ) ) ) ) ) ) )
| ( cR
@ ( sk1
@ ^ [A: $i] : ( cR @ A @ ( cQ @ ( sk2 @ A ) ) ) )
@ ( cQ
@ ( sk2
@ ( sk1
@ ^ [A: $i] : ( cR @ A @ ( cQ @ ( sk2 @ A ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[968:[bind(A,$thf( sk1 @ ^ [C: $i] : ( cR @ C @ ( cQ @ ( sk2 @ C ) ) ) )),bind(B,$thf( ^ [C: $i] : ( cR @ C @ ( cQ @ ( sk2 @ C ) ) ) ))]]) ).
thf(1308,plain,
! [B: $i,A: $i] :
( ( cR
@ ( sk1
@ ^ [C: $i] : ( cR @ C @ ( cQ @ ( sk2 @ C ) ) ) )
@ ( cQ
@ ( sk2
@ ( sk1
@ ^ [C: $i] : ( cR @ C @ ( cQ @ ( sk2 @ C ) ) ) ) ) ) )
| ( cR @ B @ ( cQ @ ( sk2 @ B ) ) )
| ~ $true
| ( ( cR
@ ( sk1
@ ^ [C: $i] : ( cR @ C @ ( cQ @ ( sk2 @ C ) ) ) )
@ ( cQ
@ ( sk6
@ ( sk1
@ ^ [C: $i] : ( cR @ C @ ( cQ @ ( sk2 @ C ) ) ) ) ) ) )
!= ( cR @ B @ ( cQ @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[1010,298]) ).
thf(1309,plain,
! [B: $i,A: $i] :
( ( cR
@ ( sk1
@ ^ [C: $i] : ( cR @ C @ ( cQ @ ( sk2 @ C ) ) ) )
@ ( cQ
@ ( sk2
@ ( sk1
@ ^ [C: $i] : ( cR @ C @ ( cQ @ ( sk2 @ C ) ) ) ) ) ) )
| ( cR @ B @ ( cQ @ ( sk2 @ B ) ) )
| ( ( cR
@ ( sk1
@ ^ [C: $i] : ( cR @ C @ ( cQ @ ( sk2 @ C ) ) ) )
@ ( cQ
@ ( sk6
@ ( sk1
@ ^ [C: $i] : ( cR @ C @ ( cQ @ ( sk2 @ C ) ) ) ) ) ) )
!= ( cR @ B @ ( cQ @ A ) ) ) ),
inference(simp,[status(thm)],[1308]) ).
thf(1310,plain,
( ( cR
@ ( sk1
@ ^ [A: $i] : ( cR @ A @ ( cQ @ ( sk2 @ A ) ) ) )
@ ( cQ
@ ( sk2
@ ( sk1
@ ^ [A: $i] : ( cR @ A @ ( cQ @ ( sk2 @ A ) ) ) ) ) ) )
| ( cR
@ ( sk1
@ ^ [A: $i] : ( cR @ A @ ( cQ @ ( sk2 @ A ) ) ) )
@ ( cQ
@ ( sk2
@ ( sk1
@ ^ [A: $i] : ( cR @ A @ ( cQ @ ( sk2 @ A ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1309:[bind(A,$thf( sk6 @ ( sk1 @ ^ [C: $i] : ( cR @ C @ ( cQ @ ( sk2 @ C ) ) ) ) )),bind(B,$thf( sk1 @ ^ [C: $i] : ( cR @ C @ ( cQ @ ( sk2 @ C ) ) ) ))]]) ).
thf(1346,plain,
( cR
@ ( sk1
@ ^ [A: $i] : ( cR @ A @ ( cQ @ ( sk2 @ A ) ) ) )
@ ( cQ
@ ( sk2
@ ( sk1
@ ^ [A: $i] : ( cR @ A @ ( cQ @ ( sk2 @ A ) ) ) ) ) ) ),
inference(simp,[status(thm)],[1310]) ).
thf(587,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( cR @ B @ ( cQ @ A ) )
| ~ ( cR @ C @ ( cQ @ D ) )
| ~ $true
| ( ( cR @ B @ ( cQ @ ( sk2 @ B ) ) )
!= ( cR @ ( cS @ C ) @ ( cQ @ E ) ) ) ),
inference(paramod_ordered,[status(thm)],[298,15]) ).
thf(588,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( cR @ B @ ( cQ @ A ) )
| ~ ( cR @ C @ ( cQ @ D ) )
| ( ( cR @ B @ ( cQ @ ( sk2 @ B ) ) )
!= ( cR @ ( cS @ C ) @ ( cQ @ E ) ) ) ),
inference(simp,[status(thm)],[587]) ).
thf(589,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( cR @ ( cS @ C ) @ ( cQ @ A ) )
| ~ ( cR @ C @ ( cQ @ B ) ) ),
inference(pattern_uni,[status(thm)],[588:[bind(A,$thf( A )),bind(B,$thf( cS @ H )),bind(C,$thf( H )),bind(D,$thf( D )),bind(E,$thf( sk2 @ ( cS @ H ) ))]]) ).
thf(624,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( cR @ ( cS @ C ) @ ( cQ @ A ) )
| ~ ( cR @ C @ ( cQ @ B ) ) ),
inference(simp,[status(thm)],[589]) ).
thf(1383,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( cR @ ( cS @ C ) @ ( cQ @ A ) )
| ~ $true
| ( ( cR
@ ( sk1
@ ^ [D: $i] : ( cR @ D @ ( cQ @ ( sk2 @ D ) ) ) )
@ ( cQ
@ ( sk2
@ ( sk1
@ ^ [D: $i] : ( cR @ D @ ( cQ @ ( sk2 @ D ) ) ) ) ) ) )
!= ( cR @ C @ ( cQ @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[1346,624]) ).
thf(1384,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( cR @ ( cS @ C ) @ ( cQ @ A ) )
| ( ( cR
@ ( sk1
@ ^ [D: $i] : ( cR @ D @ ( cQ @ ( sk2 @ D ) ) ) )
@ ( cQ
@ ( sk2
@ ( sk1
@ ^ [D: $i] : ( cR @ D @ ( cQ @ ( sk2 @ D ) ) ) ) ) ) )
!= ( cR @ C @ ( cQ @ B ) ) ) ),
inference(simp,[status(thm)],[1383]) ).
thf(1385,plain,
! [A: $i] :
~ ( cR
@ ( cS
@ ( sk1
@ ^ [B: $i] : ( cR @ B @ ( cQ @ ( sk2 @ B ) ) ) ) )
@ ( cQ @ A ) ),
inference(pattern_uni,[status(thm)],[1384:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk1 @ ^ [D: $i] : ( cR @ D @ ( cQ @ ( sk2 @ D ) ) ) ) )),bind(C,$thf( sk1 @ ^ [D: $i] : ( cR @ D @ ( cQ @ ( sk2 @ D ) ) ) ))]]) ).
thf(1444,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ ( sk1 @ A ) )
| ~ $true
| ( ( A @ ( cS @ ( sk1 @ A ) ) )
!= ( cR
@ ( cS
@ ( sk1
@ ^ [C: $i] : ( cR @ C @ ( cQ @ ( sk2 @ C ) ) ) ) )
@ ( cQ @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,1385]) ).
thf(1445,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ ( sk1 @ A ) )
| ( ( A @ ( cS @ ( sk1 @ A ) ) )
!= ( cR
@ ( cS
@ ( sk1
@ ^ [C: $i] : ( cR @ C @ ( cQ @ ( sk2 @ C ) ) ) ) )
@ ( cQ @ B ) ) ) ),
inference(simp,[status(thm)],[1444]) ).
thf(1473,plain,
~ ( cR
@ ( sk1
@ ^ [A: $i] : ( cR @ A @ ( cQ @ ( sk2 @ A ) ) ) )
@ ( cQ
@ ( sk2
@ ( sk1
@ ^ [A: $i] : ( cR @ A @ ( cQ @ ( sk2 @ A ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[1445:[bind(A,$thf( ^ [C: $i] : ( cR @ C @ ( cQ @ ( sk2 @ C ) ) ) )),bind(B,$thf( sk2 @ ( cS @ ( sk1 @ ^ [C: $i] : ( cR @ C @ ( cQ @ ( sk2 @ C ) ) ) ) ) ))]]) ).
thf(1478,plain,
~ $true,
inference(rewrite,[status(thm)],[1473,1346]) ).
thf(1479,plain,
$false,
inference(simp,[status(thm)],[1478]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO309^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % 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
% 0.10/0.18 % Computer : n010.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 16:45:03 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 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
% 0.88/0.77 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/0.95 % [INFO] Parsing done (179ms).
% 1.19/0.97 % [INFO] Running in sequential loop mode.
% 1.78/1.36 % [INFO] eprover registered as external prover.
% 1.78/1.37 % [INFO] Scanning for conjecture ...
% 1.97/1.47 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.13/1.50 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.13/1.50 % [INFO] Problem is higher-order (TPTP THF).
% 2.13/1.51 % [INFO] Type checking passed.
% 2.13/1.51 % [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 ...
% 16.90/4.72 % [INFO] Killing All external provers ...
% 16.90/4.73 % Time passed: 4392ms (effective reasoning time: 3751ms)
% 16.90/4.73 % 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)>
% 16.90/4.73 % Axioms used in derivation (0):
% 16.90/4.73 % No. of inferences in proof: 51
% 16.90/4.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4392 ms resp. 3751 ms w/o parsing
% 14.94/4.81 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.94/4.81 % [INFO] Killing All external provers ...
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