%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO224^5 : 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 : n007.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 08:45:25 AM UTC 2026
% Result : Theorem 14.39s 4.03s
% Output : Refutation 15.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 3
% Syntax : Number of formulae : 94 ( 6 unt; 0 typ; 2 def)
% Number of atoms : 508 ( 111 equ; 0 cnn)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 1076 ( 196 ~; 235 |; 88 &; 548 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 93 ( 36 ^; 33 !; 22 ?; 93 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(cJ_decl,type,
cJ: $i ).
thf(cLIKE_decl,type,
cLIKE: $i > $i > $o ).
thf(cWRH_decl,type,
cWRH: $i > $o ).
thf(cW_decl,type,
cW: $i > $o ).
thf(cUNIQUE_decl,type,
cUNIQUE: $i > $o ).
thf(cS_decl,type,
cS: $i ).
thf(cP_decl,type,
cP: $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk3_decl,type,
sk3: ( $i > $o ) > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
( ( cUNIQUE @ A )
& ( cW @ A )
& ( cWRH @ A )
& ( cLIKE @ cJ @ A ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i > $o] :
@+[B: $i] :
( ( cUNIQUE @ B )
& ( cW @ B )
& ( cWRH @ B )
& ( cLIKE @ cJ @ B ) ) ) ) ).
thf(1,conjecture,
( ( ! [A: $i] :
( ( cUNIQUE @ A )
=> ! [B: $i] :
( ( ( cWRH @ B )
& ( cW @ B ) )
=> ( A = B ) ) )
& ( cUNIQUE @ cS )
& ( cW @ cS )
& ( cWRH @ cS ) )
=> ? [A: $i > $o] :
( ( ( A @ cP )
= ( cLIKE @ cP @ cS ) )
& ( ( A @ cJ )
= ( ? [B: $i] :
( ( cUNIQUE @ B )
& ( cW @ B )
& ( cWRH @ B )
& ( cLIKE @ cJ @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cLING1) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i] :
( ( cUNIQUE @ A )
=> ! [B: $i] :
( ( ( cWRH @ B )
& ( cW @ B ) )
=> ( A = B ) ) )
& ( cUNIQUE @ cS )
& ( cW @ cS )
& ( cWRH @ cS ) )
=> ? [A: $i > $o] :
( ( ( A @ cP )
= ( cLIKE @ cP @ cS ) )
& ( ( A @ cJ )
= ( ? [B: $i] :
( ( cUNIQUE @ B )
& ( cW @ B )
& ( cWRH @ B )
& ( cLIKE @ cJ @ B ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ! [A: $i] :
( ( cUNIQUE @ A )
=> ! [B: $i] :
( ( ( cWRH @ B )
& ( cW @ B ) )
=> ( A = B ) ) )
& ( cUNIQUE @ cS )
& ( cW @ cS )
& ( cWRH @ cS ) )
=> ? [A: $i > $o] :
( ( ( A @ cP )
= ( cLIKE @ cP @ cS ) )
& ( ( A @ cJ )
= ( ? [B: $i] :
( ( cUNIQUE @ B )
& ( cW @ B )
& ( cWRH @ B )
& ( cLIKE @ cJ @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [C: $i > $o,B: $i,A: $i] :
( ( ~ ( cUNIQUE @ A )
| ~ ( cWRH @ B )
| ~ ( cW @ B )
| ( A = B ) )
& ( cUNIQUE @ cS )
& ( cW @ cS )
& ( cWRH @ cS )
& ( ( ( C @ cP )
!= ( cLIKE @ cP @ cS ) )
| ( ( C @ cJ )
!= ( ? [D: $i] :
( ( cUNIQUE @ D )
& ( cW @ D )
& ( cWRH @ D )
& ( cLIKE @ cJ @ D ) ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
! [A: $i > $o] :
( ( ( A @ cP )
!= ( cLIKE @ cP @ cS ) )
| ( ( A @ cJ )
!= ( ? [B: $i] :
( ( cUNIQUE @ B )
& ( cW @ B )
& ( cWRH @ B )
& ( cLIKE @ cJ @ B ) ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(10,plain,
! [A: $i > $o] :
( ( ( A @ cP )
!= ( cLIKE @ cP @ cS ) )
| ( ( A @ cJ )
!= ( ? [B: $i] :
( ( cUNIQUE @ B )
& ( cW @ B )
& ( cWRH @ B )
& ( cLIKE @ cJ @ B ) ) ) ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(11,plain,
! [A: $i > $o] :
( ( ( A @ cP )
!= ( cLIKE @ cP @ cS ) )
| ( ( A @ cJ )
!= ( ? [B: $i] :
( ( cUNIQUE @ B )
& ( cW @ B )
& ( cWRH @ B )
& ( cLIKE @ cJ @ B ) ) ) ) ),
inference(simp,[status(thm)],[10]) ).
thf(16,plain,
! [A: $i > $o] :
( ( A @ cP )
| ( cLIKE @ cP @ cS )
| ( A @ cJ )
| ? [B: $i] :
( ( cUNIQUE @ B )
& ( cW @ B )
& ( cWRH @ B )
& ( cLIKE @ cJ @ B ) ) ),
inference(bool_ext,[status(thm)],[11]) ).
thf(50,plain,
! [A: $i > $o] :
( ( ( A @ cP )
| ( cLIKE @ cP @ cS )
| ( A @ cJ )
| ( cUNIQUE @ ( sk3 @ A ) ) )
& ( ( A @ cP )
| ( cLIKE @ cP @ cS )
| ( A @ cJ )
| ( cW @ ( sk3 @ A ) ) )
& ( ( A @ cP )
| ( cLIKE @ cP @ cS )
| ( A @ cJ )
| ( cWRH @ ( sk3 @ A ) ) )
& ( ( A @ cP )
| ( cLIKE @ cP @ cS )
| ( A @ cJ )
| ( cLIKE @ cJ @ ( sk3 @ A ) ) ) ),
inference(cnf,[status(esa)],[16]) ).
thf(51,plain,
! [A: $i > $o] :
( ( A @ cP )
| ( cLIKE @ cP @ cS )
| ( A @ cJ )
| ( cUNIQUE @ ( sk3 @ A ) ) ),
inference(cnfConj,[status(thm)],[50]) ).
thf(84,plain,
( $false
| ( cLIKE @ cP @ cS )
| $false
| ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) ) ),
inference(prim_subst,[status(thm)],[51:[bind(A,$thf( ^ [B: $i] : $false ))]]) ).
thf(113,plain,
( ( cLIKE @ cP @ cS )
| ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) ) ),
inference(simp,[status(thm)],[84]) ).
thf(5,plain,
cUNIQUE @ cS,
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
cW @ cS,
inference(cnfConj,[status(thm)],[4]) ).
thf(21,plain,
! [A: $i > $o] :
( ~ ( cLIKE @ cP @ cS )
| ( ( A @ cJ )
!= ( ? [B: $i] :
( ( cUNIQUE @ B )
& ( cW @ B )
& ( cWRH @ B )
& ( cLIKE @ cJ @ B ) ) ) )
| ( ( cW @ cS )
!= ( A @ cP ) ) ),
inference(paramod_ordered,[status(thm)],[9,11]) ).
thf(29,plain,
( ~ ( cLIKE @ cP @ cS )
| ( ( cW @ cS )
!= ( ? [A: $i] :
( ( cUNIQUE @ A )
& ( cW @ A )
& ( cWRH @ A )
& ( cLIKE @ cJ @ A ) ) ) ) ),
inference(pre_uni,[status(thm)],[21:[bind(A,$thf( ^ [B: $i] : ( cW @ cS ) ))]]) ).
thf(57,plain,
( ~ ( cLIKE @ cP @ cS )
| ~ ? [A: $i] :
( ( cUNIQUE @ A )
& ( cW @ A )
& ( cWRH @ A )
& ( cLIKE @ cJ @ A ) ) ),
inference(rewrite,[status(thm)],[29,9]) ).
thf(58,plain,
! [A: $i] :
( ~ ( cLIKE @ cP @ cS )
| ~ ( cUNIQUE @ A )
| ~ ( cW @ A )
| ~ ( cWRH @ A )
| ~ ( cLIKE @ cJ @ A ) ),
inference(cnf,[status(esa)],[57]) ).
thf(367,plain,
! [A: $i] :
( ~ ( cLIKE @ cP @ cS )
| ~ $true
| ~ ( cW @ A )
| ~ ( cWRH @ A )
| ~ ( cLIKE @ cJ @ A )
| ( ( cUNIQUE @ cS )
!= ( cUNIQUE @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5,58]) ).
thf(368,plain,
! [A: $i] :
( ~ ( cLIKE @ cP @ cS )
| ~ ( cW @ A )
| ~ ( cWRH @ A )
| ~ ( cLIKE @ cJ @ A )
| ( ( cUNIQUE @ cS )
!= ( cUNIQUE @ A ) ) ),
inference(simp,[status(thm)],[367]) ).
thf(369,plain,
( ~ ( cLIKE @ cP @ cS )
| ~ ( cW @ cS )
| ~ ( cWRH @ cS )
| ~ ( cLIKE @ cJ @ cS ) ),
inference(pattern_uni,[status(thm)],[368:[bind(A,$thf( cS ))]]) ).
thf(6,plain,
cWRH @ cS,
inference(cnfConj,[status(thm)],[4]) ).
thf(436,plain,
( ~ ( cLIKE @ cP @ cS )
| ~ $true
| ~ $true
| ~ ( cLIKE @ cJ @ cS ) ),
inference(rewrite,[status(thm)],[369,6,9]) ).
thf(437,plain,
( ~ ( cLIKE @ cP @ cS )
| ~ ( cLIKE @ cJ @ cS ) ),
inference(simp,[status(thm)],[436]) ).
thf(466,plain,
( ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) )
| ~ $true
| ~ ( cLIKE @ cJ @ cS )
| ( ( cLIKE @ cP @ cS )
!= ( cLIKE @ cP @ cS ) ) ),
inference(paramod_ordered,[status(thm)],[113,437]) ).
thf(467,plain,
( ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) )
| ~ ( cLIKE @ cJ @ cS )
| ( ( cLIKE @ cP @ cS )
!= ( cLIKE @ cP @ cS ) ) ),
inference(simp,[status(thm)],[466]) ).
thf(468,plain,
( ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) )
| ~ ( cLIKE @ cJ @ cS ) ),
inference(pattern_uni,[status(thm)],[467:[]]) ).
thf(8,plain,
! [B: $i,A: $i] :
( ~ ( cUNIQUE @ A )
| ~ ( cWRH @ B )
| ~ ( cW @ B )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( cUNIQUE @ A )
| ~ ( cWRH @ B )
| ~ ( cW @ B ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(474,plain,
( ~ ( cLIKE @ cJ @ cS )
| ( ( cLIKE @ cP @ cS )
!= ( cLIKE @ cJ @ cS ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[437]) ).
thf(476,plain,
( ~ ( cLIKE @ cJ @ cS )
| ( cP != cJ )
| ( cS != cS ) ),
inference(simp,[status(thm)],[474]) ).
thf(485,plain,
( ~ ( cLIKE @ cJ @ cS )
| ( cP != cJ ) ),
inference(simp,[status(thm)],[476]) ).
thf(564,plain,
! [B: $i,A: $i] :
( ~ ( cUNIQUE @ A )
| ~ ( cWRH @ B )
| ~ ( cW @ B )
| ~ ( cLIKE @ cJ @ cS )
| ( B != cJ )
| ( A != cP ) ),
inference(paramod_ordered,[status(thm)],[12,485]) ).
thf(565,plain,
! [A: $i] :
( ~ ( cUNIQUE @ cP )
| ~ ( cWRH @ A )
| ~ ( cW @ A )
| ~ ( cLIKE @ cJ @ cS )
| ( A != cJ ) ),
inference(pattern_uni,[status(thm)],[564:[bind(A,$thf( cP ))]]) ).
thf(587,plain,
( ~ ( cUNIQUE @ cP )
| ~ ( cWRH @ cJ )
| ~ ( cW @ cJ )
| ~ ( cLIKE @ cJ @ cS ) ),
inference(simp,[status(thm)],[565]) ).
thf(15,plain,
! [A: $i > $o] :
( ~ ( A @ cP )
| ~ ( cLIKE @ cP @ cS )
| ( A @ cJ )
| ? [B: $i] :
( ( cUNIQUE @ B )
& ( cW @ B )
& ( cWRH @ B )
& ( cLIKE @ cJ @ B ) ) ),
inference(bool_ext,[status(thm)],[11]) ).
thf(25,plain,
( ( cP != cP )
| ~ ( cLIKE @ cP @ cS )
| ( cP = cJ )
| ? [A: $i] :
( ( cUNIQUE @ A )
& ( cW @ A )
& ( cWRH @ A )
& ( cLIKE @ cJ @ A ) ) ),
inference(replace_leibeq,[status(thm)],[15:[bind(A,$thf( (=) @ $i @ cP ))]]) ).
thf(27,plain,
( ( cP != cP )
| ( cP = cJ )
| ~ ( cLIKE @ cP @ cS )
| ? [A: $i] :
( ( cUNIQUE @ A )
& ( cW @ A )
& ( cWRH @ A )
& ( cLIKE @ cJ @ A ) ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(34,plain,
( ? [A: $i] :
( ( cUNIQUE @ A )
& ( cW @ A )
& ( cWRH @ A )
& ( cLIKE @ cJ @ A ) )
| ~ ( cLIKE @ cP @ cS )
| ( cP = cJ ) ),
inference(pattern_uni,[status(thm)],[27:[]]) ).
thf(37,plain,
( ( ( cUNIQUE @ sk1 )
| ~ ( cLIKE @ cP @ cS )
| ( cP = cJ ) )
& ( ( cW @ sk1 )
| ~ ( cLIKE @ cP @ cS )
| ( cP = cJ ) )
& ( ( cWRH @ sk1 )
| ~ ( cLIKE @ cP @ cS )
| ( cP = cJ ) )
& ( ( cLIKE @ cJ @ sk1 )
| ~ ( cLIKE @ cP @ cS )
| ( cP = cJ ) ) ),
inference(cnf,[status(esa)],[34]) ).
thf(38,plain,
( ( cUNIQUE @ sk1 )
| ~ ( cLIKE @ cP @ cS )
| ( cP = cJ ) ),
inference(cnfConj,[status(thm)],[37]) ).
thf(39,plain,
( ( cW @ sk1 )
| ~ ( cLIKE @ cP @ cS )
| ( cP = cJ ) ),
inference(cnfConj,[status(thm)],[37]) ).
thf(355,plain,
( ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) )
| ( cW @ sk1 )
| ~ $true
| ( cP = cJ )
| ( ( cLIKE @ cP @ cS )
!= ( cLIKE @ cP @ cS ) ) ),
inference(paramod_ordered,[status(thm)],[113,39]) ).
thf(356,plain,
( ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) )
| ( cW @ sk1 )
| ( cP = cJ )
| ( ( cLIKE @ cP @ cS )
!= ( cLIKE @ cP @ cS ) ) ),
inference(simp,[status(thm)],[355]) ).
thf(357,plain,
( ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) )
| ( cW @ sk1 )
| ( cP = cJ ) ),
inference(pattern_uni,[status(thm)],[356:[]]) ).
thf(575,plain,
( ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) )
| ~ $true
| ( cP != cJ )
| ( ( cLIKE @ cP @ cS )
!= ( cLIKE @ cJ @ cS ) ) ),
inference(paramod_ordered,[status(thm)],[113,485]) ).
thf(576,plain,
( ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) )
| ( cP != cJ )
| ( ( cLIKE @ cP @ cS )
!= ( cLIKE @ cJ @ cS ) ) ),
inference(simp,[status(thm)],[575]) ).
thf(582,plain,
( ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) )
| ( cP != cJ )
| ( cP != cJ )
| ( cS != cS ) ),
inference(simp,[status(thm)],[576]) ).
thf(584,plain,
( ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) )
| ( cP != cJ ) ),
inference(simp,[status(thm)],[582]) ).
thf(845,plain,
( ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) )
| ( cW @ sk1 )
| ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) )
| ( cJ != cJ )
| ( cP != cP ) ),
inference(paramod_ordered,[status(thm)],[357,584]) ).
thf(846,plain,
( ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) )
| ( cW @ sk1 )
| ( cP != cP ) ),
inference(simp,[status(thm)],[845]) ).
thf(847,plain,
( ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) )
| ( cW @ sk1 ) ),
inference(pattern_uni,[status(thm)],[846:[]]) ).
thf(41,plain,
( ( cLIKE @ cJ @ sk1 )
| ~ ( cLIKE @ cP @ cS )
| ( cP = cJ ) ),
inference(cnfConj,[status(thm)],[37]) ).
thf(142,plain,
( ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) )
| ( cUNIQUE @ sk1 )
| ~ $true
| ( cP = cJ )
| ( ( cLIKE @ cP @ cS )
!= ( cLIKE @ cP @ cS ) ) ),
inference(paramod_ordered,[status(thm)],[113,38]) ).
thf(143,plain,
( ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) )
| ( cUNIQUE @ sk1 )
| ( cP = cJ )
| ( ( cLIKE @ cP @ cS )
!= ( cLIKE @ cP @ cS ) ) ),
inference(simp,[status(thm)],[142]) ).
thf(144,plain,
( ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) )
| ( cUNIQUE @ sk1 )
| ( cP = cJ ) ),
inference(pattern_uni,[status(thm)],[143:[]]) ).
thf(609,plain,
( ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) )
| ( cUNIQUE @ sk1 )
| ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) )
| ( cJ != cJ )
| ( cP != cP ) ),
inference(paramod_ordered,[status(thm)],[144,584]) ).
thf(610,plain,
( ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) )
| ( cUNIQUE @ sk1 )
| ( cP != cP ) ),
inference(simp,[status(thm)],[609]) ).
thf(611,plain,
( ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) )
| ( cUNIQUE @ sk1 ) ),
inference(pattern_uni,[status(thm)],[610:[]]) ).
thf(638,plain,
( ( cUNIQUE @ sk1 )
| ( ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) )
!= ( cUNIQUE @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[611]) ).
thf(640,plain,
( ( cUNIQUE @ sk1 )
| ( ( sk3
@ ^ [A: $i] : $false )
!= sk1 ) ),
inference(simp,[status(thm)],[638]) ).
thf(780,plain,
( ~ ( cUNIQUE @ cP )
| ~ $true
| ~ ( cW @ cJ )
| ~ ( cLIKE @ cJ @ cS )
| ( ( cWRH @ cS )
!= ( cWRH @ cJ ) ) ),
inference(paramod_ordered,[status(thm)],[6,587]) ).
thf(781,plain,
( ~ ( cUNIQUE @ cP )
| ~ ( cW @ cJ )
| ~ ( cLIKE @ cJ @ cS )
| ( ( cWRH @ cS )
!= ( cWRH @ cJ ) ) ),
inference(simp,[status(thm)],[780]) ).
thf(819,plain,
( ~ ( cUNIQUE @ cP )
| ~ ( cW @ cJ )
| ~ ( cLIKE @ cJ @ cS )
| ( cS != cJ ) ),
inference(simp,[status(thm)],[781]) ).
thf(1326,plain,
( ~ ( cUNIQUE @ cP )
| ~ $true
| ~ ( cLIKE @ cJ @ cS )
| ( cS != cJ )
| ( ( cW @ cS )
!= ( cW @ cJ ) ) ),
inference(paramod_ordered,[status(thm)],[9,819]) ).
thf(1327,plain,
( ~ ( cUNIQUE @ cP )
| ~ ( cLIKE @ cJ @ cS )
| ( cS != cJ )
| ( ( cW @ cS )
!= ( cW @ cJ ) ) ),
inference(simp,[status(thm)],[1326]) ).
thf(1381,plain,
( ~ ( cUNIQUE @ cP )
| ~ ( cLIKE @ cJ @ cS )
| ( cS != cJ )
| ( cS != cJ ) ),
inference(simp,[status(thm)],[1327]) ).
thf(1397,plain,
( ~ ( cUNIQUE @ cP )
| ~ ( cLIKE @ cJ @ cS )
| ( cS != cJ ) ),
inference(simp,[status(thm)],[1381]) ).
thf(1398,plain,
( ~ $true
| ~ ( cLIKE @ cJ @ cS )
| ( cS != cJ )
| ( ( cUNIQUE @ cP )
!= ( cUNIQUE @ cS ) ) ),
inference(paramod_ordered,[status(thm)],[5,1397]) ).
thf(1399,plain,
( ~ ( cLIKE @ cJ @ cS )
| ( cS != cJ )
| ( ( cUNIQUE @ cP )
!= ( cUNIQUE @ cS ) ) ),
inference(simp,[status(thm)],[1398]) ).
thf(1453,plain,
( ~ ( cLIKE @ cJ @ cS )
| ( cS != cJ )
| ( cP != cS ) ),
inference(simp,[status(thm)],[1399]) ).
thf(639,plain,
( ( cUNIQUE @ sk1 )
| ( ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) )
!= ( cUNIQUE @ sk1 ) ) ),
inference(simp,[status(thm)],[638]) ).
thf(40,plain,
( ( cWRH @ sk1 )
| ~ ( cLIKE @ cP @ cS )
| ( cP = cJ ) ),
inference(cnfConj,[status(thm)],[37]) ).
thf(998,plain,
( ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) )
| ( cWRH @ sk1 )
| ~ $true
| ( cP = cJ )
| ( ( cLIKE @ cP @ cS )
!= ( cLIKE @ cP @ cS ) ) ),
inference(paramod_ordered,[status(thm)],[113,40]) ).
thf(999,plain,
( ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) )
| ( cWRH @ sk1 )
| ( cP = cJ )
| ( ( cLIKE @ cP @ cS )
!= ( cLIKE @ cP @ cS ) ) ),
inference(simp,[status(thm)],[998]) ).
thf(1000,plain,
( ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) )
| ( cWRH @ sk1 )
| ( cP = cJ ) ),
inference(pattern_uni,[status(thm)],[999:[]]) ).
thf(1125,plain,
( ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) )
| ( cWRH @ sk1 )
| ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) )
| ( cJ != cJ )
| ( cP != cP ) ),
inference(paramod_ordered,[status(thm)],[1000,584]) ).
thf(1126,plain,
( ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) )
| ( cWRH @ sk1 )
| ( cP != cP ) ),
inference(simp,[status(thm)],[1125]) ).
thf(1127,plain,
( ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : $false ) )
| ( cWRH @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1126:[]]) ).
thf(14,plain,
! [A: $i > $o] :
( ( A @ cP )
| ( cLIKE @ cP @ cS )
| ~ ( A @ cJ )
| ~ ? [B: $i] :
( ( cUNIQUE @ B )
& ( cW @ B )
& ( cWRH @ B )
& ( cLIKE @ cJ @ B ) ) ),
inference(bool_ext,[status(thm)],[11]) ).
thf(24,plain,
( ( cJ = cP )
| ( cLIKE @ cP @ cS )
| ( cJ != cJ )
| ~ ? [A: $i] :
( ( cUNIQUE @ A )
& ( cW @ A )
& ( cWRH @ A )
& ( cLIKE @ cJ @ A ) ) ),
inference(replace_leibeq,[status(thm)],[14:[bind(A,$thf( (=) @ $i @ cJ ))]]) ).
thf(26,plain,
( ( cP = cJ )
| ( cJ != cJ )
| ( cLIKE @ cP @ cS )
| ~ ? [A: $i] :
( ( cUNIQUE @ A )
& ( cW @ A )
& ( cWRH @ A )
& ( cLIKE @ cJ @ A ) ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(35,plain,
( ~ ? [A: $i] :
( ( cUNIQUE @ A )
& ( cW @ A )
& ( cWRH @ A )
& ( cLIKE @ cJ @ A ) )
| ( cLIKE @ cP @ cS )
| ( cP = cJ ) ),
inference(pattern_uni,[status(thm)],[26:[]]) ).
thf(42,plain,
! [A: $i] :
( ~ ( cUNIQUE @ A )
| ~ ( cW @ A )
| ~ ( cWRH @ A )
| ~ ( cLIKE @ cJ @ A )
| ( cLIKE @ cP @ cS )
| ( cP = cJ ) ),
inference(cnf,[status(esa)],[35]) ).
thf(475,plain,
( ~ ( cLIKE @ cJ @ cS )
| ( ( cLIKE @ cP @ cS )
!= ( cLIKE @ cJ @ cS ) ) ),
inference(simp,[status(thm)],[474]) ).
thf(74,plain,
! [A: $i > $o] :
( ( A @ cP )
| ( A @ cJ )
| ( cUNIQUE @ ( sk3 @ A ) )
| ( ( cLIKE @ cP @ cS )
!= ( A @ cJ ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[51]) ).
thf(90,plain,
( ( cLIKE @ cP @ cS )
| ( cLIKE @ cP @ cS )
| ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : ( cLIKE @ cP @ cS ) ) ) ),
inference(pre_uni,[status(thm)],[74:[bind(A,$thf( ^ [B: $i] : ( cLIKE @ cP @ cS ) ))]]) ).
thf(117,plain,
( ( cLIKE @ cP @ cS )
| ( cUNIQUE
@ ( sk3
@ ^ [A: $i] : ( cLIKE @ cP @ cS ) ) ) ),
inference(simp,[status(thm)],[90]) ).
thf(570,plain,
! [B: $i,A: $i] :
( ~ ( cUNIQUE @ A )
| ~ ( cWRH @ B )
| ~ ( cW @ B )
| ~ ( cLIKE @ cJ @ cS )
| ( A != cJ )
| ( B != cP ) ),
inference(paramod_ordered,[status(thm)],[12,485]) ).
thf(571,plain,
! [A: $i] :
( ~ ( cUNIQUE @ A )
| ~ ( cWRH @ cP )
| ~ ( cW @ cP )
| ~ ( cLIKE @ cJ @ cS )
| ( A != cJ ) ),
inference(pattern_uni,[status(thm)],[570:[bind(A,$thf( A )),bind(B,$thf( cP ))]]) ).
thf(588,plain,
( ~ ( cUNIQUE @ cJ )
| ~ ( cWRH @ cP )
| ~ ( cW @ cP )
| ~ ( cLIKE @ cJ @ cS ) ),
inference(simp,[status(thm)],[571]) ).
thf(2050,plain,
$false,
inference(e,[status(thm)],[468,5,587,38,847,41,584,3,640,11,1453,58,51,437,639,1127,42,475,485,6,117,9,1397,12,611,113,39,588,40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO224^5 : 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
% 0.11/0.21 % Computer : n007.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 16:38:11 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 0.70/0.51 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.90/0.60 % [INFO] Parsing done (96ms).
% 0.90/0.61 % [INFO] Running in sequential loop mode.
% 1.34/0.80 % [INFO] eprover registered as external prover.
% 1.34/0.80 % [INFO] Scanning for conjecture ...
% 1.34/0.89 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.53/0.93 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.53/0.93 % [INFO] Problem is higher-order (TPTP THF).
% 1.53/0.94 % [INFO] Type checking passed.
% 1.53/0.95 % [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 ...
% 14.39/4.02 % External prover 'e' found a proof!
% 14.39/4.02 % [INFO] Killing All external provers ...
% 14.39/4.02 % Time passed: 3731ms (effective reasoning time: 3410ms)
% 14.39/4.02 % 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)>
% 14.39/4.02 % Axioms used in derivation (0):
% 14.39/4.02 % No. of inferences in proof: 92
% 14.39/4.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3731 ms resp. 3410 ms w/o parsing
% 15.05/4.07 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.05/4.07 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------