%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL096-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 07:53:44 AM UTC 2026
% Result : Unsatisfiable 13.93s 55.02s
% Output : CNFRefutation 13.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of clauses : 27 ( 27 unt; 0 nHn; 3 RR)
% Number of literals : 27 ( 26 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 108 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ifeq_axiom,axiom,
ifeq(X0,X0,X1,X2) = X1 ).
cnf(condensed_detachment,axiom,
ifeq('is$ua$utheorem'(equivalent(X0,X1)),true,ifeq('is$ua$utheorem'(X0),true,'is$ua$utheorem'(X1),true),true) = true ).
cnf(lg_2,axiom,
'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),equivalent(X1,X2)),X3),X3)) = true ).
cnf(lg_3,axiom,
'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),X3),equivalent(equivalent(X1,X2),X3)),X4),X4)) = true ).
cnf(lg_4,axiom,
'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(X0,X1),X2),X3),equivalent(equivalent(equivalent(X0,X4),X2),equivalent(equivalent(X1,X4),X3)))) = true ).
cnf(prove_lg_1,negated_conjecture,
'is$ua$utheorem'(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)) != true ).
cnf(c0,plain,
ifeq(X0,X0,X1,X2) = X1,
inference(clausification,[status(esa)],[ifeq_axiom]) ).
cnf(c1,plain,
ifeq('is$ua$utheorem'(equivalent(X0,X1)),true,ifeq('is$ua$utheorem'(X0),true,'is$ua$utheorem'(X1),true),true) = true,
inference(clausification,[status(esa)],[condensed_detachment]) ).
cnf(c2,plain,
'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),equivalent(X1,X2)),X3),X3)) = true,
inference(clausification,[status(esa)],[lg_2]) ).
cnf(c3,plain,
'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),X3),equivalent(equivalent(X1,X2),X3)),X4),X4)) = true,
inference(clausification,[status(esa)],[lg_3]) ).
cnf(c4,plain,
'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(X0,X1),X2),X3),equivalent(equivalent(equivalent(X0,X4),X2),equivalent(equivalent(X1,X4),X3)))) = true,
inference(clausification,[status(esa)],[lg_4]) ).
cnf(c5,plain,
'is$ua$utheorem'(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)) != true,
inference(clausification,[status(esa)],[prove_lg_1]) ).
cnf(d0,plain,
ifeq('is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),equivalent(X1,X2)),X3),X3),X4)),true,ifeq(true,true,'is$ua$utheorem'(X4),true),true) = true,
inference(superposition,[status(thm)],[c2,c1]) ).
cnf(d1,plain,
ifeq('is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),equivalent(X2,X3)),X4),X4),X0)),true,'is$ua$utheorem'(X0),true) = true,
inference(demodulation,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
ifeq(true,true,'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),X4),X3),equivalent(equivalent(equivalent(X1,X2),X4),X3))),true) = true,
inference(superposition,[status(thm)],[c4,d1]) ).
cnf(d3,plain,
'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),X3),X4),equivalent(equivalent(equivalent(X1,X2),X3),X4))) = true,
inference(demodulation,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
ifeq(true,true,ifeq('is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),X3),X4)),true,'is$ua$utheorem'(equivalent(equivalent(equivalent(X1,X2),X3),X4)),true),true) = true,
inference(superposition,[status(thm)],[d3,c1]) ).
cnf(d5,plain,
ifeq('is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),X3),X4)),true,'is$ua$utheorem'(equivalent(equivalent(equivalent(X1,X2),X3),X4)),true) = true,
inference(demodulation,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
ifeq('is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),X3),equivalent(equivalent(X1,X2),X3)),X4),X4),X5)),true,ifeq(true,true,'is$ua$utheorem'(X5),true),true) = true,
inference(superposition,[status(thm)],[c3,c1]) ).
cnf(d7,plain,
ifeq('is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),X4),equivalent(equivalent(X2,X3),X4)),X5),X5),X0)),true,'is$ua$utheorem'(X0),true) = true,
inference(demodulation,[status(thm)],[d6,c0]) ).
cnf(d8,plain,
ifeq(true,true,'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),X3),X5),X4),equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X5),X4))),true) = true,
inference(superposition,[status(thm)],[c4,d7]) ).
cnf(d9,plain,
'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),X3),X4),X5),equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X4),X5))) = true,
inference(demodulation,[status(thm)],[d8,c0]) ).
cnf(d10,plain,
ifeq(true,true,'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X2),X3),equivalent(equivalent(X1,X2),equivalent(equivalent(X0,X1),X3))),X4),X4)),true) = true,
inference(superposition,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),X2),equivalent(equivalent(X3,X1),equivalent(equivalent(X0,X3),X2))),X4),X4)) = true,
inference(demodulation,[status(thm)],[d10,c0]) ).
cnf(d12,plain,
ifeq(true,true,'is$ua$utheorem'(equivalent(equivalent(equivalent(X2,equivalent(equivalent(X0,X0),X2)),X3),X3)),true) = true,
inference(superposition,[status(thm)],[d11,d5]) ).
cnf(d13,plain,
'is$ua$utheorem'(equivalent(equivalent(equivalent(X0,equivalent(equivalent(X1,X1),X0)),X2),X2)) = true,
inference(demodulation,[status(thm)],[d12,c0]) ).
cnf(d14,plain,
$false,
inference(resolution,[status(thm)],[d13,c5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL096-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n026.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Fri Sep 25 21:53:31 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.93/55.02 % SZS status Unsatisfiable for theBenchmark.p
% 13.93/55.02 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------