%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP305-1 : 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 07:23:34 AM UTC 2026
% Result : Unsatisfiable 115.57s 28.48s
% Output : CNFRefutation 115.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 71
% Number of leaves : 21
% Syntax : Number of clauses : 251 ( 62 unt; 160 nHn; 195 RR)
% Number of literals : 715 ( 714 equ; 289 neg)
% Maximal clause size : 10 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 101 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this_1,negated_conjecture,
( multiply('sk$uc5','sk$uc6') = 'sk$uc4'
| multiply('sk$uc6','sk$uc5') = 'sk$uc4' ) ).
cnf(prove_this_2,negated_conjecture,
( inverse('sk$uc2') = 'sk$uc6'
| multiply('sk$uc6','sk$uc5') = 'sk$uc4' ) ).
cnf(prove_this_4,negated_conjecture,
( inverse('sk$uc3') = 'sk$uc5'
| multiply('sk$uc6','sk$uc5') = 'sk$uc4' ) ).
cnf(prove_this_10,negated_conjecture,
( multiply('sk$uc3','sk$uc4') = 'sk$uc5'
| multiply('sk$uc5','sk$uc4') = 'sk$uc6' ) ).
cnf(prove_this_12,negated_conjecture,
( inverse('sk$uc2') = 'sk$uc6'
| inverse('sk$uc6') = 'sk$uc4' ) ).
cnf(prove_this_13,negated_conjecture,
( multiply('sk$uc2','sk$uc5') = 'sk$uc6'
| inverse('sk$uc6') = 'sk$uc4' ) ).
cnf(prove_this_14,negated_conjecture,
( inverse('sk$uc3') = 'sk$uc5'
| inverse('sk$uc6') = 'sk$uc4' ) ).
cnf(prove_this_16,negated_conjecture,
( multiply('sk$uc5','sk$uc6') = 'sk$uc4'
| multiply('sk$uc1','sk$uc6') = 'sk$uc4' ) ).
cnf(prove_this_17,negated_conjecture,
( inverse('sk$uc2') = 'sk$uc6'
| multiply('sk$uc1','sk$uc6') = 'sk$uc4' ) ).
cnf(prove_this_18,negated_conjecture,
( multiply('sk$uc2','sk$uc5') = 'sk$uc6'
| multiply('sk$uc1','sk$uc6') = 'sk$uc4' ) ).
cnf(prove_this_19,negated_conjecture,
( inverse('sk$uc3') = 'sk$uc5'
| multiply('sk$uc1','sk$uc6') = 'sk$uc4' ) ).
cnf(prove_this_20,negated_conjecture,
( multiply('sk$uc3','sk$uc4') = 'sk$uc5'
| multiply('sk$uc1','sk$uc6') = 'sk$uc4' ) ).
cnf(prove_this_21,negated_conjecture,
( multiply('sk$uc5','sk$uc6') = 'sk$uc4'
| inverse('sk$uc1') = 'sk$uc6' ) ).
cnf(prove_this_22,negated_conjecture,
( inverse('sk$uc2') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc6' ) ).
cnf(prove_this_23,negated_conjecture,
( multiply('sk$uc2','sk$uc5') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc6' ) ).
cnf(prove_this_24,negated_conjecture,
( inverse('sk$uc3') = 'sk$uc5'
| inverse('sk$uc1') = 'sk$uc6' ) ).
cnf(prove_this_25,negated_conjecture,
( multiply('sk$uc3','sk$uc4') = 'sk$uc5'
| inverse('sk$uc1') = 'sk$uc6' ) ).
cnf(prove_this_26,negated_conjecture,
( multiply(X2,'sk$uc4') != 'sk$uc5'
| inverse(X2) != 'sk$uc5'
| multiply(X1,'sk$uc5') != 'sk$uc6'
| inverse(X1) != 'sk$uc6'
| multiply('sk$uc5','sk$uc6') != 'sk$uc4'
| inverse(X0) != 'sk$uc6'
| multiply(X0,'sk$uc6') != 'sk$uc4'
| inverse('sk$uc6') != 'sk$uc4'
| multiply('sk$uc5','sk$uc4') != 'sk$uc6'
| multiply('sk$uc6','sk$uc5') != 'sk$uc4' ) ).
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$uc5','sk$uc6') = 'sk$uc4'
| multiply('sk$uc6','sk$uc5') = 'sk$uc4' ),
inference(clausification,[status(esa)],[prove_this_1]) ).
cnf(c1,plain,
( inverse('sk$uc2') = 'sk$uc6'
| multiply('sk$uc6','sk$uc5') = 'sk$uc4' ),
inference(clausification,[status(esa)],[prove_this_2]) ).
cnf(c3,plain,
( inverse('sk$uc3') = 'sk$uc5'
| multiply('sk$uc6','sk$uc5') = 'sk$uc4' ),
inference(clausification,[status(esa)],[prove_this_4]) ).
cnf(c9,plain,
( multiply('sk$uc3','sk$uc4') = 'sk$uc5'
| multiply('sk$uc5','sk$uc4') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_10]) ).
cnf(c11,plain,
( inverse('sk$uc2') = 'sk$uc6'
| inverse('sk$uc6') = 'sk$uc4' ),
inference(clausification,[status(esa)],[prove_this_12]) ).
cnf(c12,plain,
( multiply('sk$uc2','sk$uc5') = 'sk$uc6'
| inverse('sk$uc6') = 'sk$uc4' ),
inference(clausification,[status(esa)],[prove_this_13]) ).
cnf(c13,plain,
( inverse('sk$uc3') = 'sk$uc5'
| inverse('sk$uc6') = 'sk$uc4' ),
inference(clausification,[status(esa)],[prove_this_14]) ).
cnf(c15,plain,
( multiply('sk$uc5','sk$uc6') = 'sk$uc4'
| multiply('sk$uc1','sk$uc6') = 'sk$uc4' ),
inference(clausification,[status(esa)],[prove_this_16]) ).
cnf(c16,plain,
( inverse('sk$uc2') = 'sk$uc6'
| multiply('sk$uc1','sk$uc6') = 'sk$uc4' ),
inference(clausification,[status(esa)],[prove_this_17]) ).
cnf(c17,plain,
( multiply('sk$uc2','sk$uc5') = 'sk$uc6'
| multiply('sk$uc1','sk$uc6') = 'sk$uc4' ),
inference(clausification,[status(esa)],[prove_this_18]) ).
cnf(c18,plain,
( inverse('sk$uc3') = 'sk$uc5'
| multiply('sk$uc1','sk$uc6') = 'sk$uc4' ),
inference(clausification,[status(esa)],[prove_this_19]) ).
cnf(c19,plain,
( multiply('sk$uc3','sk$uc4') = 'sk$uc5'
| multiply('sk$uc1','sk$uc6') = 'sk$uc4' ),
inference(clausification,[status(esa)],[prove_this_20]) ).
cnf(c20,plain,
( multiply('sk$uc5','sk$uc6') = 'sk$uc4'
| inverse('sk$uc1') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_21]) ).
cnf(c21,plain,
( inverse('sk$uc2') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_22]) ).
cnf(c22,plain,
( multiply('sk$uc2','sk$uc5') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_23]) ).
cnf(c23,plain,
( inverse('sk$uc3') = 'sk$uc5'
| inverse('sk$uc1') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_24]) ).
cnf(c24,plain,
( multiply('sk$uc3','sk$uc4') = 'sk$uc5'
| inverse('sk$uc1') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_25]) ).
cnf(c25,plain,
( multiply(X2,'sk$uc4') != 'sk$uc5'
| inverse(X2) != 'sk$uc5'
| inverse('sk$uc6') != 'sk$uc4'
| multiply('sk$uc5','sk$uc4') != 'sk$uc6'
| multiply('sk$uc5','sk$uc6') != 'sk$uc4'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| multiply('sk$uc6','sk$uc5') != 'sk$uc4'
| multiply(X1,'sk$uc5') != 'sk$uc6'
| multiply(X0,'sk$uc6') != 'sk$uc4' ),
inference(clausification,[status(esa)],[prove_this_26]) ).
cnf(c26,plain,
multiply(identity,X0) = X0,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c27,plain,
multiply(inverse(X0),X0) = identity,
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c28,plain,
multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(clausification,[status(esa)],[associativity]) ).
cnf(d0,plain,
multiply(identity,multiply(X0,X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c26,c28]) ).
cnf(d1,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d0,c26]) ).
cnf(d2,plain,
( multiply('sk$uc1','sk$uc6') = 'sk$uc4'
| 'sk$uc4' = multiply('sk$uc5','sk$uc6') ),
inference(superposition,[status(thm)],[c15,d1]) ).
cnf(d3,plain,
identity = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[c27,d1]) ).
cnf(d4,plain,
multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c27,c28]) ).
cnf(d5,plain,
multiply(inverse(X1),multiply(X1,X0)) = X0,
inference(demodulation,[status(thm)],[d4,c26]) ).
cnf(d6,plain,
X0 = multiply(identity,X0),
inference(superposition,[status(thm)],[c26,d1]) ).
cnf(d7,plain,
multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
multiply(inverse(inverse(identity)),X0) = X0,
inference(superposition,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[d8,c27]) ).
cnf(d10,plain,
identity = multiply(identity,identity),
inference(superposition,[status(thm)],[d9,d3]) ).
cnf(d11,plain,
identity = identity,
inference(demodulation,[status(thm)],[d10,c26]) ).
cnf(d12,plain,
multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[d5,d5]) ).
cnf(d13,plain,
multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[d3,d5]) ).
cnf(d14,plain,
X0 = multiply(inverse(inverse(X0)),identity),
inference(superposition,[status(thm)],[d13,d1]) ).
cnf(d15,plain,
X0 = multiply(X0,identity),
inference(demodulation,[status(thm)],[d14,d12]) ).
cnf(d16,plain,
multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[d13,d12]) ).
cnf(d17,plain,
multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d12,d16]) ).
cnf(d18,plain,
X0 = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d17,d15]) ).
cnf(d19,plain,
multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[d12,c27]) ).
cnf(d20,plain,
( inverse('sk$uc1') = 'sk$uc6'
| multiply('sk$uc2','sk$uc6') = identity ),
inference(superposition,[status(thm)],[c21,d19]) ).
cnf(d21,plain,
( inverse('sk$uc1') = 'sk$uc6'
| multiply(inverse('sk$uc5'),'sk$uc4') = 'sk$uc6' ),
inference(superposition,[status(thm)],[c20,d5]) ).
cnf(d22,plain,
inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[status(thm)],[d15,d12]) ).
cnf(d23,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d22,d15]) ).
cnf(d24,plain,
( inverse('sk$uc1') = 'sk$uc6'
| inverse('sk$uc5') = 'sk$uc3' ),
inference(superposition,[status(thm)],[c23,d23]) ).
cnf(d25,plain,
( inverse('sk$uc1') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc6'
| multiply('sk$uc3','sk$uc4') = 'sk$uc6' ),
inference(superposition,[status(thm)],[d24,d21]) ).
cnf(d26,plain,
( inverse('sk$uc1') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc6'
| 'sk$uc6' = 'sk$uc5' ),
inference(superposition,[status(thm)],[d25,c24]) ).
cnf(d27,plain,
( inverse('sk$uc1') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc6'
| multiply('sk$uc2','sk$uc6') = 'sk$uc6' ),
inference(superposition,[status(thm)],[d26,c22]) ).
cnf(d28,plain,
( inverse('sk$uc1') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc6'
| 'sk$uc6' = identity ),
inference(superposition,[status(thm)],[d27,d20]) ).
cnf(d29,plain,
( inverse('sk$uc1') = 'sk$uc6'
| inverse('sk$uc6') = identity ),
inference(superposition,[status(thm)],[d28,d9]) ).
cnf(d30,plain,
( inverse('sk$uc1') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc6'
| inverse('sk$uc6') = 'sk$uc3' ),
inference(superposition,[status(thm)],[d26,d24]) ).
cnf(d31,plain,
( inverse('sk$uc1') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc6'
| 'sk$uc3' = identity ),
inference(superposition,[status(thm)],[d30,d29]) ).
cnf(d32,plain,
( 'sk$uc3' = identity
| 'sk$uc1' = inverse('sk$uc6') ),
inference(superposition,[status(thm)],[d31,d18]) ).
cnf(d33,plain,
( 'sk$uc1' = inverse('sk$uc6')
| inverse('sk$uc3') = identity ),
inference(superposition,[status(thm)],[d32,d9]) ).
cnf(d34,plain,
( inverse('sk$uc1') = 'sk$uc6'
| multiply('sk$uc3',multiply('sk$uc4',X0)) = multiply('sk$uc5',X0) ),
inference(superposition,[status(thm)],[c24,c28]) ).
cnf(d35,plain,
( inverse('sk$uc1') = 'sk$uc6'
| multiply('sk$uc3',identity) = multiply('sk$uc5',inverse('sk$uc4')) ),
inference(superposition,[status(thm)],[d19,d34]) ).
cnf(d36,plain,
( inverse('sk$uc1') = 'sk$uc6'
| 'sk$uc3' = multiply('sk$uc5',inverse('sk$uc4')) ),
inference(demodulation,[status(thm)],[d35,d15]) ).
cnf(d37,plain,
( inverse('sk$uc1') = 'sk$uc6'
| multiply('sk$uc3','sk$uc5') = identity ),
inference(superposition,[status(thm)],[c23,d19]) ).
cnf(d38,plain,
( inverse('sk$uc1') = 'sk$uc6'
| 'sk$uc5' = multiply('sk$uc3','sk$uc4') ),
inference(superposition,[status(thm)],[c24,d1]) ).
cnf(d39,plain,
( inverse('sk$uc1') = 'sk$uc6'
| multiply('sk$uc6','sk$uc2') = identity ),
inference(superposition,[status(thm)],[c21,c27]) ).
cnf(d40,plain,
( inverse('sk$uc1') = 'sk$uc6'
| multiply('sk$uc6',multiply('sk$uc2',X0)) = multiply(identity,X0) ),
inference(superposition,[status(thm)],[d39,c28]) ).
cnf(d41,plain,
( inverse('sk$uc1') = 'sk$uc6'
| multiply('sk$uc6',multiply('sk$uc2',X0)) = X0 ),
inference(demodulation,[status(thm)],[d40,c26]) ).
cnf(d42,plain,
( inverse('sk$uc1') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc6'
| multiply('sk$uc6','sk$uc6') = 'sk$uc5' ),
inference(superposition,[status(thm)],[c22,d41]) ).
cnf(d43,plain,
( inverse('sk$uc1') = 'sk$uc6'
| 'sk$uc5' = multiply('sk$uc6','sk$uc6') ),
inference(superposition,[status(thm)],[d42,d1]) ).
cnf(d44,plain,
( inverse('sk$uc1') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc6'
| multiply('sk$uc6','sk$uc6') = 'sk$uc4' ),
inference(superposition,[status(thm)],[d26,c20]) ).
cnf(d45,plain,
( inverse('sk$uc1') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc6'
| 'sk$uc5' = 'sk$uc4' ),
inference(superposition,[status(thm)],[d44,d43]) ).
cnf(d46,plain,
( inverse('sk$uc1') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc6'
| 'sk$uc5' = multiply('sk$uc3','sk$uc5') ),
inference(superposition,[status(thm)],[d45,d38]) ).
cnf(d47,plain,
( inverse('sk$uc1') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc6'
| 'sk$uc5' = identity ),
inference(superposition,[status(thm)],[d46,d37]) ).
cnf(d48,plain,
( inverse('sk$uc1') = 'sk$uc6'
| multiply('sk$uc5',X0) = X0 ),
inference(superposition,[status(thm)],[d47,c26]) ).
cnf(d49,plain,
( inverse('sk$uc1') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc6'
| 'sk$uc3' = inverse('sk$uc4') ),
inference(superposition,[status(thm)],[d48,d36]) ).
cnf(d50,plain,
( 'sk$uc3' = inverse('sk$uc4')
| 'sk$uc1' = inverse('sk$uc6') ),
inference(superposition,[status(thm)],[d49,d18]) ).
cnf(d51,plain,
( 'sk$uc1' = inverse('sk$uc6')
| 'sk$uc4' = inverse('sk$uc3') ),
inference(superposition,[status(thm)],[d50,d18]) ).
cnf(d52,plain,
( 'sk$uc1' = inverse('sk$uc6')
| 'sk$uc1' = inverse('sk$uc6')
| 'sk$uc4' = identity ),
inference(superposition,[status(thm)],[d51,d33]) ).
cnf(d53,plain,
( 'sk$uc1' = inverse('sk$uc6')
| identity = 'sk$uc4' ),
inference(superposition,[status(thm)],[d52,d11]) ).
cnf(d54,plain,
( identity = 'sk$uc4'
| identity = multiply('sk$uc1','sk$uc6') ),
inference(superposition,[status(thm)],[d53,d3]) ).
cnf(d55,plain,
( identity = 'sk$uc4'
| 'sk$uc4' = multiply('sk$uc5','sk$uc6')
| identity = 'sk$uc4' ),
inference(superposition,[status(thm)],[d54,d2]) ).
cnf(d56,plain,
( identity = 'sk$uc4'
| multiply('sk$uc5','sk$uc6') = 'sk$uc4' ),
inference(superposition,[status(thm)],[d55,d1]) ).
cnf(d57,plain,
( multiply('sk$uc1','sk$uc6') = 'sk$uc4'
| 'sk$uc5' = multiply('sk$uc3','sk$uc4') ),
inference(superposition,[status(thm)],[c19,d1]) ).
cnf(d58,plain,
( identity = 'sk$uc4'
| 'sk$uc5' = multiply('sk$uc3','sk$uc4')
| identity = 'sk$uc4' ),
inference(superposition,[status(thm)],[d54,d57]) ).
cnf(d59,plain,
X1 = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[status(thm)],[d5,d1]) ).
cnf(d60,plain,
( multiply('sk$uc1','sk$uc6') = 'sk$uc4'
| 'sk$uc6' = multiply(inverse('sk$uc5'),'sk$uc4') ),
inference(superposition,[status(thm)],[c15,d59]) ).
cnf(d61,plain,
( identity = 'sk$uc4'
| 'sk$uc6' = multiply(inverse('sk$uc5'),'sk$uc4')
| identity = 'sk$uc4' ),
inference(superposition,[status(thm)],[d54,d60]) ).
cnf(d62,plain,
( identity = 'sk$uc4'
| inverse('sk$uc3') = 'sk$uc5'
| identity = 'sk$uc4' ),
inference(superposition,[status(thm)],[d54,c18]) ).
cnf(d63,plain,
( identity = 'sk$uc4'
| 'sk$uc3' = inverse('sk$uc5') ),
inference(superposition,[status(thm)],[d62,d18]) ).
cnf(d64,plain,
( identity = 'sk$uc4'
| identity = 'sk$uc4'
| 'sk$uc6' = multiply('sk$uc3','sk$uc4') ),
inference(superposition,[status(thm)],[d63,d61]) ).
cnf(d65,plain,
( identity = 'sk$uc4'
| identity = 'sk$uc4'
| 'sk$uc5' = 'sk$uc6' ),
inference(superposition,[status(thm)],[d64,d58]) ).
cnf(d66,plain,
( identity = 'sk$uc4'
| identity = 'sk$uc4'
| multiply('sk$uc6','sk$uc6') = 'sk$uc4' ),
inference(superposition,[status(thm)],[d65,d56]) ).
cnf(d67,plain,
( identity = 'sk$uc4'
| inverse('sk$uc2') = 'sk$uc6'
| identity = 'sk$uc4' ),
inference(superposition,[status(thm)],[d54,c16]) ).
cnf(d68,plain,
( identity = 'sk$uc4'
| identity = multiply('sk$uc6','sk$uc2') ),
inference(superposition,[status(thm)],[d67,d3]) ).
cnf(d69,plain,
identity = multiply(X0,inverse(X0)),
inference(superposition,[status(thm)],[d12,d3]) ).
cnf(d70,plain,
( identity = 'sk$uc4'
| identity = multiply('sk$uc2','sk$uc6') ),
inference(superposition,[status(thm)],[d67,d69]) ).
cnf(d71,plain,
( multiply('sk$uc1','sk$uc6') = 'sk$uc4'
| 'sk$uc6' = multiply('sk$uc2','sk$uc5') ),
inference(superposition,[status(thm)],[c17,d1]) ).
cnf(d72,plain,
( identity = 'sk$uc4'
| 'sk$uc6' = multiply('sk$uc2','sk$uc5')
| identity = 'sk$uc4' ),
inference(superposition,[status(thm)],[d54,d71]) ).
cnf(d73,plain,
( identity = 'sk$uc4'
| multiply('sk$uc2','sk$uc5') = 'sk$uc6' ),
inference(superposition,[status(thm)],[d72,d1]) ).
cnf(d74,plain,
( identity = 'sk$uc4'
| identity = 'sk$uc4'
| multiply('sk$uc2','sk$uc6') = 'sk$uc6' ),
inference(superposition,[status(thm)],[d65,d73]) ).
cnf(d75,plain,
( identity = 'sk$uc4'
| identity = 'sk$uc4'
| identity = 'sk$uc6' ),
inference(superposition,[status(thm)],[d74,d70]) ).
cnf(d76,plain,
( identity = 'sk$uc4'
| 'sk$uc2' = inverse('sk$uc6') ),
inference(superposition,[status(thm)],[d67,d18]) ).
cnf(d77,plain,
( identity = 'sk$uc4'
| multiply('sk$uc2','sk$uc6') = identity ),
inference(superposition,[status(thm)],[d67,d19]) ).
cnf(d78,plain,
( identity = 'sk$uc4'
| identity = 'sk$uc4'
| 'sk$uc6' = identity ),
inference(superposition,[status(thm)],[d74,d77]) ).
cnf(d79,plain,
( identity = 'sk$uc4'
| inverse('sk$uc6') = identity ),
inference(superposition,[status(thm)],[d78,d9]) ).
cnf(d80,plain,
( identity = 'sk$uc4'
| identity = 'sk$uc4'
| 'sk$uc2' = identity ),
inference(superposition,[status(thm)],[d79,d76]) ).
cnf(d81,plain,
( identity = 'sk$uc4'
| identity = 'sk$uc4'
| 'sk$uc2' = 'sk$uc6' ),
inference(superposition,[status(thm)],[d80,d75]) ).
cnf(d82,plain,
( identity = 'sk$uc4'
| identity = 'sk$uc4'
| identity = multiply('sk$uc6','sk$uc6') ),
inference(superposition,[status(thm)],[d81,d68]) ).
cnf(d83,plain,
( identity = 'sk$uc4'
| identity = 'sk$uc4'
| identity = 'sk$uc4' ),
inference(superposition,[status(thm)],[d82,d66]) ).
cnf(d84,plain,
multiply(X0,'sk$uc4') = X0,
inference(demodulation,[status(thm)],[d16,d83]) ).
cnf(d85,plain,
multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[status(thm)],[c28,d5]) ).
cnf(d86,plain,
multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[d12,d5]) ).
cnf(d87,plain,
multiply(inverse(multiply(X2,X0)),multiply(X2,X1)) = multiply(inverse(X0),X1),
inference(superposition,[status(thm)],[d86,d85]) ).
cnf(d88,plain,
( multiply('sk$uc6','sk$uc5') = 'sk$uc4'
| multiply(inverse('sk$uc5'),'sk$uc4') = 'sk$uc6' ),
inference(superposition,[status(thm)],[c0,d5]) ).
cnf(d89,plain,
( multiply(inverse('sk$uc5'),'sk$uc4') = 'sk$uc6'
| multiply(inverse(multiply(X0,'sk$uc6')),multiply(X0,'sk$uc4')) = 'sk$uc5' ),
inference(superposition,[status(thm)],[d88,d85]) ).
cnf(d90,plain,
( multiply(inverse('sk$uc5'),'sk$uc4') = 'sk$uc6'
| multiply(inverse('sk$uc6'),'sk$uc4') = 'sk$uc5' ),
inference(demodulation,[status(thm)],[d89,d87]) ).
cnf(d91,plain,
( multiply(inverse('sk$uc5'),'sk$uc4') = 'sk$uc6'
| inverse('sk$uc6') = 'sk$uc5' ),
inference(demodulation,[status(thm)],[d90,d84]) ).
cnf(d92,plain,
( inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc6') = 'sk$uc5' ),
inference(demodulation,[status(thm)],[d91,d84]) ).
cnf(d93,plain,
( inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc5') = 'sk$uc6' ),
inference(superposition,[status(thm)],[d92,d23]) ).
cnf(d94,plain,
X0 = multiply('sk$uc6',multiply('sk$uc5',X0)),
inference(superposition,[status(thm)],[d93,d59]) ).
cnf(d95,plain,
'sk$uc4' = multiply(inverse(X0),X0),
inference(demodulation,[status(thm)],[d3,d83]) ).
cnf(d96,plain,
( multiply('sk$uc6','sk$uc5') = 'sk$uc4'
| 'sk$uc4' = multiply('sk$uc5','sk$uc6') ),
inference(superposition,[status(thm)],[c0,d1]) ).
cnf(d97,plain,
( 'sk$uc4' = multiply('sk$uc5','sk$uc6')
| multiply(inverse(multiply(X0,'sk$uc6')),multiply(X0,'sk$uc4')) = 'sk$uc5' ),
inference(superposition,[status(thm)],[d96,d85]) ).
cnf(d98,plain,
( 'sk$uc4' = multiply('sk$uc5','sk$uc6')
| multiply(inverse('sk$uc6'),'sk$uc4') = 'sk$uc5' ),
inference(demodulation,[status(thm)],[d97,d87]) ).
cnf(d99,plain,
( 'sk$uc4' = multiply('sk$uc5','sk$uc6')
| inverse('sk$uc6') = 'sk$uc5' ),
inference(demodulation,[status(thm)],[d98,d84]) ).
cnf(d100,plain,
( 'sk$uc4' = multiply('sk$uc5','sk$uc6')
| 'sk$uc4' = multiply('sk$uc5','sk$uc6') ),
inference(superposition,[status(thm)],[d99,d95]) ).
cnf(d101,plain,
'sk$uc6' = multiply('sk$uc6','sk$uc4'),
inference(superposition,[status(thm)],[d100,d94]) ).
cnf(d102,plain,
'sk$uc6' = 'sk$uc6',
inference(demodulation,[status(thm)],[d101,d84]) ).
cnf(d103,plain,
multiply('sk$uc4',X0) = X0,
inference(demodulation,[status(thm)],[c26,d83]) ).
cnf(d104,plain,
multiply(X0,inverse(X0)) = 'sk$uc4',
inference(demodulation,[status(thm)],[d19,d83]) ).
cnf(d105,plain,
identity = inverse(identity),
inference(superposition,[status(thm)],[d8,d3]) ).
cnf(d106,plain,
'sk$uc4' = inverse(identity),
inference(demodulation,[status(thm)],[d105,d83]) ).
cnf(d107,plain,
'sk$uc4' = inverse('sk$uc4'),
inference(demodulation,[status(thm)],[d106,d83]) ).
cnf(d108,plain,
multiply('sk$uc4','sk$uc4') = 'sk$uc4',
inference(superposition,[status(thm)],[d107,d104]) ).
cnf(d109,plain,
'sk$uc4' = 'sk$uc4',
inference(demodulation,[status(thm)],[d108,d103]) ).
cnf(d110,plain,
inverse('sk$uc4') = identity,
inference(demodulation,[status(thm)],[d9,d83]) ).
cnf(d111,plain,
inverse('sk$uc4') = 'sk$uc4',
inference(demodulation,[status(thm)],[d110,d83]) ).
cnf(d112,plain,
( inverse('sk$uc2') = 'sk$uc6'
| multiply('sk$uc4','sk$uc6') = identity ),
inference(superposition,[status(thm)],[c11,c27]) ).
cnf(d113,plain,
( inverse('sk$uc2') = 'sk$uc6'
| multiply('sk$uc4',multiply('sk$uc6',X0)) = multiply(identity,X0) ),
inference(superposition,[status(thm)],[d112,c28]) ).
cnf(d114,plain,
( inverse('sk$uc2') = 'sk$uc6'
| multiply('sk$uc4',multiply('sk$uc6',X0)) = X0 ),
inference(demodulation,[status(thm)],[d113,c26]) ).
cnf(d115,plain,
( inverse('sk$uc2') = 'sk$uc6'
| 'sk$uc4' = multiply('sk$uc6','sk$uc5') ),
inference(superposition,[status(thm)],[c1,d1]) ).
cnf(d116,plain,
( inverse('sk$uc2') = 'sk$uc6'
| inverse('sk$uc2') = 'sk$uc6'
| multiply('sk$uc4','sk$uc4') = 'sk$uc5' ),
inference(superposition,[status(thm)],[d115,d114]) ).
cnf(d117,plain,
( inverse('sk$uc2') = 'sk$uc6'
| multiply('sk$uc1',multiply('sk$uc6',X0)) = multiply('sk$uc4',X0) ),
inference(superposition,[status(thm)],[c16,c28]) ).
cnf(d118,plain,
( inverse('sk$uc2') = 'sk$uc6'
| multiply('sk$uc4',X0) = multiply('sk$uc1',multiply('sk$uc6',X0)) ),
inference(superposition,[status(thm)],[d117,d1]) ).
cnf(d119,plain,
( inverse('sk$uc2') = 'sk$uc6'
| multiply('sk$uc6','sk$uc4') = identity ),
inference(superposition,[status(thm)],[c11,d19]) ).
cnf(d120,plain,
( inverse('sk$uc2') = 'sk$uc6'
| inverse('sk$uc2') = 'sk$uc6'
| multiply('sk$uc4','sk$uc4') = multiply('sk$uc1',identity) ),
inference(superposition,[status(thm)],[d119,d118]) ).
cnf(d121,plain,
( inverse('sk$uc2') = 'sk$uc6'
| multiply('sk$uc4','sk$uc4') = 'sk$uc1' ),
inference(demodulation,[status(thm)],[d120,d15]) ).
cnf(d122,plain,
( inverse('sk$uc2') = 'sk$uc6'
| inverse('sk$uc2') = 'sk$uc6'
| 'sk$uc1' = 'sk$uc5' ),
inference(superposition,[status(thm)],[d121,d116]) ).
cnf(d123,plain,
( 'sk$uc1' = 'sk$uc5'
| identity = multiply('sk$uc2','sk$uc6') ),
inference(superposition,[status(thm)],[d122,d69]) ).
cnf(d124,plain,
( inverse('sk$uc1') = 'sk$uc6'
| 'sk$uc2' = inverse('sk$uc6') ),
inference(superposition,[status(thm)],[c21,d18]) ).
cnf(d125,plain,
( 'sk$uc2' = inverse('sk$uc6')
| inverse('sk$uc6') = 'sk$uc1' ),
inference(superposition,[status(thm)],[d124,d23]) ).
cnf(d126,plain,
( 'sk$uc2' = inverse('sk$uc6')
| inverse('sk$uc2') = 'sk$uc6'
| 'sk$uc1' = 'sk$uc4' ),
inference(superposition,[status(thm)],[d125,c11]) ).
cnf(d127,plain,
( 'sk$uc1' = 'sk$uc4'
| 'sk$uc2' = inverse('sk$uc6')
| 'sk$uc2' = inverse('sk$uc6') ),
inference(superposition,[status(thm)],[d126,d18]) ).
cnf(d128,plain,
( 'sk$uc1' = 'sk$uc4'
| identity = multiply('sk$uc2','sk$uc6') ),
inference(superposition,[status(thm)],[d127,d3]) ).
cnf(d129,plain,
( identity = multiply('sk$uc2','sk$uc6')
| identity = multiply('sk$uc2','sk$uc6')
| 'sk$uc4' = 'sk$uc5' ),
inference(superposition,[status(thm)],[d128,d123]) ).
cnf(d130,plain,
( 'sk$uc4' = multiply('sk$uc2','sk$uc6')
| 'sk$uc4' = 'sk$uc5' ),
inference(demodulation,[status(thm)],[d129,d83]) ).
cnf(d131,plain,
'sk$uc5' = inverse('sk$uc6'),
inference(superposition,[status(thm)],[d93,d18]) ).
cnf(d132,plain,
( inverse('sk$uc6') = 'sk$uc4'
| 'sk$uc6' = multiply('sk$uc2','sk$uc5') ),
inference(superposition,[status(thm)],[c12,d1]) ).
cnf(d133,plain,
( 'sk$uc5' = 'sk$uc4'
| 'sk$uc6' = multiply('sk$uc2','sk$uc5') ),
inference(demodulation,[status(thm)],[d132,d131]) ).
cnf(d134,plain,
( 'sk$uc6' = multiply('sk$uc2','sk$uc5')
| 'sk$uc4' = 'sk$uc5' ),
inference(superposition,[status(thm)],[d133,d109]) ).
cnf(d135,plain,
X1 = multiply(X0,multiply(inverse(X0),X1)),
inference(superposition,[status(thm)],[d12,d59]) ).
cnf(d136,plain,
X0 = multiply('sk$uc5',multiply('sk$uc6',X0)),
inference(superposition,[status(thm)],[d93,d135]) ).
cnf(d137,plain,
multiply(inverse(X0),X0) = 'sk$uc4',
inference(demodulation,[status(thm)],[c27,d83]) ).
cnf(d138,plain,
multiply('sk$uc6','sk$uc5') = 'sk$uc4',
inference(superposition,[status(thm)],[d93,d137]) ).
cnf(d139,plain,
'sk$uc5' = multiply('sk$uc5','sk$uc4'),
inference(superposition,[status(thm)],[d138,d136]) ).
cnf(d140,plain,
'sk$uc5' = 'sk$uc5',
inference(demodulation,[status(thm)],[d139,d84]) ).
cnf(d141,plain,
multiply('sk$uc6',multiply('sk$uc5',X0)) = X0,
inference(superposition,[status(thm)],[d93,d5]) ).
cnf(d142,plain,
( inverse('sk$uc3') = 'sk$uc5'
| multiply('sk$uc4','sk$uc6') = identity ),
inference(superposition,[status(thm)],[c13,c27]) ).
cnf(d143,plain,
( inverse('sk$uc3') = 'sk$uc5'
| multiply('sk$uc4',multiply('sk$uc6',X0)) = multiply(identity,X0) ),
inference(superposition,[status(thm)],[d142,c28]) ).
cnf(d144,plain,
( inverse('sk$uc3') = 'sk$uc5'
| multiply('sk$uc4',multiply('sk$uc6',X0)) = X0 ),
inference(demodulation,[status(thm)],[d143,c26]) ).
cnf(d145,plain,
( inverse('sk$uc3') = 'sk$uc5'
| inverse('sk$uc3') = 'sk$uc5'
| multiply('sk$uc4','sk$uc4') = 'sk$uc5' ),
inference(superposition,[status(thm)],[c3,d144]) ).
cnf(d146,plain,
( inverse('sk$uc3') = 'sk$uc5'
| multiply('sk$uc1',multiply('sk$uc6',X0)) = multiply('sk$uc4',X0) ),
inference(superposition,[status(thm)],[c18,c28]) ).
cnf(d147,plain,
( inverse('sk$uc3') = 'sk$uc5'
| multiply('sk$uc4',X0) = multiply('sk$uc1',multiply('sk$uc6',X0)) ),
inference(superposition,[status(thm)],[d146,d1]) ).
cnf(d148,plain,
( inverse('sk$uc3') = 'sk$uc5'
| multiply('sk$uc6','sk$uc4') = identity ),
inference(superposition,[status(thm)],[c13,d19]) ).
cnf(d149,plain,
( inverse('sk$uc3') = 'sk$uc5'
| inverse('sk$uc3') = 'sk$uc5'
| multiply('sk$uc4','sk$uc4') = multiply('sk$uc1',identity) ),
inference(superposition,[status(thm)],[d148,d147]) ).
cnf(d150,plain,
( inverse('sk$uc3') = 'sk$uc5'
| multiply('sk$uc4','sk$uc4') = 'sk$uc1' ),
inference(demodulation,[status(thm)],[d149,d15]) ).
cnf(d151,plain,
( inverse('sk$uc3') = 'sk$uc5'
| inverse('sk$uc3') = 'sk$uc5'
| 'sk$uc1' = 'sk$uc5' ),
inference(superposition,[status(thm)],[d150,d145]) ).
cnf(d152,plain,
( 'sk$uc1' = 'sk$uc5'
| identity = multiply('sk$uc5','sk$uc3') ),
inference(superposition,[status(thm)],[d151,d3]) ).
cnf(d153,plain,
( inverse('sk$uc1') = 'sk$uc6'
| 'sk$uc3' = inverse('sk$uc5') ),
inference(superposition,[status(thm)],[c23,d18]) ).
cnf(d154,plain,
( 'sk$uc3' = inverse('sk$uc5')
| inverse('sk$uc6') = 'sk$uc1' ),
inference(superposition,[status(thm)],[d153,d23]) ).
cnf(d155,plain,
( 'sk$uc3' = inverse('sk$uc5')
| inverse('sk$uc3') = 'sk$uc5'
| 'sk$uc1' = 'sk$uc4' ),
inference(superposition,[status(thm)],[d154,c13]) ).
cnf(d156,plain,
( 'sk$uc1' = 'sk$uc4'
| 'sk$uc3' = inverse('sk$uc5')
| 'sk$uc3' = inverse('sk$uc5') ),
inference(superposition,[status(thm)],[d155,d18]) ).
cnf(d157,plain,
( 'sk$uc1' = 'sk$uc4'
| identity = multiply('sk$uc5','sk$uc3') ),
inference(superposition,[status(thm)],[d156,d69]) ).
cnf(d158,plain,
( identity = multiply('sk$uc5','sk$uc3')
| identity = multiply('sk$uc5','sk$uc3')
| 'sk$uc4' = 'sk$uc5' ),
inference(superposition,[status(thm)],[d157,d152]) ).
cnf(d159,plain,
( 'sk$uc4' = multiply('sk$uc5','sk$uc3')
| 'sk$uc4' = 'sk$uc5' ),
inference(demodulation,[status(thm)],[d158,d83]) ).
cnf(d160,plain,
( 'sk$uc4' = 'sk$uc5'
| multiply('sk$uc6','sk$uc4') = 'sk$uc3' ),
inference(superposition,[status(thm)],[d159,d141]) ).
cnf(d161,plain,
( 'sk$uc4' = 'sk$uc5'
| 'sk$uc6' = 'sk$uc3' ),
inference(demodulation,[status(thm)],[d160,d84]) ).
cnf(d162,plain,
( multiply('sk$uc3','sk$uc4') = 'sk$uc5'
| 'sk$uc6' = multiply('sk$uc5','sk$uc4') ),
inference(superposition,[status(thm)],[c9,d1]) ).
cnf(d163,plain,
( 'sk$uc6' = multiply('sk$uc5','sk$uc4')
| 'sk$uc5' = multiply('sk$uc3','sk$uc4') ),
inference(superposition,[status(thm)],[d162,d1]) ).
cnf(d164,plain,
( 'sk$uc6' = multiply('sk$uc5','sk$uc4')
| 'sk$uc5' = 'sk$uc3' ),
inference(demodulation,[status(thm)],[d163,d84]) ).
cnf(d165,plain,
( 'sk$uc6' = 'sk$uc5'
| 'sk$uc5' = 'sk$uc3' ),
inference(demodulation,[status(thm)],[d164,d84]) ).
cnf(d166,plain,
( 'sk$uc6' = 'sk$uc5'
| 'sk$uc4' = 'sk$uc5'
| 'sk$uc6' = 'sk$uc5' ),
inference(superposition,[status(thm)],[d165,d161]) ).
cnf(d167,plain,
( 'sk$uc4' = 'sk$uc5'
| 'sk$uc5' = 'sk$uc6' ),
inference(superposition,[status(thm)],[d166,d140]) ).
cnf(d168,plain,
( 'sk$uc4' = 'sk$uc5'
| 'sk$uc4' = 'sk$uc5'
| 'sk$uc6' = multiply('sk$uc2','sk$uc6') ),
inference(superposition,[status(thm)],[d167,d134]) ).
cnf(d169,plain,
( 'sk$uc4' = 'sk$uc5'
| 'sk$uc4' = 'sk$uc5'
| 'sk$uc4' = 'sk$uc6' ),
inference(superposition,[status(thm)],[d168,d130]) ).
cnf(d170,plain,
( 'sk$uc4' = 'sk$uc6'
| inverse('sk$uc5') = 'sk$uc4' ),
inference(superposition,[status(thm)],[d169,d111]) ).
cnf(d171,plain,
( 'sk$uc6' = 'sk$uc4'
| 'sk$uc4' = 'sk$uc6' ),
inference(demodulation,[status(thm)],[d170,d93]) ).
cnf(d172,plain,
( 'sk$uc6' = 'sk$uc4'
| 'sk$uc6' = 'sk$uc4' ),
inference(superposition,[status(thm)],[d171,d109]) ).
cnf(d173,plain,
identity = 'sk$uc6',
inference(demodulation,[status(thm)],[d83,d172]) ).
cnf(d174,plain,
( 'sk$uc6' = 'sk$uc5'
| 'sk$uc6' = 'sk$uc5' ),
inference(demodulation,[status(thm)],[d166,d172]) ).
cnf(d175,plain,
'sk$uc6' = inverse('sk$uc4'),
inference(demodulation,[status(thm)],[d107,d172]) ).
cnf(d176,plain,
'sk$uc6' = inverse('sk$uc6'),
inference(demodulation,[status(thm)],[d175,d172]) ).
cnf(d177,plain,
multiply(X0,inverse(X0)) = 'sk$uc6',
inference(demodulation,[status(thm)],[d104,d172]) ).
cnf(d178,plain,
multiply('sk$uc6',X0) = X0,
inference(demodulation,[status(thm)],[d103,d172]) ).
cnf(d179,plain,
multiply(X0,'sk$uc6') = X0,
inference(demodulation,[status(thm)],[d84,d172]) ).
cnf(d180,plain,
( inverse('sk$uc6') != 'sk$uc4'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| inverse(identity) != 'sk$uc5'
| multiply('sk$uc6','sk$uc5') != 'sk$uc4'
| multiply('sk$uc5','sk$uc4') != 'sk$uc6'
| multiply('sk$uc5','sk$uc6') != 'sk$uc4'
| multiply(X1,'sk$uc5') != 'sk$uc6'
| multiply(X0,'sk$uc6') != 'sk$uc4'
| 'sk$uc4' != 'sk$uc5' ),
inference(superposition,[status(thm)],[c26,c25]) ).
cnf(d181,plain,
( inverse(identity) != 'sk$uc5'
| inverse('sk$uc6') != 'sk$uc4'
| inverse(X0) != 'sk$uc6'
| inverse(identity) != 'sk$uc6'
| 'sk$uc4' != 'sk$uc5'
| multiply('sk$uc6','sk$uc5') != 'sk$uc4'
| multiply('sk$uc5','sk$uc4') != 'sk$uc6'
| multiply('sk$uc5','sk$uc6') != 'sk$uc4'
| multiply(X0,'sk$uc6') != 'sk$uc4'
| 'sk$uc5' != 'sk$uc6' ),
inference(superposition,[status(thm)],[d6,d180]) ).
cnf(d182,plain,
( inverse(identity) != 'sk$uc6'
| identity != 'sk$uc5'
| inverse('sk$uc6') != 'sk$uc4'
| inverse(X0) != 'sk$uc6'
| 'sk$uc4' != 'sk$uc5'
| 'sk$uc5' != 'sk$uc6'
| multiply('sk$uc6','sk$uc5') != 'sk$uc4'
| multiply('sk$uc5','sk$uc4') != 'sk$uc6'
| multiply('sk$uc5','sk$uc6') != 'sk$uc4'
| multiply(X0,'sk$uc6') != 'sk$uc4' ),
inference(demodulation,[status(thm)],[d181,d9]) ).
cnf(d183,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc5'
| inverse('sk$uc6') != 'sk$uc4'
| inverse(X0) != 'sk$uc6'
| 'sk$uc4' != 'sk$uc5'
| 'sk$uc5' != 'sk$uc6'
| multiply('sk$uc6','sk$uc5') != 'sk$uc4'
| multiply('sk$uc5','sk$uc4') != 'sk$uc6'
| multiply('sk$uc5','sk$uc6') != 'sk$uc4'
| multiply(X0,'sk$uc6') != 'sk$uc4' ),
inference(demodulation,[status(thm)],[d182,d9]) ).
cnf(d184,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(superposition,[status(thm)],[c28,d1]) ).
cnf(d185,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc5'
| inverse('sk$uc6') != 'sk$uc4'
| inverse(multiply(X0,X1)) != 'sk$uc6'
| 'sk$uc4' != 'sk$uc5'
| 'sk$uc5' != 'sk$uc6'
| multiply('sk$uc6','sk$uc5') != 'sk$uc4'
| multiply('sk$uc5','sk$uc4') != 'sk$uc6'
| multiply('sk$uc5','sk$uc6') != 'sk$uc4'
| multiply(X0,multiply(X1,'sk$uc6')) != 'sk$uc4' ),
inference(superposition,[status(thm)],[d184,d183]) ).
cnf(d186,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc5'
| inverse('sk$uc6') != 'sk$uc4'
| inverse(multiply(X0,inverse(X0))) != 'sk$uc6'
| 'sk$uc4' != 'sk$uc5'
| 'sk$uc5' != 'sk$uc6'
| multiply('sk$uc6','sk$uc5') != 'sk$uc4'
| multiply('sk$uc5','sk$uc4') != 'sk$uc6'
| multiply('sk$uc5','sk$uc6') != 'sk$uc4'
| 'sk$uc6' != 'sk$uc4' ),
inference(superposition,[status(thm)],[d86,d185]) ).
cnf(d187,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc5'
| inverse('sk$uc6') != 'sk$uc4'
| inverse(multiply(X0,inverse(X0))) != 'sk$uc6'
| 'sk$uc4' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc4'
| 'sk$uc5' != 'sk$uc6'
| multiply('sk$uc6','sk$uc5') != 'sk$uc4'
| multiply('sk$uc5','sk$uc4') != 'sk$uc6'
| 'sk$uc5' != 'sk$uc4' ),
inference(demodulation,[status(thm)],[d186,d179]) ).
cnf(d188,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc5'
| inverse('sk$uc6') != 'sk$uc4'
| inverse(multiply(X0,inverse(X0))) != 'sk$uc6'
| 'sk$uc4' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc4'
| 'sk$uc5' != 'sk$uc6'
| multiply('sk$uc6','sk$uc5') != 'sk$uc4'
| multiply('sk$uc5','sk$uc4') != 'sk$uc6'
| 'sk$uc6' != 'sk$uc4' ),
inference(demodulation,[status(thm)],[d187,d174]) ).
cnf(d189,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc5'
| inverse('sk$uc6') != 'sk$uc4'
| inverse(multiply(X0,inverse(X0))) != 'sk$uc6'
| 'sk$uc4' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc4'
| 'sk$uc5' != 'sk$uc6'
| multiply('sk$uc6','sk$uc5') != 'sk$uc4'
| multiply('sk$uc5','sk$uc4') != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d188,d172]) ).
cnf(d190,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc5'
| inverse('sk$uc6') != 'sk$uc4'
| inverse(multiply(X0,inverse(X0))) != 'sk$uc6'
| 'sk$uc4' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc4'
| 'sk$uc5' != 'sk$uc6'
| multiply('sk$uc6','sk$uc5') != 'sk$uc4'
| multiply('sk$uc6','sk$uc4') != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d189,d174]) ).
cnf(d191,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc5'
| inverse('sk$uc6') != 'sk$uc4'
| inverse(multiply(X0,inverse(X0))) != 'sk$uc6'
| 'sk$uc4' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc4'
| 'sk$uc5' != 'sk$uc6'
| multiply('sk$uc6','sk$uc5') != 'sk$uc4'
| 'sk$uc4' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d190,d178]) ).
cnf(d192,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc5'
| inverse('sk$uc6') != 'sk$uc4'
| inverse(multiply(X0,inverse(X0))) != 'sk$uc6'
| 'sk$uc4' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc4'
| 'sk$uc5' != 'sk$uc6'
| multiply('sk$uc6','sk$uc5') != 'sk$uc4'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d191,d172]) ).
cnf(d193,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc5'
| inverse('sk$uc6') != 'sk$uc4'
| inverse(multiply(X0,inverse(X0))) != 'sk$uc6'
| 'sk$uc4' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc4'
| 'sk$uc5' != 'sk$uc6'
| 'sk$uc5' != 'sk$uc4'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d192,d178]) ).
cnf(d194,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc5'
| inverse('sk$uc6') != 'sk$uc4'
| inverse(multiply(X0,inverse(X0))) != 'sk$uc6'
| 'sk$uc4' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc4'
| 'sk$uc5' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc4'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d193,d174]) ).
cnf(d195,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc5'
| inverse('sk$uc6') != 'sk$uc4'
| inverse(multiply(X0,inverse(X0))) != 'sk$uc6'
| 'sk$uc4' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc4'
| 'sk$uc5' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d194,d172]) ).
cnf(d196,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc5'
| inverse('sk$uc6') != 'sk$uc4'
| inverse(multiply(X0,inverse(X0))) != 'sk$uc6'
| 'sk$uc4' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc4'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d195,d174]) ).
cnf(d197,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc5'
| inverse('sk$uc6') != 'sk$uc4'
| inverse(multiply(X0,inverse(X0))) != 'sk$uc6'
| 'sk$uc4' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d196,d172]) ).
cnf(d198,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc5'
| inverse('sk$uc6') != 'sk$uc4'
| inverse(multiply(X0,inverse(X0))) != 'sk$uc6'
| 'sk$uc6' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d197,d172]) ).
cnf(d199,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc5'
| inverse('sk$uc6') != 'sk$uc4'
| inverse(multiply(X0,inverse(X0))) != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d198,d174]) ).
cnf(d200,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc5'
| inverse('sk$uc6') != 'sk$uc4'
| inverse('sk$uc6') != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d199,d177]) ).
cnf(d201,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc5'
| inverse('sk$uc6') != 'sk$uc4'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d200,d176]) ).
cnf(d202,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc5'
| 'sk$uc6' != 'sk$uc4'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d201,d176]) ).
cnf(d203,plain,
( identity != 'sk$uc6'
| identity != 'sk$uc5'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d202,d172]) ).
cnf(d204,plain,
( identity != 'sk$uc6'
| 'sk$uc6' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d203,d173]) ).
cnf(d205,plain,
( identity != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d204,d174]) ).
cnf(d206,plain,
( 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d205,d173]) ).
cnf(d207,plain,
( 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6' ),
inference(resolution,[status(thm)],[d102,d206]) ).
cnf(d208,plain,
$false,
inference(resolution,[status(thm)],[d207,d102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP305-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 14:45:03 UTC 2026
% 0.12/0.35 % CPUTime :
% 0.12/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 115.57/28.48 % SZS status Unsatisfiable for theBenchmark.p
% 115.57/28.48 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------