%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ANA025-2 : 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 : 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 06:50:39 AM UTC 2026
% Result : Unsatisfiable 10.07s 1.68s
% Output : CNFRefutation 10.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of clauses : 43 ( 15 unt; 3 nHn; 36 RR)
% Number of literals : 91 ( 0 equ; 57 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 48 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
( 'c$ulessequals'('c$u0','c$uHOL$uOabs'(X1,X0),X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ) ).
cnf(cls_Orderings_Olinorder__not__le_0,axiom,
( 'c$ulessequals'(X2,X1,X0)
| 'c$uless'(X1,X2,X0)
| ~ 'class$uOrderings$uOlinorder'(X0) ) ).
cnf(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2,axiom,
( 'c$ulessequals'('c$uOrderings$uOmax'(X3,X1,X0),X2,X0)
| ~ 'c$ulessequals'(X3,X2,X0)
| ~ 'c$ulessequals'(X1,X2,X0)
| ~ 'class$uOrderings$uOlinorder'(X0) ) ).
cnf(cls_Orderings_Oorder__class_Oorder__trans_0,axiom,
( 'c$ulessequals'(X3,X2,X0)
| ~ 'c$ulessequals'(X3,X1,X0)
| ~ 'c$ulessequals'(X1,X2,X0)
| ~ 'class$uOrderings$uOorder'(X0) ) ).
cnf(cls_Orderings_Oorder__less__imp__le_0,axiom,
( 'c$ulessequals'(X1,X2,X0)
| ~ 'c$uless'(X1,X2,X0)
| ~ 'class$uOrderings$uOorder'(X0) ) ).
cnf(cls_conjecture_2,negated_conjecture,
~ 'c$ulessequals'('c$u0','c$uminus'('v$uk'('v$ux'),'v$ug'('v$ux'),'t$ub'),'t$ub') ).
cnf(cls_conjecture_3,negated_conjecture,
~ 'c$ulessequals'('c$uOrderings$uOmax'('c$uminus'('v$uk'('v$ux'),'v$ug'('v$ux'),'t$ub'),'c$u0','t$ub'),'c$uHOL$uOabs'('c$uminus'('v$uf'('v$ux'),'v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub') ).
cnf(clsrel_LOrder_Ojoin__semilorder_1,axiom,
( 'class$uOrderings$uOorder'(X0)
| ~ 'class$uLOrder$uOjoin$u$usemilorder'(X0) ) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_15,axiom,
( 'class$uLOrder$uOjoin$u$usemilorder'(X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_33,axiom,
( 'class$uOrderings$uOlinorder'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
( 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ) ).
cnf(tfree_tcs,negated_conjecture,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ub') ).
cnf(c0,plain,
( 'c$ulessequals'('c$u0','c$uHOL$uOabs'(X1,X0),X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Oabs__ge__zero_0]) ).
cnf(c1,plain,
( 'c$ulessequals'(X2,X1,X0)
| 'c$uless'(X1,X2,X0)
| ~ 'class$uOrderings$uOlinorder'(X0) ),
inference(clausification,[status(esa)],[cls_Orderings_Olinorder__not__le_0]) ).
cnf(c2,plain,
( 'c$ulessequals'('c$uOrderings$uOmax'(X3,X1,X0),X2,X0)
| ~ 'c$ulessequals'(X3,X2,X0)
| ~ 'c$ulessequals'(X1,X2,X0)
| ~ 'class$uOrderings$uOlinorder'(X0) ),
inference(clausification,[status(esa)],[cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2]) ).
cnf(c3,plain,
( 'c$ulessequals'(X3,X2,X0)
| ~ 'c$ulessequals'(X3,X1,X0)
| ~ 'c$ulessequals'(X1,X2,X0)
| ~ 'class$uOrderings$uOorder'(X0) ),
inference(clausification,[status(esa)],[cls_Orderings_Oorder__class_Oorder__trans_0]) ).
cnf(c4,plain,
( 'c$ulessequals'(X1,X2,X0)
| ~ 'c$uless'(X1,X2,X0)
| ~ 'class$uOrderings$uOorder'(X0) ),
inference(clausification,[status(esa)],[cls_Orderings_Oorder__less__imp__le_0]) ).
cnf(c5,plain,
~ 'c$ulessequals'('c$u0','c$uminus'('v$uk'('v$ux'),'v$ug'('v$ux'),'t$ub'),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c6,plain,
~ 'c$ulessequals'('c$uOrderings$uOmax'('c$uminus'('v$uk'('v$ux'),'v$ug'('v$ux'),'t$ub'),'c$u0','t$ub'),'c$uHOL$uOabs'('c$uminus'('v$uf'('v$ux'),'v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_3]) ).
cnf(c7,plain,
( 'class$uOrderings$uOorder'(X0)
| ~ 'class$uLOrder$uOjoin$u$usemilorder'(X0) ),
inference(clausification,[status(esa)],[clsrel_LOrder_Ojoin__semilorder_1]) ).
cnf(c8,plain,
( 'class$uLOrder$uOjoin$u$usemilorder'(X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ),
inference(clausification,[status(esa)],[clsrel_OrderedGroup_Olordered__ab__group__abs_15]) ).
cnf(c9,plain,
( 'class$uOrderings$uOlinorder'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ),
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Oordered__idom_33]) ).
cnf(c10,plain,
( 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ),
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Oordered__idom_50]) ).
cnf(c11,plain,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ub'),
inference(clausification,[status(esa)],[tfree_tcs]) ).
cnf(d0,plain,
( ~ 'class$uOrderings$uOlinorder'(X2)
| 'c$ulessequals'(X1,X0,X2)
| ~ 'class$uOrderings$uOorder'(X2)
| 'c$ulessequals'(X0,X1,X2) ),
inference(resolution,[status(thm)],[c4,c1]) ).
cnf(d1,plain,
( ~ 'class$uOrderings$uOorder'(X1)
| ~ 'class$uOrderings$uOlinorder'(X1)
| 'c$ulessequals'(X0,X0,X1) ),
inference(factoring,[status(thm)],[d0]) ).
cnf(d2,plain,
( ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X2)
| ~ 'class$uOrderings$uOorder'(X2)
| ~ 'c$ulessequals'(X0,'c$u0',X2)
| 'c$ulessequals'(X0,'c$uHOL$uOabs'(X1,X2),X2) ),
inference(resolution,[status(thm)],[c3,c0]) ).
cnf(d3,plain,
( ~ 'class$uOrderings$uOorder'('t$ub')
| ~ 'c$ulessequals'('c$uOrderings$uOmax'('c$uminus'('v$uk'('v$ux'),'v$ug'('v$ux'),'t$ub'),'c$u0','t$ub'),'c$u0','t$ub')
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'('t$ub') ),
inference(resolution,[status(thm)],[d2,c6]) ).
cnf(d4,plain,
'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'('t$ub'),
inference(resolution,[status(thm)],[c10,c11]) ).
cnf(d5,plain,
( ~ 'class$uOrderings$uOorder'('t$ub')
| ~ 'c$ulessequals'('c$uOrderings$uOmax'('c$uminus'('v$uk'('v$ux'),'v$ug'('v$ux'),'t$ub'),'c$u0','t$ub'),'c$u0','t$ub') ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
'class$uLOrder$uOjoin$u$usemilorder'('t$ub'),
inference(resolution,[status(thm)],[d4,c8]) ).
cnf(d7,plain,
'class$uOrderings$uOorder'('t$ub'),
inference(resolution,[status(thm)],[d6,c7]) ).
cnf(d8,plain,
~ 'c$ulessequals'('c$uOrderings$uOmax'('c$uminus'('v$uk'('v$ux'),'v$ug'('v$ux'),'t$ub'),'c$u0','t$ub'),'c$u0','t$ub'),
inference(resolution,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
( ~ 'class$uOrderings$uOlinorder'('t$ub')
| ~ 'c$ulessequals'('c$u0','c$u0','t$ub')
| ~ 'c$ulessequals'('c$uminus'('v$uk'('v$ux'),'v$ug'('v$ux'),'t$ub'),'c$u0','t$ub') ),
inference(resolution,[status(thm)],[d8,c2]) ).
cnf(d10,plain,
'class$uOrderings$uOlinorder'('t$ub'),
inference(resolution,[status(thm)],[c9,c11]) ).
cnf(d11,plain,
( ~ 'c$ulessequals'('c$uminus'('v$uk'('v$ux'),'v$ug'('v$ux'),'t$ub'),'c$u0','t$ub')
| ~ 'c$ulessequals'('c$u0','c$u0','t$ub') ),
inference(resolution,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
( ~ 'class$uOrderings$uOorder'('t$ub')
| ~ 'class$uOrderings$uOlinorder'('t$ub')
| 'c$ulessequals'('c$uminus'('v$uk'('v$ux'),'v$ug'('v$ux'),'t$ub'),'c$u0','t$ub') ),
inference(resolution,[status(thm)],[d0,c5]) ).
cnf(d13,plain,
( ~ 'class$uOrderings$uOorder'('t$ub')
| 'c$ulessequals'('c$uminus'('v$uk'('v$ux'),'v$ug'('v$ux'),'t$ub'),'c$u0','t$ub') ),
inference(resolution,[status(thm)],[d10,d12]) ).
cnf(d14,plain,
'c$ulessequals'('c$uminus'('v$uk'('v$ux'),'v$ug'('v$ux'),'t$ub'),'c$u0','t$ub'),
inference(resolution,[status(thm)],[d7,d13]) ).
cnf(d15,plain,
~ 'c$ulessequals'('c$u0','c$u0','t$ub'),
inference(resolution,[status(thm)],[d14,d11]) ).
cnf(d16,plain,
( ~ 'class$uOrderings$uOorder'('t$ub')
| ~ 'class$uOrderings$uOlinorder'('t$ub') ),
inference(resolution,[status(thm)],[d15,d1]) ).
cnf(d17,plain,
~ 'class$uOrderings$uOorder'('t$ub'),
inference(resolution,[status(thm)],[d10,d16]) ).
cnf(d18,plain,
$false,
inference(resolution,[status(thm)],[d7,d17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ANA025-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sat Sep 26 22:06:35 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.07/1.68 % SZS status Unsatisfiable for theBenchmark.p
% 10.07/1.68 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------