%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP363-1 : 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 : n020.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 07:23:39 AM UTC 2026
% Result : Unsatisfiable 84.20s 18.44s
% Output : CNFRefutation 84.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 18
% Syntax : Number of clauses : 161 ( 48 unt; 86 nHn; 113 RR)
% Number of literals : 483 ( 482 equ; 248 neg)
% Maximal clause size : 10 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 117 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this_2,negated_conjecture,
( multiply('sk$uc2','sk$uc6') = 'sk$uc7'
| multiply('sk$uc6','sk$uc5') = 'sk$uc7' ) ).
cnf(prove_this_3,negated_conjecture,
( inverse('sk$uc2') = 'sk$uc6'
| multiply('sk$uc6','sk$uc5') = 'sk$uc7' ) ).
cnf(prove_this_6,negated_conjecture,
( inverse('sk$uc3') = 'sk$uc7'
| multiply('sk$uc6','sk$uc5') = 'sk$uc7' ) ).
cnf(prove_this_7,negated_conjecture,
( multiply('sk$uc6','sk$uc7') = 'sk$uc5'
| inverse('sk$uc6') = 'sk$uc5' ) ).
cnf(prove_this_8,negated_conjecture,
( multiply('sk$uc2','sk$uc6') = 'sk$uc7'
| inverse('sk$uc6') = 'sk$uc5' ) ).
cnf(prove_this_9,negated_conjecture,
( inverse('sk$uc2') = 'sk$uc6'
| inverse('sk$uc6') = 'sk$uc5' ) ).
cnf(prove_this_13,negated_conjecture,
( multiply('sk$uc6','sk$uc7') = 'sk$uc5'
| multiply('sk$uc1','sk$uc6') = 'sk$uc5' ) ).
cnf(prove_this_16,negated_conjecture,
( multiply('sk$uc7','sk$uc4') = 'sk$uc6'
| multiply('sk$uc1','sk$uc6') = 'sk$uc5' ) ).
cnf(prove_this_17,negated_conjecture,
( multiply('sk$uc3','sk$uc7') = 'sk$uc4'
| multiply('sk$uc1','sk$uc6') = 'sk$uc5' ) ).
cnf(prove_this_18,negated_conjecture,
( inverse('sk$uc3') = 'sk$uc7'
| multiply('sk$uc1','sk$uc6') = 'sk$uc5' ) ).
cnf(prove_this_19,negated_conjecture,
( multiply('sk$uc6','sk$uc7') = 'sk$uc5'
| inverse('sk$uc1') = 'sk$uc6' ) ).
cnf(prove_this_22,negated_conjecture,
( multiply('sk$uc7','sk$uc4') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc6' ) ).
cnf(prove_this_23,negated_conjecture,
( multiply('sk$uc3','sk$uc7') = 'sk$uc4'
| inverse('sk$uc1') = 'sk$uc6' ) ).
cnf(prove_this_24,negated_conjecture,
( inverse('sk$uc3') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc6' ) ).
cnf(prove_this_25,negated_conjecture,
( inverse(X3) != 'sk$uc7'
| multiply(X3,'sk$uc7') != X2
| multiply('sk$uc7',X2) != 'sk$uc6'
| inverse(X1) != 'sk$uc6'
| multiply(X1,'sk$uc6') != 'sk$uc7'
| multiply('sk$uc6','sk$uc7') != 'sk$uc5'
| inverse(X0) != 'sk$uc6'
| multiply(X0,'sk$uc6') != 'sk$uc5'
| inverse('sk$uc6') != 'sk$uc5'
| multiply('sk$uc6','sk$uc5') != 'sk$uc7' ) ).
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,
( multiply('sk$uc2','sk$uc6') = 'sk$uc7'
| multiply('sk$uc6','sk$uc5') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_2]) ).
cnf(c2,plain,
( inverse('sk$uc2') = 'sk$uc6'
| multiply('sk$uc6','sk$uc5') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_3]) ).
cnf(c5,plain,
( inverse('sk$uc3') = 'sk$uc7'
| multiply('sk$uc6','sk$uc5') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_6]) ).
cnf(c6,plain,
( multiply('sk$uc6','sk$uc7') = 'sk$uc5'
| inverse('sk$uc6') = 'sk$uc5' ),
inference(clausification,[status(esa)],[prove_this_7]) ).
cnf(c7,plain,
( multiply('sk$uc2','sk$uc6') = 'sk$uc7'
| inverse('sk$uc6') = 'sk$uc5' ),
inference(clausification,[status(esa)],[prove_this_8]) ).
cnf(c8,plain,
( inverse('sk$uc2') = 'sk$uc6'
| inverse('sk$uc6') = 'sk$uc5' ),
inference(clausification,[status(esa)],[prove_this_9]) ).
cnf(c12,plain,
( multiply('sk$uc6','sk$uc7') = 'sk$uc5'
| multiply('sk$uc1','sk$uc6') = 'sk$uc5' ),
inference(clausification,[status(esa)],[prove_this_13]) ).
cnf(c15,plain,
( multiply('sk$uc7','sk$uc4') = 'sk$uc6'
| multiply('sk$uc1','sk$uc6') = 'sk$uc5' ),
inference(clausification,[status(esa)],[prove_this_16]) ).
cnf(c16,plain,
( multiply('sk$uc3','sk$uc7') = 'sk$uc4'
| multiply('sk$uc1','sk$uc6') = 'sk$uc5' ),
inference(clausification,[status(esa)],[prove_this_17]) ).
cnf(c17,plain,
( inverse('sk$uc3') = 'sk$uc7'
| multiply('sk$uc1','sk$uc6') = 'sk$uc5' ),
inference(clausification,[status(esa)],[prove_this_18]) ).
cnf(c18,plain,
( multiply('sk$uc6','sk$uc7') = 'sk$uc5'
| inverse('sk$uc1') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_19]) ).
cnf(c21,plain,
( multiply('sk$uc7','sk$uc4') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_22]) ).
cnf(c22,plain,
( multiply('sk$uc3','sk$uc7') = 'sk$uc4'
| inverse('sk$uc1') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_23]) ).
cnf(c23,plain,
( inverse('sk$uc3') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_24]) ).
cnf(c24,plain,
( multiply('sk$uc6','sk$uc5') != 'sk$uc7'
| inverse(X2) != 'sk$uc7'
| multiply(X1,'sk$uc6') != 'sk$uc7'
| multiply('sk$uc7',X3) != 'sk$uc6'
| multiply(X2,'sk$uc7') != X3
| multiply('sk$uc6','sk$uc7') != 'sk$uc5'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| multiply(X0,'sk$uc6') != 'sk$uc5'
| inverse('sk$uc6') != 'sk$uc5' ),
inference(clausification,[status(esa)],[prove_this_25]) ).
cnf(c25,plain,
multiply(identity,X0) = X0,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c26,plain,
multiply(inverse(X0),X0) = identity,
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c27,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(clausification,[status(esa)],[associativity]) ).
cnf(d0,plain,
multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[status(thm)],[c26,c27]) ).
cnf(d1,plain,
X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(demodulation,[status(thm)],[d0,c25]) ).
cnf(d2,plain,
multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(superposition,[status(thm)],[d1,d1]) ).
cnf(d3,plain,
multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[d2,c26]) ).
cnf(d4,plain,
( inverse('sk$uc6') = 'sk$uc5'
| multiply('sk$uc6','sk$uc2') = identity ),
inference(superposition,[status(thm)],[c8,c26]) ).
cnf(d5,plain,
( inverse('sk$uc6') = 'sk$uc5'
| multiply(identity,X0) = multiply('sk$uc6',multiply('sk$uc2',X0)) ),
inference(superposition,[status(thm)],[d4,c27]) ).
cnf(d6,plain,
( inverse('sk$uc6') = 'sk$uc5'
| X0 = multiply('sk$uc6',multiply('sk$uc2',X0)) ),
inference(demodulation,[status(thm)],[d5,c25]) ).
cnf(d7,plain,
( inverse('sk$uc6') = 'sk$uc5'
| inverse('sk$uc6') = 'sk$uc5'
| 'sk$uc6' = multiply('sk$uc6','sk$uc7') ),
inference(superposition,[status(thm)],[c7,d6]) ).
cnf(d8,plain,
( inverse('sk$uc6') = 'sk$uc5'
| 'sk$uc7' = multiply(inverse('sk$uc6'),'sk$uc6') ),
inference(superposition,[status(thm)],[d7,d1]) ).
cnf(d9,plain,
( inverse('sk$uc6') = 'sk$uc5'
| 'sk$uc7' = identity ),
inference(demodulation,[status(thm)],[d8,c26]) ).
cnf(d10,plain,
( 'sk$uc7' = identity
| multiply('sk$uc6','sk$uc5') = identity ),
inference(superposition,[status(thm)],[d9,d3]) ).
cnf(d11,plain,
multiply(X0,X1) = multiply(identity,multiply(X0,X1)),
inference(superposition,[status(thm)],[c25,c27]) ).
cnf(d12,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d11,c25]) ).
cnf(d13,plain,
( multiply('sk$uc6','sk$uc5') = 'sk$uc7'
| 'sk$uc7' = multiply('sk$uc2','sk$uc6') ),
inference(superposition,[status(thm)],[c1,d12]) ).
cnf(d14,plain,
( inverse('sk$uc2') = 'sk$uc6'
| 'sk$uc7' = multiply('sk$uc6','sk$uc5') ),
inference(superposition,[status(thm)],[c2,d12]) ).
cnf(d15,plain,
( 'sk$uc7' = identity
| inverse('sk$uc2') = 'sk$uc6'
| 'sk$uc7' = identity ),
inference(superposition,[status(thm)],[d10,d14]) ).
cnf(d16,plain,
( 'sk$uc7' = identity
| multiply('sk$uc2','sk$uc6') = identity ),
inference(superposition,[status(thm)],[d15,d3]) ).
cnf(d17,plain,
( 'sk$uc7' = identity
| multiply('sk$uc6','sk$uc5') = 'sk$uc7'
| 'sk$uc7' = identity ),
inference(superposition,[status(thm)],[d16,d13]) ).
cnf(d18,plain,
( 'sk$uc7' = identity
| 'sk$uc7' = identity
| 'sk$uc7' = identity ),
inference(superposition,[status(thm)],[d17,d10]) ).
cnf(d19,plain,
identity = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[c26,d12]) ).
cnf(d20,plain,
X0 = multiply(inverse(identity),X0),
inference(superposition,[status(thm)],[c25,d1]) ).
cnf(d21,plain,
X0 = multiply(inverse(inverse(identity)),X0),
inference(superposition,[status(thm)],[d20,d1]) ).
cnf(d22,plain,
identity = inverse(identity),
inference(superposition,[status(thm)],[d21,d19]) ).
cnf(d23,plain,
'sk$uc7' = inverse(identity),
inference(demodulation,[status(thm)],[d22,d18]) ).
cnf(d24,plain,
'sk$uc7' = inverse('sk$uc7'),
inference(demodulation,[status(thm)],[d23,d18]) ).
cnf(d25,plain,
X0 = multiply(inverse(inverse(X0)),identity),
inference(superposition,[status(thm)],[d19,d1]) ).
cnf(d26,plain,
X0 = multiply(X0,identity),
inference(demodulation,[status(thm)],[d25,d2]) ).
cnf(d27,plain,
multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d26,d2]) ).
cnf(d28,plain,
X0 = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d27,d26]) ).
cnf(d29,plain,
( inverse('sk$uc3') = 'sk$uc7'
| multiply('sk$uc6','sk$uc1') = identity ),
inference(superposition,[status(thm)],[c23,c26]) ).
cnf(d30,plain,
( inverse('sk$uc3') = 'sk$uc7'
| multiply(identity,X0) = multiply('sk$uc6',multiply('sk$uc1',X0)) ),
inference(superposition,[status(thm)],[d29,c27]) ).
cnf(d31,plain,
( inverse('sk$uc3') = 'sk$uc7'
| X0 = multiply('sk$uc6',multiply('sk$uc1',X0)) ),
inference(demodulation,[status(thm)],[d30,c25]) ).
cnf(d32,plain,
( inverse('sk$uc3') = 'sk$uc7'
| inverse('sk$uc3') = 'sk$uc7'
| 'sk$uc6' = multiply('sk$uc6','sk$uc5') ),
inference(superposition,[status(thm)],[c17,d31]) ).
cnf(d33,plain,
( inverse('sk$uc3') = 'sk$uc7'
| inverse('sk$uc3') = 'sk$uc7'
| 'sk$uc6' = 'sk$uc7' ),
inference(superposition,[status(thm)],[d32,c5]) ).
cnf(d34,plain,
( 'sk$uc6' = 'sk$uc7'
| 'sk$uc3' = inverse('sk$uc7') ),
inference(superposition,[status(thm)],[d33,d28]) ).
cnf(d35,plain,
( 'sk$uc3' = 'sk$uc7'
| 'sk$uc6' = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d34,d24]) ).
cnf(d36,plain,
inverse(X0) = multiply(inverse(X0),identity),
inference(superposition,[status(thm)],[d3,d1]) ).
cnf(d37,plain,
inverse(X0) = inverse(X0),
inference(demodulation,[status(thm)],[d36,d26]) ).
cnf(d38,plain,
multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[d25,d12]) ).
cnf(d39,plain,
multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[d38,d2]) ).
cnf(d40,plain,
multiply(X0,'sk$uc7') = X0,
inference(demodulation,[status(thm)],[d39,d18]) ).
cnf(d41,plain,
( inverse('sk$uc1') = 'sk$uc6'
| 'sk$uc3' = 'sk$uc4' ),
inference(demodulation,[status(thm)],[c22,d40]) ).
cnf(d42,plain,
( 'sk$uc3' = 'sk$uc4'
| 'sk$uc6' = inverse('sk$uc1') ),
inference(superposition,[status(thm)],[d41,d37]) ).
cnf(d43,plain,
identity = multiply(X0,inverse(X0)),
inference(superposition,[status(thm)],[d2,d19]) ).
cnf(d44,plain,
'sk$uc7' = multiply(X0,inverse(X0)),
inference(demodulation,[status(thm)],[d43,d18]) ).
cnf(d45,plain,
( multiply('sk$uc1','sk$uc6') = 'sk$uc5'
| 'sk$uc6' = 'sk$uc5' ),
inference(demodulation,[status(thm)],[c12,d40]) ).
cnf(d46,plain,
( inverse('sk$uc1') = 'sk$uc6'
| 'sk$uc6' = 'sk$uc5' ),
inference(demodulation,[status(thm)],[c18,d40]) ).
cnf(d47,plain,
( 'sk$uc6' = 'sk$uc5'
| 'sk$uc7' = multiply('sk$uc1','sk$uc6') ),
inference(superposition,[status(thm)],[d46,d44]) ).
cnf(d48,plain,
( 'sk$uc6' = 'sk$uc5'
| 'sk$uc6' = 'sk$uc5'
| 'sk$uc7' = 'sk$uc5' ),
inference(superposition,[status(thm)],[d47,d45]) ).
cnf(d49,plain,
( inverse('sk$uc6') = 'sk$uc5'
| inverse('sk$uc6') = 'sk$uc5'
| 'sk$uc6' = 'sk$uc5' ),
inference(superposition,[status(thm)],[d7,c6]) ).
cnf(d50,plain,
( 'sk$uc6' = 'sk$uc5'
| 'sk$uc6' = inverse('sk$uc5') ),
inference(superposition,[status(thm)],[d49,d28]) ).
cnf(d51,plain,
( 'sk$uc6' = 'sk$uc5'
| inverse('sk$uc5') = 'sk$uc6' ),
inference(superposition,[status(thm)],[d50,d37]) ).
cnf(d52,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[d21,c26]) ).
cnf(d53,plain,
inverse('sk$uc7') = identity,
inference(demodulation,[status(thm)],[d52,d18]) ).
cnf(d54,plain,
inverse('sk$uc7') = 'sk$uc7',
inference(demodulation,[status(thm)],[d53,d18]) ).
cnf(d55,plain,
X2 = multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))),
inference(superposition,[status(thm)],[c27,d1]) ).
cnf(d56,plain,
multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(superposition,[status(thm)],[d1,d12]) ).
cnf(d57,plain,
multiply(X0,X1) = multiply(inverse(multiply(X2,inverse(X0))),multiply(X2,X1)),
inference(superposition,[status(thm)],[d56,d55]) ).
cnf(d58,plain,
( multiply('sk$uc6','sk$uc7') = 'sk$uc5'
| 'sk$uc6' = multiply(inverse('sk$uc1'),'sk$uc5') ),
inference(superposition,[status(thm)],[c12,d1]) ).
cnf(d59,plain,
( multiply('sk$uc6','sk$uc7') = 'sk$uc5'
| 'sk$uc5' = multiply(inverse(multiply(X0,inverse('sk$uc1'))),multiply(X0,'sk$uc6')) ),
inference(superposition,[status(thm)],[d58,d55]) ).
cnf(d60,plain,
( 'sk$uc5' = multiply(inverse(multiply(X0,inverse('sk$uc1'))),multiply(X0,'sk$uc6'))
| 'sk$uc6' = 'sk$uc5' ),
inference(demodulation,[status(thm)],[d59,d40]) ).
cnf(d61,plain,
( 'sk$uc5' = multiply('sk$uc1','sk$uc6')
| 'sk$uc6' = 'sk$uc5' ),
inference(demodulation,[status(thm)],[d60,d57]) ).
cnf(d62,plain,
( 'sk$uc6' = 'sk$uc5'
| 'sk$uc6' = 'sk$uc5'
| 'sk$uc5' = 'sk$uc7' ),
inference(superposition,[status(thm)],[d47,d61]) ).
cnf(d63,plain,
( 'sk$uc6' = 'sk$uc5'
| inverse('sk$uc5') = 'sk$uc7' ),
inference(superposition,[status(thm)],[d62,d54]) ).
cnf(d64,plain,
( 'sk$uc6' = 'sk$uc5'
| 'sk$uc6' = 'sk$uc5'
| 'sk$uc7' = 'sk$uc6' ),
inference(superposition,[status(thm)],[d63,d51]) ).
cnf(d65,plain,
( 'sk$uc6' = 'sk$uc5'
| 'sk$uc6' = 'sk$uc5'
| 'sk$uc6' = 'sk$uc5' ),
inference(superposition,[status(thm)],[d64,d48]) ).
cnf(d66,plain,
( multiply('sk$uc3','sk$uc7') = 'sk$uc4'
| multiply('sk$uc5',X0) = multiply('sk$uc1',multiply('sk$uc6',X0)) ),
inference(superposition,[status(thm)],[c16,c27]) ).
cnf(d67,plain,
( multiply('sk$uc3','sk$uc7') = 'sk$uc4'
| multiply('sk$uc6',X0) = multiply(inverse('sk$uc1'),multiply('sk$uc5',X0)) ),
inference(superposition,[status(thm)],[d66,d1]) ).
cnf(d68,plain,
( multiply('sk$uc3','sk$uc7') = 'sk$uc4'
| multiply('sk$uc6',inverse('sk$uc5')) = multiply(inverse('sk$uc1'),identity) ),
inference(superposition,[status(thm)],[d3,d67]) ).
cnf(d69,plain,
( multiply('sk$uc3','sk$uc7') = 'sk$uc4'
| multiply('sk$uc6',inverse('sk$uc6')) = multiply(inverse('sk$uc1'),identity) ),
inference(demodulation,[status(thm)],[d68,d65]) ).
cnf(d70,plain,
( multiply('sk$uc3','sk$uc7') = 'sk$uc4'
| 'sk$uc7' = multiply(inverse('sk$uc1'),identity) ),
inference(demodulation,[status(thm)],[d69,d44]) ).
cnf(d71,plain,
( multiply('sk$uc3','sk$uc7') = 'sk$uc4'
| 'sk$uc7' = multiply(inverse('sk$uc1'),'sk$uc7') ),
inference(demodulation,[status(thm)],[d70,d18]) ).
cnf(d72,plain,
( multiply('sk$uc3','sk$uc7') = 'sk$uc4'
| 'sk$uc7' = inverse('sk$uc1') ),
inference(demodulation,[status(thm)],[d71,d40]) ).
cnf(d73,plain,
( 'sk$uc3' = 'sk$uc4'
| 'sk$uc7' = inverse('sk$uc1') ),
inference(demodulation,[status(thm)],[d72,d40]) ).
cnf(d74,plain,
( 'sk$uc3' = 'sk$uc4'
| 'sk$uc3' = 'sk$uc4'
| 'sk$uc6' = 'sk$uc7' ),
inference(superposition,[status(thm)],[d73,d42]) ).
cnf(d75,plain,
( 'sk$uc6' = 'sk$uc7'
| 'sk$uc6' = 'sk$uc7'
| 'sk$uc4' = 'sk$uc7' ),
inference(superposition,[status(thm)],[d74,d35]) ).
cnf(d76,plain,
X0 = multiply(identity,X0),
inference(superposition,[status(thm)],[c25,d12]) ).
cnf(d77,plain,
X0 = multiply('sk$uc7',X0),
inference(demodulation,[status(thm)],[d76,d18]) ).
cnf(d78,plain,
( multiply('sk$uc7','sk$uc4') = 'sk$uc6'
| 'sk$uc6' = multiply(inverse('sk$uc1'),'sk$uc5') ),
inference(superposition,[status(thm)],[c15,d1]) ).
cnf(d79,plain,
( multiply('sk$uc7','sk$uc4') = 'sk$uc6'
| 'sk$uc5' = multiply(inverse(multiply(X0,inverse('sk$uc1'))),multiply(X0,'sk$uc6')) ),
inference(superposition,[status(thm)],[d78,d55]) ).
cnf(d80,plain,
( 'sk$uc5' = multiply(inverse(multiply(X0,inverse('sk$uc1'))),multiply(X0,'sk$uc6'))
| 'sk$uc4' = 'sk$uc6' ),
inference(demodulation,[status(thm)],[d79,d77]) ).
cnf(d81,plain,
( 'sk$uc5' = multiply('sk$uc1','sk$uc6')
| 'sk$uc4' = 'sk$uc6' ),
inference(demodulation,[status(thm)],[d80,d57]) ).
cnf(d82,plain,
( inverse('sk$uc1') = 'sk$uc6'
| 'sk$uc4' = multiply(inverse(multiply(X0,'sk$uc7')),multiply(X0,'sk$uc6')) ),
inference(superposition,[status(thm)],[c21,d55]) ).
cnf(d83,plain,
( 'sk$uc4' = multiply(inverse(X0),multiply(X0,'sk$uc6'))
| inverse('sk$uc1') = 'sk$uc6' ),
inference(demodulation,[status(thm)],[d82,d40]) ).
cnf(d84,plain,
( 'sk$uc4' = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc6' ),
inference(demodulation,[status(thm)],[d83,d56]) ).
cnf(d85,plain,
( 'sk$uc4' = 'sk$uc6'
| 'sk$uc7' = multiply('sk$uc1','sk$uc6') ),
inference(superposition,[status(thm)],[d84,d44]) ).
cnf(d86,plain,
( 'sk$uc4' = 'sk$uc6'
| 'sk$uc4' = 'sk$uc6'
| 'sk$uc5' = 'sk$uc7' ),
inference(superposition,[status(thm)],[d85,d81]) ).
cnf(d87,plain,
( 'sk$uc4' = 'sk$uc6'
| 'sk$uc6' = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d86,d65]) ).
cnf(d88,plain,
( 'sk$uc6' = 'sk$uc7'
| 'sk$uc6' = 'sk$uc7'
| 'sk$uc6' = 'sk$uc7' ),
inference(superposition,[status(thm)],[d87,d75]) ).
cnf(d89,plain,
inverse('sk$uc6') = 'sk$uc7',
inference(demodulation,[status(thm)],[d54,d88]) ).
cnf(d90,plain,
inverse('sk$uc6') = 'sk$uc6',
inference(demodulation,[status(thm)],[d89,d88]) ).
cnf(d91,plain,
'sk$uc6' = identity,
inference(demodulation,[status(thm)],[d18,d88]) ).
cnf(d92,plain,
multiply('sk$uc7',X0) = X0,
inference(demodulation,[status(thm)],[c25,d18]) ).
cnf(d93,plain,
multiply('sk$uc6',X0) = X0,
inference(demodulation,[status(thm)],[d92,d88]) ).
cnf(d94,plain,
multiply(X0,'sk$uc6') = X0,
inference(demodulation,[status(thm)],[d40,d88]) ).
cnf(d95,plain,
( inverse('sk$uc6') != 'sk$uc5'
| inverse(X2) != 'sk$uc6'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc7'
| multiply('sk$uc6','sk$uc7') != 'sk$uc5'
| multiply('sk$uc6','sk$uc5') != 'sk$uc7'
| multiply(X2,'sk$uc6') != 'sk$uc7'
| multiply(X1,'sk$uc6') != 'sk$uc5'
| multiply(X0,'sk$uc7') != inverse('sk$uc7')
| identity != 'sk$uc6' ),
inference(superposition,[status(thm)],[d3,c24]) ).
cnf(d96,plain,
( identity != 'sk$uc6'
| inverse('sk$uc6') != 'sk$uc5'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| multiply('sk$uc6','sk$uc7') != 'sk$uc5'
| multiply('sk$uc6','sk$uc5') != 'sk$uc7'
| multiply(X1,'sk$uc6') != 'sk$uc5'
| multiply(X0,'sk$uc6') != 'sk$uc7'
| identity != inverse('sk$uc7') ),
inference(superposition,[status(thm)],[d19,d95]) ).
cnf(d97,plain,
( identity != inverse('sk$uc7')
| identity != 'sk$uc6'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse('sk$uc6') != 'sk$uc5'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| multiply('sk$uc6','sk$uc7') != 'sk$uc5'
| multiply('sk$uc6','sk$uc5') != 'sk$uc7'
| multiply(X1,'sk$uc6') != 'sk$uc7'
| X0 != 'sk$uc5' ),
inference(demodulation,[status(thm)],[d96,d94]) ).
cnf(d98,plain,
( identity != inverse('sk$uc7')
| identity != 'sk$uc6'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse('sk$uc6') != 'sk$uc5'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| multiply('sk$uc6','sk$uc7') != 'sk$uc5'
| multiply('sk$uc6','sk$uc5') != 'sk$uc7'
| multiply(X1,'sk$uc6') != 'sk$uc7'
| X0 != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d97,d65]) ).
cnf(d99,plain,
( identity != inverse('sk$uc7')
| identity != 'sk$uc6'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse('sk$uc6') != 'sk$uc5'
| inverse(X0) != 'sk$uc6'
| inverse(X1) != 'sk$uc6'
| multiply('sk$uc6','sk$uc7') != 'sk$uc5'
| multiply('sk$uc6','sk$uc5') != 'sk$uc7'
| X0 != 'sk$uc7'
| X1 != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d98,d94]) ).
cnf(d100,plain,
( identity != inverse('sk$uc7')
| identity != 'sk$uc6'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse('sk$uc6') != 'sk$uc5'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| multiply('sk$uc6','sk$uc7') != 'sk$uc5'
| multiply('sk$uc6','sk$uc5') != 'sk$uc7'
| X1 != 'sk$uc6'
| X0 != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d99,d88]) ).
cnf(d101,plain,
( identity != inverse('sk$uc7')
| identity != 'sk$uc6'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse('sk$uc6') != 'sk$uc5'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| multiply('sk$uc6','sk$uc7') != 'sk$uc5'
| 'sk$uc5' != 'sk$uc7'
| X1 != 'sk$uc6'
| X0 != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d100,d93]) ).
cnf(d102,plain,
( identity != inverse('sk$uc7')
| identity != 'sk$uc6'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse('sk$uc6') != 'sk$uc5'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| multiply('sk$uc6','sk$uc7') != 'sk$uc5'
| 'sk$uc6' != 'sk$uc7'
| X1 != 'sk$uc6'
| X0 != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d101,d65]) ).
cnf(d103,plain,
( identity != inverse('sk$uc7')
| identity != 'sk$uc6'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse('sk$uc6') != 'sk$uc5'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| multiply('sk$uc6','sk$uc7') != 'sk$uc5'
| 'sk$uc6' != 'sk$uc6'
| X1 != 'sk$uc6'
| X0 != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d102,d88]) ).
cnf(d104,plain,
( identity != inverse('sk$uc7')
| identity != 'sk$uc6'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse('sk$uc6') != 'sk$uc5'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| 'sk$uc7' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc6'
| X1 != 'sk$uc6'
| X0 != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d103,d93]) ).
cnf(d105,plain,
( identity != inverse('sk$uc7')
| identity != 'sk$uc6'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse('sk$uc6') != 'sk$uc5'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| 'sk$uc6' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc6'
| X1 != 'sk$uc6'
| X0 != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d104,d88]) ).
cnf(d106,plain,
( identity != inverse('sk$uc7')
| identity != 'sk$uc6'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse('sk$uc6') != 'sk$uc5'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| X1 != 'sk$uc6'
| X0 != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d105,d65]) ).
cnf(d107,plain,
( identity != inverse('sk$uc7')
| identity != 'sk$uc6'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| 'sk$uc6' != 'sk$uc5'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| X1 != 'sk$uc6'
| X0 != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d106,d90]) ).
cnf(d108,plain,
( identity != inverse('sk$uc7')
| identity != 'sk$uc6'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| 'sk$uc6' != 'sk$uc6'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| X1 != 'sk$uc6'
| X0 != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d107,d65]) ).
cnf(d109,plain,
( identity != inverse('sk$uc7')
| identity != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc6' != 'sk$uc6'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| X1 != 'sk$uc6'
| X0 != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d108,d28]) ).
cnf(d110,plain,
( identity != inverse('sk$uc7')
| identity != 'sk$uc6'
| 'sk$uc6' != 'sk$uc7'
| 'sk$uc6' != 'sk$uc6'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| X1 != 'sk$uc6'
| X0 != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d109,d88]) ).
cnf(d111,plain,
( identity != inverse('sk$uc7')
| identity != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| X1 != 'sk$uc6'
| X0 != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d110,d88]) ).
cnf(d112,plain,
( identity != inverse('sk$uc7')
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| X1 != 'sk$uc6'
| X0 != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d111,d91]) ).
cnf(d113,plain,
( 'sk$uc6' != inverse('sk$uc7')
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| X1 != 'sk$uc6'
| X0 != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d112,d91]) ).
cnf(d114,plain,
( 'sk$uc6' != inverse('sk$uc6')
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| X1 != 'sk$uc6'
| X0 != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d113,d88]) ).
cnf(d115,plain,
( 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| X1 != 'sk$uc6'
| X0 != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d114,d90]) ).
cnf(d116,plain,
multiply(X0,inverse(X0)) = 'sk$uc7',
inference(demodulation,[status(thm)],[d3,d18]) ).
cnf(d117,plain,
multiply(X0,inverse(X0)) = 'sk$uc6',
inference(demodulation,[status(thm)],[d116,d88]) ).
cnf(d118,plain,
multiply('sk$uc6','sk$uc6') = 'sk$uc6',
inference(superposition,[status(thm)],[d90,d117]) ).
cnf(d119,plain,
'sk$uc6' = 'sk$uc6',
inference(demodulation,[status(thm)],[d118,d93]) ).
cnf(d120,plain,
( 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| X1 != 'sk$uc6'
| X0 != 'sk$uc6' ),
inference(resolution,[status(thm)],[d119,d115]) ).
cnf(d121,plain,
( inverse(X0) != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| X0 != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6' ),
inference(superposition,[status(thm)],[d90,d120]) ).
cnf(d122,plain,
( inverse(X0) != 'sk$uc6'
| X0 != 'sk$uc6' ),
inference(resolution,[status(thm)],[d119,d121]) ).
cnf(d123,plain,
( 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6' ),
inference(superposition,[status(thm)],[d90,d122]) ).
cnf(d124,plain,
$false,
inference(resolution,[status(thm)],[d119,d123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP363-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n020.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 14:49:35 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 84.20/18.44 % SZS status Unsatisfiable for theBenchmark.p
% 84.20/18.44 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------