%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL416-10 : 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 : 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 07:54:33 AM UTC 2026
% Result : Unsatisfiable 96.32s 29.06s
% Output : CNFRefutation 96.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 4
% Syntax : Number of clauses : 61 ( 61 unt; 0 nHn; 3 RR)
% Number of literals : 61 ( 60 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 14 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-4 aty)
% Number of variables : 300 ( 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(xcb,axiom,
'is$ua$utheorem'(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2))) = true ).
cnf(prove_reflexivity,negated_conjecture,
'is$ua$utheorem'(equivalent(a,a)) != 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(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2))) = true,
inference(clausification,[status(esa)],[xcb]) ).
cnf(c3,plain,
'is$ua$utheorem'(equivalent(a,a)) != true,
inference(clausification,[status(esa)],[prove_reflexivity]) ).
cnf(d0,plain,
ifeq('is$ua$utheorem'(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),X3)),true,ifeq(true,true,'is$ua$utheorem'(X3),true),true) = true,
inference(superposition,[status(thm)],[c2,c1]) ).
cnf(d1,plain,
ifeq('is$ua$utheorem'(equivalent(equivalent(X1,equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X3)),X0)),true,'is$ua$utheorem'(X0),true) = true,
inference(demodulation,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
ifeq(true,true,ifeq('is$ua$utheorem'(X0),true,'is$ua$utheorem'(equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),true),true) = true,
inference(superposition,[status(thm)],[c2,c1]) ).
cnf(d3,plain,
ifeq('is$ua$utheorem'(X0),true,'is$ua$utheorem'(equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),true) = true,
inference(demodulation,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
ifeq(true,true,'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),X3),equivalent(X4,X3)),X4)),true) = true,
inference(superposition,[status(thm)],[c2,d3]) ).
cnf(d5,plain,
'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),X3),equivalent(X4,X3)),X4)) = true,
inference(demodulation,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
ifeq(true,true,'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),X3),X4),equivalent(X3,X4))),true) = true,
inference(superposition,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),X3),X4),equivalent(X3,X4))) = true,
inference(demodulation,[status(thm)],[d6,c0]) ).
cnf(d8,plain,
ifeq(true,true,ifeq('is$ua$utheorem'(equivalent(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),X3),X4)),true,'is$ua$utheorem'(equivalent(X3,X4)),true),true) = true,
inference(superposition,[status(thm)],[d7,c1]) ).
cnf(d9,plain,
ifeq('is$ua$utheorem'(equivalent(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),X3),X4)),true,'is$ua$utheorem'(equivalent(X3,X4)),true) = true,
inference(demodulation,[status(thm)],[d8,c0]) ).
cnf(d10,plain,
ifeq(true,true,ifeq('is$ua$utheorem'(equivalent(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),X3),equivalent(X4,X3))),true,'is$ua$utheorem'(X4),true),true) = true,
inference(superposition,[status(thm)],[d5,c1]) ).
cnf(d11,plain,
ifeq('is$ua$utheorem'(equivalent(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),X3),equivalent(X4,X3))),true,'is$ua$utheorem'(X4),true) = true,
inference(demodulation,[status(thm)],[d10,c0]) ).
cnf(d12,plain,
ifeq('is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),X3),X4),equivalent(X3,X4)),X5)),true,ifeq(true,true,'is$ua$utheorem'(X5),true),true) = true,
inference(superposition,[status(thm)],[d7,c1]) ).
cnf(d13,plain,
ifeq('is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(X1,equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X3)),X4),X5),equivalent(X4,X5)),X0)),true,'is$ua$utheorem'(X0),true) = true,
inference(demodulation,[status(thm)],[d12,c0]) ).
cnf(d14,plain,
ifeq(true,true,'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),X3),equivalent(X4,X3)),X4),X5),equivalent(X6,X5)),X6)),true) = true,
inference(superposition,[status(thm)],[d5,d3]) ).
cnf(d15,plain,
'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),X3),equivalent(X4,X3)),X4),X5),equivalent(X6,X5)),X6)) = true,
inference(demodulation,[status(thm)],[d14,c0]) ).
cnf(d16,plain,
ifeq(true,true,'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),X3),equivalent(X4,X3)),X4),X5),X6),equivalent(X5,X6))),true) = true,
inference(superposition,[status(thm)],[d15,d1]) ).
cnf(d17,plain,
'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),X3),equivalent(X4,X3)),X4),X5),X6),equivalent(X5,X6))) = true,
inference(demodulation,[status(thm)],[d16,c0]) ).
cnf(d18,plain,
ifeq(true,true,ifeq('is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),X3),equivalent(X4,X3)),X4),X5),X6)),true,'is$ua$utheorem'(equivalent(X5,X6)),true),true) = true,
inference(superposition,[status(thm)],[d17,c1]) ).
cnf(d19,plain,
ifeq('is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),X3),equivalent(X4,X3)),X4),X5),X6)),true,'is$ua$utheorem'(equivalent(X5,X6)),true) = true,
inference(demodulation,[status(thm)],[d18,c0]) ).
cnf(d20,plain,
ifeq(true,true,'is$ua$utheorem'(equivalent(X3,equivalent(equivalent(equivalent(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),X3),X4),equivalent(X5,X4)),X5))),true) = true,
inference(superposition,[status(thm)],[d7,d1]) ).
cnf(d21,plain,
'is$ua$utheorem'(equivalent(X0,equivalent(equivalent(equivalent(equivalent(equivalent(X1,equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X3)),X0),X4),equivalent(X5,X4)),X5))) = true,
inference(demodulation,[status(thm)],[d20,c0]) ).
cnf(d22,plain,
ifeq(true,true,'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(X3,equivalent(equivalent(equivalent(X3,X4),equivalent(X5,X4)),X5)),equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2))),X6),equivalent(X7,X6)),X7)),true) = true,
inference(superposition,[status(thm)],[d21,d1]) ).
cnf(d23,plain,
'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),equivalent(X3,equivalent(equivalent(equivalent(X3,X4),equivalent(X5,X4)),X5))),X6),equivalent(X7,X6)),X7)) = true,
inference(demodulation,[status(thm)],[d22,c0]) ).
cnf(d24,plain,
ifeq(true,true,'is$ua$utheorem'(equivalent(equivalent(X5,equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2))),X5)),true) = true,
inference(superposition,[status(thm)],[d23,d19]) ).
cnf(d25,plain,
'is$ua$utheorem'(equivalent(equivalent(X0,equivalent(X1,equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X3))),X0)) = true,
inference(demodulation,[status(thm)],[d24,c0]) ).
cnf(d26,plain,
ifeq(true,true,'is$ua$utheorem'(equivalent(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),X3),equivalent(equivalent(equivalent(X3,X4),equivalent(X5,X4)),X5))),true) = true,
inference(superposition,[status(thm)],[d25,d13]) ).
cnf(d27,plain,
'is$ua$utheorem'(equivalent(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),X3),equivalent(equivalent(equivalent(X3,X4),equivalent(X5,X4)),X5))) = true,
inference(demodulation,[status(thm)],[d26,c0]) ).
cnf(d28,plain,
ifeq(true,true,'is$ua$utheorem'(equivalent(equivalent(X3,X4),equivalent(X3,X4))),true) = true,
inference(superposition,[status(thm)],[d27,d11]) ).
cnf(d29,plain,
'is$ua$utheorem'(equivalent(equivalent(X0,X1),equivalent(X0,X1))) = true,
inference(demodulation,[status(thm)],[d28,c0]) ).
cnf(d30,plain,
ifeq(true,true,'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X1)),X2),equivalent(X3,X2)),X3)),true) = true,
inference(superposition,[status(thm)],[d29,d3]) ).
cnf(d31,plain,
'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X1)),X2),equivalent(X3,X2)),X3)) = true,
inference(demodulation,[status(thm)],[d30,c0]) ).
cnf(d32,plain,
ifeq(true,true,'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X1)),X2),X3),equivalent(X2,X3))),true) = true,
inference(superposition,[status(thm)],[d31,d1]) ).
cnf(d33,plain,
'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X1)),X2),X3),equivalent(X2,X3))) = true,
inference(demodulation,[status(thm)],[d32,c0]) ).
cnf(d34,plain,
ifeq(true,true,'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X1)),X2),X3),equivalent(X2,X3)),X4),equivalent(X5,X4)),X5)),true) = true,
inference(superposition,[status(thm)],[d33,d3]) ).
cnf(d35,plain,
'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X1)),X2),X3),equivalent(X2,X3)),X4),equivalent(X5,X4)),X5)) = true,
inference(demodulation,[status(thm)],[d34,c0]) ).
cnf(d36,plain,
ifeq(true,true,ifeq('is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X1)),X2),X3),equivalent(X2,X3)),X4),equivalent(X5,X4))),true,'is$ua$utheorem'(X5),true),true) = true,
inference(superposition,[status(thm)],[d35,c1]) ).
cnf(d37,plain,
ifeq('is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X1)),X2),X3),equivalent(X2,X3)),X4),equivalent(X5,X4))),true,'is$ua$utheorem'(X5),true) = true,
inference(demodulation,[status(thm)],[d36,c0]) ).
cnf(d38,plain,
ifeq(true,true,'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),X3),X4),equivalent(X3,X4)),X5),equivalent(X6,X5)),X6)),true) = true,
inference(superposition,[status(thm)],[d7,d3]) ).
cnf(d39,plain,
'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),X3),X4),equivalent(X3,X4)),X5),equivalent(X6,X5)),X6)) = true,
inference(demodulation,[status(thm)],[d38,c0]) ).
cnf(d40,plain,
ifeq(true,true,'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),X3),X4),equivalent(X3,X4)),X5),X6),equivalent(X5,X6))),true) = true,
inference(superposition,[status(thm)],[d39,d1]) ).
cnf(d41,plain,
'is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),X3),X4),equivalent(X3,X4)),X5),X6),equivalent(X5,X6))) = true,
inference(demodulation,[status(thm)],[d40,c0]) ).
cnf(d42,plain,
ifeq(true,true,ifeq('is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),X3),X4),equivalent(X3,X4)),X5),X6)),true,'is$ua$utheorem'(equivalent(X5,X6)),true),true) = true,
inference(superposition,[status(thm)],[d41,c1]) ).
cnf(d43,plain,
ifeq('is$ua$utheorem'(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),X3),X4),equivalent(X3,X4)),X5),X6)),true,'is$ua$utheorem'(equivalent(X5,X6)),true) = true,
inference(demodulation,[status(thm)],[d42,c0]) ).
cnf(d44,plain,
ifeq(true,true,'is$ua$utheorem'(equivalent(equivalent(X6,equivalent(equivalent(X5,equivalent(equivalent(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),X3),equivalent(X4,X3)),X4)),X5)),X6)),true) = true,
inference(superposition,[status(thm)],[d15,d43]) ).
cnf(d45,plain,
'is$ua$utheorem'(equivalent(equivalent(X0,equivalent(equivalent(X1,equivalent(equivalent(equivalent(equivalent(X2,equivalent(equivalent(equivalent(X2,X3),equivalent(X4,X3)),X4)),X5),equivalent(X6,X5)),X6)),X1)),X0)) = true,
inference(demodulation,[status(thm)],[d44,c0]) ).
cnf(d46,plain,
ifeq(true,true,'is$ua$utheorem'(equivalent(equivalent(equivalent(X3,equivalent(equivalent(equivalent(equivalent(X4,equivalent(equivalent(equivalent(X4,X5),equivalent(X6,X5)),X6)),X7),equivalent(X8,X7)),X8)),X3),equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)))),true) = true,
inference(superposition,[status(thm)],[d45,d9]) ).
cnf(d47,plain,
'is$ua$utheorem'(equivalent(equivalent(equivalent(X0,equivalent(equivalent(equivalent(equivalent(X1,equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X3)),X4),equivalent(X5,X4)),X5)),X0),equivalent(X6,equivalent(equivalent(equivalent(X6,X7),equivalent(X8,X7)),X8)))) = true,
inference(demodulation,[status(thm)],[d46,c0]) ).
cnf(d48,plain,
ifeq(true,true,'is$ua$utheorem'(equivalent(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),X3),X3)),true) = true,
inference(superposition,[status(thm)],[d47,d37]) ).
cnf(d49,plain,
'is$ua$utheorem'(equivalent(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2)),X3),X3)) = true,
inference(demodulation,[status(thm)],[d48,c0]) ).
cnf(d50,plain,
ifeq(true,true,'is$ua$utheorem'(equivalent(X3,X3)),true) = true,
inference(superposition,[status(thm)],[d49,d9]) ).
cnf(d51,plain,
'is$ua$utheorem'(equivalent(X0,X0)) = true,
inference(demodulation,[status(thm)],[d50,c0]) ).
cnf(d52,plain,
$false,
inference(resolution,[status(thm)],[d51,c3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL416-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.46 % Computer : n002.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Fri Sep 25 22:31:36 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 96.32/29.06 % SZS status Unsatisfiable for theBenchmark.p
% 96.32/29.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------