%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LAT274-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 : Sun Sep 27 07:48:04 AM UTC 2026
% Result : Unsatisfiable 18.80s 2.87s
% Output : CNFRefutation 18.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 15
% Syntax : Number of clauses : 84 ( 15 unt; 48 nHn; 61 RR)
% Number of literals : 262 ( 18 equ; 96 neg)
% Maximal clause size : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-4 aty)
% Number of variables : 143 ( 23 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0,axiom,
( X0 = 'c$uemptyset'
| 'c$uin'('v$usko$u$u4mk'(X3,X0,'v$ur'),X0,'t$ua')
| 'c$uin'('v$usko$u$u4mj'(X0,X2,'v$ur'),X0,'t$ua')
| 'c$uin'('c$uPair'(X2,X3,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$ulessequals'(X0,X1,'tc$uset'('t$ua')) ) ).
cnf(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_1,axiom,
( X1 = 'c$uemptyset'
| 'c$uin'('v$usko$u$u4mj'(X1,X3,'v$ur'),X1,'t$ua')
| 'c$uin'('c$uPair'(X3,X0,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$ulessequals'(X1,X2,'tc$uset'('t$ua'))
| ~ 'c$uin'('c$uPair'('v$usko$u$u4mk'(X0,X1,'v$ur'),X0,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')) ) ).
cnf(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_2,axiom,
( X1 = 'c$uemptyset'
| 'c$uin'('v$usko$u$u4mk'(X3,X1,'v$ur'),X1,'t$ua')
| 'c$uin'('c$uPair'(X0,X3,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$ulessequals'(X1,X2,'tc$uset'('t$ua'))
| ~ 'c$uin'('c$uPair'(X0,'v$usko$u$u4mj'(X1,X0,'v$ur'),'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')) ) ).
cnf(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_3,axiom,
( X1 = 'c$uemptyset'
| 'c$uin'('c$uPair'(X0,X2,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$ulessequals'(X1,X3,'tc$uset'('t$ua'))
| ~ 'c$uin'('c$uPair'('v$usko$u$u4mk'(X2,X1,'v$ur'),X2,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'('c$uPair'(X0,'v$usko$u$u4mj'(X1,X0,'v$ur'),'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')) ) ).
cnf(cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ia1_M_Ax1_J_A_58_Ar_A_61_61_ATrue_0,axiom,
( 'c$uin'('c$uPair'(X4,X0,X2,X2),X3,'tc$uprod'(X2,X2))
| ~ 'c$ulessequals'(X1,'c$uTarski$uOinterval'(X3,X4,X5,X2),'tc$uset'(X2))
| ~ 'c$uin'(X0,X1,X2) ) ).
cnf(cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Ab1_J_A_58_Ar_A_61_61_ATrue_0,axiom,
( 'c$uin'('c$uPair'(X0,X5,X2,X2),X3,'tc$uprod'(X2,X2))
| ~ 'c$ulessequals'(X1,'c$uTarski$uOinterval'(X3,X4,X5,X2),'tc$uset'(X2))
| ~ 'c$uin'(X0,X1,X2) ) ).
cnf(cls_Tarski_O_91_124_A_Ia1_M_Ax1_J_A_58_Ar_59_A_Ix1_M_Ab1_J_A_58_Ar_A_124_93_A_61_61_62_Ax1_A_58_Ainterval_Ar_Aa1_Ab1_A_61_61_ATrue_0,axiom,
( 'c$uin'(X0,'c$uTarski$uOinterval'(X3,X4,X1,X2),X2)
| ~ 'c$uin'('c$uPair'(X4,X0,X2,X2),X3,'tc$uprod'(X2,X2))
| ~ 'c$uin'('c$uPair'(X0,X1,X2,X2),X3,'tc$uprod'(X2,X2)) ) ).
cnf(cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Ay1_A_58_AS1_A_124_93_A_61_61_62_A_Iy1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0,axiom,
( 'c$uin'('c$uPair'(X2,X1,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'(X2,X0,'t$ua')
| ~ 'c$uTarski$uOisLub'(X0,'v$ucl',X1,'t$ua') ) ).
cnf(cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_0,axiom,
( 'c$uin'('v$usko$u$u4mi'(X0,'v$ur',X2),X0,'t$ua')
| 'c$uin'('c$uPair'(X1,X2,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'(X2,'v$uA','t$ua')
| ~ 'c$uTarski$uOisLub'(X0,'v$ucl',X1,'t$ua') ) ).
cnf(cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_1,axiom,
( 'c$uin'('c$uPair'(X1,X2,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'('c$uPair'('v$usko$u$u4mi'(X0,'v$ur',X2),X2,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'(X2,'v$uA','t$ua')
| ~ 'c$uTarski$uOisLub'(X0,'v$ucl',X1,'t$ua') ) ).
cnf(cls_conjecture_1,negated_conjecture,
'c$uin'('v$ub','v$uA','t$ua') ).
cnf(cls_conjecture_2,negated_conjecture,
'c$ulessequals'('v$uS','c$uTarski$uOinterval'('v$ur','v$ua','v$ub','t$ua'),'tc$uset'('t$ua')) ).
cnf(cls_conjecture_3,negated_conjecture,
'v$uS' != 'c$uemptyset' ).
cnf(cls_conjecture_4,negated_conjecture,
'c$uTarski$uOisLub'('v$uS','v$ucl','v$uL','t$ua') ).
cnf(cls_conjecture_6,negated_conjecture,
~ 'c$uin'('v$uL','c$uTarski$uOinterval'('v$ur','v$ua','v$ub','t$ua'),'t$ua') ).
cnf(c0,plain,
( 'c$uin'('v$usko$u$u4mj'(X1,X2,'v$ur'),X1,'t$ua')
| ~ 'c$ulessequals'(X1,X3,'tc$uset'('t$ua'))
| 'c$uin'('c$uPair'(X2,X0,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| X1 = 'c$uemptyset'
| 'c$uin'('v$usko$u$u4mk'(X0,X1,'v$ur'),X1,'t$ua') ),
inference(clausification,[status(esa)],[cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0]) ).
cnf(c1,plain,
( ~ 'c$uin'('c$uPair'('v$usko$u$u4mk'(X3,X0,'v$ur'),X3,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| 'c$uin'('c$uPair'(X2,X3,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| X0 = 'c$uemptyset'
| 'c$uin'('v$usko$u$u4mj'(X0,X2,'v$ur'),X0,'t$ua')
| ~ 'c$ulessequals'(X0,X1,'tc$uset'('t$ua')) ),
inference(clausification,[status(esa)],[cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_1]) ).
cnf(c2,plain,
( X0 = 'c$uemptyset'
| 'c$uin'('v$usko$u$u4mk'(X3,X0,'v$ur'),X0,'t$ua')
| ~ 'c$uin'('c$uPair'(X2,'v$usko$u$u4mj'(X0,X2,'v$ur'),'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| 'c$uin'('c$uPair'(X2,X3,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$ulessequals'(X0,X1,'tc$uset'('t$ua')) ),
inference(clausification,[status(esa)],[cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_2]) ).
cnf(c3,plain,
( ~ 'c$uin'('c$uPair'('v$usko$u$u4mk'(X3,X0,'v$ur'),X3,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| 'c$uin'('c$uPair'(X2,X3,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'('c$uPair'(X2,'v$usko$u$u4mj'(X0,X2,'v$ur'),'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$ulessequals'(X0,X1,'tc$uset'('t$ua'))
| X0 = 'c$uemptyset' ),
inference(clausification,[status(esa)],[cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_3]) ).
cnf(c4,plain,
( 'c$uin'('c$uPair'(X4,X0,X2,X2),X3,'tc$uprod'(X2,X2))
| ~ 'c$ulessequals'(X1,'c$uTarski$uOinterval'(X3,X4,X5,X2),'tc$uset'(X2))
| ~ 'c$uin'(X0,X1,X2) ),
inference(clausification,[status(esa)],[cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ia1_M_Ax1_J_A_58_Ar_A_61_61_ATrue_0]) ).
cnf(c5,plain,
( 'c$uin'('c$uPair'(X0,X5,X2,X2),X3,'tc$uprod'(X2,X2))
| ~ 'c$ulessequals'(X1,'c$uTarski$uOinterval'(X3,X4,X5,X2),'tc$uset'(X2))
| ~ 'c$uin'(X0,X1,X2) ),
inference(clausification,[status(esa)],[cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Ab1_J_A_58_Ar_A_61_61_ATrue_0]) ).
cnf(c6,plain,
( 'c$uin'(X0,'c$uTarski$uOinterval'(X3,X4,X1,X2),X2)
| ~ 'c$uin'('c$uPair'(X4,X0,X2,X2),X3,'tc$uprod'(X2,X2))
| ~ 'c$uin'('c$uPair'(X0,X1,X2,X2),X3,'tc$uprod'(X2,X2)) ),
inference(clausification,[status(esa)],[cls_Tarski_O_91_124_A_Ia1_M_Ax1_J_A_58_Ar_59_A_Ix1_M_Ab1_J_A_58_Ar_A_124_93_A_61_61_62_Ax1_A_58_Ainterval_Ar_Aa1_Ab1_A_61_61_ATrue_0]) ).
cnf(c7,plain,
( 'c$uin'('c$uPair'(X2,X1,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'(X2,X0,'t$ua')
| ~ 'c$uTarski$uOisLub'(X0,'v$ucl',X1,'t$ua') ),
inference(clausification,[status(esa)],[cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Ay1_A_58_AS1_A_124_93_A_61_61_62_A_Iy1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0]) ).
cnf(c8,plain,
( 'c$uin'('v$usko$u$u4mi'(X0,'v$ur',X2),X0,'t$ua')
| 'c$uin'('c$uPair'(X1,X2,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'(X2,'v$uA','t$ua')
| ~ 'c$uTarski$uOisLub'(X0,'v$ucl',X1,'t$ua') ),
inference(clausification,[status(esa)],[cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_0]) ).
cnf(c9,plain,
( 'c$uin'('c$uPair'(X1,X2,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'('c$uPair'('v$usko$u$u4mi'(X0,'v$ur',X2),X2,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'(X2,'v$uA','t$ua')
| ~ 'c$uTarski$uOisLub'(X0,'v$ucl',X1,'t$ua') ),
inference(clausification,[status(esa)],[cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_1]) ).
cnf(c10,plain,
'c$uin'('v$ub','v$uA','t$ua'),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c11,plain,
'c$ulessequals'('v$uS','c$uTarski$uOinterval'('v$ur','v$ua','v$ub','t$ua'),'tc$uset'('t$ua')),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c12,plain,
'v$uS' != 'c$uemptyset',
inference(clausification,[status(esa)],[cls_conjecture_3]) ).
cnf(c13,plain,
'c$uTarski$uOisLub'('v$uS','v$ucl','v$uL','t$ua'),
inference(clausification,[status(esa)],[cls_conjecture_4]) ).
cnf(c14,plain,
~ 'c$uin'('v$uL','c$uTarski$uOinterval'('v$ur','v$ua','v$ub','t$ua'),'t$ua'),
inference(clausification,[status(esa)],[cls_conjecture_6]) ).
cnf(d0,plain,
( 'c$uin'('c$uPair'('v$ua',X0,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'(X0,'v$uS','t$ua') ),
inference(resolution,[status(thm)],[c4,c11]) ).
cnf(d1,plain,
( 'c$uin'('c$uPair'(X0,'v$uL','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'(X0,'v$uS','t$ua') ),
inference(resolution,[status(thm)],[c7,c13]) ).
cnf(d2,plain,
( ~ 'c$uin'('c$uPair'(X2,'v$usko$u$u4mj'(X0,X2,'v$ur'),'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| 'c$uin'('c$uPair'(X2,'v$uL','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$ulessequals'(X0,X1,'tc$uset'('t$ua'))
| X0 = 'c$uemptyset'
| ~ 'c$uin'('v$usko$u$u4mk'('v$uL',X0,'v$ur'),'v$uS','t$ua') ),
inference(resolution,[status(thm)],[d1,c3]) ).
cnf(d3,plain,
( ~ 'c$uin'('v$usko$u$u4mj'(X0,'v$ua','v$ur'),'v$uS','t$ua')
| ~ 'c$uin'('v$usko$u$u4mk'('v$uL',X0,'v$ur'),'v$uS','t$ua')
| 'c$uin'('c$uPair'('v$ua','v$uL','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$ulessequals'(X0,X1,'tc$uset'('t$ua'))
| X0 = 'c$uemptyset' ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( 'c$uin'('v$usko$u$u4mk'(X2,X0,'v$ur'),X0,'t$ua')
| 'c$uin'('c$uPair'('v$ua',X2,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$ulessequals'(X0,X1,'tc$uset'('t$ua'))
| X0 = 'c$uemptyset'
| ~ 'c$uin'('v$usko$u$u4mj'(X0,'v$ua','v$ur'),'v$uS','t$ua') ),
inference(resolution,[status(thm)],[d0,c2]) ).
cnf(d5,plain,
( 'c$uin'('c$uPair'(X2,'v$uL','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| 'c$uin'('v$usko$u$u4mj'(X0,X2,'v$ur'),X0,'t$ua')
| ~ 'c$ulessequals'(X0,X1,'tc$uset'('t$ua'))
| X0 = 'c$uemptyset'
| ~ 'c$uin'('v$usko$u$u4mk'('v$uL',X0,'v$ur'),'v$uS','t$ua') ),
inference(resolution,[status(thm)],[d1,c1]) ).
cnf(d6,plain,
( 'c$uin'('v$usko$u$u4mk'(X1,'v$uS','v$ur'),'v$uS','t$ua')
| 'c$uin'('c$uPair'(X0,X1,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| 'c$uin'('v$usko$u$u4mj'('v$uS',X0,'v$ur'),'v$uS','t$ua')
| 'v$uS' = 'c$uemptyset' ),
inference(resolution,[status(thm)],[c11,c0]) ).
cnf(d7,plain,
( 'c$uin'('v$usko$u$u4mk'(X1,'v$uS','v$ur'),'v$uS','t$ua')
| 'c$uin'('c$uPair'(X0,X1,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| 'c$uin'('v$usko$u$u4mj'('v$uS',X0,'v$ur'),'v$uS','t$ua') ),
inference(resolution,[status(thm)],[c12,d6]) ).
cnf(d8,plain,
( ~ 'c$uin'('c$uPair'(X1,X2,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| 'c$uin'(X1,'c$uTarski$uOinterval'('v$ur',X0,X2,'t$ua'),'t$ua')
| 'c$uin'('v$usko$u$u4mk'(X1,'v$uS','v$ur'),'v$uS','t$ua')
| 'c$uin'('v$usko$u$u4mj'('v$uS',X0,'v$ur'),'v$uS','t$ua') ),
inference(resolution,[status(thm)],[d7,c6]) ).
cnf(d9,plain,
( 'c$uin'('c$uPair'(X0,'v$ub','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'(X0,'v$uS','t$ua') ),
inference(resolution,[status(thm)],[c5,c11]) ).
cnf(d10,plain,
( ~ 'c$uin'('v$usko$u$u4mi'(X1,'v$ur','v$ub'),'v$uS','t$ua')
| ~ 'c$uTarski$uOisLub'(X1,'v$ucl',X0,'t$ua')
| 'c$uin'('c$uPair'(X0,'v$ub','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'('v$ub','v$uA','t$ua') ),
inference(resolution,[status(thm)],[c9,d9]) ).
cnf(d11,plain,
( ~ 'c$uTarski$uOisLub'(X1,'v$ucl',X0,'t$ua')
| ~ 'c$uin'('v$usko$u$u4mi'(X1,'v$ur','v$ub'),'v$uS','t$ua')
| 'c$uin'('c$uPair'(X0,'v$ub','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')) ),
inference(resolution,[status(thm)],[c10,d10]) ).
cnf(d12,plain,
( 'c$uin'('v$usko$u$u4mi'('v$uS','v$ur',X0),'v$uS','t$ua')
| 'c$uin'('c$uPair'('v$uL',X0,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'(X0,'v$uA','t$ua') ),
inference(resolution,[status(thm)],[c8,c13]) ).
cnf(d13,plain,
( 'c$uin'('v$usko$u$u4mi'('v$uS','v$ur',X1),'v$uS','t$ua')
| ~ 'c$uin'(X1,'v$uA','t$ua')
| 'c$uin'('v$usko$u$u4mk'('v$uL','v$uS','v$ur'),'v$uS','t$ua')
| 'c$uin'('v$usko$u$u4mj'('v$uS',X0,'v$ur'),'v$uS','t$ua')
| 'c$uin'('v$uL','c$uTarski$uOinterval'('v$ur',X0,X1,'t$ua'),'t$ua') ),
inference(resolution,[status(thm)],[d8,d12]) ).
cnf(d14,plain,
( 'c$uin'('v$usko$u$u4mi'('v$uS','v$ur','v$ub'),'v$uS','t$ua')
| 'c$uin'('v$usko$u$u4mk'('v$uL','v$uS','v$ur'),'v$uS','t$ua')
| 'c$uin'('v$usko$u$u4mj'('v$uS','v$ua','v$ur'),'v$uS','t$ua')
| ~ 'c$uin'('v$ub','v$uA','t$ua') ),
inference(resolution,[status(thm)],[d13,c14]) ).
cnf(d15,plain,
( 'c$uin'('v$usko$u$u4mi'('v$uS','v$ur','v$ub'),'v$uS','t$ua')
| 'c$uin'('v$usko$u$u4mk'('v$uL','v$uS','v$ur'),'v$uS','t$ua')
| 'c$uin'('v$usko$u$u4mj'('v$uS','v$ua','v$ur'),'v$uS','t$ua') ),
inference(resolution,[status(thm)],[c10,d14]) ).
cnf(d16,plain,
( ~ 'c$uTarski$uOisLub'('v$uS','v$ucl',X0,'t$ua')
| 'c$uin'('c$uPair'(X0,'v$ub','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| 'c$uin'('v$usko$u$u4mk'('v$uL','v$uS','v$ur'),'v$uS','t$ua')
| 'c$uin'('v$usko$u$u4mj'('v$uS','v$ua','v$ur'),'v$uS','t$ua') ),
inference(resolution,[status(thm)],[d15,d11]) ).
cnf(d17,plain,
( 'c$uin'('v$usko$u$u4mk'(X0,'v$uS','v$ur'),'v$uS','t$ua')
| 'c$uin'('v$usko$u$u4mj'('v$uS',X1,'v$ur'),'v$uS','t$ua')
| 'c$uin'(X0,'c$uTarski$uOinterval'('v$ur',X1,'v$ub','t$ua'),'t$ua')
| ~ 'c$uTarski$uOisLub'('v$uS','v$ucl',X0,'t$ua')
| 'c$uin'('v$usko$u$u4mk'('v$uL','v$uS','v$ur'),'v$uS','t$ua')
| 'c$uin'('v$usko$u$u4mj'('v$uS','v$ua','v$ur'),'v$uS','t$ua') ),
inference(resolution,[status(thm)],[d16,d8]) ).
cnf(d18,plain,
( ~ 'c$uTarski$uOisLub'('v$uS','v$ucl','v$uL','t$ua')
| 'c$uin'('v$usko$u$u4mk'('v$uL','v$uS','v$ur'),'v$uS','t$ua')
| 'c$uin'('v$usko$u$u4mk'('v$uL','v$uS','v$ur'),'v$uS','t$ua')
| 'c$uin'('v$usko$u$u4mj'('v$uS','v$ua','v$ur'),'v$uS','t$ua')
| 'c$uin'('v$usko$u$u4mj'('v$uS','v$ua','v$ur'),'v$uS','t$ua') ),
inference(resolution,[status(thm)],[d17,c14]) ).
cnf(d19,plain,
( 'c$uin'('v$usko$u$u4mk'('v$uL','v$uS','v$ur'),'v$uS','t$ua')
| 'c$uin'('v$usko$u$u4mj'('v$uS','v$ua','v$ur'),'v$uS','t$ua') ),
inference(resolution,[status(thm)],[c13,d18]) ).
cnf(d20,plain,
( 'c$uin'('c$uPair'(X1,'v$uL','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| 'c$uin'('v$usko$u$u4mj'('v$uS',X1,'v$ur'),'v$uS','t$ua')
| ~ 'c$ulessequals'('v$uS',X0,'tc$uset'('t$ua'))
| 'v$uS' = 'c$uemptyset'
| 'c$uin'('v$usko$u$u4mj'('v$uS','v$ua','v$ur'),'v$uS','t$ua') ),
inference(resolution,[status(thm)],[d19,d5]) ).
cnf(d21,plain,
( 'c$uin'('c$uPair'(X1,'v$uL','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| 'c$uin'('v$usko$u$u4mj'('v$uS','v$ua','v$ur'),'v$uS','t$ua')
| 'c$uin'('v$usko$u$u4mj'('v$uS',X1,'v$ur'),'v$uS','t$ua')
| ~ 'c$ulessequals'('v$uS',X0,'tc$uset'('t$ua')) ),
inference(resolution,[status(thm)],[c12,d20]) ).
cnf(d22,plain,
( 'c$uin'('c$uPair'(X0,'v$uL','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| 'c$uin'('v$usko$u$u4mj'('v$uS','v$ua','v$ur'),'v$uS','t$ua')
| 'c$uin'('v$usko$u$u4mj'('v$uS',X0,'v$ur'),'v$uS','t$ua') ),
inference(resolution,[status(thm)],[d21,c11]) ).
cnf(d23,plain,
( ~ 'c$uin'('c$uPair'('v$uL',X1,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| 'c$uin'('v$uL','c$uTarski$uOinterval'('v$ur',X0,X1,'t$ua'),'t$ua')
| 'c$uin'('v$usko$u$u4mj'('v$uS','v$ua','v$ur'),'v$uS','t$ua')
| 'c$uin'('v$usko$u$u4mj'('v$uS',X0,'v$ur'),'v$uS','t$ua') ),
inference(resolution,[status(thm)],[d22,c6]) ).
cnf(d24,plain,
( 'c$uin'('v$usko$u$u4mi'('v$uS','v$ur',X1),'v$uS','t$ua')
| ~ 'c$uin'(X1,'v$uA','t$ua')
| 'c$uin'('v$uL','c$uTarski$uOinterval'('v$ur',X0,X1,'t$ua'),'t$ua')
| 'c$uin'('v$usko$u$u4mj'('v$uS','v$ua','v$ur'),'v$uS','t$ua')
| 'c$uin'('v$usko$u$u4mj'('v$uS',X0,'v$ur'),'v$uS','t$ua') ),
inference(resolution,[status(thm)],[d23,d12]) ).
cnf(d25,plain,
( 'c$uin'('v$usko$u$u4mi'('v$uS','v$ur','v$ub'),'v$uS','t$ua')
| 'c$uin'('v$usko$u$u4mj'('v$uS','v$ua','v$ur'),'v$uS','t$ua')
| 'c$uin'('v$usko$u$u4mj'('v$uS','v$ua','v$ur'),'v$uS','t$ua')
| ~ 'c$uin'('v$ub','v$uA','t$ua') ),
inference(resolution,[status(thm)],[d24,c14]) ).
cnf(d26,plain,
( 'c$uin'('v$usko$u$u4mi'('v$uS','v$ur','v$ub'),'v$uS','t$ua')
| 'c$uin'('v$usko$u$u4mj'('v$uS','v$ua','v$ur'),'v$uS','t$ua') ),
inference(resolution,[status(thm)],[c10,d25]) ).
cnf(d27,plain,
( ~ 'c$uTarski$uOisLub'('v$uS','v$ucl',X0,'t$ua')
| 'c$uin'('c$uPair'(X0,'v$ub','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| 'c$uin'('v$usko$u$u4mj'('v$uS','v$ua','v$ur'),'v$uS','t$ua') ),
inference(resolution,[status(thm)],[d26,d11]) ).
cnf(d28,plain,
( 'c$uin'('v$uL','c$uTarski$uOinterval'('v$ur',X0,'v$ub','t$ua'),'t$ua')
| 'c$uin'('v$usko$u$u4mj'('v$uS','v$ua','v$ur'),'v$uS','t$ua')
| 'c$uin'('v$usko$u$u4mj'('v$uS',X0,'v$ur'),'v$uS','t$ua')
| ~ 'c$uTarski$uOisLub'('v$uS','v$ucl','v$uL','t$ua')
| 'c$uin'('v$usko$u$u4mj'('v$uS','v$ua','v$ur'),'v$uS','t$ua') ),
inference(resolution,[status(thm)],[d27,d23]) ).
cnf(d29,plain,
( 'c$uin'('v$uL','c$uTarski$uOinterval'('v$ur',X0,'v$ub','t$ua'),'t$ua')
| 'c$uin'('v$usko$u$u4mj'('v$uS','v$ua','v$ur'),'v$uS','t$ua')
| 'c$uin'('v$usko$u$u4mj'('v$uS',X0,'v$ur'),'v$uS','t$ua') ),
inference(resolution,[status(thm)],[c13,d28]) ).
cnf(d30,plain,
( 'c$uin'('v$usko$u$u4mj'('v$uS','v$ua','v$ur'),'v$uS','t$ua')
| 'c$uin'('v$usko$u$u4mj'('v$uS','v$ua','v$ur'),'v$uS','t$ua') ),
inference(resolution,[status(thm)],[d29,c14]) ).
cnf(d31,plain,
( 'c$uin'('v$usko$u$u4mk'(X1,'v$uS','v$ur'),'v$uS','t$ua')
| 'c$uin'('c$uPair'('v$ua',X1,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$ulessequals'('v$uS',X0,'tc$uset'('t$ua'))
| 'v$uS' = 'c$uemptyset' ),
inference(resolution,[status(thm)],[d30,d4]) ).
cnf(d32,plain,
( 'c$uin'('v$usko$u$u4mk'(X1,'v$uS','v$ur'),'v$uS','t$ua')
| 'c$uin'('c$uPair'('v$ua',X1,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$ulessequals'('v$uS',X0,'tc$uset'('t$ua')) ),
inference(resolution,[status(thm)],[c12,d31]) ).
cnf(d33,plain,
( 'c$uin'('v$usko$u$u4mk'(X0,'v$uS','v$ur'),'v$uS','t$ua')
| 'c$uin'('c$uPair'('v$ua',X0,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')) ),
inference(resolution,[status(thm)],[d32,c11]) ).
cnf(d34,plain,
( ~ 'c$uin'('c$uPair'(X0,X1,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| 'c$uin'(X0,'c$uTarski$uOinterval'('v$ur','v$ua',X1,'t$ua'),'t$ua')
| 'c$uin'('v$usko$u$u4mk'(X0,'v$uS','v$ur'),'v$uS','t$ua') ),
inference(resolution,[status(thm)],[d33,c6]) ).
cnf(d35,plain,
( 'c$uin'('v$usko$u$u4mi'('v$uS','v$ur',X0),'v$uS','t$ua')
| ~ 'c$uin'(X0,'v$uA','t$ua')
| 'c$uin'('v$usko$u$u4mk'('v$uL','v$uS','v$ur'),'v$uS','t$ua')
| 'c$uin'('v$uL','c$uTarski$uOinterval'('v$ur','v$ua',X0,'t$ua'),'t$ua') ),
inference(resolution,[status(thm)],[d34,d12]) ).
cnf(d36,plain,
( 'c$uin'('v$usko$u$u4mi'('v$uS','v$ur','v$ub'),'v$uS','t$ua')
| 'c$uin'('v$usko$u$u4mk'('v$uL','v$uS','v$ur'),'v$uS','t$ua')
| ~ 'c$uin'('v$ub','v$uA','t$ua') ),
inference(resolution,[status(thm)],[d35,c14]) ).
cnf(d37,plain,
( 'c$uin'('v$usko$u$u4mi'('v$uS','v$ur','v$ub'),'v$uS','t$ua')
| 'c$uin'('v$usko$u$u4mk'('v$uL','v$uS','v$ur'),'v$uS','t$ua') ),
inference(resolution,[status(thm)],[c10,d36]) ).
cnf(d38,plain,
( ~ 'c$uTarski$uOisLub'('v$uS','v$ucl',X0,'t$ua')
| 'c$uin'('c$uPair'(X0,'v$ub','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| 'c$uin'('v$usko$u$u4mk'('v$uL','v$uS','v$ur'),'v$uS','t$ua') ),
inference(resolution,[status(thm)],[d37,d11]) ).
cnf(d39,plain,
( 'c$uin'('v$usko$u$u4mk'(X0,'v$uS','v$ur'),'v$uS','t$ua')
| 'c$uin'(X0,'c$uTarski$uOinterval'('v$ur','v$ua','v$ub','t$ua'),'t$ua')
| ~ 'c$uTarski$uOisLub'('v$uS','v$ucl',X0,'t$ua')
| 'c$uin'('v$usko$u$u4mk'('v$uL','v$uS','v$ur'),'v$uS','t$ua') ),
inference(resolution,[status(thm)],[d38,d34]) ).
cnf(d40,plain,
( ~ 'c$uTarski$uOisLub'('v$uS','v$ucl','v$uL','t$ua')
| 'c$uin'('v$usko$u$u4mk'('v$uL','v$uS','v$ur'),'v$uS','t$ua')
| 'c$uin'('v$usko$u$u4mk'('v$uL','v$uS','v$ur'),'v$uS','t$ua') ),
inference(resolution,[status(thm)],[d39,c14]) ).
cnf(d41,plain,
'c$uin'('v$usko$u$u4mk'('v$uL','v$uS','v$ur'),'v$uS','t$ua'),
inference(resolution,[status(thm)],[c13,d40]) ).
cnf(d42,plain,
( 'c$uin'('c$uPair'('v$ua','v$uL','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'('v$usko$u$u4mj'('v$uS','v$ua','v$ur'),'v$uS','t$ua')
| ~ 'c$ulessequals'('v$uS',X0,'tc$uset'('t$ua'))
| 'v$uS' = 'c$uemptyset' ),
inference(resolution,[status(thm)],[d41,d3]) ).
cnf(d43,plain,
( 'c$uin'('c$uPair'('v$ua','v$uL','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'('v$usko$u$u4mj'('v$uS','v$ua','v$ur'),'v$uS','t$ua')
| ~ 'c$ulessequals'('v$uS',X0,'tc$uset'('t$ua')) ),
inference(resolution,[status(thm)],[c12,d42]) ).
cnf(d44,plain,
( 'c$uin'('c$uPair'('v$ua','v$uL','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$ulessequals'('v$uS',X0,'tc$uset'('t$ua')) ),
inference(resolution,[status(thm)],[d30,d43]) ).
cnf(d45,plain,
'c$uin'('c$uPair'('v$ua','v$uL','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')),
inference(resolution,[status(thm)],[d44,c11]) ).
cnf(d46,plain,
( ~ 'c$uin'('c$uPair'('v$uL',X0,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| 'c$uin'('v$uL','c$uTarski$uOinterval'('v$ur','v$ua',X0,'t$ua'),'t$ua') ),
inference(resolution,[status(thm)],[d45,c6]) ).
cnf(d47,plain,
( 'c$uin'('v$usko$u$u4mi'('v$uS','v$ur',X0),'v$uS','t$ua')
| ~ 'c$uin'(X0,'v$uA','t$ua')
| 'c$uin'('v$uL','c$uTarski$uOinterval'('v$ur','v$ua',X0,'t$ua'),'t$ua') ),
inference(resolution,[status(thm)],[d46,d12]) ).
cnf(d48,plain,
( 'c$uin'('v$usko$u$u4mi'('v$uS','v$ur','v$ub'),'v$uS','t$ua')
| ~ 'c$uin'('v$ub','v$uA','t$ua') ),
inference(resolution,[status(thm)],[d47,c14]) ).
cnf(d49,plain,
'c$uin'('v$usko$u$u4mi'('v$uS','v$ur','v$ub'),'v$uS','t$ua'),
inference(resolution,[status(thm)],[c10,d48]) ).
cnf(d50,plain,
( ~ 'c$uTarski$uOisLub'('v$uS','v$ucl',X0,'t$ua')
| 'c$uin'('c$uPair'(X0,'v$ub','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')) ),
inference(resolution,[status(thm)],[d49,d11]) ).
cnf(d51,plain,
( 'c$uin'('v$uL','c$uTarski$uOinterval'('v$ur','v$ua','v$ub','t$ua'),'t$ua')
| ~ 'c$uTarski$uOisLub'('v$uS','v$ucl','v$uL','t$ua') ),
inference(resolution,[status(thm)],[d50,d46]) ).
cnf(d52,plain,
'c$uin'('v$uL','c$uTarski$uOinterval'('v$ur','v$ua','v$ub','t$ua'),'t$ua'),
inference(resolution,[status(thm)],[c13,d51]) ).
cnf(d53,plain,
$false,
inference(resolution,[status(thm)],[c14,d52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT274-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 20:20:54 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.80/2.87 % SZS status Unsatisfiable for theBenchmark.p
% 18.80/2.87 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------