%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP357-1 : 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 07:23:38 AM UTC 2026
% Result : Unsatisfiable 224.42s 37.94s
% Output : CNFRefutation 224.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 57
% Number of leaves : 18
% Syntax : Number of clauses : 162 ( 46 unt; 91 nHn; 107 RR)
% Number of literals : 484 ( 483 equ; 242 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 : 127 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this_1,negated_conjecture,
( multiply('sk$uc8','sk$uc7') = 'sk$uc6'
| multiply('sk$uc7','sk$uc6') = 'sk$uc8' ) ).
cnf(prove_this_7,negated_conjecture,
( multiply('sk$uc8','sk$uc7') = 'sk$uc6'
| inverse('sk$uc8') = 'sk$uc6' ) ).
cnf(prove_this_8,negated_conjecture,
( multiply('sk$uc3','sk$uc8') = 'sk$uc7'
| inverse('sk$uc8') = 'sk$uc6' ) ).
cnf(prove_this_9,negated_conjecture,
( inverse('sk$uc3') = 'sk$uc8'
| inverse('sk$uc8') = 'sk$uc6' ) ).
cnf(prove_this_14,negated_conjecture,
( multiply('sk$uc3','sk$uc8') = 'sk$uc7'
| multiply('sk$uc1','sk$uc2') = 'sk$uc8' ) ).
cnf(prove_this_15,negated_conjecture,
( inverse('sk$uc3') = 'sk$uc8'
| multiply('sk$uc1','sk$uc2') = 'sk$uc8' ) ).
cnf(prove_this_16,negated_conjecture,
( multiply('sk$uc8','sk$uc5') = 'sk$uc7'
| multiply('sk$uc1','sk$uc2') = 'sk$uc8' ) ).
cnf(prove_this_17,negated_conjecture,
( multiply('sk$uc4','sk$uc8') = 'sk$uc5'
| multiply('sk$uc1','sk$uc2') = 'sk$uc8' ) ).
cnf(prove_this_18,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc8'
| multiply('sk$uc1','sk$uc2') = 'sk$uc8' ) ).
cnf(prove_this_20,negated_conjecture,
( multiply('sk$uc3','sk$uc8') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc2' ) ).
cnf(prove_this_21,negated_conjecture,
( inverse('sk$uc3') = 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc2' ) ).
cnf(prove_this_22,negated_conjecture,
( multiply('sk$uc8','sk$uc5') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc2' ) ).
cnf(prove_this_23,negated_conjecture,
( multiply('sk$uc4','sk$uc8') = 'sk$uc5'
| inverse('sk$uc1') = 'sk$uc2' ) ).
cnf(prove_this_24,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc2' ) ).
cnf(prove_this_31,negated_conjecture,
( inverse(X4) != 'sk$uc8'
| multiply(X4,'sk$uc8') != X3
| multiply('sk$uc8',X3) != 'sk$uc7'
| inverse(X2) != 'sk$uc8'
| multiply(X2,'sk$uc8') != 'sk$uc7'
| multiply('sk$uc8','sk$uc7') != 'sk$uc6'
| multiply(X1,'sk$uc7') != 'sk$uc8'
| inverse(X0) != X1
| multiply(X0,X1) != 'sk$uc8'
| inverse('sk$uc8') != 'sk$uc6'
| multiply('sk$uc7','sk$uc6') != 'sk$uc8' ) ).
cnf(left_identity,axiom,
multiply(identity,X0) = X0 ).
cnf(left_inverse,axiom,
multiply(inverse(X0),X0) = identity ).
cnf(associativity,axiom,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)) ).
cnf(c0,plain,
( multiply('sk$uc8','sk$uc7') = 'sk$uc6'
| multiply('sk$uc7','sk$uc6') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_1]) ).
cnf(c6,plain,
( multiply('sk$uc8','sk$uc7') = 'sk$uc6'
| inverse('sk$uc8') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_7]) ).
cnf(c7,plain,
( multiply('sk$uc3','sk$uc8') = 'sk$uc7'
| inverse('sk$uc8') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_8]) ).
cnf(c8,plain,
( inverse('sk$uc3') = 'sk$uc8'
| inverse('sk$uc8') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_9]) ).
cnf(c13,plain,
( multiply('sk$uc3','sk$uc8') = 'sk$uc7'
| multiply('sk$uc1','sk$uc2') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_14]) ).
cnf(c14,plain,
( inverse('sk$uc3') = 'sk$uc8'
| multiply('sk$uc1','sk$uc2') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_15]) ).
cnf(c15,plain,
( multiply('sk$uc8','sk$uc5') = 'sk$uc7'
| multiply('sk$uc1','sk$uc2') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_16]) ).
cnf(c16,plain,
( multiply('sk$uc4','sk$uc8') = 'sk$uc5'
| multiply('sk$uc1','sk$uc2') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_17]) ).
cnf(c17,plain,
( inverse('sk$uc4') = 'sk$uc8'
| multiply('sk$uc1','sk$uc2') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_18]) ).
cnf(c19,plain,
( multiply('sk$uc3','sk$uc8') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc2' ),
inference(clausification,[status(esa)],[prove_this_20]) ).
cnf(c20,plain,
( inverse('sk$uc3') = 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc2' ),
inference(clausification,[status(esa)],[prove_this_21]) ).
cnf(c21,plain,
( multiply('sk$uc8','sk$uc5') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc2' ),
inference(clausification,[status(esa)],[prove_this_22]) ).
cnf(c22,plain,
( multiply('sk$uc4','sk$uc8') = 'sk$uc5'
| inverse('sk$uc1') = 'sk$uc2' ),
inference(clausification,[status(esa)],[prove_this_23]) ).
cnf(c23,plain,
( inverse('sk$uc4') = 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc2' ),
inference(clausification,[status(esa)],[prove_this_24]) ).
cnf(c30,plain,
( multiply('sk$uc8',X4) != 'sk$uc7'
| multiply(X3,'sk$uc8') != X4
| multiply('sk$uc8','sk$uc7') != 'sk$uc6'
| inverse(X3) != 'sk$uc8'
| inverse(X2) != X0
| multiply(X1,'sk$uc8') != 'sk$uc7'
| inverse('sk$uc8') != 'sk$uc6'
| multiply(X2,X0) != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| multiply('sk$uc7','sk$uc6') != 'sk$uc8'
| multiply(X0,'sk$uc7') != 'sk$uc8' ),
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,
X0 = multiply(inverse(inverse(X0)),identity),
inference(superposition,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
X0 = multiply(X0,identity),
inference(demodulation,[status(thm)],[d7,d2]) ).
cnf(d9,plain,
multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[d6,d2]) ).
cnf(d10,plain,
multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d2,d9]) ).
cnf(d11,plain,
X0 = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
X0 = multiply(identity,X0),
inference(superposition,[status(thm)],[c31,d4]) ).
cnf(d13,plain,
multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[d12,d1]) ).
cnf(d14,plain,
multiply(inverse(inverse(identity)),X0) = X0,
inference(superposition,[status(thm)],[d13,d1]) ).
cnf(d15,plain,
identity = inverse(identity),
inference(superposition,[status(thm)],[d14,d5]) ).
cnf(d16,plain,
( multiply('sk$uc1','sk$uc2') = 'sk$uc8'
| 'sk$uc7' = multiply('sk$uc3','sk$uc8') ),
inference(superposition,[status(thm)],[c13,d4]) ).
cnf(d17,plain,
multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[d2,c32]) ).
cnf(d18,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[d14,c32]) ).
cnf(d19,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[d18,c32]) ).
cnf(d20,plain,
identity = identity,
inference(demodulation,[status(thm)],[d19,c31]) ).
cnf(d21,plain,
( inverse('sk$uc1') = 'sk$uc2'
| 'sk$uc7' = multiply('sk$uc3','sk$uc8') ),
inference(superposition,[status(thm)],[c19,d4]) ).
cnf(d22,plain,
( inverse('sk$uc1') = 'sk$uc2'
| multiply('sk$uc3','sk$uc8') = identity ),
inference(superposition,[status(thm)],[c20,d17]) ).
cnf(d23,plain,
( inverse('sk$uc1') = 'sk$uc2'
| inverse('sk$uc1') = 'sk$uc2'
| 'sk$uc7' = identity ),
inference(superposition,[status(thm)],[d22,d21]) ).
cnf(d24,plain,
( inverse('sk$uc1') = 'sk$uc2'
| inverse('sk$uc7') = identity ),
inference(superposition,[status(thm)],[d23,d18]) ).
cnf(d25,plain,
( inverse('sk$uc1') = 'sk$uc2'
| 'sk$uc7' = multiply('sk$uc8','sk$uc5') ),
inference(superposition,[status(thm)],[c21,d4]) ).
cnf(d26,plain,
( inverse('sk$uc1') = 'sk$uc2'
| multiply('sk$uc8','sk$uc4') = identity ),
inference(superposition,[status(thm)],[c23,c32]) ).
cnf(d27,plain,
( inverse('sk$uc1') = 'sk$uc2'
| multiply('sk$uc8',multiply('sk$uc4',X0)) = multiply(identity,X0) ),
inference(superposition,[status(thm)],[d26,c33]) ).
cnf(d28,plain,
( inverse('sk$uc1') = 'sk$uc2'
| multiply('sk$uc8',multiply('sk$uc4',X0)) = X0 ),
inference(demodulation,[status(thm)],[d27,c31]) ).
cnf(d29,plain,
( inverse('sk$uc1') = 'sk$uc2'
| inverse('sk$uc1') = 'sk$uc2'
| multiply('sk$uc8','sk$uc5') = 'sk$uc8' ),
inference(superposition,[status(thm)],[c22,d28]) ).
cnf(d30,plain,
( inverse('sk$uc1') = 'sk$uc2'
| inverse('sk$uc1') = 'sk$uc2'
| 'sk$uc7' = 'sk$uc8' ),
inference(superposition,[status(thm)],[d29,d25]) ).
cnf(d31,plain,
( inverse('sk$uc1') = 'sk$uc2'
| inverse('sk$uc1') = 'sk$uc2'
| inverse('sk$uc8') = identity ),
inference(superposition,[status(thm)],[d30,d24]) ).
cnf(d32,plain,
( inverse('sk$uc1') = 'sk$uc2'
| 'sk$uc8' = inverse(identity) ),
inference(superposition,[status(thm)],[d31,d11]) ).
cnf(d33,plain,
( inverse('sk$uc1') = 'sk$uc2'
| 'sk$uc8' = identity ),
inference(demodulation,[status(thm)],[d32,d18]) ).
cnf(d34,plain,
( inverse('sk$uc1') = 'sk$uc2'
| identity = 'sk$uc8' ),
inference(superposition,[status(thm)],[d33,d20]) ).
cnf(d35,plain,
( identity = 'sk$uc8'
| multiply('sk$uc1','sk$uc2') = identity ),
inference(superposition,[status(thm)],[d34,d17]) ).
cnf(d36,plain,
( identity = 'sk$uc8'
| 'sk$uc7' = multiply('sk$uc3','sk$uc8')
| identity = 'sk$uc8' ),
inference(superposition,[status(thm)],[d35,d16]) ).
cnf(d37,plain,
( identity = 'sk$uc8'
| inverse('sk$uc3') = 'sk$uc8'
| identity = 'sk$uc8' ),
inference(superposition,[status(thm)],[d35,c14]) ).
cnf(d38,plain,
( identity = 'sk$uc8'
| multiply('sk$uc3','sk$uc8') = identity ),
inference(superposition,[status(thm)],[d37,d17]) ).
cnf(d39,plain,
( identity = 'sk$uc8'
| identity = 'sk$uc8'
| 'sk$uc7' = identity ),
inference(superposition,[status(thm)],[d38,d36]) ).
cnf(d40,plain,
( identity = 'sk$uc8'
| identity = inverse('sk$uc7') ),
inference(superposition,[status(thm)],[d39,d15]) ).
cnf(d41,plain,
( identity = inverse('sk$uc7')
| identity = inverse('sk$uc8') ),
inference(superposition,[status(thm)],[d40,d15]) ).
cnf(d42,plain,
( multiply('sk$uc1','sk$uc2') = 'sk$uc8'
| 'sk$uc7' = multiply('sk$uc8','sk$uc5') ),
inference(superposition,[status(thm)],[c15,d4]) ).
cnf(d43,plain,
( identity = 'sk$uc8'
| 'sk$uc7' = multiply('sk$uc8','sk$uc5')
| identity = 'sk$uc8' ),
inference(superposition,[status(thm)],[d35,d42]) ).
cnf(d44,plain,
( multiply('sk$uc1','sk$uc2') = 'sk$uc8'
| 'sk$uc5' = multiply('sk$uc4','sk$uc8') ),
inference(superposition,[status(thm)],[c16,d4]) ).
cnf(d45,plain,
( identity = 'sk$uc8'
| 'sk$uc5' = multiply('sk$uc4','sk$uc8')
| identity = 'sk$uc8' ),
inference(superposition,[status(thm)],[d35,d44]) ).
cnf(d46,plain,
( identity = 'sk$uc8'
| inverse('sk$uc4') = 'sk$uc8'
| identity = 'sk$uc8' ),
inference(superposition,[status(thm)],[d35,c17]) ).
cnf(d47,plain,
( identity = 'sk$uc8'
| multiply('sk$uc4','sk$uc8') = identity ),
inference(superposition,[status(thm)],[d46,d17]) ).
cnf(d48,plain,
( identity = 'sk$uc8'
| identity = 'sk$uc8'
| 'sk$uc5' = identity ),
inference(superposition,[status(thm)],[d47,d45]) ).
cnf(d49,plain,
( identity = 'sk$uc8'
| X0 = multiply(X0,'sk$uc5') ),
inference(superposition,[status(thm)],[d48,d8]) ).
cnf(d50,plain,
( identity = 'sk$uc8'
| identity = 'sk$uc8'
| 'sk$uc7' = 'sk$uc8' ),
inference(superposition,[status(thm)],[d49,d43]) ).
cnf(d51,plain,
( identity = 'sk$uc8'
| identity = inverse('sk$uc8')
| identity = inverse('sk$uc8') ),
inference(superposition,[status(thm)],[d50,d41]) ).
cnf(d52,plain,
( identity = inverse('sk$uc8')
| identity = inverse('sk$uc8') ),
inference(superposition,[status(thm)],[d51,d15]) ).
cnf(d53,plain,
'sk$uc8' = inverse(identity),
inference(superposition,[status(thm)],[d52,d11]) ).
cnf(d54,plain,
'sk$uc8' = identity,
inference(demodulation,[status(thm)],[d18,d53]) ).
cnf(d55,plain,
inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[status(thm)],[d8,d2]) ).
cnf(d56,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d55,d8]) ).
cnf(d57,plain,
inverse(identity) = 'sk$uc8',
inference(superposition,[status(thm)],[d52,d56]) ).
cnf(d58,plain,
inverse('sk$uc8') = 'sk$uc8',
inference(demodulation,[status(thm)],[d57,d54]) ).
cnf(d59,plain,
multiply(X0,'sk$uc8') = X0,
inference(demodulation,[status(thm)],[d9,d54]) ).
cnf(d60,plain,
X0 = multiply('sk$uc8',X0),
inference(demodulation,[status(thm)],[d12,d54]) ).
cnf(d61,plain,
( inverse('sk$uc8') = 'sk$uc6'
| multiply('sk$uc8',multiply('sk$uc7',X0)) = multiply('sk$uc6',X0) ),
inference(superposition,[status(thm)],[c6,c33]) ).
cnf(d62,plain,
multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d63,plain,
( inverse('sk$uc8') = 'sk$uc6'
| multiply('sk$uc8',X0) = multiply('sk$uc6',multiply(inverse('sk$uc7'),X0)) ),
inference(superposition,[status(thm)],[d62,d61]) ).
cnf(d64,plain,
( inverse('sk$uc8') = 'sk$uc6'
| X0 = multiply('sk$uc6',multiply(inverse('sk$uc7'),X0)) ),
inference(demodulation,[status(thm)],[d63,d60]) ).
cnf(d65,plain,
( 'sk$uc8' = 'sk$uc6'
| X0 = multiply('sk$uc6',multiply(inverse('sk$uc7'),X0)) ),
inference(demodulation,[status(thm)],[d64,d58]) ).
cnf(d66,plain,
X1 = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[status(thm)],[d1,d4]) ).
cnf(d67,plain,
X0 = multiply(X0,'sk$uc8'),
inference(demodulation,[status(thm)],[d8,d54]) ).
cnf(d68,plain,
( inverse('sk$uc3') = 'sk$uc8'
| multiply('sk$uc6','sk$uc8') = identity ),
inference(superposition,[status(thm)],[c8,c32]) ).
cnf(d69,plain,
( inverse('sk$uc3') = 'sk$uc8'
| identity = multiply('sk$uc6','sk$uc8') ),
inference(superposition,[status(thm)],[d68,d4]) ).
cnf(d70,plain,
( identity = multiply('sk$uc6','sk$uc8')
| multiply(inverse('sk$uc8'),X0) = multiply('sk$uc3',X0) ),
inference(superposition,[status(thm)],[d69,d2]) ).
cnf(d71,plain,
( identity = multiply('sk$uc6','sk$uc8')
| multiply('sk$uc8',X0) = multiply('sk$uc3',X0) ),
inference(demodulation,[status(thm)],[d70,d58]) ).
cnf(d72,plain,
( identity = multiply('sk$uc6','sk$uc8')
| X0 = multiply('sk$uc3',X0) ),
inference(demodulation,[status(thm)],[d71,d60]) ).
cnf(d73,plain,
( 'sk$uc8' = multiply('sk$uc6','sk$uc8')
| X0 = multiply('sk$uc3',X0) ),
inference(demodulation,[status(thm)],[d72,d54]) ).
cnf(d74,plain,
( 'sk$uc8' = 'sk$uc6'
| X0 = multiply('sk$uc3',X0) ),
inference(demodulation,[status(thm)],[d73,d67]) ).
cnf(d75,plain,
( inverse('sk$uc8') = 'sk$uc6'
| multiply('sk$uc3',multiply('sk$uc8',X0)) = multiply('sk$uc7',X0) ),
inference(superposition,[status(thm)],[c7,c33]) ).
cnf(d76,plain,
( inverse('sk$uc8') = 'sk$uc6'
| multiply('sk$uc3','sk$uc8') = multiply('sk$uc7',identity) ),
inference(superposition,[status(thm)],[d8,d75]) ).
cnf(d77,plain,
( inverse('sk$uc8') = 'sk$uc6'
| 'sk$uc3' = multiply('sk$uc7',identity) ),
inference(demodulation,[status(thm)],[d76,d67]) ).
cnf(d78,plain,
( inverse('sk$uc8') = 'sk$uc6'
| 'sk$uc3' = multiply('sk$uc7','sk$uc8') ),
inference(demodulation,[status(thm)],[d77,d54]) ).
cnf(d79,plain,
( inverse('sk$uc8') = 'sk$uc6'
| 'sk$uc3' = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d78,d67]) ).
cnf(d80,plain,
( 'sk$uc8' = 'sk$uc6'
| 'sk$uc3' = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d79,d58]) ).
cnf(d81,plain,
( 'sk$uc8' = 'sk$uc6'
| 'sk$uc8' = 'sk$uc6'
| X0 = multiply('sk$uc7',X0) ),
inference(superposition,[status(thm)],[d80,d74]) ).
cnf(d82,plain,
( 'sk$uc8' = 'sk$uc6'
| X0 = multiply(inverse('sk$uc7'),X0) ),
inference(superposition,[status(thm)],[d81,d66]) ).
cnf(d83,plain,
( 'sk$uc8' = 'sk$uc6'
| 'sk$uc8' = 'sk$uc6'
| X0 = multiply('sk$uc6',X0) ),
inference(superposition,[status(thm)],[d82,d65]) ).
cnf(d84,plain,
( 'sk$uc8' = 'sk$uc6'
| 'sk$uc8' = 'sk$uc6' ),
inference(superposition,[status(thm)],[d83,d59]) ).
cnf(d85,plain,
( multiply('sk$uc8','sk$uc7') = 'sk$uc6'
| multiply('sk$uc7',multiply('sk$uc6',X0)) = multiply('sk$uc8',X0) ),
inference(superposition,[status(thm)],[c0,c33]) ).
cnf(d86,plain,
( multiply('sk$uc8','sk$uc7') = 'sk$uc6'
| multiply('sk$uc8',X0) = multiply('sk$uc7',multiply('sk$uc6',X0)) ),
inference(superposition,[status(thm)],[d85,d4]) ).
cnf(d87,plain,
( multiply('sk$uc8','sk$uc7') = 'sk$uc6'
| multiply('sk$uc7',multiply('sk$uc6',X0)) = multiply('sk$uc8',X0) ),
inference(superposition,[status(thm)],[d86,d4]) ).
cnf(d88,plain,
( multiply('sk$uc8','sk$uc7') = 'sk$uc6'
| multiply('sk$uc7',multiply('sk$uc8',X0)) = multiply('sk$uc8',X0) ),
inference(demodulation,[status(thm)],[d87,d84]) ).
cnf(d89,plain,
( multiply('sk$uc8','sk$uc7') = 'sk$uc6'
| multiply('sk$uc7',X0) = multiply('sk$uc8',X0) ),
inference(demodulation,[status(thm)],[d88,d60]) ).
cnf(d90,plain,
( multiply('sk$uc8','sk$uc7') = 'sk$uc6'
| multiply('sk$uc7',X0) = X0 ),
inference(demodulation,[status(thm)],[d89,d60]) ).
cnf(d91,plain,
( 'sk$uc7' = 'sk$uc6'
| multiply('sk$uc7',X0) = X0 ),
inference(demodulation,[status(thm)],[d90,d60]) ).
cnf(d92,plain,
( 'sk$uc7' = 'sk$uc8'
| multiply('sk$uc7',X0) = X0 ),
inference(demodulation,[status(thm)],[d91,d84]) ).
cnf(d93,plain,
( 'sk$uc7' = 'sk$uc8'
| 'sk$uc7' = 'sk$uc8' ),
inference(superposition,[status(thm)],[d92,d67]) ).
cnf(d94,plain,
( inverse('sk$uc8') != 'sk$uc6'
| inverse(X3) != 'sk$uc8'
| inverse(X1) != X2
| inverse(inverse('sk$uc8')) != 'sk$uc8'
| multiply('sk$uc8','sk$uc7') != 'sk$uc6'
| multiply('sk$uc8',X0) != 'sk$uc7'
| multiply('sk$uc7','sk$uc6') != 'sk$uc8'
| multiply(X3,'sk$uc8') != 'sk$uc7'
| multiply(X2,'sk$uc7') != 'sk$uc8'
| multiply(X1,X2) != 'sk$uc8'
| identity != X0 ),
inference(superposition,[status(thm)],[c32,c30]) ).
cnf(d95,plain,
( identity != X2
| inverse(inverse('sk$uc8')) != 'sk$uc8'
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X1) != X0
| inverse(inverse(identity)) != 'sk$uc8'
| multiply('sk$uc8','sk$uc7') != 'sk$uc6'
| multiply('sk$uc8',X2) != 'sk$uc7'
| multiply('sk$uc7','sk$uc6') != 'sk$uc8'
| multiply(X1,X0) != 'sk$uc8'
| multiply(X0,'sk$uc7') != 'sk$uc8'
| 'sk$uc8' != 'sk$uc7' ),
inference(superposition,[status(thm)],[d13,d94]) ).
cnf(d96,plain,
( identity != X2
| inverse(inverse(identity)) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X0) != X1
| 'sk$uc8' != 'sk$uc7'
| multiply('sk$uc8','sk$uc7') != 'sk$uc6'
| multiply('sk$uc8',X2) != 'sk$uc7'
| multiply('sk$uc7','sk$uc6') != 'sk$uc8'
| multiply(X1,'sk$uc7') != 'sk$uc8'
| multiply(X0,X1) != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d95,d56]) ).
cnf(d97,plain,
( identity != X2
| identity != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X0) != X1
| 'sk$uc8' != 'sk$uc7'
| multiply('sk$uc8','sk$uc7') != 'sk$uc6'
| multiply('sk$uc8',X2) != 'sk$uc7'
| multiply('sk$uc7','sk$uc6') != 'sk$uc8'
| multiply(X1,'sk$uc7') != 'sk$uc8'
| multiply(X0,X1) != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d96,d56]) ).
cnf(d98,plain,
( identity != X1
| identity != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X0) != inverse(X0)
| 'sk$uc8' != 'sk$uc7'
| multiply('sk$uc8','sk$uc7') != 'sk$uc6'
| multiply('sk$uc8',X1) != 'sk$uc7'
| multiply('sk$uc7','sk$uc6') != 'sk$uc8'
| multiply(inverse(X0),'sk$uc7') != 'sk$uc8'
| identity != 'sk$uc8' ),
inference(superposition,[status(thm)],[d17,d97]) ).
cnf(d99,plain,
( identity != 'sk$uc8'
| identity != X0
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X1) != inverse(X1)
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc7'
| multiply(inverse(X1),'sk$uc7') != 'sk$uc8'
| multiply('sk$uc8','sk$uc7') != 'sk$uc6'
| multiply('sk$uc8',X0) != 'sk$uc7'
| multiply('sk$uc8','sk$uc6') != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d98,d93]) ).
cnf(d100,plain,
( identity != 'sk$uc8'
| identity != X0
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X1) != inverse(X1)
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc7'
| multiply(inverse(X1),'sk$uc7') != 'sk$uc8'
| multiply('sk$uc8','sk$uc7') != 'sk$uc6'
| multiply('sk$uc8',X0) != 'sk$uc7'
| 'sk$uc6' != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d99,d60]) ).
cnf(d101,plain,
( identity != 'sk$uc8'
| identity != X0
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X1) != inverse(X1)
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc7'
| multiply(inverse(X1),'sk$uc7') != 'sk$uc8'
| multiply('sk$uc8','sk$uc7') != 'sk$uc6'
| multiply('sk$uc8',X0) != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d100,d84]) ).
cnf(d102,plain,
( identity != 'sk$uc8'
| identity != X0
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X1) != inverse(X1)
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc7'
| multiply(inverse(X1),'sk$uc7') != 'sk$uc8'
| multiply('sk$uc8','sk$uc7') != 'sk$uc6'
| X0 != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d101,d60]) ).
cnf(d103,plain,
( identity != 'sk$uc8'
| identity != X0
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X1) != inverse(X1)
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc7'
| multiply(inverse(X1),'sk$uc7') != 'sk$uc8'
| multiply('sk$uc8','sk$uc7') != 'sk$uc6'
| X0 != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d102,d93]) ).
cnf(d104,plain,
( identity != 'sk$uc8'
| identity != X0
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X1) != inverse(X1)
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc7'
| multiply(inverse(X1),'sk$uc7') != 'sk$uc8'
| 'sk$uc7' != 'sk$uc6'
| X0 != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d103,d60]) ).
cnf(d105,plain,
( identity != 'sk$uc8'
| identity != X0
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X1) != inverse(X1)
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc7'
| multiply(inverse(X1),'sk$uc7') != 'sk$uc8'
| 'sk$uc8' != 'sk$uc6'
| X0 != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d104,d93]) ).
cnf(d106,plain,
( identity != 'sk$uc8'
| identity != X0
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X1) != inverse(X1)
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc7'
| multiply(inverse(X1),'sk$uc7') != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d105,d84]) ).
cnf(d107,plain,
( identity != 'sk$uc8'
| identity != X0
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X1) != inverse(X1)
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc7'
| multiply(inverse(X1),'sk$uc8') != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d106,d93]) ).
cnf(d108,plain,
( identity != 'sk$uc8'
| identity != X1
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X0) != inverse(X0)
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc7'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X1 != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d107,d67]) ).
cnf(d109,plain,
( identity != 'sk$uc8'
| identity != X0
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X1) != inverse(X1)
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d108,d93]) ).
cnf(d110,plain,
( identity != 'sk$uc8'
| identity != X0
| 'sk$uc8' != 'sk$uc6'
| inverse(X1) != inverse(X1)
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d109,d58]) ).
cnf(d111,plain,
( identity != 'sk$uc8'
| identity != X0
| 'sk$uc8' != 'sk$uc8'
| inverse(X1) != inverse(X1)
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d110,d84]) ).
cnf(d112,plain,
( identity != 'sk$uc8'
| 'sk$uc8' != X0
| 'sk$uc8' != 'sk$uc8'
| inverse(X1) != inverse(X1)
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d111,d54]) ).
cnf(d113,plain,
( 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != X0
| 'sk$uc8' != 'sk$uc8'
| inverse(X1) != inverse(X1)
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d112,d54]) ).
cnf(d114,plain,
inverse(X0) = multiply(inverse(X0),identity),
inference(superposition,[status(thm)],[d17,d66]) ).
cnf(d115,plain,
inverse(X0) = inverse(X0),
inference(demodulation,[status(thm)],[d114,d8]) ).
cnf(d116,plain,
( 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != X0
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8' ),
inference(resolution,[status(thm)],[d115,d113]) ).
cnf(d117,plain,
identity = multiply(identity,'sk$uc8'),
inference(superposition,[status(thm)],[d52,d5]) ).
cnf(d118,plain,
'sk$uc8' = multiply(identity,'sk$uc8'),
inference(demodulation,[status(thm)],[d117,d54]) ).
cnf(d119,plain,
'sk$uc8' = multiply('sk$uc8','sk$uc8'),
inference(demodulation,[status(thm)],[d118,d54]) ).
cnf(d120,plain,
multiply('sk$uc8','sk$uc8') = 'sk$uc8',
inference(superposition,[status(thm)],[d119,d4]) ).
cnf(d121,plain,
'sk$uc8' = 'sk$uc8',
inference(demodulation,[status(thm)],[d120,d60]) ).
cnf(d122,plain,
( inverse(X1) != 'sk$uc8'
| 'sk$uc8' != X0
| X0 != 'sk$uc8' ),
inference(resolution,[status(thm)],[d121,d116]) ).
cnf(d123,plain,
( inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8' ),
inference(equality_resolution,[status(thm)],[d122]) ).
cnf(d124,plain,
inverse(X0) != 'sk$uc8',
inference(resolution,[status(thm)],[d121,d123]) ).
cnf(d125,plain,
$false,
inference(resolution,[status(thm)],[d124,d58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP357-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 14:48:39 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 224.42/37.94 % SZS status Unsatisfiable for theBenchmark.p
% 224.42/37.94 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------