%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL050-10 : 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 : n006.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 07:53:37 AM UTC 2026
% Result : Unsatisfiable 27.02s 23.69s
% Output : CNFRefutation 27.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 6
% Syntax : Number of clauses : 87 ( 87 unt; 0 nHn; 3 RR)
% Number of literals : 87 ( 86 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 222 ( 56 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ifeq_axiom,axiom,
ifeq(X0,X0,X1,X2) = X1 ).
cnf(condensed_detachment,axiom,
ifeq('is$ua$utheorem'(implies(X0,X1)),true,ifeq('is$ua$utheorem'(X0),true,'is$ua$utheorem'(X1),true),true) = true ).
cnf(cn_1,axiom,
'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) = true ).
cnf(cn_2,axiom,
'is$ua$utheorem'(implies(implies(not(X0),X0),X0)) = true ).
cnf(cn_3,axiom,
'is$ua$utheorem'(implies(X0,implies(not(X0),X1))) = true ).
cnf(prove_cn_21,negated_conjecture,
'is$ua$utheorem'(implies(implies(a,implies(b,c)),implies(b,implies(a,c)))) != true ).
cnf(c0,plain,
ifeq(X0,X0,X1,X2) = X1,
inference(clausification,[status(esa)],[ifeq_axiom]) ).
cnf(c1,plain,
ifeq('is$ua$utheorem'(implies(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'(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) = true,
inference(clausification,[status(esa)],[cn_1]) ).
cnf(c3,plain,
'is$ua$utheorem'(implies(implies(not(X0),X0),X0)) = true,
inference(clausification,[status(esa)],[cn_2]) ).
cnf(c4,plain,
'is$ua$utheorem'(implies(X0,implies(not(X0),X1))) = true,
inference(clausification,[status(esa)],[cn_3]) ).
cnf(c5,plain,
'is$ua$utheorem'(implies(implies(a,implies(b,c)),implies(b,implies(a,c)))) != true,
inference(clausification,[status(esa)],[prove_cn_21]) ).
cnf(d0,plain,
ifeq(true,true,ifeq('is$ua$utheorem'(implies(X0,X1)),true,'is$ua$utheorem'(implies(implies(X1,X2),implies(X0,X2))),true),true) = true,
inference(superposition,[status(thm)],[c2,c1]) ).
cnf(d1,plain,
ifeq('is$ua$utheorem'(implies(X0,X1)),true,'is$ua$utheorem'(implies(implies(X1,X2),implies(X0,X2))),true) = true,
inference(demodulation,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
ifeq(true,true,'is$ua$utheorem'(implies(implies(implies(implies(X1,X2),implies(X0,X2)),X3),implies(implies(X0,X1),X3))),true) = true,
inference(superposition,[status(thm)],[c2,d1]) ).
cnf(d3,plain,
'is$ua$utheorem'(implies(implies(implies(implies(X0,X1),implies(X2,X1)),X3),implies(implies(X2,X0),X3))) = true,
inference(demodulation,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
ifeq(true,true,ifeq('is$ua$utheorem'(implies(implies(implies(X0,X1),implies(X2,X1)),X3)),true,'is$ua$utheorem'(implies(implies(X2,X0),X3)),true),true) = true,
inference(superposition,[status(thm)],[d3,c1]) ).
cnf(d5,plain,
ifeq('is$ua$utheorem'(implies(implies(implies(X0,X1),implies(X2,X1)),X3)),true,'is$ua$utheorem'(implies(implies(X2,X0),X3)),true) = true,
inference(demodulation,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
ifeq('is$ua$utheorem'(implies(implies(X0,implies(not(X0),X1)),X2)),true,ifeq(true,true,'is$ua$utheorem'(X2),true),true) = true,
inference(superposition,[status(thm)],[c4,c1]) ).
cnf(d7,plain,
ifeq('is$ua$utheorem'(implies(implies(X1,implies(not(X1),X2)),X0)),true,'is$ua$utheorem'(X0),true) = true,
inference(demodulation,[status(thm)],[d6,c0]) ).
cnf(d8,plain,
ifeq(true,true,'is$ua$utheorem'(implies(implies(implies(not(X0),X1),X2),implies(X0,X2))),true) = true,
inference(superposition,[status(thm)],[c2,d7]) ).
cnf(d9,plain,
'is$ua$utheorem'(implies(implies(implies(not(X0),X1),X2),implies(X0,X2))) = true,
inference(demodulation,[status(thm)],[d8,c0]) ).
cnf(d10,plain,
ifeq('is$ua$utheorem'(implies(implies(implies(implies(not(X0),X1),X2),implies(X0,X2)),X3)),true,ifeq(true,true,'is$ua$utheorem'(X3),true),true) = true,
inference(superposition,[status(thm)],[d9,c1]) ).
cnf(d11,plain,
ifeq('is$ua$utheorem'(implies(implies(implies(implies(not(X1),X2),X3),implies(X1,X3)),X0)),true,'is$ua$utheorem'(X0),true) = true,
inference(demodulation,[status(thm)],[d10,c0]) ).
cnf(d12,plain,
ifeq(true,true,ifeq('is$ua$utheorem'(implies(implies(not(X0),X1),X2)),true,'is$ua$utheorem'(implies(X0,X2)),true),true) = true,
inference(superposition,[status(thm)],[d9,c1]) ).
cnf(d13,plain,
ifeq('is$ua$utheorem'(implies(implies(not(X0),X1),X2)),true,'is$ua$utheorem'(implies(X0,X2)),true) = true,
inference(demodulation,[status(thm)],[d12,c0]) ).
cnf(d14,plain,
ifeq('is$ua$utheorem'(implies(implies(implies(not(X0),X0),X0),X1)),true,ifeq(true,true,'is$ua$utheorem'(X1),true),true) = true,
inference(superposition,[status(thm)],[c3,c1]) ).
cnf(d15,plain,
ifeq('is$ua$utheorem'(implies(implies(implies(not(X1),X1),X1),X0)),true,'is$ua$utheorem'(X0),true) = true,
inference(demodulation,[status(thm)],[d14,c0]) ).
cnf(d16,plain,
ifeq(true,true,'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(not(X0),X0),X1))),true) = true,
inference(superposition,[status(thm)],[c2,d15]) ).
cnf(d17,plain,
'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(not(X0),X0),X1))) = true,
inference(demodulation,[status(thm)],[d16,c0]) ).
cnf(d18,plain,
ifeq(true,true,'is$ua$utheorem'(implies(implies(not(X0),X0),implies(not(X0),X1))),true) = true,
inference(superposition,[status(thm)],[d17,d7]) ).
cnf(d19,plain,
'is$ua$utheorem'(implies(implies(not(X0),X0),implies(not(X0),X1))) = true,
inference(demodulation,[status(thm)],[d18,c0]) ).
cnf(d20,plain,
ifeq('is$ua$utheorem'(implies(implies(implies(not(X0),X0),implies(not(X0),X1)),X2)),true,ifeq(true,true,'is$ua$utheorem'(X2),true),true) = true,
inference(superposition,[status(thm)],[d19,c1]) ).
cnf(d21,plain,
ifeq('is$ua$utheorem'(implies(implies(implies(not(X1),X1),implies(not(X1),X2)),X0)),true,'is$ua$utheorem'(X0),true) = true,
inference(demodulation,[status(thm)],[d20,c0]) ).
cnf(d22,plain,
ifeq('is$ua$utheorem'(implies(implies(implies(X0,X1),implies(implies(not(X0),X0),X1)),X2)),true,ifeq(true,true,'is$ua$utheorem'(X2),true),true) = true,
inference(superposition,[status(thm)],[d17,c1]) ).
cnf(d23,plain,
ifeq('is$ua$utheorem'(implies(implies(implies(X1,X2),implies(implies(not(X1),X1),X2)),X0)),true,'is$ua$utheorem'(X0),true) = true,
inference(demodulation,[status(thm)],[d22,c0]) ).
cnf(d24,plain,
ifeq(true,true,ifeq('is$ua$utheorem'(X0),true,'is$ua$utheorem'(implies(not(X0),X1)),true),true) = true,
inference(superposition,[status(thm)],[c4,c1]) ).
cnf(d25,plain,
ifeq('is$ua$utheorem'(X0),true,'is$ua$utheorem'(implies(not(X0),X1)),true) = true,
inference(demodulation,[status(thm)],[d24,c0]) ).
cnf(d26,plain,
ifeq(true,true,'is$ua$utheorem'(implies(X0,X0)),true) = true,
inference(superposition,[status(thm)],[d9,d15]) ).
cnf(d27,plain,
'is$ua$utheorem'(implies(X0,X0)) = true,
inference(demodulation,[status(thm)],[d26,c0]) ).
cnf(d28,plain,
ifeq(true,true,'is$ua$utheorem'(implies(not(implies(X0,X0)),X1)),true) = true,
inference(superposition,[status(thm)],[d27,d25]) ).
cnf(d29,plain,
'is$ua$utheorem'(implies(not(implies(X0,X0)),X1)) = true,
inference(demodulation,[status(thm)],[d28,c0]) ).
cnf(d30,plain,
ifeq(true,true,'is$ua$utheorem'(implies(implies(X1,X2),implies(not(implies(X0,X0)),X2))),true) = true,
inference(superposition,[status(thm)],[d29,d1]) ).
cnf(d31,plain,
'is$ua$utheorem'(implies(implies(X0,X1),implies(not(implies(X2,X2)),X1))) = true,
inference(demodulation,[status(thm)],[d30,c0]) ).
cnf(d32,plain,
ifeq(true,true,'is$ua$utheorem'(implies(X0,implies(not(implies(X2,X2)),X1))),true) = true,
inference(superposition,[status(thm)],[d31,d13]) ).
cnf(d33,plain,
'is$ua$utheorem'(implies(X0,implies(not(implies(X1,X1)),X2))) = true,
inference(demodulation,[status(thm)],[d32,c0]) ).
cnf(d34,plain,
ifeq(true,true,'is$ua$utheorem'(implies(implies(implies(not(implies(X1,X1)),X2),X3),implies(X0,X3))),true) = true,
inference(superposition,[status(thm)],[d33,d1]) ).
cnf(d35,plain,
'is$ua$utheorem'(implies(implies(implies(not(implies(X0,X0)),X1),X2),implies(X3,X2))) = true,
inference(demodulation,[status(thm)],[d34,c0]) ).
cnf(d36,plain,
ifeq(true,true,'is$ua$utheorem'(implies(X1,implies(X0,X0))),true) = true,
inference(superposition,[status(thm)],[d35,d15]) ).
cnf(d37,plain,
'is$ua$utheorem'(implies(X0,implies(X1,X1))) = true,
inference(demodulation,[status(thm)],[d36,c0]) ).
cnf(d38,plain,
ifeq(true,true,'is$ua$utheorem'(implies(implies(implies(X1,X1),X2),implies(X0,X2))),true) = true,
inference(superposition,[status(thm)],[d37,d1]) ).
cnf(d39,plain,
'is$ua$utheorem'(implies(implies(implies(X0,X0),X1),implies(X2,X1))) = true,
inference(demodulation,[status(thm)],[d38,c0]) ).
cnf(d40,plain,
ifeq(true,true,'is$ua$utheorem'(implies(X1,implies(implies(not(X0),X0),X0))),true) = true,
inference(superposition,[status(thm)],[d39,d23]) ).
cnf(d41,plain,
'is$ua$utheorem'(implies(X0,implies(implies(not(X1),X1),X1))) = true,
inference(demodulation,[status(thm)],[d40,c0]) ).
cnf(d42,plain,
ifeq('is$ua$utheorem'(implies(implies(X0,implies(implies(not(X1),X1),X1)),X2)),true,ifeq(true,true,'is$ua$utheorem'(X2),true),true) = true,
inference(superposition,[status(thm)],[d41,c1]) ).
cnf(d43,plain,
ifeq('is$ua$utheorem'(implies(implies(X1,implies(implies(not(X2),X2),X2)),X0)),true,'is$ua$utheorem'(X0),true) = true,
inference(demodulation,[status(thm)],[d42,c0]) ).
cnf(d44,plain,
ifeq(true,true,'is$ua$utheorem'(implies(implies(implies(implies(not(X1),X1),X1),X2),implies(X0,X2))),true) = true,
inference(superposition,[status(thm)],[d41,d1]) ).
cnf(d45,plain,
'is$ua$utheorem'(implies(implies(implies(implies(not(X0),X0),X0),X1),implies(X2,X1))) = true,
inference(demodulation,[status(thm)],[d44,c0]) ).
cnf(d46,plain,
ifeq(true,true,'is$ua$utheorem'(implies(implies(X1,implies(not(X0),X0)),implies(X2,implies(X1,X0)))),true) = true,
inference(superposition,[status(thm)],[d45,d5]) ).
cnf(d47,plain,
'is$ua$utheorem'(implies(implies(X0,implies(not(X1),X1)),implies(X2,implies(X0,X1)))) = true,
inference(demodulation,[status(thm)],[d46,c0]) ).
cnf(d48,plain,
ifeq(true,true,'is$ua$utheorem'(implies(implies(not(X1),X0),implies(X2,implies(implies(X0,X1),X1)))),true) = true,
inference(superposition,[status(thm)],[d47,d5]) ).
cnf(d49,plain,
'is$ua$utheorem'(implies(implies(not(X0),X1),implies(X2,implies(implies(X1,X0),X0)))) = true,
inference(demodulation,[status(thm)],[d48,c0]) ).
cnf(d50,plain,
ifeq(true,true,'is$ua$utheorem'(implies(X2,implies(implies(implies(implies(not(X1),X1),X1),X0),X0))),true) = true,
inference(superposition,[status(thm)],[d49,d43]) ).
cnf(d51,plain,
'is$ua$utheorem'(implies(X0,implies(implies(implies(implies(not(X1),X1),X1),X2),X2))) = true,
inference(demodulation,[status(thm)],[d50,c0]) ).
cnf(d52,plain,
ifeq(true,true,'is$ua$utheorem'(implies(implies(implies(implies(not(X2),X2),X2),X3),X3)),true) = true,
inference(superposition,[status(thm)],[d51,d21]) ).
cnf(d53,plain,
'is$ua$utheorem'(implies(implies(implies(implies(not(X0),X0),X0),X1),X1)) = true,
inference(demodulation,[status(thm)],[d52,c0]) ).
cnf(d54,plain,
ifeq(true,true,'is$ua$utheorem'(implies(implies(X1,implies(not(X0),X0)),implies(X1,X0))),true) = true,
inference(superposition,[status(thm)],[d53,d5]) ).
cnf(d55,plain,
'is$ua$utheorem'(implies(implies(X0,implies(not(X1),X1)),implies(X0,X1))) = true,
inference(demodulation,[status(thm)],[d54,c0]) ).
cnf(d56,plain,
ifeq(true,true,'is$ua$utheorem'(implies(implies(not(X1),X0),implies(implies(X0,X1),X1))),true) = true,
inference(superposition,[status(thm)],[d55,d5]) ).
cnf(d57,plain,
'is$ua$utheorem'(implies(implies(not(X0),X1),implies(implies(X1,X0),X0))) = true,
inference(demodulation,[status(thm)],[d56,c0]) ).
cnf(d58,plain,
ifeq(true,true,'is$ua$utheorem'(implies(X0,implies(implies(X1,X0),X0))),true) = true,
inference(superposition,[status(thm)],[d57,d13]) ).
cnf(d59,plain,
'is$ua$utheorem'(implies(X0,implies(implies(X1,X0),X0))) = true,
inference(demodulation,[status(thm)],[d58,c0]) ).
cnf(d60,plain,
ifeq(true,true,'is$ua$utheorem'(implies(implies(implies(implies(X1,X0),X0),X2),implies(X0,X2))),true) = true,
inference(superposition,[status(thm)],[d59,d1]) ).
cnf(d61,plain,
'is$ua$utheorem'(implies(implies(implies(implies(X0,X1),X1),X2),implies(X1,X2))) = true,
inference(demodulation,[status(thm)],[d60,c0]) ).
cnf(d62,plain,
ifeq(true,true,'is$ua$utheorem'(implies(X1,implies(X0,X1))),true) = true,
inference(superposition,[status(thm)],[d61,d11]) ).
cnf(d63,plain,
'is$ua$utheorem'(implies(X0,implies(X1,X0))) = true,
inference(demodulation,[status(thm)],[d62,c0]) ).
cnf(d64,plain,
ifeq(true,true,'is$ua$utheorem'(implies(implies(implies(X1,X0),X2),implies(X0,X2))),true) = true,
inference(superposition,[status(thm)],[d63,d1]) ).
cnf(d65,plain,
'is$ua$utheorem'(implies(implies(implies(X0,X1),X2),implies(X1,X2))) = true,
inference(demodulation,[status(thm)],[d64,c0]) ).
cnf(d66,plain,
ifeq(true,true,ifeq('is$ua$utheorem'(implies(implies(X0,X1),X2)),true,'is$ua$utheorem'(implies(X1,X2)),true),true) = true,
inference(superposition,[status(thm)],[d65,c1]) ).
cnf(d67,plain,
ifeq('is$ua$utheorem'(implies(implies(X0,X1),X2)),true,'is$ua$utheorem'(implies(X1,X2)),true) = true,
inference(demodulation,[status(thm)],[d66,c0]) ).
cnf(d68,plain,
ifeq(true,true,'is$ua$utheorem'(implies(X1,implies(implies(X1,X0),X0))),true) = true,
inference(superposition,[status(thm)],[d57,d67]) ).
cnf(d69,plain,
'is$ua$utheorem'(implies(X0,implies(implies(X0,X1),X1))) = true,
inference(demodulation,[status(thm)],[d68,c0]) ).
cnf(d70,plain,
ifeq(true,true,'is$ua$utheorem'(implies(implies(implies(implies(X0,X1),X1),X2),implies(X0,X2))),true) = true,
inference(superposition,[status(thm)],[d69,d1]) ).
cnf(d71,plain,
'is$ua$utheorem'(implies(implies(implies(implies(X0,X1),X1),X2),implies(X0,X2))) = true,
inference(demodulation,[status(thm)],[d70,c0]) ).
cnf(d72,plain,
ifeq(true,true,'is$ua$utheorem'(implies(implies(X2,implies(X0,X1)),implies(X0,implies(X2,X1)))),true) = true,
inference(superposition,[status(thm)],[d71,d5]) ).
cnf(d73,plain,
'is$ua$utheorem'(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2)))) = true,
inference(demodulation,[status(thm)],[d72,c0]) ).
cnf(d74,plain,
$false,
inference(resolution,[status(thm)],[d73,c5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL050-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n006.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Fri Sep 25 21:46:10 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.02/23.69 % SZS status Unsatisfiable for theBenchmark.p
% 27.02/23.69 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------