%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LAT273-2 : 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 : n004.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 9.61s 11.65s
% Output : CNFRefutation 9.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 23 ( 11 unt; 3 nHn; 23 RR)
% Number of literals : 49 ( 0 equ; 26 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-4 aty)
% Number of variables : 31 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
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_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_4,negated_conjecture,
'c$uTarski$uOisLub'('v$uS','v$ucl','v$uL','t$ua') ).
cnf(cls_conjecture_6,negated_conjecture,
~ 'c$uin'('c$uPair'('v$uL','v$ub','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')) ).
cnf(c0,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(c1,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$ua') ),
inference(clausification,[status(esa)],[cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_0]) ).
cnf(c2,plain,
( 'c$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(c3,plain,
'c$uin'('v$ub','v$uA','t$ua'),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c4,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(c5,plain,
'c$uTarski$uOisLub'('v$uS','v$ucl','v$uL','t$ua'),
inference(clausification,[status(esa)],[cls_conjecture_4]) ).
cnf(c6,plain,
~ 'c$uin'('c$uPair'('v$uL','v$ub','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')),
inference(clausification,[status(esa)],[cls_conjecture_6]) ).
cnf(d0,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)],[c1,c5]) ).
cnf(d1,plain,
( 'c$uin'('v$usko$u$u4mi'('v$uS','v$ur','v$ub'),'v$uS','t$ua')
| ~ 'c$uin'('v$ub','v$uA','t$ua') ),
inference(resolution,[status(thm)],[d0,c6]) ).
cnf(d2,plain,
'c$uin'('v$usko$u$u4mi'('v$uS','v$ur','v$ub'),'v$uS','t$ua'),
inference(resolution,[status(thm)],[c3,d1]) ).
cnf(d3,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)],[c4,c0]) ).
cnf(d4,plain,
( ~ 'c$uTarski$uOisLub'(X0,'v$ucl',X1,'t$ua')
| 'c$uin'('c$uPair'(X1,'v$ub','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'('v$ub','v$uA','t$ua')
| ~ 'c$uin'('v$usko$u$u4mi'(X0,'v$ur','v$ub'),'v$uS','t$ua') ),
inference(resolution,[status(thm)],[d3,c2]) ).
cnf(d5,plain,
( ~ 'c$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)],[c3,d4]) ).
cnf(d6,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)],[d5,d2]) ).
cnf(d7,plain,
~ 'c$uTarski$uOisLub'('v$uS','v$ucl','v$uL','t$ua'),
inference(resolution,[status(thm)],[d6,c6]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[c5,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT273-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/10.37 % Computer : n004.cluster.edu
% 0.08/10.37 % Model : x86_64 x86_64
% 0.08/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.37 % Memory : 8046.5625MB
% 0.08/10.37 % OS : Linux 6.8.0-71-generic
% 0.08/10.37 % CPULimit : 300
% 0.08/10.37 % WCLimit : 300
% 0.08/10.37 % DateTime : Fri Sep 25 20:23:04 UTC 2026
% 0.08/10.37 % CPUTime :
% 0.08/10.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.61/11.65 % SZS status Unsatisfiable for theBenchmark.p
% 9.61/11.65 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------