%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP358-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 07:23:38 AM UTC 2026
% Result : Unsatisfiable 197.91s 59.60s
% Output : CNFRefutation 197.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 21
% Syntax : Number of clauses : 183 ( 53 unt; 104 nHn; 129 RR)
% Number of literals : 521 ( 520 equ; 239 neg)
% Maximal clause size : 11 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 105 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this_2,negated_conjecture,
( inverse('sk$uc3') = 'sk$uc8'
| multiply('sk$uc7','sk$uc6') = 'sk$uc8' ) ).
cnf(prove_this_3,negated_conjecture,
( multiply('sk$uc4','sk$uc7') = 'sk$uc6'
| multiply('sk$uc7','sk$uc6') = 'sk$uc8' ) ).
cnf(prove_this_4,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc7','sk$uc6') = 'sk$uc8' ) ).
cnf(prove_this_11,negated_conjecture,
( inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc8') = 'sk$uc6' ) ).
cnf(prove_this_12,negated_conjecture,
( multiply('sk$uc5','sk$uc8') = 'sk$uc6'
| inverse('sk$uc8') = 'sk$uc6' ) ).
cnf(prove_this_13,negated_conjecture,
( multiply('sk$uc3','sk$uc8') = 'sk$uc7'
| multiply('sk$uc8','sk$uc2') = 'sk$uc7' ) ).
cnf(prove_this_14,negated_conjecture,
( inverse('sk$uc3') = 'sk$uc8'
| multiply('sk$uc8','sk$uc2') = 'sk$uc7' ) ).
cnf(prove_this_15,negated_conjecture,
( multiply('sk$uc4','sk$uc7') = 'sk$uc6'
| multiply('sk$uc8','sk$uc2') = 'sk$uc7' ) ).
cnf(prove_this_16,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc8','sk$uc2') = 'sk$uc7' ) ).
cnf(prove_this_19,negated_conjecture,
( multiply('sk$uc3','sk$uc8') = 'sk$uc7'
| multiply('sk$uc1','sk$uc8') = 'sk$uc2' ) ).
cnf(prove_this_20,negated_conjecture,
( inverse('sk$uc3') = 'sk$uc8'
| multiply('sk$uc1','sk$uc8') = 'sk$uc2' ) ).
cnf(prove_this_21,negated_conjecture,
( multiply('sk$uc4','sk$uc7') = 'sk$uc6'
| multiply('sk$uc1','sk$uc8') = 'sk$uc2' ) ).
cnf(prove_this_22,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc1','sk$uc8') = 'sk$uc2' ) ).
cnf(prove_this_25,negated_conjecture,
( multiply('sk$uc3','sk$uc8') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc8' ) ).
cnf(prove_this_26,negated_conjecture,
( inverse('sk$uc3') = 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc8' ) ).
cnf(prove_this_27,negated_conjecture,
( multiply('sk$uc4','sk$uc7') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc8' ) ).
cnf(prove_this_28,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc8' ) ).
cnf(prove_this_31,negated_conjecture,
( multiply(X4,'sk$uc8') != 'sk$uc6'
| inverse(X4) != 'sk$uc6'
| inverse(X3) != 'sk$uc7'
| multiply(X3,'sk$uc7') != 'sk$uc6'
| inverse(X2) != 'sk$uc8'
| multiply(X2,'sk$uc8') != 'sk$uc7'
| inverse(X1) != 'sk$uc8'
| multiply(X1,'sk$uc8') != X0
| multiply('sk$uc8',X0) != 'sk$uc7'
| inverse('sk$uc8') != 'sk$uc6'
| multiply('sk$uc7','sk$uc6') != 'sk$uc8' ) ).
cnf(left_identity,axiom,
multiply(identity,X0) = X0 ).
cnf(left_inverse,axiom,
multiply(inverse(X0),X0) = identity ).
cnf(associativity,axiom,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)) ).
cnf(c1,plain,
( inverse('sk$uc3') = 'sk$uc8'
| multiply('sk$uc7','sk$uc6') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_2]) ).
cnf(c2,plain,
( multiply('sk$uc4','sk$uc7') = 'sk$uc6'
| multiply('sk$uc7','sk$uc6') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_3]) ).
cnf(c3,plain,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc7','sk$uc6') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_4]) ).
cnf(c10,plain,
( inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc8') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_11]) ).
cnf(c11,plain,
( multiply('sk$uc5','sk$uc8') = 'sk$uc6'
| inverse('sk$uc8') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_12]) ).
cnf(c12,plain,
( multiply('sk$uc3','sk$uc8') = 'sk$uc7'
| multiply('sk$uc8','sk$uc2') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_13]) ).
cnf(c13,plain,
( inverse('sk$uc3') = 'sk$uc8'
| multiply('sk$uc8','sk$uc2') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_14]) ).
cnf(c14,plain,
( multiply('sk$uc4','sk$uc7') = 'sk$uc6'
| multiply('sk$uc8','sk$uc2') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_15]) ).
cnf(c15,plain,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc8','sk$uc2') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_16]) ).
cnf(c18,plain,
( multiply('sk$uc3','sk$uc8') = 'sk$uc7'
| multiply('sk$uc1','sk$uc8') = 'sk$uc2' ),
inference(clausification,[status(esa)],[prove_this_19]) ).
cnf(c19,plain,
( inverse('sk$uc3') = 'sk$uc8'
| multiply('sk$uc1','sk$uc8') = 'sk$uc2' ),
inference(clausification,[status(esa)],[prove_this_20]) ).
cnf(c20,plain,
( multiply('sk$uc4','sk$uc7') = 'sk$uc6'
| multiply('sk$uc1','sk$uc8') = 'sk$uc2' ),
inference(clausification,[status(esa)],[prove_this_21]) ).
cnf(c21,plain,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc1','sk$uc8') = 'sk$uc2' ),
inference(clausification,[status(esa)],[prove_this_22]) ).
cnf(c24,plain,
( multiply('sk$uc3','sk$uc8') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_25]) ).
cnf(c25,plain,
( inverse('sk$uc3') = 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_26]) ).
cnf(c26,plain,
( multiply('sk$uc4','sk$uc7') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_27]) ).
cnf(c27,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_28]) ).
cnf(c30,plain,
( inverse(X3) != 'sk$uc8'
| inverse(X4) != 'sk$uc7'
| inverse(X1) != 'sk$uc8'
| multiply('sk$uc8',X2) != 'sk$uc7'
| multiply(X4,'sk$uc7') != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| inverse('sk$uc8') != 'sk$uc6'
| multiply('sk$uc7','sk$uc6') != 'sk$uc8'
| multiply(X3,'sk$uc8') != 'sk$uc7'
| multiply(X1,'sk$uc8') != X2
| multiply(X0,'sk$uc8') != 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_31]) ).
cnf(c31,plain,
multiply(identity,X0) = X0,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c32,plain,
multiply(inverse(X0),X0) = identity,
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c33,plain,
multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(clausification,[status(esa)],[associativity]) ).
cnf(d0,plain,
multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c32,c33]) ).
cnf(d1,plain,
multiply(inverse(X1),multiply(X1,X0)) = X0,
inference(demodulation,[status(thm)],[d0,c31]) ).
cnf(d2,plain,
multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[d1,d1]) ).
cnf(d3,plain,
multiply(identity,multiply(X0,X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c31,c33]) ).
cnf(d4,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d3,c31]) ).
cnf(d5,plain,
identity = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[c32,d4]) ).
cnf(d6,plain,
multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[status(thm)],[d7,d2]) ).
cnf(d9,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
identity = multiply(X0,inverse(X0)),
inference(superposition,[status(thm)],[d2,d5]) ).
cnf(d11,plain,
multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[d2,c32]) ).
cnf(d12,plain,
( inverse('sk$uc1') = 'sk$uc8'
| multiply('sk$uc4','sk$uc7') = identity ),
inference(superposition,[status(thm)],[c27,d11]) ).
cnf(d13,plain,
( inverse('sk$uc1') = 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc8'
| identity = 'sk$uc6' ),
inference(superposition,[status(thm)],[d12,c26]) ).
cnf(d14,plain,
( identity = 'sk$uc6'
| multiply('sk$uc1','sk$uc8') = identity ),
inference(superposition,[status(thm)],[d13,d11]) ).
cnf(d15,plain,
multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c31,d1]) ).
cnf(d16,plain,
multiply(inverse(inverse(identity)),X0) = X0,
inference(superposition,[status(thm)],[d15,d1]) ).
cnf(d17,plain,
identity = inverse(identity),
inference(superposition,[status(thm)],[d16,d5]) ).
cnf(d18,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[d17,c32]) ).
cnf(d19,plain,
identity = identity,
inference(demodulation,[status(thm)],[d18,c31]) ).
cnf(d20,plain,
( multiply('sk$uc1','sk$uc8') = 'sk$uc2'
| 'sk$uc6' = multiply('sk$uc4','sk$uc7') ),
inference(superposition,[status(thm)],[c20,d4]) ).
cnf(d21,plain,
( 'sk$uc6' = multiply('sk$uc4','sk$uc7')
| 'sk$uc2' = multiply('sk$uc1','sk$uc8') ),
inference(superposition,[status(thm)],[d20,d4]) ).
cnf(d22,plain,
( inverse('sk$uc4') = 'sk$uc7'
| 'sk$uc2' = multiply('sk$uc1','sk$uc8') ),
inference(superposition,[status(thm)],[c21,d4]) ).
cnf(d23,plain,
( 'sk$uc2' = multiply('sk$uc1','sk$uc8')
| multiply('sk$uc4','sk$uc7') = identity ),
inference(superposition,[status(thm)],[d22,d11]) ).
cnf(d24,plain,
( 'sk$uc2' = multiply('sk$uc1','sk$uc8')
| 'sk$uc2' = multiply('sk$uc1','sk$uc8')
| 'sk$uc6' = identity ),
inference(superposition,[status(thm)],[d23,d21]) ).
cnf(d25,plain,
( 'sk$uc2' = multiply('sk$uc1','sk$uc8')
| identity = 'sk$uc6' ),
inference(superposition,[status(thm)],[d24,d19]) ).
cnf(d26,plain,
( identity = 'sk$uc6'
| identity = 'sk$uc6'
| 'sk$uc2' = identity ),
inference(superposition,[status(thm)],[d25,d14]) ).
cnf(d27,plain,
( identity = 'sk$uc6'
| multiply(X0,'sk$uc2') = X0 ),
inference(superposition,[status(thm)],[d26,d7]) ).
cnf(d28,plain,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc7',multiply('sk$uc6',X0)) = multiply('sk$uc8',X0) ),
inference(superposition,[status(thm)],[c3,c33]) ).
cnf(d29,plain,
( inverse('sk$uc4') = 'sk$uc7'
| multiply(inverse('sk$uc7'),multiply('sk$uc8',X0)) = multiply('sk$uc6',X0) ),
inference(superposition,[status(thm)],[d28,d1]) ).
cnf(d30,plain,
( inverse('sk$uc4') = 'sk$uc7'
| 'sk$uc7' = multiply('sk$uc8','sk$uc2') ),
inference(superposition,[status(thm)],[c15,d4]) ).
cnf(d31,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| multiply(inverse('sk$uc7'),'sk$uc7') = multiply('sk$uc6','sk$uc2') ),
inference(superposition,[status(thm)],[d30,d29]) ).
cnf(d32,plain,
( inverse('sk$uc4') = 'sk$uc7'
| identity = multiply('sk$uc6','sk$uc2') ),
inference(demodulation,[status(thm)],[d31,c32]) ).
cnf(d33,plain,
( inverse('sk$uc4') = 'sk$uc7'
| identity = 'sk$uc6'
| identity = 'sk$uc6' ),
inference(superposition,[status(thm)],[d32,d27]) ).
cnf(d34,plain,
( identity = 'sk$uc6'
| identity = multiply('sk$uc4','sk$uc7') ),
inference(superposition,[status(thm)],[d33,d10]) ).
cnf(d35,plain,
( multiply('sk$uc4','sk$uc7') = 'sk$uc6'
| multiply('sk$uc7',multiply('sk$uc6',X0)) = multiply('sk$uc8',X0) ),
inference(superposition,[status(thm)],[c2,c33]) ).
cnf(d36,plain,
( multiply('sk$uc4','sk$uc7') = 'sk$uc6'
| multiply(inverse('sk$uc7'),multiply('sk$uc8',X0)) = multiply('sk$uc6',X0) ),
inference(superposition,[status(thm)],[d35,d1]) ).
cnf(d37,plain,
( multiply('sk$uc4','sk$uc7') = 'sk$uc6'
| multiply('sk$uc4','sk$uc7') = 'sk$uc6'
| multiply(inverse('sk$uc7'),'sk$uc7') = multiply('sk$uc6','sk$uc2') ),
inference(superposition,[status(thm)],[c14,d36]) ).
cnf(d38,plain,
( multiply('sk$uc4','sk$uc7') = 'sk$uc6'
| identity = multiply('sk$uc6','sk$uc2') ),
inference(demodulation,[status(thm)],[d37,c32]) ).
cnf(d39,plain,
( multiply('sk$uc4','sk$uc7') = 'sk$uc6'
| identity = 'sk$uc6'
| identity = 'sk$uc6' ),
inference(superposition,[status(thm)],[d38,d27]) ).
cnf(d40,plain,
( identity = 'sk$uc6'
| identity = 'sk$uc6'
| identity = 'sk$uc6' ),
inference(superposition,[status(thm)],[d39,d34]) ).
cnf(d41,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[d16,c32]) ).
cnf(d42,plain,
inverse('sk$uc6') = identity,
inference(demodulation,[status(thm)],[d41,d40]) ).
cnf(d43,plain,
inverse('sk$uc6') = 'sk$uc6',
inference(demodulation,[status(thm)],[d42,d40]) ).
cnf(d44,plain,
multiply(X0,inverse(X0)) = 'sk$uc6',
inference(demodulation,[status(thm)],[d11,d40]) ).
cnf(d45,plain,
multiply(X0,'sk$uc6') = X0,
inference(demodulation,[status(thm)],[d7,d40]) ).
cnf(d46,plain,
multiply('sk$uc6',X0) = X0,
inference(demodulation,[status(thm)],[c31,d40]) ).
cnf(d47,plain,
( inverse('sk$uc8') = 'sk$uc6'
| multiply('sk$uc5',multiply('sk$uc8',X0)) = multiply('sk$uc6',X0) ),
inference(superposition,[status(thm)],[c11,c33]) ).
cnf(d48,plain,
( inverse('sk$uc8') = 'sk$uc6'
| multiply(inverse('sk$uc5'),multiply('sk$uc6',X0)) = multiply('sk$uc8',X0) ),
inference(superposition,[status(thm)],[d47,d1]) ).
cnf(d49,plain,
( inverse('sk$uc5') = 'sk$uc6'
| identity = multiply('sk$uc8','sk$uc6') ),
inference(superposition,[status(thm)],[c10,d10]) ).
cnf(d50,plain,
( identity = multiply('sk$uc8','sk$uc6')
| inverse('sk$uc8') = 'sk$uc6'
| multiply('sk$uc6',multiply('sk$uc6',X0)) = multiply('sk$uc8',X0) ),
inference(superposition,[status(thm)],[d49,d48]) ).
cnf(d51,plain,
( identity = multiply('sk$uc8','sk$uc6')
| inverse('sk$uc8') = 'sk$uc6'
| multiply('sk$uc6',X0) = multiply('sk$uc8',X0) ),
inference(demodulation,[status(thm)],[d50,d46]) ).
cnf(d52,plain,
( identity = multiply('sk$uc8','sk$uc6')
| inverse('sk$uc8') = 'sk$uc6'
| X0 = multiply('sk$uc8',X0) ),
inference(demodulation,[status(thm)],[d51,d46]) ).
cnf(d53,plain,
( 'sk$uc6' = multiply('sk$uc8','sk$uc6')
| inverse('sk$uc8') = 'sk$uc6'
| X0 = multiply('sk$uc8',X0) ),
inference(demodulation,[status(thm)],[d52,d40]) ).
cnf(d54,plain,
( 'sk$uc6' = 'sk$uc8'
| inverse('sk$uc8') = 'sk$uc6'
| X0 = multiply('sk$uc8',X0) ),
inference(demodulation,[status(thm)],[d53,d45]) ).
cnf(d55,plain,
( 'sk$uc6' = 'sk$uc8'
| inverse('sk$uc8') = 'sk$uc6'
| inverse('sk$uc8') = 'sk$uc6' ),
inference(superposition,[status(thm)],[d54,d44]) ).
cnf(d56,plain,
( inverse('sk$uc8') = 'sk$uc6'
| inverse('sk$uc8') = 'sk$uc6' ),
inference(superposition,[status(thm)],[d55,d43]) ).
cnf(d57,plain,
inverse('sk$uc6') = 'sk$uc8',
inference(superposition,[status(thm)],[d56,d9]) ).
cnf(d58,plain,
'sk$uc8' = 'sk$uc6',
inference(demodulation,[status(thm)],[d43,d57]) ).
cnf(d59,plain,
identity = 'sk$uc8',
inference(demodulation,[status(thm)],[d40,d58]) ).
cnf(d60,plain,
multiply(inverse(X0),identity) = inverse(X0),
inference(superposition,[status(thm)],[d10,d1]) ).
cnf(d61,plain,
inverse(X0) = inverse(X0),
inference(demodulation,[status(thm)],[d60,d7]) ).
cnf(d62,plain,
inverse('sk$uc8') = 'sk$uc6',
inference(superposition,[status(thm)],[d56,d61]) ).
cnf(d63,plain,
inverse('sk$uc8') = 'sk$uc8',
inference(demodulation,[status(thm)],[d62,d58]) ).
cnf(d64,plain,
( inverse('sk$uc1') = 'sk$uc8'
| multiply('sk$uc3','sk$uc8') = identity ),
inference(superposition,[status(thm)],[c25,d11]) ).
cnf(d65,plain,
( inverse('sk$uc1') = 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc8'
| identity = 'sk$uc7' ),
inference(superposition,[status(thm)],[d64,c24]) ).
cnf(d66,plain,
( identity = 'sk$uc7'
| multiply('sk$uc1','sk$uc8') = identity ),
inference(superposition,[status(thm)],[d65,d11]) ).
cnf(d67,plain,
( multiply('sk$uc1','sk$uc8') = 'sk$uc2'
| 'sk$uc7' = multiply('sk$uc3','sk$uc8') ),
inference(superposition,[status(thm)],[c18,d4]) ).
cnf(d68,plain,
( 'sk$uc7' = multiply('sk$uc3','sk$uc8')
| 'sk$uc2' = multiply('sk$uc1','sk$uc8') ),
inference(superposition,[status(thm)],[d67,d4]) ).
cnf(d69,plain,
( inverse('sk$uc3') = 'sk$uc8'
| 'sk$uc2' = multiply('sk$uc1','sk$uc8') ),
inference(superposition,[status(thm)],[c19,d4]) ).
cnf(d70,plain,
( 'sk$uc2' = multiply('sk$uc1','sk$uc8')
| multiply('sk$uc3','sk$uc8') = identity ),
inference(superposition,[status(thm)],[d69,d11]) ).
cnf(d71,plain,
( 'sk$uc2' = multiply('sk$uc1','sk$uc8')
| 'sk$uc2' = multiply('sk$uc1','sk$uc8')
| 'sk$uc7' = identity ),
inference(superposition,[status(thm)],[d70,d68]) ).
cnf(d72,plain,
( 'sk$uc2' = multiply('sk$uc1','sk$uc8')
| identity = 'sk$uc7' ),
inference(superposition,[status(thm)],[d71,d19]) ).
cnf(d73,plain,
( identity = 'sk$uc7'
| identity = 'sk$uc7'
| 'sk$uc2' = identity ),
inference(superposition,[status(thm)],[d72,d66]) ).
cnf(d74,plain,
( identity = 'sk$uc7'
| identity = inverse('sk$uc2') ),
inference(superposition,[status(thm)],[d73,d17]) ).
cnf(d75,plain,
( identity = inverse('sk$uc2')
| inverse('sk$uc7') = identity ),
inference(superposition,[status(thm)],[d74,d41]) ).
cnf(d76,plain,
( identity = inverse('sk$uc2')
| inverse('sk$uc7') = 'sk$uc6' ),
inference(demodulation,[status(thm)],[d75,d40]) ).
cnf(d77,plain,
( 'sk$uc6' = inverse('sk$uc2')
| inverse('sk$uc7') = 'sk$uc6' ),
inference(demodulation,[status(thm)],[d76,d40]) ).
cnf(d78,plain,
( inverse('sk$uc7') = 'sk$uc6'
| 'sk$uc8' = inverse('sk$uc2') ),
inference(demodulation,[status(thm)],[d77,d58]) ).
cnf(d79,plain,
( inverse('sk$uc7') = 'sk$uc8'
| 'sk$uc8' = inverse('sk$uc2') ),
inference(demodulation,[status(thm)],[d78,d58]) ).
cnf(d80,plain,
X0 = multiply(identity,X0),
inference(superposition,[status(thm)],[c31,d4]) ).
cnf(d81,plain,
X0 = multiply('sk$uc6',X0),
inference(demodulation,[status(thm)],[d80,d40]) ).
cnf(d82,plain,
X0 = multiply('sk$uc8',X0),
inference(demodulation,[status(thm)],[d81,d58]) ).
cnf(d83,plain,
X1 = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[status(thm)],[d1,d4]) ).
cnf(d84,plain,
( inverse('sk$uc3') = 'sk$uc8'
| multiply('sk$uc8',multiply('sk$uc2',X0)) = multiply('sk$uc7',X0) ),
inference(superposition,[status(thm)],[c13,c33]) ).
cnf(d85,plain,
( inverse('sk$uc3') = 'sk$uc8'
| multiply(inverse('sk$uc8'),multiply('sk$uc7',X0)) = multiply('sk$uc2',X0) ),
inference(superposition,[status(thm)],[d84,d1]) ).
cnf(d86,plain,
( inverse('sk$uc3') = 'sk$uc8'
| multiply('sk$uc7',multiply('sk$uc6',X0)) = multiply('sk$uc8',X0) ),
inference(superposition,[status(thm)],[c1,c33]) ).
cnf(d87,plain,
( inverse('sk$uc3') = 'sk$uc8'
| multiply('sk$uc8',X0) = multiply('sk$uc7',multiply('sk$uc6',X0)) ),
inference(superposition,[status(thm)],[d86,d4]) ).
cnf(d88,plain,
( inverse('sk$uc3') = 'sk$uc8'
| inverse('sk$uc3') = 'sk$uc8'
| multiply(inverse('sk$uc8'),multiply('sk$uc8',X0)) = multiply('sk$uc2',multiply('sk$uc6',X0)) ),
inference(superposition,[status(thm)],[d87,d85]) ).
cnf(d89,plain,
( inverse('sk$uc3') = 'sk$uc8'
| X0 = multiply('sk$uc2',multiply('sk$uc6',X0)) ),
inference(demodulation,[status(thm)],[d88,d83]) ).
cnf(d90,plain,
( inverse('sk$uc3') = 'sk$uc8'
| X0 = multiply('sk$uc2',multiply('sk$uc8',X0)) ),
inference(demodulation,[status(thm)],[d89,d58]) ).
cnf(d91,plain,
( inverse('sk$uc3') = 'sk$uc8'
| X0 = multiply('sk$uc2',X0) ),
inference(demodulation,[status(thm)],[d90,d82]) ).
cnf(d92,plain,
( inverse('sk$uc3') = 'sk$uc8'
| multiply(inverse('sk$uc8'),identity) = multiply('sk$uc2',inverse('sk$uc7')) ),
inference(superposition,[status(thm)],[d10,d85]) ).
cnf(d93,plain,
( inverse('sk$uc3') = 'sk$uc8'
| multiply('sk$uc8',identity) = multiply('sk$uc2',inverse('sk$uc7')) ),
inference(demodulation,[status(thm)],[d92,d63]) ).
cnf(d94,plain,
( inverse('sk$uc3') = 'sk$uc8'
| identity = multiply('sk$uc2',inverse('sk$uc7')) ),
inference(demodulation,[status(thm)],[d93,d82]) ).
cnf(d95,plain,
( inverse('sk$uc3') = 'sk$uc8'
| 'sk$uc8' = multiply('sk$uc2',inverse('sk$uc7')) ),
inference(demodulation,[status(thm)],[d94,d59]) ).
cnf(d96,plain,
( inverse('sk$uc3') = 'sk$uc8'
| inverse('sk$uc3') = 'sk$uc8'
| inverse('sk$uc7') = 'sk$uc8' ),
inference(superposition,[status(thm)],[d95,d91]) ).
cnf(d97,plain,
X0 = multiply(inverse(inverse(X0)),identity),
inference(superposition,[status(thm)],[d6,d4]) ).
cnf(d98,plain,
X0 = multiply(X0,identity),
inference(demodulation,[status(thm)],[d97,d2]) ).
cnf(d99,plain,
X0 = multiply(X0,'sk$uc6'),
inference(demodulation,[status(thm)],[d98,d40]) ).
cnf(d100,plain,
X0 = multiply(X0,'sk$uc8'),
inference(demodulation,[status(thm)],[d99,d58]) ).
cnf(d101,plain,
( multiply('sk$uc8','sk$uc2') = 'sk$uc7'
| 'sk$uc7' = multiply('sk$uc3','sk$uc8') ),
inference(superposition,[status(thm)],[c12,d4]) ).
cnf(d102,plain,
( 'sk$uc7' = multiply('sk$uc3','sk$uc8')
| 'sk$uc7' = multiply('sk$uc8','sk$uc2') ),
inference(superposition,[status(thm)],[d101,d4]) ).
cnf(d103,plain,
( 'sk$uc7' = 'sk$uc2'
| 'sk$uc7' = multiply('sk$uc3','sk$uc8') ),
inference(demodulation,[status(thm)],[d102,d82]) ).
cnf(d104,plain,
( 'sk$uc7' = 'sk$uc2'
| 'sk$uc7' = 'sk$uc3' ),
inference(demodulation,[status(thm)],[d103,d100]) ).
cnf(d105,plain,
( 'sk$uc7' = 'sk$uc2'
| inverse('sk$uc7') = 'sk$uc8'
| inverse('sk$uc7') = 'sk$uc8' ),
inference(superposition,[status(thm)],[d104,d96]) ).
cnf(d106,plain,
( inverse('sk$uc7') = 'sk$uc8'
| inverse('sk$uc7') = 'sk$uc8'
| 'sk$uc8' = inverse('sk$uc7') ),
inference(superposition,[status(thm)],[d105,d79]) ).
cnf(d107,plain,
( inverse('sk$uc7') = 'sk$uc8'
| inverse('sk$uc7') = 'sk$uc8' ),
inference(superposition,[status(thm)],[d106,d61]) ).
cnf(d108,plain,
inverse('sk$uc8') = 'sk$uc7',
inference(superposition,[status(thm)],[d107,d9]) ).
cnf(d109,plain,
'sk$uc8' = 'sk$uc7',
inference(demodulation,[status(thm)],[d108,d63]) ).
cnf(d110,plain,
( inverse('sk$uc8') != 'sk$uc6'
| inverse(X3) != 'sk$uc8'
| inverse(X2) != 'sk$uc7'
| inverse(X0) != 'sk$uc8'
| inverse(inverse('sk$uc8')) != 'sk$uc6'
| multiply('sk$uc7','sk$uc6') != 'sk$uc8'
| multiply('sk$uc8',X1) != 'sk$uc7'
| multiply(X3,'sk$uc8') != 'sk$uc7'
| multiply(X2,'sk$uc7') != 'sk$uc6'
| multiply(X0,'sk$uc8') != X1
| identity != 'sk$uc6' ),
inference(superposition,[status(thm)],[c32,c30]) ).
cnf(d111,plain,
( identity != 'sk$uc6'
| inverse(inverse('sk$uc8')) != 'sk$uc6'
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc7'
| inverse(inverse('sk$uc8')) != 'sk$uc8'
| multiply('sk$uc7','sk$uc6') != 'sk$uc8'
| multiply('sk$uc8',X2) != 'sk$uc7'
| multiply(X1,'sk$uc8') != X2
| multiply(X0,'sk$uc7') != 'sk$uc6'
| identity != 'sk$uc7' ),
inference(superposition,[status(thm)],[c32,d110]) ).
cnf(d112,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc7'
| inverse(inverse('sk$uc8')) != 'sk$uc6'
| inverse(inverse('sk$uc8')) != 'sk$uc8'
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X1) != 'sk$uc7'
| inverse(inverse('sk$uc8')) != 'sk$uc8'
| multiply('sk$uc7','sk$uc6') != 'sk$uc8'
| multiply('sk$uc8',X0) != 'sk$uc7'
| multiply(X1,'sk$uc7') != 'sk$uc6'
| identity != X0 ),
inference(superposition,[status(thm)],[d5,d111]) ).
cnf(d113,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc7'
| identity != X1
| inverse(inverse('sk$uc8')) != 'sk$uc6'
| 'sk$uc8' != 'sk$uc8'
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X0) != 'sk$uc7'
| multiply('sk$uc7','sk$uc6') != 'sk$uc8'
| multiply('sk$uc8',X1) != 'sk$uc7'
| multiply(X0,'sk$uc7') != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d112,d9]) ).
cnf(d114,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc7'
| identity != X1
| 'sk$uc8' != 'sk$uc6'
| 'sk$uc8' != 'sk$uc8'
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X0) != 'sk$uc7'
| multiply('sk$uc7','sk$uc6') != 'sk$uc8'
| multiply('sk$uc8',X1) != 'sk$uc7'
| multiply(X0,'sk$uc7') != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d113,d9]) ).
cnf(d115,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc7'
| identity != X0
| 'sk$uc8' != 'sk$uc6'
| 'sk$uc8' != 'sk$uc8'
| inverse('sk$uc8') != 'sk$uc6'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| multiply('sk$uc7','sk$uc6') != 'sk$uc8'
| multiply('sk$uc8',X0) != 'sk$uc7'
| identity != 'sk$uc6' ),
inference(superposition,[status(thm)],[d5,d114]) ).
cnf(d116,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc7'
| identity != X0
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse('sk$uc8') != 'sk$uc6'
| 'sk$uc8' != 'sk$uc6'
| 'sk$uc8' != 'sk$uc8'
| multiply('sk$uc7','sk$uc6') != 'sk$uc8'
| X0 != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d115,d82]) ).
cnf(d117,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc7'
| identity != X0
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse('sk$uc8') != 'sk$uc6'
| 'sk$uc8' != 'sk$uc6'
| 'sk$uc8' != 'sk$uc8'
| multiply('sk$uc7','sk$uc6') != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d116,d109]) ).
cnf(d118,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc7'
| identity != X0
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse('sk$uc8') != 'sk$uc6'
| 'sk$uc8' != 'sk$uc6'
| 'sk$uc8' != 'sk$uc8'
| multiply('sk$uc8','sk$uc6') != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d117,d109]) ).
cnf(d119,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc7'
| identity != X0
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse('sk$uc8') != 'sk$uc6'
| 'sk$uc8' != 'sk$uc6'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc6' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d118,d82]) ).
cnf(d120,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc7'
| identity != X0
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse('sk$uc8') != 'sk$uc6'
| 'sk$uc8' != 'sk$uc6'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d119,d58]) ).
cnf(d121,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc7'
| identity != X0
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse('sk$uc8') != 'sk$uc6'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d120,d58]) ).
cnf(d122,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc7'
| identity != X0
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| 'sk$uc8' != 'sk$uc6'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d121,d63]) ).
cnf(d123,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc7'
| identity != X0
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d122,d58]) ).
cnf(d124,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc7'
| identity != X0
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d123,d9]) ).
cnf(d125,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc7'
| identity != X0
| 'sk$uc8' != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d124,d109]) ).
cnf(d126,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc7'
| identity != X0
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d125,d109]) ).
cnf(d127,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc7'
| 'sk$uc8' != X0
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d126,d59]) ).
cnf(d128,plain,
( identity != 'sk$uc6'
| 'sk$uc8' != 'sk$uc7'
| 'sk$uc8' != X0
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d127,d59]) ).
cnf(d129,plain,
( identity != 'sk$uc6'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != X0
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d128,d109]) ).
cnf(d130,plain,
( 'sk$uc8' != 'sk$uc6'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != X0
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d129,d59]) ).
cnf(d131,plain,
( 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != X0
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d130,d58]) ).
cnf(d132,plain,
multiply(inverse(X0),X0) = 'sk$uc6',
inference(demodulation,[status(thm)],[c32,d40]) ).
cnf(d133,plain,
multiply('sk$uc6','sk$uc8') = 'sk$uc6',
inference(superposition,[status(thm)],[d56,d132]) ).
cnf(d134,plain,
multiply('sk$uc8','sk$uc8') = 'sk$uc6',
inference(demodulation,[status(thm)],[d133,d58]) ).
cnf(d135,plain,
multiply('sk$uc8','sk$uc8') = 'sk$uc8',
inference(demodulation,[status(thm)],[d134,d58]) ).
cnf(d136,plain,
multiply('sk$uc8','sk$uc8') = 'sk$uc8',
inference(superposition,[status(thm)],[d135,d4]) ).
cnf(d137,plain,
'sk$uc8' = 'sk$uc8',
inference(demodulation,[status(thm)],[d136,d82]) ).
cnf(d138,plain,
( 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != X0
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(resolution,[status(thm)],[d137,d131]) ).
cnf(d139,plain,
( 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8' ),
inference(equality_resolution,[status(thm)],[d138]) ).
cnf(d140,plain,
$false,
inference(resolution,[status(thm)],[d137,d139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP358-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 14:47:58 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 197.91/59.60 % SZS status Unsatisfiable for theBenchmark.p
% 197.91/59.60 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------