%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP226-1 : 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 : n004.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 07:23:27 AM UTC 2026
% Result : Unsatisfiable 166.85s 36.62s
% Output : CNFRefutation 166.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 21
% Syntax : Number of clauses : 263 ( 43 unt; 198 nHn; 190 RR)
% Number of literals : 710 ( 709 equ; 206 neg)
% Maximal clause size : 9 ( 2 avg)
% Maximal term depth : 4 ( 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 : 147 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this_1,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7' ) ).
cnf(prove_this_2,negated_conjecture,
( multiply('sk$uc4','sk$uc6') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7' ) ).
cnf(prove_this_3,negated_conjecture,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7' ) ).
cnf(prove_this_4,negated_conjecture,
( inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc7' ) ).
cnf(prove_this_5,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc1','sk$uc6') = 'sk$uc7' ) ).
cnf(prove_this_6,negated_conjecture,
( multiply('sk$uc4','sk$uc6') = 'sk$uc7'
| multiply('sk$uc1','sk$uc6') = 'sk$uc7' ) ).
cnf(prove_this_7,negated_conjecture,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| multiply('sk$uc1','sk$uc6') = 'sk$uc7' ) ).
cnf(prove_this_8,negated_conjecture,
( inverse('sk$uc5') = 'sk$uc6'
| multiply('sk$uc1','sk$uc6') = 'sk$uc7' ) ).
cnf(prove_this_9,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc7','sk$uc3') = 'sk$uc6' ) ).
cnf(prove_this_11,negated_conjecture,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| multiply('sk$uc7','sk$uc3') = 'sk$uc6' ) ).
cnf(prove_this_12,negated_conjecture,
( inverse('sk$uc5') = 'sk$uc6'
| multiply('sk$uc7','sk$uc3') = 'sk$uc6' ) ).
cnf(prove_this_13,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc2','sk$uc7') = 'sk$uc3' ) ).
cnf(prove_this_15,negated_conjecture,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| multiply('sk$uc2','sk$uc7') = 'sk$uc3' ) ).
cnf(prove_this_16,negated_conjecture,
( inverse('sk$uc5') = 'sk$uc6'
| multiply('sk$uc2','sk$uc7') = 'sk$uc3' ) ).
cnf(prove_this_17,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc2') = 'sk$uc7' ) ).
cnf(prove_this_19,negated_conjecture,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| inverse('sk$uc2') = 'sk$uc7' ) ).
cnf(prove_this_20,negated_conjecture,
( inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc2') = 'sk$uc7' ) ).
cnf(prove_this_21,negated_conjecture,
( inverse(X4) != 'sk$uc6'
| multiply(X4,'sk$uc6') != 'sk$uc7'
| multiply(X3,'sk$uc6') != 'sk$uc7'
| inverse(X3) != 'sk$uc7'
| inverse(X2) != 'sk$uc7'
| multiply(X2,'sk$uc7') != X1
| multiply('sk$uc7',X1) != 'sk$uc6'
| multiply(X0,'sk$uc6') != 'sk$uc7'
| inverse(X0) != 'sk$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(c0,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_1]) ).
cnf(c1,plain,
( multiply('sk$uc4','sk$uc6') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_2]) ).
cnf(c2,plain,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_3]) ).
cnf(c3,plain,
( inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_4]) ).
cnf(c4,plain,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc1','sk$uc6') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_5]) ).
cnf(c5,plain,
( multiply('sk$uc4','sk$uc6') = 'sk$uc7'
| multiply('sk$uc1','sk$uc6') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_6]) ).
cnf(c6,plain,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| multiply('sk$uc1','sk$uc6') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_7]) ).
cnf(c7,plain,
( inverse('sk$uc5') = 'sk$uc6'
| multiply('sk$uc1','sk$uc6') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_8]) ).
cnf(c8,plain,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc7','sk$uc3') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_9]) ).
cnf(c10,plain,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| multiply('sk$uc7','sk$uc3') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_11]) ).
cnf(c11,plain,
( inverse('sk$uc5') = 'sk$uc6'
| multiply('sk$uc7','sk$uc3') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_12]) ).
cnf(c12,plain,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc2','sk$uc7') = 'sk$uc3' ),
inference(clausification,[status(esa)],[prove_this_13]) ).
cnf(c14,plain,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| multiply('sk$uc2','sk$uc7') = 'sk$uc3' ),
inference(clausification,[status(esa)],[prove_this_15]) ).
cnf(c15,plain,
( inverse('sk$uc5') = 'sk$uc6'
| multiply('sk$uc2','sk$uc7') = 'sk$uc3' ),
inference(clausification,[status(esa)],[prove_this_16]) ).
cnf(c16,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc2') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_17]) ).
cnf(c18,plain,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| inverse('sk$uc2') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_19]) ).
cnf(c19,plain,
( inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc2') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_20]) ).
cnf(c20,plain,
( multiply(X2,'sk$uc6') != 'sk$uc7'
| inverse(X0) != 'sk$uc7'
| inverse(X4) != 'sk$uc7'
| multiply(X4,'sk$uc6') != 'sk$uc7'
| multiply(X3,'sk$uc7') != X1
| inverse(X3) != 'sk$uc7'
| inverse(X2) != 'sk$uc6'
| multiply('sk$uc7',X1) != 'sk$uc6'
| multiply(X0,'sk$uc6') != 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_21]) ).
cnf(c21,plain,
multiply(identity,X0) = X0,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c22,plain,
multiply(inverse(X0),X0) = identity,
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c23,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)],[c21,c23]) ).
cnf(d1,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d0,c21]) ).
cnf(d2,plain,
multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[status(thm)],[c22,c23]) ).
cnf(d3,plain,
X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(demodulation,[status(thm)],[d2,c21]) ).
cnf(d4,plain,
multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(superposition,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc7','sk$uc2') = identity ),
inference(superposition,[status(thm)],[c16,c22]) ).
cnf(d6,plain,
( inverse('sk$uc4') = 'sk$uc7'
| multiply(identity,X0) = multiply('sk$uc7',multiply('sk$uc2',X0)) ),
inference(superposition,[status(thm)],[d5,c23]) ).
cnf(d7,plain,
( X0 = multiply('sk$uc7',multiply('sk$uc2',X0))
| inverse('sk$uc4') = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d6,c21]) ).
cnf(d8,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| 'sk$uc7' = multiply('sk$uc7','sk$uc3') ),
inference(superposition,[status(thm)],[c12,d7]) ).
cnf(d9,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| 'sk$uc7' = 'sk$uc6' ),
inference(superposition,[status(thm)],[d8,c8]) ).
cnf(d10,plain,
( 'sk$uc7' = 'sk$uc6'
| multiply('sk$uc7',multiply('sk$uc4',X0)) = X0 ),
inference(superposition,[status(thm)],[d9,d4]) ).
cnf(d11,plain,
multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(superposition,[status(thm)],[d3,d3]) ).
cnf(d12,plain,
identity = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[c22,d1]) ).
cnf(d13,plain,
X0 = multiply(inverse(inverse(X0)),identity),
inference(superposition,[status(thm)],[d12,d3]) ).
cnf(d14,plain,
multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[d13,d1]) ).
cnf(d15,plain,
multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[d14,d11]) ).
cnf(d16,plain,
multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d15,d11]) ).
cnf(d17,plain,
X0 = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d16,d15]) ).
cnf(d18,plain,
( 'sk$uc7' = 'sk$uc6'
| 'sk$uc4' = inverse('sk$uc7') ),
inference(superposition,[status(thm)],[d9,d17]) ).
cnf(d19,plain,
multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[d11,c22]) ).
cnf(d20,plain,
multiply(inverse(X0),identity) = inverse(X0),
inference(superposition,[status(thm)],[d19,d4]) ).
cnf(d21,plain,
inverse(X0) = inverse(X0),
inference(demodulation,[status(thm)],[d20,d15]) ).
cnf(d22,plain,
( inverse('sk$uc4') = 'sk$uc7'
| 'sk$uc1' = inverse('sk$uc7') ),
inference(superposition,[status(thm)],[c0,d17]) ).
cnf(d23,plain,
( 'sk$uc1' = inverse('sk$uc7')
| 'sk$uc7' = inverse('sk$uc4') ),
inference(superposition,[status(thm)],[d22,d21]) ).
cnf(d24,plain,
( inverse('sk$uc5') = 'sk$uc6'
| 'sk$uc1' = inverse('sk$uc7') ),
inference(superposition,[status(thm)],[c3,d17]) ).
cnf(d25,plain,
( inverse('sk$uc1') = 'sk$uc7'
| multiply('sk$uc7',X0) = multiply('sk$uc4',multiply('sk$uc6',X0)) ),
inference(superposition,[status(thm)],[c1,c23]) ).
cnf(d26,plain,
( inverse('sk$uc1') = 'sk$uc7'
| multiply('sk$uc6',X0) = multiply(inverse('sk$uc4'),multiply('sk$uc7',X0)) ),
inference(superposition,[status(thm)],[d25,d3]) ).
cnf(d27,plain,
identity = multiply(X0,inverse(X0)),
inference(superposition,[status(thm)],[d11,d12]) ).
cnf(d28,plain,
( inverse('sk$uc1') = 'sk$uc7'
| multiply('sk$uc6',inverse('sk$uc7')) = multiply(inverse('sk$uc4'),identity) ),
inference(superposition,[status(thm)],[d27,d26]) ).
cnf(d29,plain,
( multiply('sk$uc6',inverse('sk$uc7')) = inverse('sk$uc4')
| inverse('sk$uc1') = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d28,d15]) ).
cnf(d30,plain,
( inverse('sk$uc1') = 'sk$uc7'
| multiply('sk$uc7',X0) = multiply('sk$uc5',multiply('sk$uc6',X0)) ),
inference(superposition,[status(thm)],[c2,c23]) ).
cnf(d31,plain,
( inverse('sk$uc1') = 'sk$uc7'
| multiply('sk$uc6',X0) = multiply(inverse('sk$uc5'),multiply('sk$uc7',X0)) ),
inference(superposition,[status(thm)],[d30,d3]) ).
cnf(d32,plain,
( inverse('sk$uc1') = 'sk$uc7'
| multiply('sk$uc6',inverse('sk$uc7')) = multiply(inverse('sk$uc5'),identity) ),
inference(superposition,[status(thm)],[d27,d31]) ).
cnf(d33,plain,
( multiply('sk$uc6',inverse('sk$uc7')) = inverse('sk$uc5')
| inverse('sk$uc1') = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d32,d15]) ).
cnf(d34,plain,
( inverse('sk$uc1') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7'
| inverse('sk$uc5') = inverse('sk$uc4') ),
inference(superposition,[status(thm)],[d33,d29]) ).
cnf(d35,plain,
( inverse('sk$uc5') = inverse('sk$uc4')
| 'sk$uc1' = inverse('sk$uc7') ),
inference(superposition,[status(thm)],[d34,d17]) ).
cnf(d36,plain,
( 'sk$uc1' = inverse('sk$uc7')
| 'sk$uc1' = inverse('sk$uc7')
| inverse('sk$uc4') = 'sk$uc6' ),
inference(superposition,[status(thm)],[d35,d24]) ).
cnf(d37,plain,
( 'sk$uc1' = inverse('sk$uc7')
| 'sk$uc1' = inverse('sk$uc7')
| 'sk$uc7' = 'sk$uc6' ),
inference(superposition,[status(thm)],[d36,d23]) ).
cnf(d38,plain,
( 'sk$uc7' = 'sk$uc6'
| 'sk$uc7' = 'sk$uc6'
| 'sk$uc4' = 'sk$uc1' ),
inference(superposition,[status(thm)],[d37,d18]) ).
cnf(d39,plain,
( 'sk$uc7' = 'sk$uc6'
| multiply('sk$uc4','sk$uc6') = 'sk$uc7'
| multiply('sk$uc4','sk$uc6') = 'sk$uc7' ),
inference(superposition,[status(thm)],[d38,c5]) ).
cnf(d40,plain,
( 'sk$uc7' = 'sk$uc6'
| 'sk$uc7' = 'sk$uc6'
| multiply('sk$uc7','sk$uc7') = 'sk$uc6' ),
inference(superposition,[status(thm)],[d39,d10]) ).
cnf(d41,plain,
( inverse('sk$uc5') = 'sk$uc6'
| multiply('sk$uc3',X0) = multiply('sk$uc2',multiply('sk$uc7',X0)) ),
inference(superposition,[status(thm)],[c15,c23]) ).
cnf(d42,plain,
( inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc5') = 'sk$uc6'
| multiply('sk$uc3','sk$uc3') = multiply('sk$uc2','sk$uc6') ),
inference(superposition,[status(thm)],[c11,d41]) ).
cnf(d43,plain,
multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[d11,d4]) ).
cnf(d44,plain,
( inverse('sk$uc5') = 'sk$uc6'
| multiply('sk$uc2',multiply('sk$uc7',X0)) = X0 ),
inference(superposition,[status(thm)],[c19,d43]) ).
cnf(d45,plain,
( inverse('sk$uc5') = 'sk$uc6'
| multiply('sk$uc7','sk$uc1') = identity ),
inference(superposition,[status(thm)],[c3,c22]) ).
cnf(d46,plain,
( inverse('sk$uc5') = 'sk$uc6'
| multiply(identity,X0) = multiply('sk$uc7',multiply('sk$uc1',X0)) ),
inference(superposition,[status(thm)],[d45,c23]) ).
cnf(d47,plain,
( X0 = multiply('sk$uc7',multiply('sk$uc1',X0))
| inverse('sk$uc5') = 'sk$uc6' ),
inference(demodulation,[status(thm)],[d46,c21]) ).
cnf(d48,plain,
( inverse('sk$uc5') = 'sk$uc6'
| multiply('sk$uc7',multiply('sk$uc1',X0)) = X0 ),
inference(superposition,[status(thm)],[d47,d1]) ).
cnf(d49,plain,
( inverse('sk$uc5') = 'sk$uc6'
| 'sk$uc7' = multiply('sk$uc1','sk$uc6') ),
inference(superposition,[status(thm)],[c7,d1]) ).
cnf(d50,plain,
( inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc5') = 'sk$uc6'
| multiply('sk$uc7','sk$uc7') = 'sk$uc6' ),
inference(superposition,[status(thm)],[d49,d48]) ).
cnf(d51,plain,
( inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc5') = 'sk$uc6'
| multiply('sk$uc2','sk$uc6') = 'sk$uc7' ),
inference(superposition,[status(thm)],[d50,d44]) ).
cnf(d52,plain,
( inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc5') = 'sk$uc6'
| multiply('sk$uc3','sk$uc3') = 'sk$uc7' ),
inference(superposition,[status(thm)],[d51,d42]) ).
cnf(d53,plain,
( inverse('sk$uc5') = 'sk$uc6'
| multiply('sk$uc2','sk$uc7') = identity ),
inference(superposition,[status(thm)],[c19,d19]) ).
cnf(d54,plain,
( inverse('sk$uc5') = 'sk$uc6'
| multiply('sk$uc7','sk$uc2') = identity ),
inference(superposition,[status(thm)],[c19,c22]) ).
cnf(d55,plain,
( inverse('sk$uc5') = 'sk$uc6'
| multiply(identity,X0) = multiply('sk$uc7',multiply('sk$uc2',X0)) ),
inference(superposition,[status(thm)],[d54,c23]) ).
cnf(d56,plain,
( X0 = multiply('sk$uc7',multiply('sk$uc2',X0))
| inverse('sk$uc5') = 'sk$uc6' ),
inference(demodulation,[status(thm)],[d55,c21]) ).
cnf(d57,plain,
( inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc5') = 'sk$uc6'
| multiply('sk$uc3',multiply('sk$uc2',X0)) = multiply('sk$uc2',X0) ),
inference(superposition,[status(thm)],[d56,d41]) ).
cnf(d58,plain,
( inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc5') = 'sk$uc6'
| multiply('sk$uc3','sk$uc3') = multiply('sk$uc2','sk$uc7') ),
inference(superposition,[status(thm)],[c15,d57]) ).
cnf(d59,plain,
( inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc5') = 'sk$uc6'
| multiply('sk$uc3','sk$uc3') = identity ),
inference(superposition,[status(thm)],[d58,d53]) ).
cnf(d60,plain,
( inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc5') = 'sk$uc6'
| identity = 'sk$uc7' ),
inference(superposition,[status(thm)],[d59,d52]) ).
cnf(d61,plain,
( identity = 'sk$uc7'
| identity = multiply('sk$uc5','sk$uc6') ),
inference(superposition,[status(thm)],[d60,d27]) ).
cnf(d62,plain,
( identity = 'sk$uc7'
| multiply('sk$uc7','sk$uc3') = 'sk$uc6'
| identity = 'sk$uc7' ),
inference(superposition,[status(thm)],[d61,c10]) ).
cnf(d63,plain,
( identity = 'sk$uc7'
| inverse('sk$uc2') = 'sk$uc7'
| identity = 'sk$uc7' ),
inference(superposition,[status(thm)],[d61,c18]) ).
cnf(d64,plain,
( identity = 'sk$uc7'
| identity = multiply('sk$uc2','sk$uc7') ),
inference(superposition,[status(thm)],[d63,d27]) ).
cnf(d65,plain,
( multiply('sk$uc7',X3) != 'sk$uc6'
| multiply(X2,'sk$uc6') != 'sk$uc7'
| multiply(X2,'sk$uc6') != 'sk$uc7'
| multiply(X1,'sk$uc6') != 'sk$uc7'
| multiply(X0,'sk$uc7') != X3
| inverse(X2) != 'sk$uc7'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc7' ),
inference(factoring,[status(thm)],[c20]) ).
cnf(d66,plain,
( inverse('sk$uc5') = 'sk$uc6'
| multiply(X2,'sk$uc7') != 'sk$uc3'
| multiply(X1,'sk$uc6') != 'sk$uc7'
| multiply(X0,'sk$uc6') != 'sk$uc7'
| inverse(X2) != 'sk$uc7'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc7'
| 'sk$uc6' != 'sk$uc6' ),
inference(superposition,[status(thm)],[c11,d65]) ).
cnf(d67,plain,
( inverse('sk$uc5') = 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| multiply(X1,'sk$uc6') != 'sk$uc7'
| multiply(X0,'sk$uc7') != 'sk$uc3'
| inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc1') != 'sk$uc7'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7' ),
inference(superposition,[status(thm)],[c7,d66]) ).
cnf(d68,plain,
( 'sk$uc6' != 'sk$uc6'
| multiply(X1,'sk$uc7') != 'sk$uc3'
| multiply(X0,'sk$uc6') != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc5') = 'sk$uc6'
| inverse(X1) != 'sk$uc7'
| inverse(X0) != 'sk$uc6'
| inverse('sk$uc5') = 'sk$uc6' ),
inference(resolution,[status(thm)],[c3,d67]) ).
cnf(d69,plain,
( inverse('sk$uc5') = 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| multiply(X0,'sk$uc7') != 'sk$uc3'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc1') != 'sk$uc6'
| inverse(X0) != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7' ),
inference(superposition,[status(thm)],[d49,d68]) ).
cnf(d70,plain,
( inverse('sk$uc5') = 'sk$uc6'
| multiply('sk$uc1','sk$uc7') = identity ),
inference(superposition,[status(thm)],[c3,d19]) ).
cnf(d71,plain,
( inverse('sk$uc5') = 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc1') != 'sk$uc6'
| inverse('sk$uc1') != 'sk$uc7'
| identity != 'sk$uc3' ),
inference(superposition,[status(thm)],[d70,d69]) ).
cnf(d72,plain,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc7','sk$uc1') = identity ),
inference(superposition,[status(thm)],[c0,c22]) ).
cnf(d73,plain,
( inverse('sk$uc4') = 'sk$uc7'
| multiply(X2,'sk$uc7') != 'sk$uc1'
| multiply(X1,'sk$uc6') != 'sk$uc7'
| multiply(X0,'sk$uc6') != 'sk$uc7'
| inverse(X2) != 'sk$uc7'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc7'
| identity != 'sk$uc6' ),
inference(superposition,[status(thm)],[d72,d65]) ).
cnf(d74,plain,
( inverse('sk$uc4') = 'sk$uc7'
| identity != 'sk$uc6'
| multiply(X1,'sk$uc6') != 'sk$uc7'
| multiply(X0,'sk$uc7') != 'sk$uc1'
| inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc1') != 'sk$uc7'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7' ),
inference(superposition,[status(thm)],[c4,d73]) ).
cnf(d75,plain,
( identity != 'sk$uc6'
| multiply(X1,'sk$uc7') != 'sk$uc1'
| multiply(X0,'sk$uc6') != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| inverse(X1) != 'sk$uc7'
| inverse(X0) != 'sk$uc6'
| inverse('sk$uc4') = 'sk$uc7' ),
inference(resolution,[status(thm)],[c0,d74]) ).
cnf(d76,plain,
( inverse('sk$uc4') = 'sk$uc7'
| identity != 'sk$uc6'
| multiply(X0,'sk$uc7') != 'sk$uc1'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc1') != 'sk$uc6'
| inverse(X0) != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7' ),
inference(superposition,[status(thm)],[c4,d75]) ).
cnf(d77,plain,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc1','sk$uc7') = identity ),
inference(superposition,[status(thm)],[c0,d19]) ).
cnf(d78,plain,
( inverse('sk$uc4') = 'sk$uc7'
| identity != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc1') != 'sk$uc6'
| inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc1') != 'sk$uc7'
| identity != 'sk$uc1' ),
inference(superposition,[status(thm)],[d77,d76]) ).
cnf(d79,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc1'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc1') != 'sk$uc6'
| inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7' ),
inference(resolution,[status(thm)],[c0,d78]) ).
cnf(d80,plain,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc3',X0) = multiply('sk$uc2',multiply('sk$uc7',X0)) ),
inference(superposition,[status(thm)],[c12,c23]) ).
cnf(d81,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc3','sk$uc3') = multiply('sk$uc2','sk$uc6') ),
inference(superposition,[status(thm)],[c8,d80]) ).
cnf(d82,plain,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc2',multiply('sk$uc7',X0)) = X0 ),
inference(superposition,[status(thm)],[c16,d43]) ).
cnf(d83,plain,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc6',X0) = multiply('sk$uc7',multiply('sk$uc3',X0)) ),
inference(superposition,[status(thm)],[c8,c23]) ).
cnf(d84,plain,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc7',multiply('sk$uc3',X0)) = multiply('sk$uc6',X0) ),
inference(superposition,[status(thm)],[d83,d1]) ).
cnf(d85,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| 'sk$uc6' = multiply('sk$uc7',multiply('sk$uc3','sk$uc3')) ),
inference(superposition,[status(thm)],[d81,d7]) ).
cnf(d86,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| 'sk$uc6' = multiply('sk$uc6','sk$uc3') ),
inference(superposition,[status(thm)],[d85,d84]) ).
cnf(d87,plain,
( inverse('sk$uc4') = 'sk$uc7'
| multiply(identity,X0) = multiply('sk$uc7',multiply('sk$uc1',X0)) ),
inference(superposition,[status(thm)],[d72,c23]) ).
cnf(d88,plain,
( X0 = multiply('sk$uc7',multiply('sk$uc1',X0))
| inverse('sk$uc4') = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d87,c21]) ).
cnf(d89,plain,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc7',X0) = multiply('sk$uc1',multiply('sk$uc6',X0)) ),
inference(superposition,[status(thm)],[c4,c23]) ).
cnf(d90,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc6',X0) = multiply('sk$uc7',multiply('sk$uc7',X0)) ),
inference(superposition,[status(thm)],[d89,d88]) ).
cnf(d91,plain,
( inverse('sk$uc4') = 'sk$uc7'
| 'sk$uc6' = multiply('sk$uc7','sk$uc3') ),
inference(superposition,[status(thm)],[c8,d1]) ).
cnf(d92,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc6','sk$uc3') = multiply('sk$uc7','sk$uc6') ),
inference(superposition,[status(thm)],[d91,d90]) ).
cnf(d93,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| 'sk$uc6' = multiply('sk$uc7','sk$uc6') ),
inference(superposition,[status(thm)],[d92,d86]) ).
cnf(d94,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc2','sk$uc6') = 'sk$uc6' ),
inference(superposition,[status(thm)],[d93,d82]) ).
cnf(d95,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc3','sk$uc3') = 'sk$uc6' ),
inference(superposition,[status(thm)],[d94,d81]) ).
cnf(d96,plain,
( inverse('sk$uc4') = 'sk$uc7'
| identity = multiply('sk$uc2','sk$uc7') ),
inference(superposition,[status(thm)],[c16,d27]) ).
cnf(d97,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc3',multiply('sk$uc2',X0)) = multiply('sk$uc2',X0) ),
inference(superposition,[status(thm)],[d7,d80]) ).
cnf(d98,plain,
( inverse('sk$uc4') = 'sk$uc7'
| 'sk$uc3' = multiply('sk$uc2','sk$uc7') ),
inference(superposition,[status(thm)],[c12,d1]) ).
cnf(d99,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc3','sk$uc3') = multiply('sk$uc2','sk$uc7') ),
inference(superposition,[status(thm)],[d98,d97]) ).
cnf(d100,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| identity = multiply('sk$uc3','sk$uc3') ),
inference(superposition,[status(thm)],[d99,d96]) ).
cnf(d101,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| identity = 'sk$uc6' ),
inference(superposition,[status(thm)],[d100,d95]) ).
cnf(d102,plain,
( identity != 'sk$uc1'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc1') != 'sk$uc6'
| inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7' ),
inference(resolution,[status(thm)],[d101,d79]) ).
cnf(d103,plain,
X2 = multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))),
inference(superposition,[status(thm)],[c23,d3]) ).
cnf(d104,plain,
multiply(inverse(X0),X1) = multiply(inverse(multiply(X2,X0)),multiply(X2,X1)),
inference(superposition,[status(thm)],[d43,d103]) ).
cnf(d105,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc7',X0) = multiply('sk$uc7',multiply('sk$uc3',X0)) ),
inference(superposition,[status(thm)],[d80,d7]) ).
cnf(d106,plain,
( inverse('sk$uc4') = 'sk$uc7'
| X0 = multiply(inverse(multiply('sk$uc7','sk$uc3')),multiply('sk$uc7',X0)) ),
inference(superposition,[status(thm)],[d105,d103]) ).
cnf(d107,plain,
( inverse('sk$uc4') = 'sk$uc7'
| X0 = multiply(inverse('sk$uc3'),X0) ),
inference(demodulation,[status(thm)],[d106,d104]) ).
cnf(d108,plain,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc2',multiply('sk$uc7',X0)) = multiply('sk$uc3',X0) ),
inference(superposition,[status(thm)],[d80,d1]) ).
cnf(d109,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| X0 = multiply('sk$uc3',X0) ),
inference(superposition,[status(thm)],[d82,d108]) ).
cnf(d110,plain,
( inverse('sk$uc4') = 'sk$uc7'
| identity = inverse('sk$uc3') ),
inference(superposition,[status(thm)],[d109,d27]) ).
cnf(d111,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| X0 = multiply(identity,X0) ),
inference(superposition,[status(thm)],[d110,d107]) ).
cnf(d112,plain,
( inverse('sk$uc4') = 'sk$uc7'
| X0 = X0 ),
inference(demodulation,[status(thm)],[d111,c21]) ).
cnf(d113,plain,
( identity != 'sk$uc1'
| inverse('sk$uc1') != 'sk$uc6'
| inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7' ),
inference(resolution,[status(thm)],[d112,d102]) ).
cnf(d114,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc6','sk$uc1') = multiply('sk$uc7',identity) ),
inference(superposition,[status(thm)],[d72,d90]) ).
cnf(d115,plain,
( multiply('sk$uc6','sk$uc1') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d114,d15]) ).
cnf(d116,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc7',X0) = multiply('sk$uc6',X0) ),
inference(superposition,[status(thm)],[d105,d84]) ).
cnf(d117,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc7','sk$uc1') = 'sk$uc7' ),
inference(superposition,[status(thm)],[d116,d115]) ).
cnf(d118,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc2','sk$uc7') = 'sk$uc1' ),
inference(superposition,[status(thm)],[d117,d82]) ).
cnf(d119,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| identity = 'sk$uc1' ),
inference(superposition,[status(thm)],[d118,d96]) ).
cnf(d120,plain,
( inverse('sk$uc1') != 'sk$uc6'
| inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7' ),
inference(resolution,[status(thm)],[d119,d113]) ).
cnf(d121,plain,
( inverse('sk$uc4') = 'sk$uc7'
| 'sk$uc7' = inverse('sk$uc1') ),
inference(superposition,[status(thm)],[c0,d21]) ).
cnf(d122,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| 'sk$uc7' != 'sk$uc6' ),
inference(superposition,[status(thm)],[d121,d120]) ).
cnf(d123,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7' ),
inference(resolution,[status(thm)],[d9,d122]) ).
cnf(d124,plain,
multiply('sk$uc7',multiply('sk$uc4',X0)) = X0,
inference(superposition,[status(thm)],[d123,d4]) ).
cnf(d125,plain,
multiply('sk$uc4','sk$uc7') = identity,
inference(superposition,[status(thm)],[d123,d19]) ).
cnf(d126,plain,
multiply('sk$uc7',identity) = 'sk$uc7',
inference(superposition,[status(thm)],[d125,d124]) ).
cnf(d127,plain,
'sk$uc7' = 'sk$uc7',
inference(demodulation,[status(thm)],[d126,d15]) ).
cnf(d128,plain,
( identity != 'sk$uc3'
| 'sk$uc6' != 'sk$uc6'
| inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc1') != 'sk$uc6'
| inverse('sk$uc1') != 'sk$uc7' ),
inference(resolution,[status(thm)],[d127,d71]) ).
cnf(d129,plain,
( identity != 'sk$uc3'
| 'sk$uc6' != 'sk$uc6'
| inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc1') != 'sk$uc6'
| inverse('sk$uc5') = 'sk$uc6' ),
inference(resolution,[status(thm)],[c3,d128]) ).
cnf(d130,plain,
( inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc5') = 'sk$uc6'
| multiply('sk$uc7',X0) = multiply('sk$uc7',multiply('sk$uc3',X0)) ),
inference(superposition,[status(thm)],[d41,d56]) ).
cnf(d131,plain,
( inverse('sk$uc5') = 'sk$uc6'
| X0 = multiply(inverse(multiply('sk$uc7','sk$uc3')),multiply('sk$uc7',X0)) ),
inference(superposition,[status(thm)],[d130,d103]) ).
cnf(d132,plain,
( inverse('sk$uc5') = 'sk$uc6'
| X0 = multiply(inverse('sk$uc3'),X0) ),
inference(demodulation,[status(thm)],[d131,d104]) ).
cnf(d133,plain,
( inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc5') = 'sk$uc6'
| multiply('sk$uc3',X0) = X0 ),
inference(superposition,[status(thm)],[d44,d41]) ).
cnf(d134,plain,
( inverse('sk$uc5') = 'sk$uc6'
| identity = inverse('sk$uc3') ),
inference(superposition,[status(thm)],[d133,d27]) ).
cnf(d135,plain,
( inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc5') = 'sk$uc6'
| X0 = multiply(identity,X0) ),
inference(superposition,[status(thm)],[d134,d132]) ).
cnf(d136,plain,
( inverse('sk$uc5') = 'sk$uc6'
| X0 = X0 ),
inference(demodulation,[status(thm)],[d135,c21]) ).
cnf(d137,plain,
( identity != 'sk$uc3'
| inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc1') != 'sk$uc6'
| inverse('sk$uc5') = 'sk$uc6' ),
inference(resolution,[status(thm)],[d136,d129]) ).
cnf(d138,plain,
( inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc5') = 'sk$uc6'
| identity = 'sk$uc3' ),
inference(superposition,[status(thm)],[d53,c15]) ).
cnf(d139,plain,
( inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc1') != 'sk$uc6'
| inverse('sk$uc5') = 'sk$uc6' ),
inference(resolution,[status(thm)],[d138,d137]) ).
cnf(d140,plain,
( inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc5') = 'sk$uc6'
| 'sk$uc7' != 'sk$uc6' ),
inference(superposition,[status(thm)],[c3,d139]) ).
cnf(d141,plain,
( inverse('sk$uc5') = 'sk$uc6'
| 'sk$uc3' = multiply('sk$uc2','sk$uc7') ),
inference(superposition,[status(thm)],[c15,d1]) ).
cnf(d142,plain,
( inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc5') = 'sk$uc6'
| 'sk$uc7' = multiply('sk$uc7','sk$uc3') ),
inference(superposition,[status(thm)],[d141,d56]) ).
cnf(d143,plain,
( inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc5') = 'sk$uc6'
| 'sk$uc7' = 'sk$uc6' ),
inference(superposition,[status(thm)],[d142,c11]) ).
cnf(d144,plain,
( inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc5') = 'sk$uc6' ),
inference(resolution,[status(thm)],[d143,d140]) ).
cnf(d145,plain,
identity = multiply('sk$uc5','sk$uc6'),
inference(superposition,[status(thm)],[d144,d27]) ).
cnf(d146,plain,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| 'sk$uc3' = multiply('sk$uc2','sk$uc7') ),
inference(superposition,[status(thm)],[c14,d1]) ).
cnf(d147,plain,
( 'sk$uc3' = multiply('sk$uc2','sk$uc7')
| identity = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d146,d145]) ).
cnf(d148,plain,
( identity = 'sk$uc7'
| identity = 'sk$uc7'
| identity = 'sk$uc3' ),
inference(superposition,[status(thm)],[d147,d64]) ).
cnf(d149,plain,
( identity = 'sk$uc7'
| multiply(X0,'sk$uc3') = X0 ),
inference(superposition,[status(thm)],[d148,d15]) ).
cnf(d150,plain,
( identity = 'sk$uc7'
| identity = 'sk$uc7'
| 'sk$uc7' = 'sk$uc6' ),
inference(superposition,[status(thm)],[d149,d62]) ).
cnf(d151,plain,
( 'sk$uc7' = 'sk$uc6'
| multiply('sk$uc7',X0) = X0 ),
inference(superposition,[status(thm)],[d150,c21]) ).
cnf(d152,plain,
( 'sk$uc7' = 'sk$uc6'
| 'sk$uc7' = 'sk$uc6'
| 'sk$uc7' = 'sk$uc6' ),
inference(superposition,[status(thm)],[d151,d40]) ).
cnf(d153,plain,
( identity = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7'
| identity = 'sk$uc7' ),
inference(superposition,[status(thm)],[d61,c2]) ).
cnf(d154,plain,
( identity = 'sk$uc7'
| identity = multiply('sk$uc1','sk$uc7') ),
inference(superposition,[status(thm)],[d153,d27]) ).
cnf(d155,plain,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| 'sk$uc7' = multiply('sk$uc1','sk$uc6') ),
inference(superposition,[status(thm)],[c6,d1]) ).
cnf(d156,plain,
( identity = 'sk$uc7'
| 'sk$uc7' = multiply('sk$uc1','sk$uc6') ),
inference(demodulation,[status(thm)],[d155,d145]) ).
cnf(d157,plain,
( identity = 'sk$uc7'
| 'sk$uc7' = multiply('sk$uc1','sk$uc7') ),
inference(demodulation,[status(thm)],[d156,d152]) ).
cnf(d158,plain,
( identity = 'sk$uc7'
| identity = 'sk$uc7'
| identity = 'sk$uc7' ),
inference(superposition,[status(thm)],[d157,d154]) ).
cnf(d159,plain,
multiply(X0,'sk$uc7') = X0,
inference(demodulation,[status(thm)],[d15,d158]) ).
cnf(d160,plain,
X0 = multiply(inverse(identity),X0),
inference(superposition,[status(thm)],[c21,d3]) ).
cnf(d161,plain,
X0 = multiply(inverse(inverse(identity)),X0),
inference(superposition,[status(thm)],[d160,d3]) ).
cnf(d162,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[d161,c22]) ).
cnf(d163,plain,
identity = multiply(identity,identity),
inference(superposition,[status(thm)],[d162,d12]) ).
cnf(d164,plain,
identity = identity,
inference(demodulation,[status(thm)],[d163,c21]) ).
cnf(d165,plain,
identity = multiply('sk$uc4','sk$uc7'),
inference(superposition,[status(thm)],[d123,d27]) ).
cnf(d166,plain,
inverse(inverse(X0)) = X0,
inference(superposition,[status(thm)],[d17,d21]) ).
cnf(d167,plain,
inverse('sk$uc7') = 'sk$uc4',
inference(superposition,[status(thm)],[d123,d166]) ).
cnf(d168,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc3','sk$uc1') = multiply('sk$uc2',identity) ),
inference(superposition,[status(thm)],[d72,d80]) ).
cnf(d169,plain,
( multiply('sk$uc3','sk$uc1') = 'sk$uc2'
| inverse('sk$uc4') = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d168,d15]) ).
cnf(d170,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc6','sk$uc1') = multiply('sk$uc7','sk$uc2') ),
inference(superposition,[status(thm)],[d169,d83]) ).
cnf(d171,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| 'sk$uc7' = multiply('sk$uc7','sk$uc2') ),
inference(superposition,[status(thm)],[d115,d170]) ).
cnf(d172,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| 'sk$uc7' = identity ),
inference(superposition,[status(thm)],[d171,d5]) ).
cnf(d173,plain,
( 'sk$uc7' = identity
| inverse('sk$uc7') = 'sk$uc4' ),
inference(superposition,[status(thm)],[d172,d166]) ).
cnf(d174,plain,
( inverse('sk$uc1') = 'sk$uc7'
| 'sk$uc7' = multiply('sk$uc5','sk$uc6') ),
inference(superposition,[status(thm)],[c2,d1]) ).
cnf(d175,plain,
( inverse('sk$uc5') = 'sk$uc6'
| multiply('sk$uc2',multiply('sk$uc7',X0)) = multiply('sk$uc3',X0) ),
inference(superposition,[status(thm)],[d41,d1]) ).
cnf(d176,plain,
( inverse('sk$uc5') = 'sk$uc6'
| 'sk$uc6' = multiply('sk$uc7','sk$uc3') ),
inference(superposition,[status(thm)],[c11,d1]) ).
cnf(d177,plain,
( inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc5') = 'sk$uc6'
| multiply('sk$uc2','sk$uc6') = multiply('sk$uc3','sk$uc3') ),
inference(superposition,[status(thm)],[d176,d175]) ).
cnf(d178,plain,
( inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc5') = 'sk$uc6'
| 'sk$uc7' = multiply('sk$uc3','sk$uc3') ),
inference(superposition,[status(thm)],[d51,d177]) ).
cnf(d179,plain,
( inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc5') = 'sk$uc6'
| 'sk$uc7' = identity ),
inference(superposition,[status(thm)],[d59,d178]) ).
cnf(d180,plain,
( 'sk$uc7' = identity
| identity = multiply('sk$uc5','sk$uc6') ),
inference(superposition,[status(thm)],[d179,d27]) ).
cnf(d181,plain,
( 'sk$uc7' = identity
| inverse('sk$uc1') = 'sk$uc7'
| 'sk$uc7' = identity ),
inference(superposition,[status(thm)],[d180,d174]) ).
cnf(d182,plain,
( 'sk$uc7' = identity
| 'sk$uc1' = inverse('sk$uc7') ),
inference(superposition,[status(thm)],[d181,d17]) ).
cnf(d183,plain,
( 'sk$uc7' = identity
| 'sk$uc7' = identity
| 'sk$uc1' = 'sk$uc4' ),
inference(superposition,[status(thm)],[d182,d173]) ).
cnf(d184,plain,
( 'sk$uc1' = 'sk$uc4'
| inverse('sk$uc7') = identity ),
inference(superposition,[status(thm)],[d183,d162]) ).
cnf(d185,plain,
( 'sk$uc1' = 'sk$uc4'
| 'sk$uc4' = identity ),
inference(demodulation,[status(thm)],[d184,d167]) ).
cnf(d186,plain,
X0 = multiply(identity,X0),
inference(superposition,[status(thm)],[c21,d1]) ).
cnf(d187,plain,
( 'sk$uc1' = 'sk$uc4'
| X0 = multiply('sk$uc4',X0) ),
inference(superposition,[status(thm)],[d185,d186]) ).
cnf(d188,plain,
( 'sk$uc1' = inverse('sk$uc7')
| inverse('sk$uc6') = 'sk$uc4' ),
inference(superposition,[status(thm)],[d36,d166]) ).
cnf(d189,plain,
( 'sk$uc1' = 'sk$uc4'
| inverse('sk$uc6') = 'sk$uc4' ),
inference(demodulation,[status(thm)],[d188,d167]) ).
cnf(d190,plain,
( 'sk$uc1' = 'sk$uc4'
| identity = multiply('sk$uc4','sk$uc6') ),
inference(superposition,[status(thm)],[d189,d12]) ).
cnf(d191,plain,
( 'sk$uc1' = 'sk$uc4'
| 'sk$uc1' = 'sk$uc4'
| 'sk$uc6' = identity ),
inference(superposition,[status(thm)],[d190,d187]) ).
cnf(d192,plain,
( 'sk$uc1' = 'sk$uc4'
| 'sk$uc1' = 'sk$uc4'
| 'sk$uc4' = 'sk$uc6' ),
inference(superposition,[status(thm)],[d191,d185]) ).
cnf(d193,plain,
( 'sk$uc4' = 'sk$uc6'
| multiply('sk$uc4','sk$uc6') = 'sk$uc7'
| multiply('sk$uc4','sk$uc6') = 'sk$uc7' ),
inference(superposition,[status(thm)],[d192,c5]) ).
cnf(d194,plain,
( 'sk$uc4' = 'sk$uc6'
| 'sk$uc7' = multiply('sk$uc4','sk$uc6') ),
inference(superposition,[status(thm)],[d193,d1]) ).
cnf(d195,plain,
( 'sk$uc7' = multiply('sk$uc4','sk$uc6')
| 'sk$uc4' = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d194,d152]) ).
cnf(d196,plain,
( 'sk$uc7' = multiply('sk$uc4','sk$uc7')
| 'sk$uc4' = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d195,d152]) ).
cnf(d197,plain,
( 'sk$uc7' = identity
| 'sk$uc4' = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d196,d165]) ).
cnf(d198,plain,
( 'sk$uc4' = 'sk$uc7'
| identity = 'sk$uc7' ),
inference(superposition,[status(thm)],[d197,d164]) ).
cnf(d199,plain,
identity = inverse(identity),
inference(superposition,[status(thm)],[d161,d12]) ).
cnf(d200,plain,
( 'sk$uc4' = 'sk$uc7'
| identity = inverse('sk$uc7') ),
inference(superposition,[status(thm)],[d197,d199]) ).
cnf(d201,plain,
( identity = 'sk$uc4'
| 'sk$uc4' = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d200,d167]) ).
cnf(d202,plain,
( 'sk$uc4' = 'sk$uc7'
| 'sk$uc4' = 'sk$uc7'
| 'sk$uc4' = 'sk$uc7' ),
inference(superposition,[status(thm)],[d201,d198]) ).
cnf(d203,plain,
inverse('sk$uc7') = 'sk$uc7',
inference(demodulation,[status(thm)],[d123,d202]) ).
cnf(d204,plain,
( multiply(X2,'sk$uc7') != identity
| multiply(X1,'sk$uc6') != 'sk$uc7'
| multiply(X0,'sk$uc6') != 'sk$uc7'
| inverse(X2) != 'sk$uc7'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc7'
| 'sk$uc7' != 'sk$uc6' ),
inference(superposition,[status(thm)],[d15,d65]) ).
cnf(d205,plain,
( multiply(X1,'sk$uc6') != 'sk$uc7'
| multiply(X0,'sk$uc7') != identity
| 'sk$uc7' != 'sk$uc6'
| inverse(identity) != 'sk$uc7'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc7'
| 'sk$uc6' != 'sk$uc7' ),
inference(superposition,[status(thm)],[c21,d204]) ).
cnf(d206,plain,
( 'sk$uc6' != 'sk$uc7'
| multiply(X1,'sk$uc7') != identity
| multiply(X0,'sk$uc6') != 'sk$uc7'
| 'sk$uc7' != 'sk$uc6'
| inverse(identity) != 'sk$uc7'
| inverse(X1) != 'sk$uc7'
| inverse(X0) != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d205,d152]) ).
cnf(d207,plain,
( 'sk$uc6' != 'sk$uc7'
| multiply(X1,'sk$uc7') != identity
| multiply(X0,'sk$uc6') != 'sk$uc7'
| 'sk$uc7' != 'sk$uc6'
| inverse('sk$uc7') != 'sk$uc7'
| inverse(X1) != 'sk$uc7'
| inverse(X0) != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d206,d158]) ).
cnf(d208,plain,
( 'sk$uc6' != 'sk$uc7'
| multiply(X1,'sk$uc7') != identity
| multiply(X0,'sk$uc6') != 'sk$uc7'
| 'sk$uc7' != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| inverse(X1) != 'sk$uc7'
| inverse(X0) != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d207,d203]) ).
cnf(d209,plain,
( 'sk$uc6' != 'sk$uc7'
| multiply(X1,'sk$uc7') != identity
| multiply(X0,'sk$uc6') != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| inverse(X1) != 'sk$uc7'
| inverse(X0) != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d208,d152]) ).
cnf(d210,plain,
( 'sk$uc6' != 'sk$uc7'
| multiply(X1,'sk$uc7') != identity
| multiply(X0,'sk$uc7') != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| inverse(X1) != 'sk$uc7'
| inverse(X0) != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d209,d152]) ).
cnf(d211,plain,
( 'sk$uc6' != 'sk$uc7'
| multiply(X1,'sk$uc7') != identity
| X0 != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| inverse(X1) != 'sk$uc7'
| inverse(X0) != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d210,d159]) ).
cnf(d212,plain,
( 'sk$uc6' != 'sk$uc7'
| X0 != identity
| X1 != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| inverse(X0) != 'sk$uc7'
| inverse(X1) != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d211,d159]) ).
cnf(d213,plain,
( 'sk$uc6' != 'sk$uc7'
| X1 != 'sk$uc7'
| X0 != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| inverse(X1) != 'sk$uc7'
| inverse(X0) != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d212,d158]) ).
cnf(d214,plain,
( 'sk$uc7' != 'sk$uc7'
| X1 != 'sk$uc7'
| X0 != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| inverse(X1) != 'sk$uc7'
| inverse(X0) != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d213,d152]) ).
cnf(d215,plain,
( 'sk$uc7' != 'sk$uc7'
| X1 != 'sk$uc7'
| X0 != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| inverse(X1) != 'sk$uc7'
| inverse(X0) != 'sk$uc7' ),
inference(resolution,[status(thm)],[d127,d214]) ).
cnf(d216,plain,
( 'sk$uc7' != 'sk$uc7'
| inverse(X1) != 'sk$uc7'
| inverse(X0) != 'sk$uc7'
| X1 != 'sk$uc7'
| X0 != 'sk$uc7' ),
inference(superposition,[status(thm)],[d166,d215]) ).
cnf(d217,plain,
( 'sk$uc7' != 'sk$uc7'
| inverse(X0) != 'sk$uc7'
| inverse(X0) != 'sk$uc7'
| X0 != 'sk$uc7' ),
inference(factoring,[status(thm)],[d216]) ).
cnf(d218,plain,
( inverse(X0) != 'sk$uc7'
| X0 != 'sk$uc7' ),
inference(resolution,[status(thm)],[d127,d217]) ).
cnf(d219,plain,
( 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7' ),
inference(superposition,[status(thm)],[d203,d218]) ).
cnf(d220,plain,
$false,
inference(resolution,[status(thm)],[d127,d219]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP226-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n004.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Fri Sep 25 14:39:06 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 166.85/36.62 % SZS status Unsatisfiable for theBenchmark.p
% 166.85/36.62 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------