%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ANA023-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 11.13s 1.83s
% Output : CNFRefutation 11.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of clauses : 55 ( 55 unt; 0 nHn; 26 RR)
% Number of literals : 55 ( 54 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 4 con; 0-4 aty)
% Number of variables : 60 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ifeq_axiom,axiom,
ifeq2(X0,X0,X1,X2) = X1 ).
cnf(ifeq_axiom_001,axiom,
ifeq(X0,X0,X1,X2) = X1 ).
cnf(cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0,axiom,
ifeq2('class$uOrderedGroup$uOcomm$u$umonoid$u$uadd'(X0),true,'c$uplus'('c$u0',X1,X0),X1) = X1 ).
cnf(cls_OrderedGroup_Ocompare__rls__9_0,axiom,
ifeq('class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'(X0),true,ifeq('c$ulessequals'(X1,'c$uminus'(X2,X3,X0),X0),true,'c$ulessequals'('c$uplus'(X1,X3,X0),X2,X0),true),true) = true ).
cnf(cls_OrderedGroup_Ocompare__rls__9_1,axiom,
ifeq('class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'(X0),true,ifeq('c$ulessequals'('c$uplus'(X1,X2,X0),X3,X0),true,'c$ulessequals'(X1,'c$uminus'(X3,X2,X0),X0),true),true) = true ).
cnf(cls_Orderings_Oorder__class_Oorder__trans_0,axiom,
ifeq('class$uOrderings$uOorder'(X0),true,ifeq('c$ulessequals'(X1,X2,X0),true,ifeq('c$ulessequals'(X2,X3,X0),true,'c$ulessequals'(X1,X3,X0),true),true),true) = true ).
cnf(cls_conjecture_1,negated_conjecture,
'c$ulessequals'('c$u0','c$uminus'('v$uk'('v$ux'),'v$ug'('v$ux'),'t$ub'),'t$ub') = true ).
cnf(cls_conjecture_2,negated_conjecture,
'c$ulessequals'('v$uk'('v$ux'),'v$uf'('v$ux'),'t$ub') = true ).
cnf(cls_conjecture_3,negated_conjecture,
'c$ulessequals'('c$u0','c$uminus'('v$uf'('v$ux'),'v$ug'('v$ux'),'t$ub'),'t$ub') != true ).
cnf(clsrel_Orderings_Olinorder_4,axiom,
ifeq('class$uOrderings$uOlinorder'(X0),true,'class$uOrderings$uOorder'(X0),true) = true ).
cnf(clsrel_Ring__and__Field_Oordered__idom_23,axiom,
ifeq('class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0),true,'class$uOrderedGroup$uOcomm$u$umonoid$u$uadd'(X0),true) = true ).
cnf(clsrel_Ring__and__Field_Oordered__idom_33,axiom,
ifeq('class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0),true,'class$uOrderings$uOlinorder'(X0),true) = true ).
cnf(clsrel_Ring__and__Field_Oordered__idom_54,axiom,
ifeq('class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0),true,'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'(X0),true) = true ).
cnf(tfree_tcs,negated_conjecture,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ub') = true ).
cnf(c0,plain,
ifeq2(X0,X0,X1,X2) = X1,
inference(clausification,[status(esa)],[ifeq_axiom]) ).
cnf(c1,plain,
ifeq(X0,X0,X1,X2) = X1,
inference(clausification,[status(esa)],[ifeq_axiom_001]) ).
cnf(c2,plain,
ifeq2('class$uOrderedGroup$uOcomm$u$umonoid$u$uadd'(X0),true,'c$uplus'('c$u0',X1,X0),X1) = X1,
inference(clausification,[status(esa)],[cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0]) ).
cnf(c3,plain,
ifeq('class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'(X0),true,ifeq('c$ulessequals'(X1,'c$uminus'(X2,X3,X0),X0),true,'c$ulessequals'('c$uplus'(X1,X3,X0),X2,X0),true),true) = true,
inference(clausification,[status(esa)],[cls_OrderedGroup_Ocompare__rls__9_0]) ).
cnf(c4,plain,
ifeq('class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'(X0),true,ifeq('c$ulessequals'('c$uplus'(X1,X2,X0),X3,X0),true,'c$ulessequals'(X1,'c$uminus'(X3,X2,X0),X0),true),true) = true,
inference(clausification,[status(esa)],[cls_OrderedGroup_Ocompare__rls__9_1]) ).
cnf(c5,plain,
ifeq('class$uOrderings$uOorder'(X0),true,ifeq('c$ulessequals'(X1,X2,X0),true,ifeq('c$ulessequals'(X2,X3,X0),true,'c$ulessequals'(X1,X3,X0),true),true),true) = true,
inference(clausification,[status(esa)],[cls_Orderings_Oorder__class_Oorder__trans_0]) ).
cnf(c6,plain,
'c$ulessequals'('c$u0','c$uminus'('v$uk'('v$ux'),'v$ug'('v$ux'),'t$ub'),'t$ub') = true,
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c7,plain,
'c$ulessequals'('v$uk'('v$ux'),'v$uf'('v$ux'),'t$ub') = true,
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c8,plain,
'c$ulessequals'('c$u0','c$uminus'('v$uf'('v$ux'),'v$ug'('v$ux'),'t$ub'),'t$ub') != true,
inference(clausification,[status(esa)],[cls_conjecture_3]) ).
cnf(c9,plain,
ifeq('class$uOrderings$uOlinorder'(X0),true,'class$uOrderings$uOorder'(X0),true) = true,
inference(clausification,[status(esa)],[clsrel_Orderings_Olinorder_4]) ).
cnf(c10,plain,
ifeq('class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0),true,'class$uOrderedGroup$uOcomm$u$umonoid$u$uadd'(X0),true) = true,
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Oordered__idom_23]) ).
cnf(c11,plain,
ifeq('class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0),true,'class$uOrderings$uOlinorder'(X0),true) = true,
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Oordered__idom_33]) ).
cnf(c12,plain,
ifeq('class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0),true,'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'(X0),true) = true,
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Oordered__idom_54]) ).
cnf(c13,plain,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ub') = true,
inference(clausification,[status(esa)],[tfree_tcs]) ).
cnf(d0,plain,
ifeq(true,true,'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'('t$ub'),true) = true,
inference(superposition,[status(thm)],[c13,c12]) ).
cnf(d1,plain,
'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'('t$ub') = true,
inference(demodulation,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
ifeq(true,true,'class$uOrderedGroup$uOcomm$u$umonoid$u$uadd'('t$ub'),true) = true,
inference(superposition,[status(thm)],[c13,c10]) ).
cnf(d3,plain,
'class$uOrderedGroup$uOcomm$u$umonoid$u$uadd'('t$ub') = true,
inference(demodulation,[status(thm)],[d2,c1]) ).
cnf(d4,plain,
ifeq2(true,true,'c$uplus'('c$u0',X0,'t$ub'),X0) = X0,
inference(superposition,[status(thm)],[d3,c2]) ).
cnf(d5,plain,
'c$uplus'('c$u0',X0,'t$ub') = X0,
inference(demodulation,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
ifeq('class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'('t$ub'),true,ifeq('c$ulessequals'(X0,X1,'t$ub'),true,'c$ulessequals'('c$u0','c$uminus'(X1,X0,'t$ub'),'t$ub'),true),true) = true,
inference(superposition,[status(thm)],[d5,c4]) ).
cnf(d7,plain,
ifeq(true,true,ifeq('c$ulessequals'(X0,X1,'t$ub'),true,'c$ulessequals'('c$u0','c$uminus'(X1,X0,'t$ub'),'t$ub'),true),true) = true,
inference(demodulation,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
ifeq('c$ulessequals'(X0,X1,'t$ub'),true,'c$ulessequals'('c$u0','c$uminus'(X1,X0,'t$ub'),'t$ub'),true) = true,
inference(demodulation,[status(thm)],[d7,c1]) ).
cnf(d9,plain,
ifeq(true,true,'class$uOrderings$uOlinorder'('t$ub'),true) = true,
inference(superposition,[status(thm)],[c13,c11]) ).
cnf(d10,plain,
'class$uOrderings$uOlinorder'('t$ub') = true,
inference(demodulation,[status(thm)],[d9,c1]) ).
cnf(d11,plain,
ifeq(true,true,'class$uOrderings$uOorder'('t$ub'),true) = true,
inference(superposition,[status(thm)],[d10,c9]) ).
cnf(d12,plain,
'class$uOrderings$uOorder'('t$ub') = true,
inference(demodulation,[status(thm)],[d11,c1]) ).
cnf(d13,plain,
ifeq('class$uOrderings$uOorder'('t$ub'),true,ifeq('c$ulessequals'(X0,'v$uk'('v$ux'),'t$ub'),true,ifeq(true,true,'c$ulessequals'(X0,'v$uf'('v$ux'),'t$ub'),true),true),true) = true,
inference(superposition,[status(thm)],[c7,c5]) ).
cnf(d14,plain,
ifeq('class$uOrderings$uOorder'('t$ub'),true,ifeq('c$ulessequals'(X0,'v$uk'('v$ux'),'t$ub'),true,'c$ulessequals'(X0,'v$uf'('v$ux'),'t$ub'),true),true) = true,
inference(demodulation,[status(thm)],[d13,c1]) ).
cnf(d15,plain,
ifeq(true,true,ifeq('c$ulessequals'(X0,'v$uk'('v$ux'),'t$ub'),true,'c$ulessequals'(X0,'v$uf'('v$ux'),'t$ub'),true),true) = true,
inference(demodulation,[status(thm)],[d14,d12]) ).
cnf(d16,plain,
ifeq('c$ulessequals'(X0,'v$uk'('v$ux'),'t$ub'),true,'c$ulessequals'(X0,'v$uf'('v$ux'),'t$ub'),true) = true,
inference(demodulation,[status(thm)],[d15,c1]) ).
cnf(d17,plain,
ifeq('class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'('t$ub'),true,ifeq(true,true,'c$ulessequals'('c$uplus'('c$u0','v$ug'('v$ux'),'t$ub'),'v$uk'('v$ux'),'t$ub'),true),true) = true,
inference(superposition,[status(thm)],[c6,c3]) ).
cnf(d18,plain,
ifeq(true,true,ifeq(true,true,'c$ulessequals'('c$uplus'('c$u0','v$ug'('v$ux'),'t$ub'),'v$uk'('v$ux'),'t$ub'),true),true) = true,
inference(demodulation,[status(thm)],[d17,d1]) ).
cnf(d19,plain,
ifeq(true,true,'c$ulessequals'('c$uplus'('c$u0','v$ug'('v$ux'),'t$ub'),'v$uk'('v$ux'),'t$ub'),true) = true,
inference(demodulation,[status(thm)],[d18,c1]) ).
cnf(d20,plain,
'c$ulessequals'('c$uplus'('c$u0','v$ug'('v$ux'),'t$ub'),'v$uk'('v$ux'),'t$ub') = true,
inference(demodulation,[status(thm)],[d19,c1]) ).
cnf(d21,plain,
'c$ulessequals'('v$ug'('v$ux'),'v$uk'('v$ux'),'t$ub') = true,
inference(demodulation,[status(thm)],[d20,d5]) ).
cnf(d22,plain,
ifeq(true,true,'c$ulessequals'('v$ug'('v$ux'),'v$uf'('v$ux'),'t$ub'),true) = true,
inference(superposition,[status(thm)],[d21,d16]) ).
cnf(d23,plain,
'c$ulessequals'('v$ug'('v$ux'),'v$uf'('v$ux'),'t$ub') = true,
inference(demodulation,[status(thm)],[d22,c1]) ).
cnf(d24,plain,
ifeq(true,true,'c$ulessequals'('c$u0','c$uminus'('v$uf'('v$ux'),'v$ug'('v$ux'),'t$ub'),'t$ub'),true) = true,
inference(superposition,[status(thm)],[d23,d8]) ).
cnf(d25,plain,
'c$ulessequals'('c$u0','c$uminus'('v$uf'('v$ux'),'v$ug'('v$ux'),'t$ub'),'t$ub') = true,
inference(demodulation,[status(thm)],[d24,c1]) ).
cnf(d26,plain,
$false,
inference(resolution,[status(thm)],[c8,d25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA023-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n013.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 22:05:36 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.13/1.83 % SZS status Unsatisfiable for theBenchmark.p
% 11.13/1.83 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------