%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP250-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 07:23:29 AM UTC 2026
% Result : Unsatisfiable 116.18s 20.06s
% Output : CNFRefutation 116.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 16
% Syntax : Number of clauses : 143 ( 52 unt; 59 nHn; 104 RR)
% Number of literals : 416 ( 415 equ; 227 neg)
% Maximal clause size : 12 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 122 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this_2,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc9'
| multiply('sk$uc1','sk$uc9') = 'sk$uc8' ) ).
cnf(prove_this_5,negated_conjecture,
( inverse('sk$uc6') = 'sk$uc7'
| multiply('sk$uc1','sk$uc9') = 'sk$uc8' ) ).
cnf(prove_this_6,negated_conjecture,
( multiply('sk$uc6','sk$uc8') = 'sk$uc7'
| multiply('sk$uc1','sk$uc9') = 'sk$uc8' ) ).
cnf(prove_this_8,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc9'
| inverse('sk$uc1') = 'sk$uc9' ) ).
cnf(prove_this_11,negated_conjecture,
( inverse('sk$uc6') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc9' ) ).
cnf(prove_this_12,negated_conjecture,
( multiply('sk$uc6','sk$uc8') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc9' ) ).
cnf(prove_this_15,negated_conjecture,
( multiply('sk$uc5','sk$uc8') = 'sk$uc7'
| multiply('sk$uc2','sk$uc8') = 'sk$uc7' ) ).
cnf(prove_this_16,negated_conjecture,
( inverse('sk$uc5') = 'sk$uc8'
| multiply('sk$uc2','sk$uc8') = 'sk$uc7' ) ).
cnf(prove_this_21,negated_conjecture,
( multiply('sk$uc5','sk$uc8') = 'sk$uc7'
| inverse('sk$uc2') = 'sk$uc8' ) ).
cnf(prove_this_22,negated_conjecture,
( inverse('sk$uc5') = 'sk$uc8'
| inverse('sk$uc2') = 'sk$uc8' ) ).
cnf(prove_this_26,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc9'
| inverse('sk$uc3') = 'sk$uc8' ) ).
cnf(prove_this_32,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc9'
| multiply('sk$uc3','sk$uc7') = 'sk$uc8' ) ).
cnf(prove_this_37,negated_conjecture,
( multiply(X5,'sk$uc8') != 'sk$uc7'
| inverse(X5) != 'sk$uc7'
| inverse(X4) != 'sk$uc8'
| multiply(X4,'sk$uc8') != 'sk$uc7'
| inverse(X3) != 'sk$uc9'
| multiply(X3,'sk$uc9') != 'sk$uc8'
| multiply(X2,'sk$uc7') != 'sk$uc8'
| inverse(X2) != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| multiply(X1,'sk$uc8') != 'sk$uc7'
| inverse(X0) != 'sk$uc9'
| multiply(X0,'sk$uc9') != 'sk$uc8' ) ).
cnf(left_identity,axiom,
multiply(identity,X0) = X0 ).
cnf(left_inverse,axiom,
multiply(inverse(X0),X0) = identity ).
cnf(associativity,axiom,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)) ).
cnf(c1,plain,
( inverse('sk$uc4') = 'sk$uc9'
| multiply('sk$uc1','sk$uc9') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_2]) ).
cnf(c4,plain,
( inverse('sk$uc6') = 'sk$uc7'
| multiply('sk$uc1','sk$uc9') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_5]) ).
cnf(c5,plain,
( multiply('sk$uc6','sk$uc8') = 'sk$uc7'
| multiply('sk$uc1','sk$uc9') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_6]) ).
cnf(c7,plain,
( inverse('sk$uc4') = 'sk$uc9'
| inverse('sk$uc1') = 'sk$uc9' ),
inference(clausification,[status(esa)],[prove_this_8]) ).
cnf(c10,plain,
( inverse('sk$uc6') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc9' ),
inference(clausification,[status(esa)],[prove_this_11]) ).
cnf(c11,plain,
( multiply('sk$uc6','sk$uc8') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc9' ),
inference(clausification,[status(esa)],[prove_this_12]) ).
cnf(c14,plain,
( multiply('sk$uc5','sk$uc8') = 'sk$uc7'
| multiply('sk$uc2','sk$uc8') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_15]) ).
cnf(c15,plain,
( inverse('sk$uc5') = 'sk$uc8'
| multiply('sk$uc2','sk$uc8') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_16]) ).
cnf(c20,plain,
( multiply('sk$uc5','sk$uc8') = 'sk$uc7'
| inverse('sk$uc2') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_21]) ).
cnf(c21,plain,
( inverse('sk$uc5') = 'sk$uc8'
| inverse('sk$uc2') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_22]) ).
cnf(c25,plain,
( inverse('sk$uc4') = 'sk$uc9'
| inverse('sk$uc3') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_26]) ).
cnf(c31,plain,
( inverse('sk$uc4') = 'sk$uc9'
| multiply('sk$uc3','sk$uc7') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_32]) ).
cnf(c36,plain,
( multiply(X4,'sk$uc9') != 'sk$uc8'
| multiply(X0,'sk$uc9') != 'sk$uc8'
| multiply(X1,'sk$uc8') != 'sk$uc7'
| multiply(X5,'sk$uc7') != 'sk$uc8'
| multiply(X2,'sk$uc8') != 'sk$uc7'
| inverse(X5) != 'sk$uc8'
| inverse(X3) != 'sk$uc7'
| inverse(X4) != 'sk$uc9'
| multiply(X3,'sk$uc8') != 'sk$uc7'
| inverse(X2) != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc9' ),
inference(clausification,[status(esa)],[prove_this_37]) ).
cnf(c37,plain,
multiply(identity,X0) = X0,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c38,plain,
multiply(inverse(X0),X0) = identity,
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c39,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(clausification,[status(esa)],[associativity]) ).
cnf(d0,plain,
multiply(X0,X1) = multiply(identity,multiply(X0,X1)),
inference(superposition,[status(thm)],[c37,c39]) ).
cnf(d1,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d0,c37]) ).
cnf(d2,plain,
( inverse('sk$uc6') = 'sk$uc7'
| 'sk$uc8' = multiply('sk$uc1','sk$uc9') ),
inference(superposition,[status(thm)],[c4,d1]) ).
cnf(d3,plain,
multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[status(thm)],[c38,c39]) ).
cnf(d4,plain,
X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(demodulation,[status(thm)],[d3,c37]) ).
cnf(d5,plain,
multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(superposition,[status(thm)],[d4,d4]) ).
cnf(d6,plain,
multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[d5,c38]) ).
cnf(d7,plain,
( inverse('sk$uc5') = 'sk$uc8'
| 'sk$uc7' = multiply('sk$uc2','sk$uc8') ),
inference(superposition,[status(thm)],[c15,d1]) ).
cnf(d8,plain,
identity = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[c38,d1]) ).
cnf(d9,plain,
identity = multiply(X0,inverse(X0)),
inference(superposition,[status(thm)],[d5,d8]) ).
cnf(d10,plain,
( inverse('sk$uc5') = 'sk$uc8'
| identity = multiply('sk$uc2','sk$uc8') ),
inference(superposition,[status(thm)],[c21,d9]) ).
cnf(d11,plain,
( inverse('sk$uc5') = 'sk$uc8'
| inverse('sk$uc5') = 'sk$uc8'
| 'sk$uc7' = identity ),
inference(superposition,[status(thm)],[d10,d7]) ).
cnf(d12,plain,
( 'sk$uc7' = identity
| multiply('sk$uc5','sk$uc8') = identity ),
inference(superposition,[status(thm)],[d11,d6]) ).
cnf(d13,plain,
( multiply('sk$uc5','sk$uc8') = 'sk$uc7'
| 'sk$uc7' = multiply('sk$uc2','sk$uc8') ),
inference(superposition,[status(thm)],[c14,d1]) ).
cnf(d14,plain,
( inverse('sk$uc2') = 'sk$uc8'
| 'sk$uc7' = multiply('sk$uc5','sk$uc8') ),
inference(superposition,[status(thm)],[c20,d1]) ).
cnf(d15,plain,
( 'sk$uc7' = identity
| identity = multiply('sk$uc5','sk$uc8') ),
inference(superposition,[status(thm)],[d11,d9]) ).
cnf(d16,plain,
( 'sk$uc7' = identity
| inverse('sk$uc2') = 'sk$uc8'
| 'sk$uc7' = identity ),
inference(superposition,[status(thm)],[d15,d14]) ).
cnf(d17,plain,
( 'sk$uc7' = identity
| identity = multiply('sk$uc2','sk$uc8') ),
inference(superposition,[status(thm)],[d16,d9]) ).
cnf(d18,plain,
( 'sk$uc7' = identity
| multiply('sk$uc5','sk$uc8') = 'sk$uc7'
| 'sk$uc7' = identity ),
inference(superposition,[status(thm)],[d17,d13]) ).
cnf(d19,plain,
( 'sk$uc7' = identity
| 'sk$uc7' = identity
| 'sk$uc7' = identity ),
inference(superposition,[status(thm)],[d18,d12]) ).
cnf(d20,plain,
'sk$uc7' = multiply(X0,inverse(X0)),
inference(demodulation,[status(thm)],[d9,d19]) ).
cnf(d21,plain,
X0 = multiply(inverse(inverse(X0)),identity),
inference(superposition,[status(thm)],[c38,d4]) ).
cnf(d22,plain,
multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[d21,d1]) ).
cnf(d23,plain,
multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[d22,d5]) ).
cnf(d24,plain,
multiply(X0,'sk$uc7') = X0,
inference(demodulation,[status(thm)],[d23,d19]) ).
cnf(d25,plain,
( inverse('sk$uc1') = 'sk$uc9'
| multiply('sk$uc7','sk$uc6') = identity ),
inference(superposition,[status(thm)],[c10,c38]) ).
cnf(d26,plain,
( inverse('sk$uc1') = 'sk$uc9'
| multiply(identity,X0) = multiply('sk$uc7',multiply('sk$uc6',X0)) ),
inference(superposition,[status(thm)],[d25,c39]) ).
cnf(d27,plain,
( inverse('sk$uc1') = 'sk$uc9'
| X0 = multiply('sk$uc7',multiply('sk$uc6',X0)) ),
inference(demodulation,[status(thm)],[d26,c37]) ).
cnf(d28,plain,
( inverse('sk$uc1') = 'sk$uc9'
| inverse('sk$uc1') = 'sk$uc9'
| 'sk$uc8' = multiply('sk$uc7','sk$uc7') ),
inference(superposition,[status(thm)],[c11,d27]) ).
cnf(d29,plain,
( inverse('sk$uc1') = 'sk$uc9'
| 'sk$uc8' = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d28,d24]) ).
cnf(d30,plain,
( 'sk$uc8' = 'sk$uc7'
| 'sk$uc7' = multiply('sk$uc1','sk$uc9') ),
inference(superposition,[status(thm)],[d29,d20]) ).
cnf(d31,plain,
( 'sk$uc8' = 'sk$uc7'
| inverse('sk$uc6') = 'sk$uc7'
| 'sk$uc8' = 'sk$uc7' ),
inference(superposition,[status(thm)],[d30,d2]) ).
cnf(d32,plain,
X0 = multiply(X0,identity),
inference(demodulation,[status(thm)],[d21,d5]) ).
cnf(d33,plain,
inverse(X0) = multiply(inverse(X0),identity),
inference(superposition,[status(thm)],[d9,d4]) ).
cnf(d34,plain,
inverse(X0) = inverse(X0),
inference(demodulation,[status(thm)],[d33,d32]) ).
cnf(d35,plain,
multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d32,d5]) ).
cnf(d36,plain,
X0 = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d35,d32]) ).
cnf(d37,plain,
inverse(inverse(X0)) = X0,
inference(superposition,[status(thm)],[d36,d34]) ).
cnf(d38,plain,
multiply(X0,inverse(X0)) = 'sk$uc7',
inference(demodulation,[status(thm)],[d6,d19]) ).
cnf(d39,plain,
( 'sk$uc8' = 'sk$uc7'
| multiply('sk$uc1','sk$uc9') = 'sk$uc7' ),
inference(superposition,[status(thm)],[d29,d38]) ).
cnf(d40,plain,
multiply('sk$uc7',X0) = X0,
inference(demodulation,[status(thm)],[c37,d19]) ).
cnf(d41,plain,
( multiply('sk$uc1','sk$uc9') = 'sk$uc8'
| multiply('sk$uc7',X0) = multiply('sk$uc6',multiply('sk$uc8',X0)) ),
inference(superposition,[status(thm)],[c5,c39]) ).
cnf(d42,plain,
( multiply('sk$uc1','sk$uc9') = 'sk$uc8'
| multiply('sk$uc7',inverse('sk$uc8')) = multiply('sk$uc6',identity) ),
inference(superposition,[status(thm)],[d9,d41]) ).
cnf(d43,plain,
( inverse('sk$uc8') = multiply('sk$uc6',identity)
| multiply('sk$uc1','sk$uc9') = 'sk$uc8' ),
inference(demodulation,[status(thm)],[d42,d40]) ).
cnf(d44,plain,
( inverse('sk$uc8') = multiply('sk$uc6','sk$uc7')
| multiply('sk$uc1','sk$uc9') = 'sk$uc8' ),
inference(demodulation,[status(thm)],[d43,d19]) ).
cnf(d45,plain,
( inverse('sk$uc8') = 'sk$uc6'
| multiply('sk$uc1','sk$uc9') = 'sk$uc8' ),
inference(demodulation,[status(thm)],[d44,d24]) ).
cnf(d46,plain,
( inverse('sk$uc8') = 'sk$uc6'
| 'sk$uc8' = 'sk$uc7'
| 'sk$uc8' = 'sk$uc7' ),
inference(superposition,[status(thm)],[d45,d39]) ).
cnf(d47,plain,
( 'sk$uc8' = 'sk$uc7'
| inverse('sk$uc6') = 'sk$uc8' ),
inference(superposition,[status(thm)],[d46,d37]) ).
cnf(d48,plain,
( 'sk$uc8' = 'sk$uc7'
| 'sk$uc8' = 'sk$uc7'
| 'sk$uc8' = 'sk$uc7' ),
inference(superposition,[status(thm)],[d47,d31]) ).
cnf(d49,plain,
'sk$uc8' = identity,
inference(demodulation,[status(thm)],[d19,d48]) ).
cnf(d50,plain,
X0 = multiply(X0,'sk$uc7'),
inference(demodulation,[status(thm)],[d32,d19]) ).
cnf(d51,plain,
X0 = multiply(X0,'sk$uc8'),
inference(demodulation,[status(thm)],[d50,d48]) ).
cnf(d52,plain,
( inverse(X4) != 'sk$uc9'
| inverse(X3) != 'sk$uc9'
| inverse(X2) != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc7'
| multiply(X4,'sk$uc9') != 'sk$uc8'
| multiply(X3,'sk$uc9') != 'sk$uc8'
| multiply(X2,'sk$uc7') != 'sk$uc8'
| multiply(X1,'sk$uc8') != 'sk$uc7'
| multiply(X0,'sk$uc8') != 'sk$uc7' ),
inference(factoring,[status(thm)],[c36]) ).
cnf(d53,plain,
( inverse(X3) != 'sk$uc7'
| inverse(X2) != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc9'
| inverse(X0) != 'sk$uc9'
| multiply(X3,'sk$uc8') != 'sk$uc7'
| multiply(X2,'sk$uc8') != 'sk$uc7'
| multiply(X1,'sk$uc7') != 'sk$uc8'
| multiply(X0,'sk$uc9') != 'sk$uc8' ),
inference(factoring,[status(thm)],[d52]) ).
cnf(d54,plain,
identity = multiply(inverse(inverse(inverse(X0))),X0),
inference(superposition,[status(thm)],[d21,d4]) ).
cnf(d55,plain,
( inverse(inverse(inverse(inverse('sk$uc9')))) != 'sk$uc9'
| inverse(X2) != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc7'
| multiply(X2,'sk$uc7') != 'sk$uc8'
| multiply(X1,'sk$uc8') != 'sk$uc7'
| multiply(X0,'sk$uc8') != 'sk$uc7'
| identity != 'sk$uc8' ),
inference(superposition,[status(thm)],[d54,d53]) ).
cnf(d56,plain,
( identity != 'sk$uc8'
| inverse(inverse('sk$uc9')) != 'sk$uc9'
| inverse(X2) != 'sk$uc7'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| multiply(X2,'sk$uc8') != 'sk$uc7'
| multiply(X1,'sk$uc8') != 'sk$uc7'
| multiply(X0,'sk$uc7') != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d55,d36]) ).
cnf(d57,plain,
( identity != 'sk$uc8'
| 'sk$uc9' != 'sk$uc9'
| inverse(X2) != 'sk$uc7'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| multiply(X2,'sk$uc8') != 'sk$uc7'
| multiply(X1,'sk$uc8') != 'sk$uc7'
| multiply(X0,'sk$uc7') != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d56,d36]) ).
cnf(d58,plain,
( identity != 'sk$uc8'
| 'sk$uc9' != 'sk$uc9'
| inverse(X1) != 'sk$uc7'
| inverse(X0) != 'sk$uc8'
| inverse(inverse('sk$uc7')) != 'sk$uc8'
| multiply(X1,'sk$uc8') != 'sk$uc7'
| multiply(X0,'sk$uc8') != 'sk$uc7'
| identity != 'sk$uc8' ),
inference(superposition,[status(thm)],[c38,d57]) ).
cnf(d59,plain,
( identity != 'sk$uc8'
| inverse(inverse('sk$uc7')) != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc7'
| 'sk$uc9' != 'sk$uc9'
| multiply(X1,'sk$uc8') != 'sk$uc7'
| X0 != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d58,d51]) ).
cnf(d60,plain,
( identity != 'sk$uc8'
| inverse(inverse('sk$uc7')) != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc7'
| 'sk$uc9' != 'sk$uc9'
| multiply(X1,'sk$uc8') != 'sk$uc7'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d59,d48]) ).
cnf(d61,plain,
( identity != 'sk$uc8'
| inverse(inverse('sk$uc7')) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| inverse(X1) != 'sk$uc7'
| 'sk$uc9' != 'sk$uc9'
| X0 != 'sk$uc7'
| X1 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d60,d51]) ).
cnf(d62,plain,
( identity != 'sk$uc8'
| inverse(inverse('sk$uc7')) != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc7'
| 'sk$uc9' != 'sk$uc9'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d61,d48]) ).
cnf(d63,plain,
( identity != 'sk$uc8'
| inverse(inverse('sk$uc7')) != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc9' != 'sk$uc9'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d62,d48]) ).
cnf(d64,plain,
( identity != 'sk$uc8'
| 'sk$uc7' != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc9' != 'sk$uc9'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d63,d36]) ).
cnf(d65,plain,
( identity != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc9' != 'sk$uc9'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d64,d48]) ).
cnf(d66,plain,
( 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc9' != 'sk$uc9'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d65,d49]) ).
cnf(d67,plain,
( inverse('sk$uc4') = 'sk$uc9'
| inverse('sk$uc1') != 'sk$uc9'
| inverse(X2) != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc7'
| multiply(X2,'sk$uc7') != 'sk$uc8'
| multiply(X1,'sk$uc8') != 'sk$uc7'
| multiply(X0,'sk$uc8') != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8' ),
inference(superposition,[status(thm)],[c1,d53]) ).
cnf(d68,plain,
( inverse('sk$uc4') = 'sk$uc9'
| inverse(X2) != 'sk$uc7'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| multiply(X2,'sk$uc8') != 'sk$uc7'
| multiply(X1,'sk$uc8') != 'sk$uc7'
| multiply(X0,'sk$uc7') != 'sk$uc8'
| inverse('sk$uc4') = 'sk$uc9' ),
inference(resolution,[status(thm)],[c7,d67]) ).
cnf(d69,plain,
( inverse('sk$uc4') = 'sk$uc9'
| inverse('sk$uc4') = 'sk$uc9'
| inverse('sk$uc3') != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| multiply(X1,'sk$uc8') != 'sk$uc7'
| multiply(X0,'sk$uc8') != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8' ),
inference(superposition,[status(thm)],[c31,d68]) ).
cnf(d70,plain,
( inverse('sk$uc4') = 'sk$uc9'
| inverse(X1) != 'sk$uc7'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| multiply(X1,'sk$uc8') != 'sk$uc7'
| multiply(X0,'sk$uc8') != 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc9' ),
inference(resolution,[status(thm)],[c25,d69]) ).
cnf(d71,plain,
( inverse('sk$uc4') = 'sk$uc9'
| 'sk$uc7' = multiply(inverse('sk$uc3'),'sk$uc8') ),
inference(superposition,[status(thm)],[c31,d4]) ).
cnf(d72,plain,
( inverse('sk$uc4') = 'sk$uc9'
| inverse('sk$uc4') = 'sk$uc9'
| inverse(inverse('sk$uc3')) != 'sk$uc8'
| inverse(X0) != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| multiply(X0,'sk$uc8') != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7' ),
inference(superposition,[status(thm)],[d71,d70]) ).
cnf(d73,plain,
( 'sk$uc7' != 'sk$uc7'
| inverse(inverse('sk$uc3')) != 'sk$uc8'
| inverse('sk$uc4') = 'sk$uc9'
| inverse(X0) != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d72,d51]) ).
cnf(d74,plain,
( 'sk$uc7' != 'sk$uc7'
| inverse(inverse('sk$uc3')) != 'sk$uc8'
| inverse('sk$uc4') = 'sk$uc9'
| inverse(X0) != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d73,d48]) ).
cnf(d75,plain,
( 'sk$uc7' != 'sk$uc7'
| inverse(inverse('sk$uc3')) != 'sk$uc8'
| inverse('sk$uc4') = 'sk$uc9'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d74,d48]) ).
cnf(d76,plain,
( 'sk$uc7' != 'sk$uc7'
| 'sk$uc3' != 'sk$uc8'
| inverse('sk$uc4') = 'sk$uc9'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d75,d36]) ).
cnf(d77,plain,
( 'sk$uc8' != 'sk$uc7'
| 'sk$uc3' != 'sk$uc8'
| inverse('sk$uc4') = 'sk$uc9'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d76,d48]) ).
cnf(d78,plain,
( 'sk$uc8' != 'sk$uc8'
| 'sk$uc3' != 'sk$uc8'
| inverse('sk$uc4') = 'sk$uc9'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d77,d48]) ).
cnf(d79,plain,
X0 = multiply(identity,X0),
inference(superposition,[status(thm)],[c37,d1]) ).
cnf(d80,plain,
X0 = multiply('sk$uc7',X0),
inference(demodulation,[status(thm)],[d79,d19]) ).
cnf(d81,plain,
X0 = multiply('sk$uc8',X0),
inference(demodulation,[status(thm)],[d80,d48]) ).
cnf(d82,plain,
'sk$uc8' = multiply(X0,inverse(X0)),
inference(demodulation,[status(thm)],[d20,d48]) ).
cnf(d83,plain,
X0 = multiply(inverse(identity),X0),
inference(superposition,[status(thm)],[d79,d4]) ).
cnf(d84,plain,
X0 = multiply(inverse(inverse(identity)),X0),
inference(superposition,[status(thm)],[d83,d4]) ).
cnf(d85,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[d84,c38]) ).
cnf(d86,plain,
inverse('sk$uc7') = identity,
inference(demodulation,[status(thm)],[d85,d19]) ).
cnf(d87,plain,
inverse('sk$uc7') = 'sk$uc7',
inference(demodulation,[status(thm)],[d86,d19]) ).
cnf(d88,plain,
inverse('sk$uc8') = 'sk$uc7',
inference(demodulation,[status(thm)],[d87,d48]) ).
cnf(d89,plain,
inverse('sk$uc8') = 'sk$uc8',
inference(demodulation,[status(thm)],[d88,d48]) ).
cnf(d90,plain,
'sk$uc8' = multiply('sk$uc8','sk$uc8'),
inference(superposition,[status(thm)],[d89,d82]) ).
cnf(d91,plain,
'sk$uc8' = 'sk$uc8',
inference(demodulation,[status(thm)],[d90,d81]) ).
cnf(d92,plain,
( 'sk$uc8' != 'sk$uc8'
| 'sk$uc3' != 'sk$uc8'
| inverse('sk$uc4') = 'sk$uc9'
| inverse(X0) != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(resolution,[status(thm)],[d91,d78]) ).
cnf(d93,plain,
( inverse('sk$uc4') = 'sk$uc9'
| 'sk$uc3' = 'sk$uc8' ),
inference(demodulation,[status(thm)],[c31,d24]) ).
cnf(d94,plain,
( inverse('sk$uc4') = 'sk$uc9'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8'
| inverse('sk$uc4') = 'sk$uc9' ),
inference(resolution,[status(thm)],[d93,d92]) ).
cnf(d95,plain,
( inverse('sk$uc4') = 'sk$uc9'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8' ),
inference(superposition,[status(thm)],[d89,d94]) ).
cnf(d96,plain,
inverse('sk$uc4') = 'sk$uc9',
inference(resolution,[status(thm)],[d91,d95]) ).
cnf(d97,plain,
identity = inverse(identity),
inference(superposition,[status(thm)],[d84,d8]) ).
cnf(d98,plain,
'sk$uc7' = inverse(identity),
inference(demodulation,[status(thm)],[d97,d19]) ).
cnf(d99,plain,
'sk$uc7' = inverse('sk$uc7'),
inference(demodulation,[status(thm)],[d98,d19]) ).
cnf(d100,plain,
'sk$uc8' = inverse('sk$uc7'),
inference(demodulation,[status(thm)],[d99,d48]) ).
cnf(d101,plain,
'sk$uc8' = inverse('sk$uc8'),
inference(demodulation,[status(thm)],[d100,d48]) ).
cnf(d102,plain,
( inverse('sk$uc4') = 'sk$uc9'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8' ),
inference(superposition,[status(thm)],[d101,d94]) ).
cnf(d103,plain,
( 'sk$uc9' = 'sk$uc9'
| 'sk$uc8' != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d102,d96]) ).
cnf(d104,plain,
'sk$uc9' = 'sk$uc9',
inference(resolution,[status(thm)],[d91,d103]) ).
cnf(d105,plain,
( 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(resolution,[status(thm)],[d104,d66]) ).
cnf(d106,plain,
( inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(resolution,[status(thm)],[d91,d105]) ).
cnf(d107,plain,
( inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(superposition,[status(thm)],[d36,d106]) ).
cnf(d108,plain,
( inverse(X0) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(factoring,[status(thm)],[d107]) ).
cnf(d109,plain,
( 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8' ),
inference(superposition,[status(thm)],[d89,d108]) ).
cnf(d110,plain,
$false,
inference(resolution,[status(thm)],[d91,d109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP250-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n008.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 14:41:54 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 116.18/20.06 % SZS status Unsatisfiable for theBenchmark.p
% 116.18/20.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------