%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL443-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 07:54:38 AM UTC 2026
% Result : Unsatisfiable 33.16s 9.74s
% Output : CNFRefutation 33.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of clauses : 35 ( 35 unt; 0 nHn; 11 RR)
% Number of literals : 35 ( 34 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 64 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ifeq_axiom,axiom,
ifeq(X0,X0,X1,X2) = X1 ).
cnf(cls_PropLog_Othms_OMP_0,axiom,
ifeq('c$uin'('c$uPropLog$uOpl$uOop$uA$uN$u62'(X0,X1,X2),'c$uPropLog$uOthms'(X3,X2),'tc$uPropLog$uOpl'(X2)),true,ifeq('c$uin'(X0,'c$uPropLog$uOthms'(X3,X2),'tc$uPropLog$uOpl'(X2)),true,'c$uin'(X1,'c$uPropLog$uOthms'(X3,X2),'tc$uPropLog$uOpl'(X2)),true),true) = true ).
cnf(cls_PropLog_Odeduction_0,axiom,
ifeq('c$uin'(X0,'c$uPropLog$uOthms'('c$uinsert'(X1,X2,'tc$uPropLog$uOpl'(X3)),X3),'tc$uPropLog$uOpl'(X3)),true,'c$uin'('c$uPropLog$uOpl$uOop$uA$uN$u62'(X1,X0,X3),'c$uPropLog$uOthms'(X2,X3),'tc$uPropLog$uOpl'(X3)),true) = true ).
cnf(cls_PropLog_Othms_OH_0,axiom,
ifeq('c$uin'(X0,X1,'tc$uPropLog$uOpl'(X2)),true,'c$uin'(X0,'c$uPropLog$uOthms'(X1,X2),'tc$uPropLog$uOpl'(X2)),true) = true ).
cnf(cls_PropLog_Oweaken__left__insert_0,axiom,
ifeq('c$uin'(X0,'c$uPropLog$uOthms'(X1,X2),'tc$uPropLog$uOpl'(X2)),true,'c$uin'(X0,'c$uPropLog$uOthms'('c$uinsert'(X3,X1,'tc$uPropLog$uOpl'(X2)),X2),'tc$uPropLog$uOpl'(X2)),true) = true ).
cnf(cls_Set_OinsertCI_1,axiom,
'c$uin'(X0,'c$uinsert'(X0,X1,X2),X2) = true ).
cnf(cls_conjecture_0,negated_conjecture,
'c$uin'('v$up','c$uPropLog$uOthms'('v$uH','t$ua'),'tc$uPropLog$uOpl'('t$ua')) = true ).
cnf(cls_conjecture_1,negated_conjecture,
'c$uin'('c$uPropLog$uOpl$uOop$uA$uN$u62'('v$uq','c$uPropLog$uOpl$uOfalse','t$ua'),'c$uPropLog$uOthms'('v$uH','t$ua'),'tc$uPropLog$uOpl'('t$ua')) = true ).
cnf(cls_conjecture_2,negated_conjecture,
'c$uin'('c$uPropLog$uOpl$uOop$uA$uN$u62'('c$uPropLog$uOpl$uOop$uA$uN$u62'('v$up','v$uq','t$ua'),'c$uPropLog$uOpl$uOfalse','t$ua'),'c$uPropLog$uOthms'('v$uH','t$ua'),'tc$uPropLog$uOpl'('t$ua')) != true ).
cnf(c0,plain,
ifeq(X0,X0,X1,X2) = X1,
inference(clausification,[status(esa)],[ifeq_axiom]) ).
cnf(c1,plain,
ifeq('c$uin'('c$uPropLog$uOpl$uOop$uA$uN$u62'(X0,X1,X2),'c$uPropLog$uOthms'(X3,X2),'tc$uPropLog$uOpl'(X2)),true,ifeq('c$uin'(X0,'c$uPropLog$uOthms'(X3,X2),'tc$uPropLog$uOpl'(X2)),true,'c$uin'(X1,'c$uPropLog$uOthms'(X3,X2),'tc$uPropLog$uOpl'(X2)),true),true) = true,
inference(clausification,[status(esa)],[cls_PropLog_Othms_OMP_0]) ).
cnf(c2,plain,
ifeq('c$uin'(X0,'c$uPropLog$uOthms'('c$uinsert'(X1,X2,'tc$uPropLog$uOpl'(X3)),X3),'tc$uPropLog$uOpl'(X3)),true,'c$uin'('c$uPropLog$uOpl$uOop$uA$uN$u62'(X1,X0,X3),'c$uPropLog$uOthms'(X2,X3),'tc$uPropLog$uOpl'(X3)),true) = true,
inference(clausification,[status(esa)],[cls_PropLog_Odeduction_0]) ).
cnf(c3,plain,
ifeq('c$uin'(X0,X1,'tc$uPropLog$uOpl'(X2)),true,'c$uin'(X0,'c$uPropLog$uOthms'(X1,X2),'tc$uPropLog$uOpl'(X2)),true) = true,
inference(clausification,[status(esa)],[cls_PropLog_Othms_OH_0]) ).
cnf(c4,plain,
ifeq('c$uin'(X0,'c$uPropLog$uOthms'(X1,X2),'tc$uPropLog$uOpl'(X2)),true,'c$uin'(X0,'c$uPropLog$uOthms'('c$uinsert'(X3,X1,'tc$uPropLog$uOpl'(X2)),X2),'tc$uPropLog$uOpl'(X2)),true) = true,
inference(clausification,[status(esa)],[cls_PropLog_Oweaken__left__insert_0]) ).
cnf(c5,plain,
'c$uin'(X0,'c$uinsert'(X0,X1,X2),X2) = true,
inference(clausification,[status(esa)],[cls_Set_OinsertCI_1]) ).
cnf(c6,plain,
'c$uin'('v$up','c$uPropLog$uOthms'('v$uH','t$ua'),'tc$uPropLog$uOpl'('t$ua')) = true,
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c7,plain,
'c$uin'('c$uPropLog$uOpl$uOop$uA$uN$u62'('v$uq','c$uPropLog$uOpl$uOfalse','t$ua'),'c$uPropLog$uOthms'('v$uH','t$ua'),'tc$uPropLog$uOpl'('t$ua')) = true,
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c8,plain,
'c$uin'('c$uPropLog$uOpl$uOop$uA$uN$u62'('c$uPropLog$uOpl$uOop$uA$uN$u62'('v$up','v$uq','t$ua'),'c$uPropLog$uOpl$uOfalse','t$ua'),'c$uPropLog$uOthms'('v$uH','t$ua'),'tc$uPropLog$uOpl'('t$ua')) != true,
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(d0,plain,
ifeq(true,true,'c$uin'('c$uPropLog$uOpl$uOop$uA$uN$u62'('v$uq','c$uPropLog$uOpl$uOfalse','t$ua'),'c$uPropLog$uOthms'('c$uinsert'(X0,'v$uH','tc$uPropLog$uOpl'('t$ua')),'t$ua'),'tc$uPropLog$uOpl'('t$ua')),true) = true,
inference(superposition,[status(thm)],[c7,c4]) ).
cnf(d1,plain,
'c$uin'('c$uPropLog$uOpl$uOop$uA$uN$u62'('v$uq','c$uPropLog$uOpl$uOfalse','t$ua'),'c$uPropLog$uOthms'('c$uinsert'(X0,'v$uH','tc$uPropLog$uOpl'('t$ua')),'t$ua'),'tc$uPropLog$uOpl'('t$ua')) = true,
inference(demodulation,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
ifeq(true,true,ifeq('c$uin'('v$uq','c$uPropLog$uOthms'('c$uinsert'(X0,'v$uH','tc$uPropLog$uOpl'('t$ua')),'t$ua'),'tc$uPropLog$uOpl'('t$ua')),true,'c$uin'('c$uPropLog$uOpl$uOfalse','c$uPropLog$uOthms'('c$uinsert'(X0,'v$uH','tc$uPropLog$uOpl'('t$ua')),'t$ua'),'tc$uPropLog$uOpl'('t$ua')),true),true) = true,
inference(superposition,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
ifeq('c$uin'('v$uq','c$uPropLog$uOthms'('c$uinsert'(X0,'v$uH','tc$uPropLog$uOpl'('t$ua')),'t$ua'),'tc$uPropLog$uOpl'('t$ua')),true,'c$uin'('c$uPropLog$uOpl$uOfalse','c$uPropLog$uOthms'('c$uinsert'(X0,'v$uH','tc$uPropLog$uOpl'('t$ua')),'t$ua'),'tc$uPropLog$uOpl'('t$ua')),true) = true,
inference(demodulation,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
ifeq(true,true,'c$uin'(X0,'c$uPropLog$uOthms'('c$uinsert'(X0,X1,'tc$uPropLog$uOpl'(X2)),X2),'tc$uPropLog$uOpl'(X2)),true) = true,
inference(superposition,[status(thm)],[c5,c3]) ).
cnf(d5,plain,
'c$uin'(X0,'c$uPropLog$uOthms'('c$uinsert'(X0,X1,'tc$uPropLog$uOpl'(X2)),X2),'tc$uPropLog$uOpl'(X2)) = true,
inference(demodulation,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
ifeq(true,true,ifeq('c$uin'(X0,'c$uPropLog$uOthms'('c$uinsert'('c$uPropLog$uOpl$uOop$uA$uN$u62'(X0,X1,X2),X3,'tc$uPropLog$uOpl'(X2)),X2),'tc$uPropLog$uOpl'(X2)),true,'c$uin'(X1,'c$uPropLog$uOthms'('c$uinsert'('c$uPropLog$uOpl$uOop$uA$uN$u62'(X0,X1,X2),X3,'tc$uPropLog$uOpl'(X2)),X2),'tc$uPropLog$uOpl'(X2)),true),true) = true,
inference(superposition,[status(thm)],[d5,c1]) ).
cnf(d7,plain,
ifeq('c$uin'(X0,'c$uPropLog$uOthms'('c$uinsert'('c$uPropLog$uOpl$uOop$uA$uN$u62'(X0,X1,X2),X3,'tc$uPropLog$uOpl'(X2)),X2),'tc$uPropLog$uOpl'(X2)),true,'c$uin'(X1,'c$uPropLog$uOthms'('c$uinsert'('c$uPropLog$uOpl$uOop$uA$uN$u62'(X0,X1,X2),X3,'tc$uPropLog$uOpl'(X2)),X2),'tc$uPropLog$uOpl'(X2)),true) = true,
inference(demodulation,[status(thm)],[d6,c0]) ).
cnf(d8,plain,
ifeq(true,true,'c$uin'('v$up','c$uPropLog$uOthms'('c$uinsert'(X0,'v$uH','tc$uPropLog$uOpl'('t$ua')),'t$ua'),'tc$uPropLog$uOpl'('t$ua')),true) = true,
inference(superposition,[status(thm)],[c6,c4]) ).
cnf(d9,plain,
'c$uin'('v$up','c$uPropLog$uOthms'('c$uinsert'(X0,'v$uH','tc$uPropLog$uOpl'('t$ua')),'t$ua'),'tc$uPropLog$uOpl'('t$ua')) = true,
inference(demodulation,[status(thm)],[d8,c0]) ).
cnf(d10,plain,
ifeq(true,true,'c$uin'(X0,'c$uPropLog$uOthms'('c$uinsert'('c$uPropLog$uOpl$uOop$uA$uN$u62'('v$up',X0,'t$ua'),'v$uH','tc$uPropLog$uOpl'('t$ua')),'t$ua'),'tc$uPropLog$uOpl'('t$ua')),true) = true,
inference(superposition,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
'c$uin'(X0,'c$uPropLog$uOthms'('c$uinsert'('c$uPropLog$uOpl$uOop$uA$uN$u62'('v$up',X0,'t$ua'),'v$uH','tc$uPropLog$uOpl'('t$ua')),'t$ua'),'tc$uPropLog$uOpl'('t$ua')) = true,
inference(demodulation,[status(thm)],[d10,c0]) ).
cnf(d12,plain,
ifeq(true,true,'c$uin'('c$uPropLog$uOpl$uOfalse','c$uPropLog$uOthms'('c$uinsert'('c$uPropLog$uOpl$uOop$uA$uN$u62'('v$up','v$uq','t$ua'),'v$uH','tc$uPropLog$uOpl'('t$ua')),'t$ua'),'tc$uPropLog$uOpl'('t$ua')),true) = true,
inference(superposition,[status(thm)],[d11,d3]) ).
cnf(d13,plain,
'c$uin'('c$uPropLog$uOpl$uOfalse','c$uPropLog$uOthms'('c$uinsert'('c$uPropLog$uOpl$uOop$uA$uN$u62'('v$up','v$uq','t$ua'),'v$uH','tc$uPropLog$uOpl'('t$ua')),'t$ua'),'tc$uPropLog$uOpl'('t$ua')) = true,
inference(demodulation,[status(thm)],[d12,c0]) ).
cnf(d14,plain,
ifeq(true,true,'c$uin'('c$uPropLog$uOpl$uOop$uA$uN$u62'('c$uPropLog$uOpl$uOop$uA$uN$u62'('v$up','v$uq','t$ua'),'c$uPropLog$uOpl$uOfalse','t$ua'),'c$uPropLog$uOthms'('v$uH','t$ua'),'tc$uPropLog$uOpl'('t$ua')),true) = true,
inference(superposition,[status(thm)],[d13,c2]) ).
cnf(d15,plain,
'c$uin'('c$uPropLog$uOpl$uOop$uA$uN$u62'('c$uPropLog$uOpl$uOop$uA$uN$u62'('v$up','v$uq','t$ua'),'c$uPropLog$uOpl$uOfalse','t$ua'),'c$uPropLog$uOthms'('v$uH','t$ua'),'tc$uPropLog$uOpl'('t$ua')) = true,
inference(demodulation,[status(thm)],[d14,c0]) ).
cnf(d16,plain,
$false,
inference(resolution,[status(thm)],[c8,d15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL443-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/5.40 % Computer : n003.cluster.edu
% 0.15/5.40 % Model : x86_64 x86_64
% 0.15/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.40 % Memory : 8046.5625MB
% 0.15/5.40 % OS : Linux 6.8.0-71-generic
% 0.15/5.40 % CPULimit : 300
% 0.15/5.40 % WCLimit : 300
% 0.15/5.40 % DateTime : Fri Sep 25 22:35:45 UTC 2026
% 0.15/5.40 % CPUTime :
% 0.15/5.40 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 33.16/9.74 % SZS status Unsatisfiable for theBenchmark.p
% 33.16/9.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------