%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LAT269-1 : 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 : n012.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 07:48:02 AM UTC 2026
% Result : Unsatisfiable 38.58s 16.85s
% Output : CNFRefutation 38.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of clauses : 27 ( 16 unt; 7 nHn; 23 RR)
% Number of literals : 49 ( 20 equ; 22 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-5 aty)
% Number of variables : 12 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Tarski_OTop_Acl_A_58_AA_A_61_61_ATrue_0,axiom,
'c$uin'('c$uTarski$uOTop'('v$ucl','t$ua'),'v$uA','t$ua') ).
cnf(cls_Tarski_O_91_124_Aa2_A_58_AA_59_Ab2_A_58_AA_59_Ainterval_Ar_Aa2_Ab2_A_126_61_A_123_125_A_124_93_A_61_61_62_A_I_124_Apset_A_61_Ainterval_Ar_Aa2_Ab2_M_Aorder_A_61_Ainduced_A_Iinterval_Ar_Aa2_Ab2_J_Ar_A_124_J_A_58_ACompleteLattice_A_61_61_ATrue_0,axiom,
( 'c$uTarski$uOinterval'('v$ur',X1,X0,'t$ua') = 'c$uemptyset'
| 'c$uin'('c$uTarski$uOpotype$uOpotype$u$uext'('c$uTarski$uOinterval'('v$ur',X1,X0,'t$ua'),'c$uTarski$uOinduced'('c$uTarski$uOinterval'('v$ur',X1,X0,'t$ua'),'v$ur','t$ua'),'c$uProduct$u$uType$uOUnity','t$ua','tc$uProduct$u$uType$uOunit'),'c$uTarski$uOCompleteLattice','tc$uTarski$uOpotype$uOpotype$u$uext$u$utype'('t$ua','tc$uProduct$u$uType$uOunit'))
| ~ 'c$uin'(X1,'v$uA','t$ua')
| ~ 'c$uin'(X0,'v$uA','t$ua') ) ).
cnf(cls_Tarski_OintY1_A_61_61_Ainterval_Ar_A_Ilub_AY_Acl_J_A_ITop_Acl_J_0,axiom,
'v$uintY1' = 'c$uTarski$uOinterval'('v$ur','c$uTarski$uOlub'('v$uY','v$ucl','t$ua'),'c$uTarski$uOTop'('v$ucl','t$ua'),'t$ua') ).
cnf(cls_Tarski_Olub_AY_Acl_A_58_AA_A_61_61_ATrue_0,axiom,
'c$uin'('c$uTarski$uOlub'('v$uY','v$ucl','t$ua'),'v$uA','t$ua') ).
cnf(cls_Tarski_Ox1_A_58_AA_A_61_61_62_Ainterval_Ar_Ax1_A_ITop_Acl_J_A_61_A_123_125_A_61_61_AFalse_0,axiom,
( 'c$uTarski$uOinterval'('v$ur',X0,'c$uTarski$uOTop'('v$ucl','t$ua'),'t$ua') != 'c$uemptyset'
| ~ 'c$uin'(X0,'v$uA','t$ua') ) ).
cnf(cls_conjecture_0,negated_conjecture,
~ 'c$uin'('c$uTarski$uOpotype$uOpotype$u$uext'('v$uintY1','c$uTarski$uOinduced'('v$uintY1','v$ur','t$ua'),'c$uProduct$u$uType$uOUnity','t$ua','tc$uProduct$u$uType$uOunit'),'c$uTarski$uOCompleteLattice','tc$uTarski$uOpotype$uOpotype$u$uext$u$utype'('t$ua','tc$uProduct$u$uType$uOunit')) ).
cnf(cls_Set_OUn__absorb_0,axiom,
'c$uunion'(X0,X0,X1) = X0 ).
cnf(cls_Set_OUn__empty_2,axiom,
'c$uunion'('c$uemptyset','c$uemptyset',X0) = 'c$uemptyset' ).
cnf(c0,plain,
'c$uin'('c$uTarski$uOTop'('v$ucl','t$ua'),'v$uA','t$ua'),
inference(clausification,[status(esa)],[cls_Tarski_OTop_Acl_A_58_AA_A_61_61_ATrue_0]) ).
cnf(c1,plain,
( 'c$uTarski$uOinterval'('v$ur',X1,X0,'t$ua') = 'c$uemptyset'
| 'c$uin'('c$uTarski$uOpotype$uOpotype$u$uext'('c$uTarski$uOinterval'('v$ur',X1,X0,'t$ua'),'c$uTarski$uOinduced'('c$uTarski$uOinterval'('v$ur',X1,X0,'t$ua'),'v$ur','t$ua'),'c$uProduct$u$uType$uOUnity','t$ua','tc$uProduct$u$uType$uOunit'),'c$uTarski$uOCompleteLattice','tc$uTarski$uOpotype$uOpotype$u$uext$u$utype'('t$ua','tc$uProduct$u$uType$uOunit'))
| ~ 'c$uin'(X1,'v$uA','t$ua')
| ~ 'c$uin'(X0,'v$uA','t$ua') ),
inference(clausification,[status(esa)],[cls_Tarski_O_91_124_Aa2_A_58_AA_59_Ab2_A_58_AA_59_Ainterval_Ar_Aa2_Ab2_A_126_61_A_123_125_A_124_93_A_61_61_62_A_I_124_Apset_A_61_Ainterval_Ar_Aa2_Ab2_M_Aorder_A_61_Ainduced_A_Iinterval_Ar_Aa2_Ab2_J_Ar_A_124_J_A_58_ACompleteLattice_A_61_61_ATrue_0]) ).
cnf(c6,plain,
'v$uintY1' = 'c$uTarski$uOinterval'('v$ur','c$uTarski$uOlub'('v$uY','v$ucl','t$ua'),'c$uTarski$uOTop'('v$ucl','t$ua'),'t$ua'),
inference(clausification,[status(esa)],[cls_Tarski_OintY1_A_61_61_Ainterval_Ar_A_Ilub_AY_Acl_J_A_ITop_Acl_J_0]) ).
cnf(c7,plain,
'c$uin'('c$uTarski$uOlub'('v$uY','v$ucl','t$ua'),'v$uA','t$ua'),
inference(clausification,[status(esa)],[cls_Tarski_Olub_AY_Acl_A_58_AA_A_61_61_ATrue_0]) ).
cnf(c8,plain,
( 'c$uTarski$uOinterval'('v$ur',X0,'c$uTarski$uOTop'('v$ucl','t$ua'),'t$ua') != 'c$uemptyset'
| ~ 'c$uin'(X0,'v$uA','t$ua') ),
inference(clausification,[status(esa)],[cls_Tarski_Ox1_A_58_AA_A_61_61_62_Ainterval_Ar_Ax1_A_ITop_Acl_J_A_61_A_123_125_A_61_61_AFalse_0]) ).
cnf(c9,plain,
~ 'c$uin'('c$uTarski$uOpotype$uOpotype$u$uext'('v$uintY1','c$uTarski$uOinduced'('v$uintY1','v$ur','t$ua'),'c$uProduct$u$uType$uOUnity','t$ua','tc$uProduct$u$uType$uOunit'),'c$uTarski$uOCompleteLattice','tc$uTarski$uOpotype$uOpotype$u$uext$u$utype'('t$ua','tc$uProduct$u$uType$uOunit')),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c1493,plain,
'c$uunion'(X0,X0,X1) = X0,
inference(clausification,[status(esa)],[cls_Set_OUn__absorb_0]) ).
cnf(c1496,plain,
'c$uunion'('c$uemptyset','c$uemptyset',X0) = 'c$uemptyset',
inference(clausification,[status(esa)],[cls_Set_OUn__empty_2]) ).
cnf(d0,plain,
( ~ 'c$uin'('c$uTarski$uOlub'('v$uY','v$ucl','t$ua'),'v$uA','t$ua')
| ~ 'c$uin'('c$uTarski$uOTop'('v$ucl','t$ua'),'v$uA','t$ua')
| 'c$uTarski$uOinterval'('v$ur','c$uTarski$uOlub'('v$uY','v$ucl','t$ua'),'c$uTarski$uOTop'('v$ucl','t$ua'),'t$ua') = 'c$uemptyset'
| 'c$uin'('c$uTarski$uOpotype$uOpotype$u$uext'('c$uTarski$uOinterval'('v$ur','c$uTarski$uOlub'('v$uY','v$ucl','t$ua'),'c$uTarski$uOTop'('v$ucl','t$ua'),'t$ua'),'c$uTarski$uOinduced'('v$uintY1','v$ur','t$ua'),'c$uProduct$u$uType$uOUnity','t$ua','tc$uProduct$u$uType$uOunit'),'c$uTarski$uOCompleteLattice','tc$uTarski$uOpotype$uOpotype$u$uext$u$utype'('t$ua','tc$uProduct$u$uType$uOunit')) ),
inference(superposition,[status(thm)],[c6,c1]) ).
cnf(d1,plain,
( ~ 'c$uin'('c$uTarski$uOlub'('v$uY','v$ucl','t$ua'),'v$uA','t$ua')
| 'c$uin'('c$uTarski$uOpotype$uOpotype$u$uext'('c$uTarski$uOinterval'('v$ur','c$uTarski$uOlub'('v$uY','v$ucl','t$ua'),'c$uTarski$uOTop'('v$ucl','t$ua'),'t$ua'),'c$uTarski$uOinduced'('v$uintY1','v$ur','t$ua'),'c$uProduct$u$uType$uOUnity','t$ua','tc$uProduct$u$uType$uOunit'),'c$uTarski$uOCompleteLattice','tc$uTarski$uOpotype$uOpotype$u$uext$u$utype'('t$ua','tc$uProduct$u$uType$uOunit'))
| ~ 'c$uin'('c$uTarski$uOTop'('v$ucl','t$ua'),'v$uA','t$ua')
| 'v$uintY1' = 'c$uemptyset' ),
inference(demodulation,[status(thm)],[d0,c6]) ).
cnf(d2,plain,
( ~ 'c$uin'('c$uTarski$uOlub'('v$uY','v$ucl','t$ua'),'v$uA','t$ua')
| 'c$uin'('c$uTarski$uOpotype$uOpotype$u$uext'('v$uintY1','c$uTarski$uOinduced'('v$uintY1','v$ur','t$ua'),'c$uProduct$u$uType$uOUnity','t$ua','tc$uProduct$u$uType$uOunit'),'c$uTarski$uOCompleteLattice','tc$uTarski$uOpotype$uOpotype$u$uext$u$utype'('t$ua','tc$uProduct$u$uType$uOunit'))
| ~ 'c$uin'('c$uTarski$uOTop'('v$ucl','t$ua'),'v$uA','t$ua')
| 'v$uintY1' = 'c$uemptyset' ),
inference(demodulation,[status(thm)],[d1,c6]) ).
cnf(d3,plain,
( ~ 'c$uin'('c$uTarski$uOlub'('v$uY','v$ucl','t$ua'),'v$uA','t$ua')
| 'c$uin'('c$uTarski$uOpotype$uOpotype$u$uext'('v$uintY1','c$uTarski$uOinduced'('v$uintY1','v$ur','t$ua'),'c$uProduct$u$uType$uOUnity','t$ua','tc$uProduct$u$uType$uOunit'),'c$uTarski$uOCompleteLattice','tc$uTarski$uOpotype$uOpotype$u$uext$u$utype'('t$ua','tc$uProduct$u$uType$uOunit'))
| 'v$uintY1' = 'c$uemptyset' ),
inference(resolution,[status(thm)],[c0,d2]) ).
cnf(d4,plain,
( 'c$uin'('c$uTarski$uOpotype$uOpotype$u$uext'('v$uintY1','c$uTarski$uOinduced'('v$uintY1','v$ur','t$ua'),'c$uProduct$u$uType$uOUnity','t$ua','tc$uProduct$u$uType$uOunit'),'c$uTarski$uOCompleteLattice','tc$uTarski$uOpotype$uOpotype$u$uext$u$utype'('t$ua','tc$uProduct$u$uType$uOunit'))
| 'v$uintY1' = 'c$uemptyset' ),
inference(resolution,[status(thm)],[c7,d3]) ).
cnf(d5,plain,
'v$uintY1' = 'c$uemptyset',
inference(resolution,[status(thm)],[c9,d4]) ).
cnf(d6,plain,
( ~ 'c$uin'('c$uTarski$uOlub'('v$uY','v$ucl','t$ua'),'v$uA','t$ua')
| 'v$uintY1' != 'c$uemptyset' ),
inference(superposition,[status(thm)],[c6,c8]) ).
cnf(d7,plain,
( ~ 'c$uin'('c$uTarski$uOlub'('v$uY','v$ucl','t$ua'),'v$uA','t$ua')
| 'c$uemptyset' != 'c$uemptyset' ),
inference(demodulation,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
'c$uemptyset' != 'c$uemptyset',
inference(resolution,[status(thm)],[c7,d7]) ).
cnf(d9,plain,
'c$uemptyset' = 'c$uemptyset',
inference(demodulation,[status(thm)],[c1496,c1493]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[d9,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LAT269-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/10.32 % Computer : n012.cluster.edu
% 0.03/10.32 % Model : x86_64 x86_64
% 0.03/10.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/10.32 % Memory : 8046.5625MB
% 0.03/10.32 % OS : Linux 6.8.0-71-generic
% 0.03/10.32 % CPULimit : 300
% 0.03/10.32 % WCLimit : 300
% 0.03/10.32 % DateTime : Fri Sep 25 20:22:24 UTC 2026
% 0.03/10.32 % CPUTime :
% 0.03/10.32 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 38.58/16.85 % SZS status Unsatisfiable for theBenchmark.p
% 38.58/16.85 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------