%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP229-1 : 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 : n006.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 91.80s 25.81s
% Output : CNFRefutation 91.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 29
% Syntax : Number of clauses : 231 ( 86 unt; 116 nHn; 171 RR)
% Number of literals : 547 ( 546 equ; 205 neg)
% Maximal clause size : 11 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 162 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this_1,negated_conjecture,
( inverse('sk$uc8') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc8' ) ).
cnf(prove_this_2,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc8' ) ).
cnf(prove_this_3,negated_conjecture,
( multiply('sk$uc4','sk$uc7') = 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc8' ) ).
cnf(prove_this_4,negated_conjecture,
( multiply('sk$uc8','sk$uc6') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc8' ) ).
cnf(prove_this_5,negated_conjecture,
( multiply('sk$uc5','sk$uc8') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc8' ) ).
cnf(prove_this_6,negated_conjecture,
( inverse('sk$uc5') = 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc8' ) ).
cnf(prove_this_7,negated_conjecture,
( inverse('sk$uc8') = 'sk$uc7'
| multiply('sk$uc1','sk$uc7') = 'sk$uc8' ) ).
cnf(prove_this_8,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc8'
| multiply('sk$uc1','sk$uc7') = 'sk$uc8' ) ).
cnf(prove_this_9,negated_conjecture,
( multiply('sk$uc4','sk$uc7') = 'sk$uc8'
| multiply('sk$uc1','sk$uc7') = 'sk$uc8' ) ).
cnf(prove_this_13,negated_conjecture,
( inverse('sk$uc8') = 'sk$uc7'
| multiply('sk$uc8','sk$uc3') = 'sk$uc7' ) ).
cnf(prove_this_14,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc8'
| multiply('sk$uc8','sk$uc3') = 'sk$uc7' ) ).
cnf(prove_this_15,negated_conjecture,
( multiply('sk$uc4','sk$uc7') = 'sk$uc8'
| multiply('sk$uc8','sk$uc3') = 'sk$uc7' ) ).
cnf(prove_this_16,negated_conjecture,
( multiply('sk$uc8','sk$uc6') = 'sk$uc7'
| multiply('sk$uc8','sk$uc3') = 'sk$uc7' ) ).
cnf(prove_this_17,negated_conjecture,
( multiply('sk$uc5','sk$uc8') = 'sk$uc6'
| multiply('sk$uc8','sk$uc3') = 'sk$uc7' ) ).
cnf(prove_this_18,negated_conjecture,
( inverse('sk$uc5') = 'sk$uc8'
| multiply('sk$uc8','sk$uc3') = 'sk$uc7' ) ).
cnf(prove_this_19,negated_conjecture,
( inverse('sk$uc8') = 'sk$uc7'
| multiply('sk$uc2','sk$uc8') = 'sk$uc3' ) ).
cnf(prove_this_22,negated_conjecture,
( multiply('sk$uc8','sk$uc6') = 'sk$uc7'
| multiply('sk$uc2','sk$uc8') = 'sk$uc3' ) ).
cnf(prove_this_23,negated_conjecture,
( multiply('sk$uc5','sk$uc8') = 'sk$uc6'
| multiply('sk$uc2','sk$uc8') = 'sk$uc3' ) ).
cnf(prove_this_24,negated_conjecture,
( inverse('sk$uc5') = 'sk$uc8'
| multiply('sk$uc2','sk$uc8') = 'sk$uc3' ) ).
cnf(prove_this_25,negated_conjecture,
( inverse('sk$uc8') = 'sk$uc7'
| inverse('sk$uc2') = 'sk$uc8' ) ).
cnf(prove_this_26,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc8'
| inverse('sk$uc2') = 'sk$uc8' ) ).
cnf(prove_this_27,negated_conjecture,
( multiply('sk$uc4','sk$uc7') = 'sk$uc8'
| inverse('sk$uc2') = 'sk$uc8' ) ).
cnf(prove_this_28,negated_conjecture,
( multiply('sk$uc8','sk$uc6') = 'sk$uc7'
| inverse('sk$uc2') = 'sk$uc8' ) ).
cnf(prove_this_29,negated_conjecture,
( multiply('sk$uc5','sk$uc8') = 'sk$uc6'
| inverse('sk$uc2') = 'sk$uc8' ) ).
cnf(prove_this_30,negated_conjecture,
( inverse('sk$uc5') = 'sk$uc8'
| inverse('sk$uc2') = 'sk$uc8' ) ).
cnf(prove_this_31,negated_conjecture,
( inverse(X5) != 'sk$uc8'
| multiply(X5,'sk$uc8') != X4
| multiply('sk$uc8',X4) != 'sk$uc7'
| multiply(X3,'sk$uc7') != 'sk$uc8'
| inverse(X3) != 'sk$uc8'
| inverse('sk$uc8') != 'sk$uc7'
| inverse(X2) != 'sk$uc8'
| multiply(X2,'sk$uc8') != X1
| multiply('sk$uc8',X1) != 'sk$uc7'
| multiply(X0,'sk$uc7') != 'sk$uc8'
| inverse(X0) != 'sk$uc8' ) ).
cnf(left_identity,axiom,
multiply(identity,X0) = X0 ).
cnf(left_inverse,axiom,
multiply(inverse(X0),X0) = identity ).
cnf(associativity,axiom,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)) ).
cnf(c0,plain,
( inverse('sk$uc8') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_1]) ).
cnf(c1,plain,
( inverse('sk$uc4') = 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_2]) ).
cnf(c2,plain,
( multiply('sk$uc4','sk$uc7') = 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_3]) ).
cnf(c3,plain,
( multiply('sk$uc8','sk$uc6') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_4]) ).
cnf(c4,plain,
( multiply('sk$uc5','sk$uc8') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_5]) ).
cnf(c5,plain,
( inverse('sk$uc5') = 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_6]) ).
cnf(c6,plain,
( inverse('sk$uc8') = 'sk$uc7'
| multiply('sk$uc1','sk$uc7') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_7]) ).
cnf(c7,plain,
( inverse('sk$uc4') = 'sk$uc8'
| multiply('sk$uc1','sk$uc7') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_8]) ).
cnf(c8,plain,
( multiply('sk$uc4','sk$uc7') = 'sk$uc8'
| multiply('sk$uc1','sk$uc7') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_9]) ).
cnf(c12,plain,
( inverse('sk$uc8') = 'sk$uc7'
| multiply('sk$uc8','sk$uc3') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_13]) ).
cnf(c13,plain,
( inverse('sk$uc4') = 'sk$uc8'
| multiply('sk$uc8','sk$uc3') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_14]) ).
cnf(c14,plain,
( multiply('sk$uc4','sk$uc7') = 'sk$uc8'
| multiply('sk$uc8','sk$uc3') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_15]) ).
cnf(c15,plain,
( multiply('sk$uc8','sk$uc6') = 'sk$uc7'
| multiply('sk$uc8','sk$uc3') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_16]) ).
cnf(c16,plain,
( multiply('sk$uc5','sk$uc8') = 'sk$uc6'
| multiply('sk$uc8','sk$uc3') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_17]) ).
cnf(c17,plain,
( inverse('sk$uc5') = 'sk$uc8'
| multiply('sk$uc8','sk$uc3') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_18]) ).
cnf(c18,plain,
( inverse('sk$uc8') = 'sk$uc7'
| multiply('sk$uc2','sk$uc8') = 'sk$uc3' ),
inference(clausification,[status(esa)],[prove_this_19]) ).
cnf(c21,plain,
( multiply('sk$uc8','sk$uc6') = 'sk$uc7'
| multiply('sk$uc2','sk$uc8') = 'sk$uc3' ),
inference(clausification,[status(esa)],[prove_this_22]) ).
cnf(c22,plain,
( multiply('sk$uc5','sk$uc8') = 'sk$uc6'
| multiply('sk$uc2','sk$uc8') = 'sk$uc3' ),
inference(clausification,[status(esa)],[prove_this_23]) ).
cnf(c23,plain,
( inverse('sk$uc5') = 'sk$uc8'
| multiply('sk$uc2','sk$uc8') = 'sk$uc3' ),
inference(clausification,[status(esa)],[prove_this_24]) ).
cnf(c24,plain,
( inverse('sk$uc8') = 'sk$uc7'
| inverse('sk$uc2') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_25]) ).
cnf(c25,plain,
( inverse('sk$uc4') = 'sk$uc8'
| inverse('sk$uc2') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_26]) ).
cnf(c26,plain,
( multiply('sk$uc4','sk$uc7') = 'sk$uc8'
| inverse('sk$uc2') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_27]) ).
cnf(c27,plain,
( multiply('sk$uc8','sk$uc6') = 'sk$uc7'
| inverse('sk$uc2') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_28]) ).
cnf(c28,plain,
( multiply('sk$uc5','sk$uc8') = 'sk$uc6'
| inverse('sk$uc2') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_29]) ).
cnf(c29,plain,
( inverse('sk$uc5') = 'sk$uc8'
| inverse('sk$uc2') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_30]) ).
cnf(c30,plain,
( inverse(X0) != 'sk$uc8'
| multiply(X4,'sk$uc8') != X5
| multiply('sk$uc8',X5) != 'sk$uc7'
| inverse(X2) != 'sk$uc8'
| multiply(X1,'sk$uc8') != X3
| inverse(X4) != 'sk$uc8'
| multiply('sk$uc8',X3) != 'sk$uc7'
| multiply(X2,'sk$uc7') != 'sk$uc8'
| inverse('sk$uc8') != 'sk$uc7'
| inverse(X1) != 'sk$uc8'
| multiply(X0,'sk$uc7') != 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_31]) ).
cnf(c31,plain,
multiply(identity,X0) = X0,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c32,plain,
multiply(inverse(X0),X0) = identity,
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c33,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(clausification,[status(esa)],[associativity]) ).
cnf(d0,plain,
( multiply('sk$uc8',X4) != 'sk$uc7'
| multiply('sk$uc8',X3) != 'sk$uc7'
| multiply(X0,'sk$uc7') != 'sk$uc8'
| multiply(X2,'sk$uc8') != X4
| multiply(X1,'sk$uc8') != X3
| multiply(X0,'sk$uc7') != 'sk$uc8'
| inverse('sk$uc8') != 'sk$uc7'
| inverse(X2) != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8' ),
inference(factoring,[status(thm)],[c30]) ).
cnf(d1,plain,
( multiply('sk$uc8',X2) != 'sk$uc7'
| multiply('sk$uc8',X2) != 'sk$uc7'
| multiply(X1,'sk$uc7') != 'sk$uc8'
| multiply(X0,'sk$uc8') != X2
| inverse('sk$uc8') != 'sk$uc7'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| inverse(X0) != 'sk$uc8' ),
inference(factoring,[status(thm)],[d0]) ).
cnf(d2,plain,
( multiply('sk$uc8','sk$uc3') = 'sk$uc7'
| multiply(X1,'sk$uc8') != 'sk$uc6'
| multiply(X0,'sk$uc7') != 'sk$uc8'
| inverse('sk$uc8') != 'sk$uc7'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc7' != 'sk$uc7' ),
inference(superposition,[status(thm)],[c15,d1]) ).
cnf(d3,plain,
( multiply('sk$uc8','sk$uc3') = 'sk$uc7'
| multiply(X1,'sk$uc7') != 'sk$uc8'
| multiply(X0,'sk$uc8') != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| multiply('sk$uc8','sk$uc3') = 'sk$uc7' ),
inference(resolution,[status(thm)],[c12,d2]) ).
cnf(d4,plain,
( multiply('sk$uc8','sk$uc3') = 'sk$uc7'
| multiply('sk$uc8','sk$uc3') = 'sk$uc7'
| multiply(X0,'sk$uc7') != 'sk$uc8'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc5') != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc6' != 'sk$uc6' ),
inference(superposition,[status(thm)],[c16,d3]) ).
cnf(d5,plain,
( 'sk$uc6' != 'sk$uc6'
| multiply('sk$uc8','sk$uc3') = 'sk$uc7'
| multiply(X0,'sk$uc7') != 'sk$uc8'
| 'sk$uc7' != 'sk$uc7'
| inverse(X0) != 'sk$uc8'
| multiply('sk$uc8','sk$uc3') = 'sk$uc7' ),
inference(resolution,[status(thm)],[c17,d4]) ).
cnf(d6,plain,
multiply(X0,X1) = multiply(identity,multiply(X0,X1)),
inference(superposition,[status(thm)],[c31,c33]) ).
cnf(d7,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d6,c31]) ).
cnf(d8,plain,
( multiply('sk$uc8','sk$uc3') = 'sk$uc7'
| 'sk$uc8' = multiply('sk$uc4','sk$uc7') ),
inference(superposition,[status(thm)],[c14,d7]) ).
cnf(d9,plain,
( multiply('sk$uc8','sk$uc3') = 'sk$uc7'
| 'sk$uc6' != 'sk$uc6'
| multiply('sk$uc8','sk$uc3') = 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc4') != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8' ),
inference(superposition,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[status(thm)],[c32,c33]) ).
cnf(d11,plain,
X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(demodulation,[status(thm)],[d10,c31]) ).
cnf(d12,plain,
multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(superposition,[status(thm)],[d11,d11]) ).
cnf(d13,plain,
identity = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[c32,d7]) ).
cnf(d14,plain,
X0 = multiply(inverse(inverse(X0)),identity),
inference(superposition,[status(thm)],[d13,d11]) ).
cnf(d15,plain,
multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[d14,d7]) ).
cnf(d16,plain,
multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[d15,d12]) ).
cnf(d17,plain,
multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(superposition,[status(thm)],[d11,d7]) ).
cnf(d18,plain,
multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d16,d12]) ).
cnf(d19,plain,
X0 = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d18,d16]) ).
cnf(d20,plain,
( inverse('sk$uc2') = 'sk$uc8'
| multiply(X1,'sk$uc8') != 'sk$uc6'
| multiply(X0,'sk$uc7') != 'sk$uc8'
| inverse('sk$uc8') != 'sk$uc7'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc7' != 'sk$uc7' ),
inference(superposition,[status(thm)],[c27,d1]) ).
cnf(d21,plain,
( multiply(X1,'sk$uc7') != 'sk$uc8'
| multiply(X0,'sk$uc8') != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc2') = 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| inverse('sk$uc2') = 'sk$uc8' ),
inference(resolution,[status(thm)],[c24,d20]) ).
cnf(d22,plain,
( multiply(X0,'sk$uc7') != 'sk$uc8'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc2') = 'sk$uc8'
| inverse(inverse('sk$uc8')) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| identity != 'sk$uc6' ),
inference(superposition,[status(thm)],[c32,d21]) ).
cnf(d23,plain,
( inverse('sk$uc2') = 'sk$uc8'
| identity != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc2') = 'sk$uc8'
| inverse(inverse('sk$uc8')) != 'sk$uc8'
| inverse('sk$uc4') != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8' ),
inference(superposition,[status(thm)],[c26,d22]) ).
cnf(d24,plain,
( identity != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| inverse('sk$uc2') = 'sk$uc8'
| inverse('sk$uc4') != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d23,d19]) ).
cnf(d25,plain,
( identity != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| inverse('sk$uc2') = 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| inverse('sk$uc2') = 'sk$uc8' ),
inference(resolution,[status(thm)],[c25,d24]) ).
cnf(d26,plain,
identity = multiply(X0,inverse(X0)),
inference(superposition,[status(thm)],[d12,d13]) ).
cnf(d27,plain,
( inverse('sk$uc2') = 'sk$uc8'
| identity = multiply('sk$uc5','sk$uc8') ),
inference(superposition,[status(thm)],[c29,d26]) ).
cnf(d28,plain,
( inverse('sk$uc2') = 'sk$uc8'
| inverse('sk$uc2') = 'sk$uc8'
| identity = 'sk$uc6' ),
inference(superposition,[status(thm)],[d27,c28]) ).
cnf(d29,plain,
( 'sk$uc7' != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| inverse('sk$uc2') = 'sk$uc8'
| inverse('sk$uc2') = 'sk$uc8' ),
inference(resolution,[status(thm)],[d28,d25]) ).
cnf(d30,plain,
( 'sk$uc8' != 'sk$uc8'
| inverse('sk$uc2') = 'sk$uc8' ),
inference(equality_resolution,[status(thm)],[d29]) ).
cnf(d31,plain,
inverse('sk$uc2') = 'sk$uc8',
inference(equality_resolution,[status(thm)],[d30]) ).
cnf(d32,plain,
multiply('sk$uc8',multiply('sk$uc2',X0)) = X0,
inference(superposition,[status(thm)],[d31,d17]) ).
cnf(d33,plain,
multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[d12,c32]) ).
cnf(d34,plain,
multiply('sk$uc2','sk$uc8') = identity,
inference(superposition,[status(thm)],[d31,d33]) ).
cnf(d35,plain,
multiply('sk$uc8',identity) = 'sk$uc8',
inference(superposition,[status(thm)],[d34,d32]) ).
cnf(d36,plain,
'sk$uc8' = 'sk$uc8',
inference(demodulation,[status(thm)],[d35,d16]) ).
cnf(d37,plain,
( 'sk$uc6' != 'sk$uc6'
| multiply('sk$uc8','sk$uc3') = 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc4') != 'sk$uc8' ),
inference(resolution,[status(thm)],[d36,d9]) ).
cnf(d38,plain,
( 'sk$uc6' != 'sk$uc6'
| multiply('sk$uc8','sk$uc3') = 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| multiply('sk$uc8','sk$uc3') = 'sk$uc7' ),
inference(resolution,[status(thm)],[c13,d37]) ).
cnf(d39,plain,
( multiply('sk$uc8','sk$uc3') = 'sk$uc7'
| 'sk$uc7' != 'sk$uc7' ),
inference(equality_resolution,[status(thm)],[d38]) ).
cnf(d40,plain,
multiply('sk$uc8','sk$uc3') = 'sk$uc7',
inference(equality_resolution,[status(thm)],[d39]) ).
cnf(d41,plain,
X0 = multiply(X0,identity),
inference(demodulation,[status(thm)],[d14,d12]) ).
cnf(d42,plain,
identity = multiply('sk$uc2','sk$uc8'),
inference(superposition,[status(thm)],[d31,d26]) ).
cnf(d43,plain,
( identity = 'sk$uc3'
| multiply('sk$uc8','sk$uc6') = 'sk$uc7' ),
inference(demodulation,[status(thm)],[c21,d42]) ).
cnf(d44,plain,
( identity = 'sk$uc3'
| multiply('sk$uc5','sk$uc8') = 'sk$uc6' ),
inference(demodulation,[status(thm)],[c22,d42]) ).
cnf(d45,plain,
( identity = 'sk$uc3'
| inverse('sk$uc5') = 'sk$uc8' ),
inference(demodulation,[status(thm)],[c23,d42]) ).
cnf(d46,plain,
( identity = 'sk$uc3'
| identity = multiply('sk$uc5','sk$uc8') ),
inference(superposition,[status(thm)],[d45,d26]) ).
cnf(d47,plain,
( identity = 'sk$uc3'
| identity = 'sk$uc3'
| identity = 'sk$uc6' ),
inference(superposition,[status(thm)],[d46,d44]) ).
cnf(d48,plain,
( identity = 'sk$uc3'
| X0 = multiply(X0,'sk$uc6') ),
inference(superposition,[status(thm)],[d47,d41]) ).
cnf(d49,plain,
( identity = 'sk$uc3'
| identity = 'sk$uc3'
| 'sk$uc8' = 'sk$uc7' ),
inference(superposition,[status(thm)],[d48,d43]) ).
cnf(d50,plain,
( 'sk$uc8' = 'sk$uc7'
| X0 = multiply(X0,'sk$uc3') ),
inference(superposition,[status(thm)],[d49,d41]) ).
cnf(d51,plain,
( 'sk$uc8' = 'sk$uc7'
| 'sk$uc8' = 'sk$uc7' ),
inference(superposition,[status(thm)],[d50,d40]) ).
cnf(d52,plain,
( inverse('sk$uc1') = 'sk$uc8'
| multiply(X1,'sk$uc8') != 'sk$uc6'
| multiply(X0,'sk$uc7') != 'sk$uc8'
| inverse('sk$uc8') != 'sk$uc7'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc7' != 'sk$uc7' ),
inference(superposition,[status(thm)],[c3,d1]) ).
cnf(d53,plain,
( multiply(X1,'sk$uc7') != 'sk$uc8'
| multiply(X0,'sk$uc8') != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc8' ),
inference(resolution,[status(thm)],[c0,d52]) ).
cnf(d54,plain,
( multiply(X0,'sk$uc7') != 'sk$uc8'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc8'
| inverse(inverse('sk$uc8')) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| identity != 'sk$uc6' ),
inference(superposition,[status(thm)],[c32,d53]) ).
cnf(d55,plain,
( inverse('sk$uc1') = 'sk$uc8'
| 'sk$uc8' = multiply('sk$uc4','sk$uc7') ),
inference(superposition,[status(thm)],[c2,d7]) ).
cnf(d56,plain,
( inverse('sk$uc1') = 'sk$uc8'
| identity != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc8'
| inverse(inverse('sk$uc8')) != 'sk$uc8'
| inverse('sk$uc4') != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8' ),
inference(superposition,[status(thm)],[d55,d54]) ).
cnf(d57,plain,
( identity != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| inverse('sk$uc4') != 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc8'
| 'sk$uc8' != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d56,d19]) ).
cnf(d58,plain,
( identity != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| inverse('sk$uc4') != 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc8' ),
inference(resolution,[status(thm)],[d36,d57]) ).
cnf(d59,plain,
( identity != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc8' ),
inference(resolution,[status(thm)],[c1,d58]) ).
cnf(d60,plain,
( inverse('sk$uc1') = 'sk$uc8'
| identity = multiply('sk$uc5','sk$uc8') ),
inference(superposition,[status(thm)],[c5,d26]) ).
cnf(d61,plain,
( inverse('sk$uc1') = 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc8'
| identity = 'sk$uc6' ),
inference(superposition,[status(thm)],[d60,c4]) ).
cnf(d62,plain,
( 'sk$uc7' != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc8' ),
inference(resolution,[status(thm)],[d61,d59]) ).
cnf(d63,plain,
( 'sk$uc8' != 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc8' ),
inference(equality_resolution,[status(thm)],[d62]) ).
cnf(d64,plain,
inverse('sk$uc1') = 'sk$uc8',
inference(resolution,[status(thm)],[d36,d63]) ).
cnf(d65,plain,
'sk$uc1' = inverse('sk$uc8'),
inference(superposition,[status(thm)],[d64,d19]) ).
cnf(d66,plain,
multiply(inverse(X0),identity) = inverse(X0),
inference(superposition,[status(thm)],[d26,d17]) ).
cnf(d67,plain,
inverse(X0) = inverse(X0),
inference(demodulation,[status(thm)],[d66,d16]) ).
cnf(d68,plain,
inverse(inverse(X0)) = X0,
inference(superposition,[status(thm)],[d19,d67]) ).
cnf(d69,plain,
inverse('sk$uc8') = 'sk$uc2',
inference(superposition,[status(thm)],[d31,d68]) ).
cnf(d70,plain,
'sk$uc1' = 'sk$uc2',
inference(demodulation,[status(thm)],[d69,d65]) ).
cnf(d71,plain,
'sk$uc2' = inverse('sk$uc8'),
inference(superposition,[status(thm)],[d31,d19]) ).
cnf(d72,plain,
( inverse('sk$uc8') = 'sk$uc7'
| 'sk$uc3' = multiply('sk$uc2','sk$uc8') ),
inference(superposition,[status(thm)],[c18,d7]) ).
cnf(d73,plain,
( inverse('sk$uc8') = 'sk$uc7'
| identity = multiply('sk$uc2','sk$uc8') ),
inference(superposition,[status(thm)],[c24,d26]) ).
cnf(d74,plain,
( inverse('sk$uc8') = 'sk$uc7'
| inverse('sk$uc8') = 'sk$uc7'
| 'sk$uc3' = identity ),
inference(superposition,[status(thm)],[d73,d72]) ).
cnf(d75,plain,
( 'sk$uc3' = identity
| 'sk$uc7' = inverse('sk$uc8') ),
inference(superposition,[status(thm)],[d74,d67]) ).
cnf(d76,plain,
( 'sk$uc3' = identity
| 'sk$uc7' = 'sk$uc2' ),
inference(demodulation,[status(thm)],[d75,d71]) ).
cnf(d77,plain,
( 'sk$uc3' = identity
| 'sk$uc7' = 'sk$uc1' ),
inference(demodulation,[status(thm)],[d76,d70]) ).
cnf(d78,plain,
X0 = multiply(inverse(identity),X0),
inference(superposition,[status(thm)],[c31,d11]) ).
cnf(d79,plain,
X0 = multiply(inverse(inverse(identity)),X0),
inference(superposition,[status(thm)],[d78,d11]) ).
cnf(d80,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[d79,c32]) ).
cnf(d81,plain,
( inverse('sk$uc8') = 'sk$uc7'
| inverse('sk$uc8') = 'sk$uc7'
| identity = 'sk$uc3' ),
inference(superposition,[status(thm)],[d73,c18]) ).
cnf(d82,plain,
( identity = 'sk$uc3'
| 'sk$uc7' = inverse('sk$uc8') ),
inference(superposition,[status(thm)],[d81,d67]) ).
cnf(d83,plain,
( identity = 'sk$uc3'
| 'sk$uc7' = 'sk$uc2' ),
inference(demodulation,[status(thm)],[d82,d71]) ).
cnf(d84,plain,
( 'sk$uc7' = 'sk$uc2'
| inverse('sk$uc3') = identity ),
inference(superposition,[status(thm)],[d83,d80]) ).
cnf(d85,plain,
( 'sk$uc7' = 'sk$uc2'
| identity = inverse('sk$uc3') ),
inference(superposition,[status(thm)],[d84,d67]) ).
cnf(d86,plain,
( identity = inverse('sk$uc3')
| 'sk$uc7' = 'sk$uc1' ),
inference(demodulation,[status(thm)],[d85,d70]) ).
cnf(d87,plain,
( inverse('sk$uc8') = 'sk$uc7'
| multiply(inverse('sk$uc8'),'sk$uc7') = 'sk$uc3' ),
inference(superposition,[status(thm)],[c12,d17]) ).
cnf(d88,plain,
( inverse('sk$uc8') = 'sk$uc7'
| multiply('sk$uc8','sk$uc1') = identity ),
inference(superposition,[status(thm)],[c0,c32]) ).
cnf(d89,plain,
( inverse('sk$uc8') = 'sk$uc7'
| multiply(identity,X0) = multiply('sk$uc8',multiply('sk$uc1',X0)) ),
inference(superposition,[status(thm)],[d88,c33]) ).
cnf(d90,plain,
( X0 = multiply('sk$uc8',multiply('sk$uc1',X0))
| inverse('sk$uc8') = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d89,c31]) ).
cnf(d91,plain,
( inverse('sk$uc8') = 'sk$uc7'
| inverse('sk$uc8') = 'sk$uc7'
| 'sk$uc7' = multiply('sk$uc8','sk$uc8') ),
inference(superposition,[status(thm)],[c6,d90]) ).
cnf(d92,plain,
( inverse('sk$uc8') = 'sk$uc7'
| multiply(inverse('sk$uc8'),'sk$uc7') = 'sk$uc8' ),
inference(superposition,[status(thm)],[d91,d17]) ).
cnf(d93,plain,
( inverse('sk$uc8') = 'sk$uc7'
| inverse('sk$uc8') = 'sk$uc7'
| 'sk$uc8' = 'sk$uc3' ),
inference(superposition,[status(thm)],[d92,d87]) ).
cnf(d94,plain,
( 'sk$uc8' = 'sk$uc3'
| 'sk$uc7' = inverse('sk$uc8') ),
inference(superposition,[status(thm)],[d93,d67]) ).
cnf(d95,plain,
( 'sk$uc7' = 'sk$uc2'
| 'sk$uc8' = 'sk$uc3' ),
inference(demodulation,[status(thm)],[d94,d71]) ).
cnf(d96,plain,
( 'sk$uc7' = 'sk$uc1'
| 'sk$uc8' = 'sk$uc3' ),
inference(demodulation,[status(thm)],[d95,d70]) ).
cnf(d97,plain,
( 'sk$uc7' = 'sk$uc1'
| 'sk$uc7' = 'sk$uc1'
| identity = inverse('sk$uc8') ),
inference(superposition,[status(thm)],[d96,d86]) ).
cnf(d98,plain,
( identity = 'sk$uc1'
| 'sk$uc7' = 'sk$uc1' ),
inference(demodulation,[status(thm)],[d97,d65]) ).
cnf(d99,plain,
( 'sk$uc7' = 'sk$uc1'
| 'sk$uc7' = 'sk$uc1'
| 'sk$uc3' = 'sk$uc1' ),
inference(superposition,[status(thm)],[d98,d77]) ).
cnf(d100,plain,
multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[d12,d17]) ).
cnf(d101,plain,
multiply('sk$uc2',multiply('sk$uc8',X0)) = X0,
inference(superposition,[status(thm)],[d31,d100]) ).
cnf(d102,plain,
multiply('sk$uc2',multiply('sk$uc8',X0)) = X0,
inference(superposition,[status(thm)],[d101,d7]) ).
cnf(d103,plain,
multiply('sk$uc1',multiply('sk$uc8',X0)) = X0,
inference(demodulation,[status(thm)],[d102,d70]) ).
cnf(d104,plain,
multiply('sk$uc1','sk$uc7') = 'sk$uc3',
inference(superposition,[status(thm)],[d40,d103]) ).
cnf(d105,plain,
( 'sk$uc7' = 'sk$uc1'
| multiply('sk$uc1',X0) = X0 ),
inference(superposition,[status(thm)],[d98,c31]) ).
cnf(d106,plain,
( 'sk$uc7' = 'sk$uc1'
| 'sk$uc7' = 'sk$uc3' ),
inference(superposition,[status(thm)],[d105,d104]) ).
cnf(d107,plain,
( 'sk$uc7' = 'sk$uc1'
| 'sk$uc7' = 'sk$uc1'
| 'sk$uc7' = 'sk$uc1' ),
inference(superposition,[status(thm)],[d106,d99]) ).
cnf(d108,plain,
'sk$uc7' = 'sk$uc2',
inference(demodulation,[status(thm)],[d70,d107]) ).
cnf(d109,plain,
'sk$uc8' = 'sk$uc2',
inference(demodulation,[status(thm)],[d108,d51]) ).
cnf(d110,plain,
X0 = multiply('sk$uc2',multiply('sk$uc8',X0)),
inference(superposition,[status(thm)],[d101,d7]) ).
cnf(d111,plain,
X0 = multiply('sk$uc1',multiply('sk$uc8',X0)),
inference(demodulation,[status(thm)],[d110,d70]) ).
cnf(d112,plain,
'sk$uc3' = multiply('sk$uc1','sk$uc7'),
inference(superposition,[status(thm)],[d40,d111]) ).
cnf(d113,plain,
'sk$uc3' = multiply('sk$uc7','sk$uc7'),
inference(demodulation,[status(thm)],[d112,d107]) ).
cnf(d114,plain,
'sk$uc3' = multiply('sk$uc8','sk$uc7'),
inference(demodulation,[status(thm)],[d113,d51]) ).
cnf(d115,plain,
'sk$uc3' = multiply('sk$uc8','sk$uc8'),
inference(demodulation,[status(thm)],[d114,d51]) ).
cnf(d116,plain,
multiply('sk$uc1','sk$uc8') = identity,
inference(superposition,[status(thm)],[d64,d33]) ).
cnf(d117,plain,
multiply('sk$uc7','sk$uc8') = identity,
inference(demodulation,[status(thm)],[d116,d107]) ).
cnf(d118,plain,
multiply('sk$uc8','sk$uc8') = identity,
inference(demodulation,[status(thm)],[d117,d51]) ).
cnf(d119,plain,
'sk$uc3' = identity,
inference(demodulation,[status(thm)],[d118,d115]) ).
cnf(d120,plain,
multiply('sk$uc3',X0) = X0,
inference(demodulation,[status(thm)],[c31,d119]) ).
cnf(d121,plain,
multiply(inverse(X0),X0) = 'sk$uc3',
inference(demodulation,[status(thm)],[c32,d119]) ).
cnf(d122,plain,
inverse('sk$uc3') = identity,
inference(demodulation,[status(thm)],[d80,d119]) ).
cnf(d123,plain,
inverse('sk$uc3') = 'sk$uc3',
inference(demodulation,[status(thm)],[d122,d119]) ).
cnf(d124,plain,
multiply('sk$uc3','sk$uc3') = 'sk$uc3',
inference(superposition,[status(thm)],[d123,d121]) ).
cnf(d125,plain,
'sk$uc3' = 'sk$uc3',
inference(demodulation,[status(thm)],[d124,d120]) ).
cnf(d126,plain,
( multiply('sk$uc4','sk$uc7') = 'sk$uc8'
| 'sk$uc3' = 'sk$uc8' ),
inference(demodulation,[status(thm)],[c8,d104]) ).
cnf(d127,plain,
( 'sk$uc3' = 'sk$uc8'
| inverse('sk$uc4') = 'sk$uc8' ),
inference(demodulation,[status(thm)],[c7,d104]) ).
cnf(d128,plain,
( 'sk$uc3' = 'sk$uc8'
| 'sk$uc4' = inverse('sk$uc8') ),
inference(superposition,[status(thm)],[d127,d19]) ).
cnf(d129,plain,
( 'sk$uc3' = 'sk$uc8'
| 'sk$uc4' = 'sk$uc1' ),
inference(demodulation,[status(thm)],[d128,d65]) ).
cnf(d130,plain,
( 'sk$uc3' = 'sk$uc8'
| 'sk$uc4' = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d129,d107]) ).
cnf(d131,plain,
( 'sk$uc3' = 'sk$uc8'
| 'sk$uc3' = 'sk$uc8'
| multiply('sk$uc7','sk$uc7') = 'sk$uc8' ),
inference(superposition,[status(thm)],[d130,d126]) ).
cnf(d132,plain,
( 'sk$uc3' = 'sk$uc8'
| multiply('sk$uc8','sk$uc7') = 'sk$uc8' ),
inference(demodulation,[status(thm)],[d131,d51]) ).
cnf(d133,plain,
( 'sk$uc3' = 'sk$uc8'
| multiply('sk$uc8','sk$uc8') = 'sk$uc8' ),
inference(demodulation,[status(thm)],[d132,d51]) ).
cnf(d134,plain,
( 'sk$uc3' = 'sk$uc8'
| 'sk$uc3' = 'sk$uc8' ),
inference(demodulation,[status(thm)],[d133,d115]) ).
cnf(d135,plain,
( 'sk$uc3' = 'sk$uc8'
| 'sk$uc3' = 'sk$uc8' ),
inference(superposition,[status(thm)],[d134,d125]) ).
cnf(d136,plain,
X0 = multiply(identity,X0),
inference(superposition,[status(thm)],[c31,d7]) ).
cnf(d137,plain,
X0 = multiply('sk$uc3',X0),
inference(demodulation,[status(thm)],[d136,d119]) ).
cnf(d138,plain,
X0 = multiply('sk$uc8',X0),
inference(demodulation,[status(thm)],[d137,d135]) ).
cnf(d139,plain,
X0 = multiply(X0,'sk$uc3'),
inference(demodulation,[status(thm)],[d41,d119]) ).
cnf(d140,plain,
X0 = multiply(X0,'sk$uc8'),
inference(demodulation,[status(thm)],[d139,d135]) ).
cnf(d141,plain,
( multiply('sk$uc8',X2) != 'sk$uc7'
| multiply(X1,'sk$uc8') != X2
| multiply(X0,'sk$uc7') != 'sk$uc8'
| 'sk$uc2' != 'sk$uc7'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d1,d71]) ).
cnf(d142,plain,
( 'sk$uc2' != 'sk$uc7'
| multiply('sk$uc8',X2) != 'sk$uc7'
| multiply(X1,'sk$uc7') != 'sk$uc8'
| X0 != X2
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d141,d140]) ).
cnf(d143,plain,
( 'sk$uc2' != 'sk$uc7'
| multiply('sk$uc8',X2) != 'sk$uc7'
| multiply(X1,'sk$uc8') != 'sk$uc8'
| X0 != X2
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d142,d51]) ).
cnf(d144,plain,
( 'sk$uc2' != 'sk$uc7'
| multiply('sk$uc8',X2) != 'sk$uc7'
| X0 != 'sk$uc8'
| X1 != X2
| inverse(X0) != 'sk$uc8'
| inverse(X1) != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d143,d140]) ).
cnf(d145,plain,
( 'sk$uc2' != 'sk$uc7'
| X0 != 'sk$uc7'
| X2 != 'sk$uc8'
| X1 != X0
| inverse(X2) != 'sk$uc8'
| inverse(X1) != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d144,d138]) ).
cnf(d146,plain,
( 'sk$uc2' != 'sk$uc7'
| X2 != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != X2
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d145,d51]) ).
cnf(d147,plain,
( 'sk$uc8' != 'sk$uc7'
| X2 != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != X2
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d146,d109]) ).
cnf(d148,plain,
( 'sk$uc8' != 'sk$uc8'
| X2 != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != X2
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d147,d51]) ).
cnf(d149,plain,
'sk$uc8' = identity,
inference(demodulation,[status(thm)],[d119,d135]) ).
cnf(d150,plain,
multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(superposition,[status(thm)],[c33,d7]) ).
cnf(d151,plain,
multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = identity,
inference(superposition,[status(thm)],[d26,d150]) ).
cnf(d152,plain,
multiply(inverse(X0),identity) = multiply(X1,inverse(multiply(X0,X1))),
inference(superposition,[status(thm)],[d151,d17]) ).
cnf(d153,plain,
multiply(inverse(X0),'sk$uc8') = multiply(X1,inverse(multiply(X0,X1))),
inference(demodulation,[status(thm)],[d152,d149]) ).
cnf(d154,plain,
inverse(X0) = multiply(X1,inverse(multiply(X0,X1))),
inference(demodulation,[status(thm)],[d153,d140]) ).
cnf(d155,plain,
multiply(inverse(X0),inverse(X1)) = inverse(multiply(X1,X0)),
inference(superposition,[status(thm)],[d154,d17]) ).
cnf(d156,plain,
multiply(inverse(X1),X0) = inverse(multiply(inverse(X0),X1)),
inference(superposition,[status(thm)],[d19,d155]) ).
cnf(d157,plain,
X2 = multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))),
inference(superposition,[status(thm)],[c33,d11]) ).
cnf(d158,plain,
X3 = multiply(inverse(multiply(X0,multiply(X1,X2))),multiply(multiply(X0,X1),multiply(X2,X3))),
inference(superposition,[status(thm)],[d150,d157]) ).
cnf(d159,plain,
X3 = multiply(inverse(multiply(X0,multiply(X1,X2))),multiply(X0,multiply(X1,multiply(X2,X3)))),
inference(demodulation,[status(thm)],[d158,c33]) ).
cnf(d160,plain,
multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[status(thm)],[d150,d17]) ).
cnf(d161,plain,
X2 = multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X1))),X2),
inference(superposition,[status(thm)],[d160,d159]) ).
cnf(d162,plain,
X2 = multiply(multiply(inverse(multiply(X0,X1)),multiply(X0,X1)),X2),
inference(demodulation,[status(thm)],[d161,d156]) ).
cnf(d163,plain,
X2 = multiply(inverse(multiply(X0,X1)),multiply(multiply(X0,X1),X2)),
inference(demodulation,[status(thm)],[d162,c33]) ).
cnf(d164,plain,
X2 = X2,
inference(demodulation,[status(thm)],[d163,d17]) ).
cnf(d165,plain,
( X2 != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != X2
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8' ),
inference(resolution,[status(thm)],[d164,d148]) ).
cnf(d166,plain,
inverse('sk$uc7') = 'sk$uc8',
inference(demodulation,[status(thm)],[d64,d107]) ).
cnf(d167,plain,
inverse('sk$uc8') = 'sk$uc8',
inference(demodulation,[status(thm)],[d166,d51]) ).
cnf(d168,plain,
( inverse(X1) != 'sk$uc8'
| 'sk$uc8' != X0
| X1 != 'sk$uc8'
| X0 != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8' ),
inference(superposition,[status(thm)],[d167,d165]) ).
cnf(d169,plain,
( 'sk$uc8' != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(factoring,[status(thm)],[d168]) ).
cnf(d170,plain,
( inverse(X0) != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(resolution,[status(thm)],[d164,d169]) ).
cnf(d171,plain,
( 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8' ),
inference(superposition,[status(thm)],[d167,d170]) ).
cnf(d172,plain,
$false,
inference(resolution,[status(thm)],[d164,d171]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP229-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/10.63 % Computer : n006.cluster.edu
% 0.15/10.63 % Model : x86_64 x86_64
% 0.15/10.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/10.63 % Memory : 8046.5625MB
% 0.15/10.63 % OS : Linux 6.8.0-71-generic
% 0.15/10.63 % CPULimit : 300
% 0.15/10.63 % WCLimit : 300
% 0.15/10.63 % DateTime : Fri Sep 25 14:39:37 UTC 2026
% 0.15/10.64 % CPUTime :
% 0.15/10.64 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 91.80/25.81 % SZS status Unsatisfiable for theBenchmark.p
% 91.80/25.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------