%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LAT268-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 12.12s 2.26s
% Output : CNFRefutation 12.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of clauses : 39 ( 39 unt; 0 nHn; 19 RR)
% Number of literals : 39 ( 38 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 10 con; 0-4 aty)
% Number of variables : 50 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ifeq_axiom,axiom,
ifeq(X0,X0,X1,X2) = X1 ).
cnf(cls_conjecture_0,negated_conjecture,
'c$ulessequals'('v$uS','v$uA','tc$uset'('t$ua')) = true ).
cnf(cls_conjecture_1,negated_conjecture,
'c$uin'('v$ux','v$uS','t$ua') = true ).
cnf(cls_conjecture_2,negated_conjecture,
'c$uin'('c$uPair'('c$uTarski$uOglb'('v$uS','v$ucl','t$ua'),'v$ux','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')) != true ).
cnf(cls_Tarski_OA_A_61_61_Apset_Acl_0,axiom,
'v$uA' = 'c$uTarski$uOpotype$uOpset'('v$ucl','t$ua','tc$uProduct$u$uType$uOunit') ).
cnf(cls_Tarski_OCL_Olub__upper_0,axiom,
ifeq('c$ulessequals'(X0,'c$uTarski$uOpotype$uOpset'(X1,X2,'tc$uProduct$u$uType$uOunit'),'tc$uset'(X2)),true,ifeq('c$uin'(X1,'c$uTarski$uOCompleteLattice','tc$uTarski$uOpotype$uOpotype$u$uext$u$utype'(X2,'tc$uProduct$u$uType$uOunit')),true,ifeq('c$uin'(X1,'c$uTarski$uOPartialOrder','tc$uTarski$uOpotype$uOpotype$u$uext$u$utype'(X2,'tc$uProduct$u$uType$uOunit')),true,ifeq('c$uin'(X3,X0,X2),true,'c$uin'('c$uPair'(X3,'c$uTarski$uOlub'(X0,X1,X2),X2,X2),'c$uTarski$uOpotype$uOorder'(X1,X2,'tc$uProduct$u$uType$uOunit'),'tc$uprod'(X2,X2)),true),true),true),true) = true ).
cnf(cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0,axiom,
ifeq('c$uin'('c$uPair'(X0,X1,X2,X2),'c$uTarski$uOpotype$uOorder'('c$uTarski$uOdual'(X3,X2),X2,'tc$uProduct$u$uType$uOunit'),'tc$uprod'(X2,X2)),true,'c$uin'('c$uPair'(X1,X0,X2,X2),'c$uTarski$uOpotype$uOorder'(X3,X2,'tc$uProduct$u$uType$uOunit'),'tc$uprod'(X2,X2)),true) = true ).
cnf(cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0,axiom,
'c$uin'('c$uTarski$uOdual'('v$ucl','t$ua'),'c$uTarski$uOCompleteLattice','tc$uTarski$uOpotype$uOpotype$u$uext$u$utype'('t$ua','tc$uProduct$u$uType$uOunit')) = true ).
cnf(cls_Tarski_Odual_Acl_A_58_APartialOrder_0,axiom,
'c$uin'('c$uTarski$uOdual'('v$ucl','t$ua'),'c$uTarski$uOPartialOrder','tc$uTarski$uOpotype$uOpotype$u$uext$u$utype'('t$ua','tc$uProduct$u$uType$uOunit')) = true ).
cnf(cls_Tarski_Oglb__dual__lub_0,axiom,
'c$uTarski$uOglb'(X0,X1,X2) = 'c$uTarski$uOlub'(X0,'c$uTarski$uOdual'(X1,X2),X2) ).
cnf(cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0,axiom,
'c$uTarski$uOpotype$uOpset'('c$uTarski$uOdual'(X0,X1),X1,'tc$uProduct$u$uType$uOunit') = 'c$uTarski$uOpotype$uOpset'(X0,X1,'tc$uProduct$u$uType$uOunit') ).
cnf(cls_Tarski_Or_A_61_61_Aorder_Acl_0,axiom,
'v$ur' = 'c$uTarski$uOpotype$uOorder'('v$ucl','t$ua','tc$uProduct$u$uType$uOunit') ).
cnf(c0,plain,
ifeq(X0,X0,X1,X2) = X1,
inference(clausification,[status(esa)],[ifeq_axiom]) ).
cnf(c1,plain,
'c$ulessequals'('v$uS','v$uA','tc$uset'('t$ua')) = true,
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c2,plain,
'c$uin'('v$ux','v$uS','t$ua') = true,
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c3,plain,
'c$uin'('c$uPair'('c$uTarski$uOglb'('v$uS','v$ucl','t$ua'),'v$ux','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')) != true,
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c4,plain,
'v$uA' = 'c$uTarski$uOpotype$uOpset'('v$ucl','t$ua','tc$uProduct$u$uType$uOunit'),
inference(clausification,[status(esa)],[cls_Tarski_OA_A_61_61_Apset_Acl_0]) ).
cnf(c5,plain,
ifeq('c$ulessequals'(X0,'c$uTarski$uOpotype$uOpset'(X1,X2,'tc$uProduct$u$uType$uOunit'),'tc$uset'(X2)),true,ifeq('c$uin'(X1,'c$uTarski$uOCompleteLattice','tc$uTarski$uOpotype$uOpotype$u$uext$u$utype'(X2,'tc$uProduct$u$uType$uOunit')),true,ifeq('c$uin'(X1,'c$uTarski$uOPartialOrder','tc$uTarski$uOpotype$uOpotype$u$uext$u$utype'(X2,'tc$uProduct$u$uType$uOunit')),true,ifeq('c$uin'(X3,X0,X2),true,'c$uin'('c$uPair'(X3,'c$uTarski$uOlub'(X0,X1,X2),X2,X2),'c$uTarski$uOpotype$uOorder'(X1,X2,'tc$uProduct$u$uType$uOunit'),'tc$uprod'(X2,X2)),true),true),true),true) = true,
inference(clausification,[status(esa)],[cls_Tarski_OCL_Olub__upper_0]) ).
cnf(c6,plain,
ifeq('c$uin'('c$uPair'(X0,X1,X2,X2),'c$uTarski$uOpotype$uOorder'('c$uTarski$uOdual'(X3,X2),X2,'tc$uProduct$u$uType$uOunit'),'tc$uprod'(X2,X2)),true,'c$uin'('c$uPair'(X1,X0,X2,X2),'c$uTarski$uOpotype$uOorder'(X3,X2,'tc$uProduct$u$uType$uOunit'),'tc$uprod'(X2,X2)),true) = true,
inference(clausification,[status(esa)],[cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0]) ).
cnf(c7,plain,
'c$uin'('c$uTarski$uOdual'('v$ucl','t$ua'),'c$uTarski$uOCompleteLattice','tc$uTarski$uOpotype$uOpotype$u$uext$u$utype'('t$ua','tc$uProduct$u$uType$uOunit')) = true,
inference(clausification,[status(esa)],[cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0]) ).
cnf(c8,plain,
'c$uin'('c$uTarski$uOdual'('v$ucl','t$ua'),'c$uTarski$uOPartialOrder','tc$uTarski$uOpotype$uOpotype$u$uext$u$utype'('t$ua','tc$uProduct$u$uType$uOunit')) = true,
inference(clausification,[status(esa)],[cls_Tarski_Odual_Acl_A_58_APartialOrder_0]) ).
cnf(c9,plain,
'c$uTarski$uOglb'(X0,X1,X2) = 'c$uTarski$uOlub'(X0,'c$uTarski$uOdual'(X1,X2),X2),
inference(clausification,[status(esa)],[cls_Tarski_Oglb__dual__lub_0]) ).
cnf(c10,plain,
'c$uTarski$uOpotype$uOpset'('c$uTarski$uOdual'(X0,X1),X1,'tc$uProduct$u$uType$uOunit') = 'c$uTarski$uOpotype$uOpset'(X0,X1,'tc$uProduct$u$uType$uOunit'),
inference(clausification,[status(esa)],[cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0]) ).
cnf(c11,plain,
'v$ur' = 'c$uTarski$uOpotype$uOorder'('v$ucl','t$ua','tc$uProduct$u$uType$uOunit'),
inference(clausification,[status(esa)],[cls_Tarski_Or_A_61_61_Aorder_Acl_0]) ).
cnf(d0,plain,
ifeq('c$uin'('c$uPair'(X0,X1,'t$ua','t$ua'),'c$uTarski$uOpotype$uOorder'('c$uTarski$uOdual'('v$ucl','t$ua'),'t$ua','tc$uProduct$u$uType$uOunit'),'tc$uprod'('t$ua','t$ua')),true,'c$uin'('c$uPair'(X1,X0,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')),true) = true,
inference(superposition,[status(thm)],[c11,c6]) ).
cnf(d1,plain,
ifeq('c$ulessequals'(X0,'c$uTarski$uOpotype$uOpset'('c$uTarski$uOdual'('v$ucl','t$ua'),'t$ua','tc$uProduct$u$uType$uOunit'),'tc$uset'('t$ua')),true,ifeq(true,true,ifeq('c$uin'('c$uTarski$uOdual'('v$ucl','t$ua'),'c$uTarski$uOPartialOrder','tc$uTarski$uOpotype$uOpotype$u$uext$u$utype'('t$ua','tc$uProduct$u$uType$uOunit')),true,ifeq('c$uin'(X1,X0,'t$ua'),true,'c$uin'('c$uPair'(X1,'c$uTarski$uOlub'(X0,'c$uTarski$uOdual'('v$ucl','t$ua'),'t$ua'),'t$ua','t$ua'),'c$uTarski$uOpotype$uOorder'('c$uTarski$uOdual'('v$ucl','t$ua'),'t$ua','tc$uProduct$u$uType$uOunit'),'tc$uprod'('t$ua','t$ua')),true),true),true),true) = true,
inference(superposition,[status(thm)],[c7,c5]) ).
cnf(d2,plain,
ifeq('c$ulessequals'(X0,'c$uTarski$uOpotype$uOpset'('v$ucl','t$ua','tc$uProduct$u$uType$uOunit'),'tc$uset'('t$ua')),true,ifeq(true,true,ifeq('c$uin'('c$uTarski$uOdual'('v$ucl','t$ua'),'c$uTarski$uOPartialOrder','tc$uTarski$uOpotype$uOpotype$u$uext$u$utype'('t$ua','tc$uProduct$u$uType$uOunit')),true,ifeq('c$uin'(X1,X0,'t$ua'),true,'c$uin'('c$uPair'(X1,'c$uTarski$uOlub'(X0,'c$uTarski$uOdual'('v$ucl','t$ua'),'t$ua'),'t$ua','t$ua'),'c$uTarski$uOpotype$uOorder'('c$uTarski$uOdual'('v$ucl','t$ua'),'t$ua','tc$uProduct$u$uType$uOunit'),'tc$uprod'('t$ua','t$ua')),true),true),true),true) = true,
inference(demodulation,[status(thm)],[d1,c10]) ).
cnf(d3,plain,
ifeq('c$ulessequals'(X0,'v$uA','tc$uset'('t$ua')),true,ifeq(true,true,ifeq('c$uin'('c$uTarski$uOdual'('v$ucl','t$ua'),'c$uTarski$uOPartialOrder','tc$uTarski$uOpotype$uOpotype$u$uext$u$utype'('t$ua','tc$uProduct$u$uType$uOunit')),true,ifeq('c$uin'(X1,X0,'t$ua'),true,'c$uin'('c$uPair'(X1,'c$uTarski$uOlub'(X0,'c$uTarski$uOdual'('v$ucl','t$ua'),'t$ua'),'t$ua','t$ua'),'c$uTarski$uOpotype$uOorder'('c$uTarski$uOdual'('v$ucl','t$ua'),'t$ua','tc$uProduct$u$uType$uOunit'),'tc$uprod'('t$ua','t$ua')),true),true),true),true) = true,
inference(demodulation,[status(thm)],[d2,c4]) ).
cnf(d4,plain,
ifeq('c$ulessequals'(X1,'v$uA','tc$uset'('t$ua')),true,ifeq('c$uin'('c$uTarski$uOdual'('v$ucl','t$ua'),'c$uTarski$uOPartialOrder','tc$uTarski$uOpotype$uOpotype$u$uext$u$utype'('t$ua','tc$uProduct$u$uType$uOunit')),true,ifeq('c$uin'(X0,X1,'t$ua'),true,'c$uin'('c$uPair'(X0,'c$uTarski$uOlub'(X1,'c$uTarski$uOdual'('v$ucl','t$ua'),'t$ua'),'t$ua','t$ua'),'c$uTarski$uOpotype$uOorder'('c$uTarski$uOdual'('v$ucl','t$ua'),'t$ua','tc$uProduct$u$uType$uOunit'),'tc$uprod'('t$ua','t$ua')),true),true),true) = true,
inference(demodulation,[status(thm)],[d3,c0]) ).
cnf(d5,plain,
ifeq('c$ulessequals'(X0,'v$uA','tc$uset'('t$ua')),true,ifeq(true,true,ifeq('c$uin'(X1,X0,'t$ua'),true,'c$uin'('c$uPair'(X1,'c$uTarski$uOlub'(X0,'c$uTarski$uOdual'('v$ucl','t$ua'),'t$ua'),'t$ua','t$ua'),'c$uTarski$uOpotype$uOorder'('c$uTarski$uOdual'('v$ucl','t$ua'),'t$ua','tc$uProduct$u$uType$uOunit'),'tc$uprod'('t$ua','t$ua')),true),true),true) = true,
inference(demodulation,[status(thm)],[d4,c8]) ).
cnf(d6,plain,
ifeq('c$ulessequals'(X1,'v$uA','tc$uset'('t$ua')),true,ifeq('c$uin'(X0,X1,'t$ua'),true,'c$uin'('c$uPair'(X0,'c$uTarski$uOlub'(X1,'c$uTarski$uOdual'('v$ucl','t$ua'),'t$ua'),'t$ua','t$ua'),'c$uTarski$uOpotype$uOorder'('c$uTarski$uOdual'('v$ucl','t$ua'),'t$ua','tc$uProduct$u$uType$uOunit'),'tc$uprod'('t$ua','t$ua')),true),true) = true,
inference(demodulation,[status(thm)],[d5,c0]) ).
cnf(d7,plain,
ifeq('c$ulessequals'(X0,'v$uA','tc$uset'('t$ua')),true,ifeq('c$uin'(X1,X0,'t$ua'),true,'c$uin'('c$uPair'(X1,'c$uTarski$uOglb'(X0,'v$ucl','t$ua'),'t$ua','t$ua'),'c$uTarski$uOpotype$uOorder'('c$uTarski$uOdual'('v$ucl','t$ua'),'t$ua','tc$uProduct$u$uType$uOunit'),'tc$uprod'('t$ua','t$ua')),true),true) = true,
inference(demodulation,[status(thm)],[d6,c9]) ).
cnf(d8,plain,
ifeq(true,true,ifeq('c$uin'(X0,'v$uS','t$ua'),true,'c$uin'('c$uPair'(X0,'c$uTarski$uOglb'('v$uS','v$ucl','t$ua'),'t$ua','t$ua'),'c$uTarski$uOpotype$uOorder'('c$uTarski$uOdual'('v$ucl','t$ua'),'t$ua','tc$uProduct$u$uType$uOunit'),'tc$uprod'('t$ua','t$ua')),true),true) = true,
inference(superposition,[status(thm)],[c1,d7]) ).
cnf(d9,plain,
ifeq('c$uin'(X0,'v$uS','t$ua'),true,'c$uin'('c$uPair'(X0,'c$uTarski$uOglb'('v$uS','v$ucl','t$ua'),'t$ua','t$ua'),'c$uTarski$uOpotype$uOorder'('c$uTarski$uOdual'('v$ucl','t$ua'),'t$ua','tc$uProduct$u$uType$uOunit'),'tc$uprod'('t$ua','t$ua')),true) = true,
inference(demodulation,[status(thm)],[d8,c0]) ).
cnf(d10,plain,
ifeq(true,true,'c$uin'('c$uPair'('v$ux','c$uTarski$uOglb'('v$uS','v$ucl','t$ua'),'t$ua','t$ua'),'c$uTarski$uOpotype$uOorder'('c$uTarski$uOdual'('v$ucl','t$ua'),'t$ua','tc$uProduct$u$uType$uOunit'),'tc$uprod'('t$ua','t$ua')),true) = true,
inference(superposition,[status(thm)],[c2,d9]) ).
cnf(d11,plain,
'c$uin'('c$uPair'('v$ux','c$uTarski$uOglb'('v$uS','v$ucl','t$ua'),'t$ua','t$ua'),'c$uTarski$uOpotype$uOorder'('c$uTarski$uOdual'('v$ucl','t$ua'),'t$ua','tc$uProduct$u$uType$uOunit'),'tc$uprod'('t$ua','t$ua')) = true,
inference(demodulation,[status(thm)],[d10,c0]) ).
cnf(d12,plain,
ifeq(true,true,'c$uin'('c$uPair'('c$uTarski$uOglb'('v$uS','v$ucl','t$ua'),'v$ux','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')),true) = true,
inference(superposition,[status(thm)],[d11,d0]) ).
cnf(d13,plain,
'c$uin'('c$uPair'('c$uTarski$uOglb'('v$uS','v$ucl','t$ua'),'v$ux','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')) = true,
inference(demodulation,[status(thm)],[d12,c0]) ).
cnf(d14,plain,
$false,
inference(resolution,[status(thm)],[c3,d13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT268-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 20:24:53 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.12/2.26 % SZS status Unsatisfiable for theBenchmark.p
% 12.12/2.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------