%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP314-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 146.20s 45.18s
% Output : CNFRefutation 146.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 20
% Syntax : Number of clauses : 189 ( 56 unt; 108 nHn; 126 RR)
% Number of literals : 527 ( 526 equ; 221 neg)
% Maximal clause size : 11 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 138 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this_1,negated_conjecture,
multiply('sk$uc7','sk$uc8') = 'sk$uc6' ).
cnf(prove_this_3,negated_conjecture,
( multiply('sk$uc4','sk$uc7') = 'sk$uc8'
| multiply('sk$uc1','sk$uc8') = 'sk$uc7' ) ).
cnf(prove_this_5,negated_conjecture,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| multiply('sk$uc1','sk$uc8') = 'sk$uc7' ) ).
cnf(prove_this_6,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc8' ) ).
cnf(prove_this_7,negated_conjecture,
( multiply('sk$uc4','sk$uc7') = 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc8' ) ).
cnf(prove_this_8,negated_conjecture,
( inverse('sk$uc5') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc8' ) ).
cnf(prove_this_9,negated_conjecture,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc8' ) ).
cnf(prove_this_12,negated_conjecture,
( inverse('sk$uc5') = 'sk$uc7'
| multiply('sk$uc2','sk$uc7') = 'sk$uc6' ) ).
cnf(prove_this_14,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc8'
| inverse('sk$uc2') = 'sk$uc7' ) ).
cnf(prove_this_16,negated_conjecture,
( inverse('sk$uc5') = 'sk$uc7'
| inverse('sk$uc2') = 'sk$uc7' ) ).
cnf(prove_this_18,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc8'
| multiply('sk$uc3','sk$uc7') = 'sk$uc8' ) ).
cnf(prove_this_20,negated_conjecture,
( inverse('sk$uc5') = 'sk$uc7'
| multiply('sk$uc3','sk$uc7') = 'sk$uc8' ) ).
cnf(prove_this_21,negated_conjecture,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| multiply('sk$uc3','sk$uc7') = 'sk$uc8' ) ).
cnf(prove_this_22,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc8'
| inverse('sk$uc3') = 'sk$uc7' ) ).
cnf(prove_this_24,negated_conjecture,
( inverse('sk$uc5') = 'sk$uc7'
| inverse('sk$uc3') = 'sk$uc7' ) ).
cnf(prove_this_25,negated_conjecture,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| inverse('sk$uc3') = 'sk$uc7' ) ).
cnf(prove_this_26,negated_conjecture,
( multiply(X4,'sk$uc6') != 'sk$uc7'
| inverse(X4) != 'sk$uc7'
| multiply(X3,'sk$uc7') != 'sk$uc8'
| inverse(X3) != 'sk$uc8'
| inverse(X2) != 'sk$uc7'
| multiply(X2,'sk$uc7') != 'sk$uc8'
| inverse(X1) != 'sk$uc7'
| multiply(X1,'sk$uc7') != 'sk$uc6'
| inverse(X0) != 'sk$uc8'
| multiply(X0,'sk$uc8') != 'sk$uc7'
| multiply('sk$uc7','sk$uc8') != 'sk$uc6' ) ).
cnf(left_identity,axiom,
multiply(identity,X0) = X0 ).
cnf(left_inverse,axiom,
multiply(inverse(X0),X0) = identity ).
cnf(associativity,axiom,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)) ).
cnf(c0,plain,
multiply('sk$uc7','sk$uc8') = 'sk$uc6',
inference(clausification,[status(esa)],[prove_this_1]) ).
cnf(c2,plain,
( multiply('sk$uc4','sk$uc7') = 'sk$uc8'
| multiply('sk$uc1','sk$uc8') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_3]) ).
cnf(c4,plain,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| multiply('sk$uc1','sk$uc8') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_5]) ).
cnf(c5,plain,
( inverse('sk$uc4') = 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_6]) ).
cnf(c6,plain,
( multiply('sk$uc4','sk$uc7') = 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_7]) ).
cnf(c7,plain,
( inverse('sk$uc5') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_8]) ).
cnf(c8,plain,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_9]) ).
cnf(c11,plain,
( inverse('sk$uc5') = 'sk$uc7'
| multiply('sk$uc2','sk$uc7') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_12]) ).
cnf(c13,plain,
( inverse('sk$uc4') = 'sk$uc8'
| inverse('sk$uc2') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_14]) ).
cnf(c15,plain,
( inverse('sk$uc5') = 'sk$uc7'
| inverse('sk$uc2') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_16]) ).
cnf(c17,plain,
( inverse('sk$uc4') = 'sk$uc8'
| multiply('sk$uc3','sk$uc7') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_18]) ).
cnf(c19,plain,
( inverse('sk$uc5') = 'sk$uc7'
| multiply('sk$uc3','sk$uc7') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_20]) ).
cnf(c20,plain,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| multiply('sk$uc3','sk$uc7') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_21]) ).
cnf(c21,plain,
( inverse('sk$uc4') = 'sk$uc8'
| inverse('sk$uc3') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_22]) ).
cnf(c23,plain,
( inverse('sk$uc5') = 'sk$uc7'
| inverse('sk$uc3') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_24]) ).
cnf(c24,plain,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| inverse('sk$uc3') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_25]) ).
cnf(c25,plain,
( multiply(X4,'sk$uc8') != 'sk$uc7'
| inverse(X3) != 'sk$uc8'
| inverse(X1) != 'sk$uc7'
| inverse(X0) != 'sk$uc7'
| inverse(X4) != 'sk$uc8'
| multiply('sk$uc7','sk$uc8') != 'sk$uc6'
| multiply(X2,'sk$uc7') != 'sk$uc8'
| multiply(X3,'sk$uc7') != 'sk$uc8'
| inverse(X2) != 'sk$uc7'
| multiply(X1,'sk$uc6') != 'sk$uc7'
| multiply(X0,'sk$uc7') != 'sk$uc6' ),
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(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c27,c28]) ).
cnf(d1,plain,
multiply(inverse(X1),multiply(X1,X0)) = X0,
inference(demodulation,[status(thm)],[d0,c26]) ).
cnf(d2,plain,
multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[d1,d1]) ).
cnf(d3,plain,
multiply(identity,multiply(X0,X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c26,c28]) ).
cnf(d4,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d3,c26]) ).
cnf(d5,plain,
identity = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[c27,d4]) ).
cnf(d6,plain,
multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
X1 = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[status(thm)],[d1,d4]) ).
cnf(d9,plain,
multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[d2,c27]) ).
cnf(d10,plain,
inverse(X0) = multiply(inverse(X0),identity),
inference(superposition,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
inverse(X0) = inverse(X0),
inference(demodulation,[status(thm)],[d10,d7]) ).
cnf(d12,plain,
'sk$uc6' = multiply('sk$uc7','sk$uc8'),
inference(superposition,[status(thm)],[c0,d4]) ).
cnf(d13,plain,
multiply(inverse('sk$uc7'),'sk$uc6') = 'sk$uc8',
inference(superposition,[status(thm)],[d12,d1]) ).
cnf(d14,plain,
inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[status(thm)],[d7,d2]) ).
cnf(d15,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d14,d7]) ).
cnf(d16,plain,
multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d17,plain,
( inverse('sk$uc5') = 'sk$uc7'
| multiply('sk$uc3',multiply('sk$uc7',X0)) = X0 ),
inference(superposition,[status(thm)],[c23,d16]) ).
cnf(d18,plain,
multiply('sk$uc7',multiply('sk$uc8',X0)) = multiply('sk$uc6',X0),
inference(superposition,[status(thm)],[c0,c28]) ).
cnf(d19,plain,
( inverse('sk$uc5') = 'sk$uc7'
| multiply('sk$uc7','sk$uc3') = identity ),
inference(superposition,[status(thm)],[c23,c27]) ).
cnf(d20,plain,
( inverse('sk$uc5') = 'sk$uc7'
| multiply('sk$uc7',multiply('sk$uc3',X0)) = multiply(identity,X0) ),
inference(superposition,[status(thm)],[d19,c28]) ).
cnf(d21,plain,
( inverse('sk$uc5') = 'sk$uc7'
| multiply('sk$uc7',multiply('sk$uc3',X0)) = X0 ),
inference(demodulation,[status(thm)],[d20,c26]) ).
cnf(d22,plain,
( inverse('sk$uc5') = 'sk$uc7'
| multiply('sk$uc3',multiply('sk$uc7',X0)) = multiply('sk$uc8',X0) ),
inference(superposition,[status(thm)],[c19,c28]) ).
cnf(d23,plain,
( inverse('sk$uc5') = 'sk$uc7'
| inverse('sk$uc5') = 'sk$uc7'
| multiply('sk$uc7',multiply('sk$uc8',X0)) = multiply('sk$uc7',X0) ),
inference(superposition,[status(thm)],[d22,d21]) ).
cnf(d24,plain,
( inverse('sk$uc5') = 'sk$uc7'
| multiply('sk$uc6',X0) = multiply('sk$uc7',X0) ),
inference(demodulation,[status(thm)],[d23,d18]) ).
cnf(d25,plain,
( inverse('sk$uc5') = 'sk$uc7'
| multiply('sk$uc2',multiply('sk$uc7',X0)) = multiply('sk$uc6',X0) ),
inference(superposition,[status(thm)],[c11,c28]) ).
cnf(d26,plain,
( inverse('sk$uc5') = 'sk$uc7'
| multiply('sk$uc2',multiply('sk$uc7',X0)) = X0 ),
inference(superposition,[status(thm)],[c15,d16]) ).
cnf(d27,plain,
( inverse('sk$uc5') = 'sk$uc7'
| inverse('sk$uc5') = 'sk$uc7'
| X0 = multiply('sk$uc6',X0) ),
inference(superposition,[status(thm)],[d26,d25]) ).
cnf(d28,plain,
( inverse('sk$uc5') = 'sk$uc7'
| inverse('sk$uc5') = 'sk$uc7'
| X0 = multiply('sk$uc7',X0) ),
inference(superposition,[status(thm)],[d27,d24]) ).
cnf(d29,plain,
( inverse('sk$uc5') = 'sk$uc7'
| inverse('sk$uc5') = 'sk$uc7'
| multiply('sk$uc3',X0) = X0 ),
inference(superposition,[status(thm)],[d28,d17]) ).
cnf(d30,plain,
( inverse('sk$uc5') = 'sk$uc7'
| inverse('sk$uc5') = 'sk$uc7'
| 'sk$uc7' = 'sk$uc8' ),
inference(superposition,[status(thm)],[d29,c19]) ).
cnf(d31,plain,
( 'sk$uc7' = 'sk$uc8'
| inverse('sk$uc7') = 'sk$uc5' ),
inference(superposition,[status(thm)],[d30,d15]) ).
cnf(d32,plain,
( 'sk$uc7' = 'sk$uc8'
| multiply('sk$uc5','sk$uc6') = 'sk$uc8' ),
inference(superposition,[status(thm)],[d31,d13]) ).
cnf(d33,plain,
X0 = multiply(identity,X0),
inference(superposition,[status(thm)],[c26,d4]) ).
cnf(d34,plain,
multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d2,d7]) ).
cnf(d35,plain,
X0 = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d34,d7]) ).
cnf(d36,plain,
( inverse('sk$uc3') = 'sk$uc7'
| 'sk$uc7' = multiply('sk$uc5','sk$uc6') ),
inference(superposition,[status(thm)],[c24,d4]) ).
cnf(d37,plain,
( 'sk$uc7' = 'sk$uc8'
| inverse('sk$uc3') = 'sk$uc7'
| 'sk$uc7' = 'sk$uc8' ),
inference(superposition,[status(thm)],[d32,d36]) ).
cnf(d38,plain,
( 'sk$uc7' = 'sk$uc8'
| 'sk$uc3' = inverse('sk$uc7') ),
inference(superposition,[status(thm)],[d37,d35]) ).
cnf(d39,plain,
multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[d33,d1]) ).
cnf(d40,plain,
multiply(inverse(inverse(identity)),X0) = X0,
inference(superposition,[status(thm)],[d39,d1]) ).
cnf(d41,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[d40,c27]) ).
cnf(d42,plain,
identity = multiply(X0,inverse(X0)),
inference(superposition,[status(thm)],[d2,d5]) ).
cnf(d43,plain,
( inverse('sk$uc1') = 'sk$uc8'
| multiply('sk$uc7','sk$uc5') = identity ),
inference(superposition,[status(thm)],[c7,c27]) ).
cnf(d44,plain,
( inverse('sk$uc1') = 'sk$uc8'
| multiply('sk$uc7',multiply('sk$uc5',X0)) = multiply(identity,X0) ),
inference(superposition,[status(thm)],[d43,c28]) ).
cnf(d45,plain,
( inverse('sk$uc1') = 'sk$uc8'
| multiply('sk$uc7',multiply('sk$uc5',X0)) = X0 ),
inference(demodulation,[status(thm)],[d44,c26]) ).
cnf(d46,plain,
( inverse('sk$uc1') = 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc8'
| multiply('sk$uc7','sk$uc7') = 'sk$uc6' ),
inference(superposition,[status(thm)],[c8,d45]) ).
cnf(d47,plain,
( inverse('sk$uc1') = 'sk$uc8'
| 'sk$uc7' = multiply(inverse('sk$uc7'),'sk$uc6') ),
inference(superposition,[status(thm)],[d46,d8]) ).
cnf(d48,plain,
( inverse('sk$uc1') = 'sk$uc8'
| 'sk$uc7' = 'sk$uc8' ),
inference(demodulation,[status(thm)],[d47,d13]) ).
cnf(d49,plain,
( 'sk$uc7' = 'sk$uc8'
| identity = multiply('sk$uc1','sk$uc8') ),
inference(superposition,[status(thm)],[d48,d42]) ).
cnf(d50,plain,
( multiply('sk$uc1','sk$uc8') = 'sk$uc7'
| 'sk$uc7' = multiply('sk$uc5','sk$uc6') ),
inference(superposition,[status(thm)],[c4,d4]) ).
cnf(d51,plain,
( 'sk$uc7' = 'sk$uc8'
| multiply('sk$uc1','sk$uc8') = 'sk$uc7'
| 'sk$uc7' = 'sk$uc8' ),
inference(superposition,[status(thm)],[d32,d50]) ).
cnf(d52,plain,
( 'sk$uc7' = 'sk$uc8'
| 'sk$uc7' = 'sk$uc8'
| identity = 'sk$uc7' ),
inference(superposition,[status(thm)],[d51,d49]) ).
cnf(d53,plain,
( 'sk$uc7' = 'sk$uc8'
| inverse('sk$uc7') = identity ),
inference(superposition,[status(thm)],[d52,d41]) ).
cnf(d54,plain,
( 'sk$uc7' = 'sk$uc8'
| 'sk$uc7' = 'sk$uc8'
| 'sk$uc3' = identity ),
inference(superposition,[status(thm)],[d53,d38]) ).
cnf(d55,plain,
( 'sk$uc7' = 'sk$uc8'
| X0 = multiply('sk$uc3',X0) ),
inference(superposition,[status(thm)],[d54,d33]) ).
cnf(d56,plain,
( 'sk$uc7' = 'sk$uc8'
| multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| 'sk$uc7' = 'sk$uc8' ),
inference(superposition,[status(thm)],[d55,c20]) ).
cnf(d57,plain,
( 'sk$uc7' = 'sk$uc8'
| 'sk$uc7' = 'sk$uc8'
| 'sk$uc7' = 'sk$uc8' ),
inference(superposition,[status(thm)],[d56,d32]) ).
cnf(d58,plain,
( inverse('sk$uc4') = 'sk$uc8'
| 'sk$uc8' = multiply('sk$uc3','sk$uc7') ),
inference(superposition,[status(thm)],[c17,d4]) ).
cnf(d59,plain,
( inverse('sk$uc4') = 'sk$uc8'
| multiply('sk$uc3','sk$uc7') = identity ),
inference(superposition,[status(thm)],[c21,d9]) ).
cnf(d60,plain,
( inverse('sk$uc4') = 'sk$uc8'
| inverse('sk$uc4') = 'sk$uc8'
| 'sk$uc8' = identity ),
inference(superposition,[status(thm)],[d59,d58]) ).
cnf(d61,plain,
( 'sk$uc8' = identity
| multiply('sk$uc4','sk$uc8') = identity ),
inference(superposition,[status(thm)],[d60,d9]) ).
cnf(d62,plain,
( 'sk$uc8' = identity
| multiply('sk$uc4','sk$uc7') = identity ),
inference(demodulation,[status(thm)],[d61,d57]) ).
cnf(d63,plain,
( 'sk$uc7' = identity
| multiply('sk$uc4','sk$uc7') = identity ),
inference(demodulation,[status(thm)],[d62,d57]) ).
cnf(d64,plain,
( inverse('sk$uc1') = 'sk$uc8'
| multiply('sk$uc4',multiply('sk$uc7',X0)) = multiply('sk$uc8',X0) ),
inference(superposition,[status(thm)],[c6,c28]) ).
cnf(d65,plain,
( inverse('sk$uc1') = 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc8'
| multiply('sk$uc4',X0) = multiply('sk$uc8',multiply('sk$uc5',X0)) ),
inference(superposition,[status(thm)],[d45,d64]) ).
cnf(d66,plain,
( inverse('sk$uc5') = 'sk$uc7'
| 'sk$uc8' = multiply('sk$uc3','sk$uc7') ),
inference(superposition,[status(thm)],[c19,d4]) ).
cnf(d67,plain,
( inverse('sk$uc5') = 'sk$uc7'
| multiply('sk$uc3','sk$uc7') = identity ),
inference(superposition,[status(thm)],[c23,d9]) ).
cnf(d68,plain,
( inverse('sk$uc5') = 'sk$uc7'
| inverse('sk$uc5') = 'sk$uc7'
| 'sk$uc8' = identity ),
inference(superposition,[status(thm)],[d67,d66]) ).
cnf(d69,plain,
( 'sk$uc8' = identity
| identity = multiply('sk$uc5','sk$uc7') ),
inference(superposition,[status(thm)],[d68,d42]) ).
cnf(d70,plain,
( 'sk$uc8' = identity
| inverse('sk$uc1') = 'sk$uc8'
| multiply('sk$uc4','sk$uc7') = multiply('sk$uc8',identity) ),
inference(superposition,[status(thm)],[d69,d65]) ).
cnf(d71,plain,
( inverse('sk$uc1') = 'sk$uc8'
| 'sk$uc8' = identity
| multiply('sk$uc4','sk$uc7') = 'sk$uc8' ),
inference(demodulation,[status(thm)],[d70,d7]) ).
cnf(d72,plain,
( inverse('sk$uc1') = 'sk$uc8'
| 'sk$uc8' = identity
| multiply('sk$uc4','sk$uc7') = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d71,d57]) ).
cnf(d73,plain,
( inverse('sk$uc1') = 'sk$uc8'
| 'sk$uc7' = identity
| multiply('sk$uc4','sk$uc7') = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d72,d57]) ).
cnf(d74,plain,
( inverse('sk$uc1') = 'sk$uc7'
| 'sk$uc7' = identity
| multiply('sk$uc4','sk$uc7') = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d73,d57]) ).
cnf(d75,plain,
( inverse('sk$uc1') = 'sk$uc7'
| 'sk$uc7' = identity
| 'sk$uc7' = identity
| 'sk$uc7' = identity ),
inference(superposition,[status(thm)],[d74,d63]) ).
cnf(d76,plain,
( 'sk$uc7' = identity
| 'sk$uc7' = inverse('sk$uc1') ),
inference(superposition,[status(thm)],[d75,d11]) ).
cnf(d77,plain,
( inverse('sk$uc4') = 'sk$uc8'
| identity = multiply('sk$uc2','sk$uc7') ),
inference(superposition,[status(thm)],[c13,d42]) ).
cnf(d78,plain,
( inverse('sk$uc4') = 'sk$uc8'
| multiply('sk$uc2',multiply('sk$uc7',X0)) = X0 ),
inference(superposition,[status(thm)],[c13,d16]) ).
cnf(d79,plain,
multiply('sk$uc6',X0) = multiply('sk$uc7',multiply('sk$uc8',X0)),
inference(superposition,[status(thm)],[d18,d4]) ).
cnf(d80,plain,
( inverse('sk$uc4') = 'sk$uc8'
| multiply('sk$uc8','sk$uc1') = identity ),
inference(superposition,[status(thm)],[c5,c27]) ).
cnf(d81,plain,
( inverse('sk$uc4') = 'sk$uc8'
| multiply('sk$uc6','sk$uc1') = multiply('sk$uc7',identity) ),
inference(superposition,[status(thm)],[d80,d79]) ).
cnf(d82,plain,
( inverse('sk$uc4') = 'sk$uc8'
| multiply('sk$uc6','sk$uc1') = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d81,d7]) ).
cnf(d83,plain,
( inverse('sk$uc4') = 'sk$uc8'
| multiply('sk$uc7','sk$uc3') = identity ),
inference(superposition,[status(thm)],[c21,c27]) ).
cnf(d84,plain,
( inverse('sk$uc4') = 'sk$uc8'
| multiply('sk$uc7',multiply('sk$uc3',X0)) = multiply(identity,X0) ),
inference(superposition,[status(thm)],[d83,c28]) ).
cnf(d85,plain,
( inverse('sk$uc4') = 'sk$uc8'
| multiply('sk$uc7',multiply('sk$uc3',X0)) = X0 ),
inference(demodulation,[status(thm)],[d84,c26]) ).
cnf(d86,plain,
( inverse('sk$uc4') = 'sk$uc8'
| multiply('sk$uc3',multiply('sk$uc7',X0)) = multiply('sk$uc8',X0) ),
inference(superposition,[status(thm)],[c17,c28]) ).
cnf(d87,plain,
( inverse('sk$uc4') = 'sk$uc8'
| inverse('sk$uc4') = 'sk$uc8'
| multiply('sk$uc7',multiply('sk$uc8',X0)) = multiply('sk$uc7',X0) ),
inference(superposition,[status(thm)],[d86,d85]) ).
cnf(d88,plain,
( inverse('sk$uc4') = 'sk$uc8'
| multiply('sk$uc6',X0) = multiply('sk$uc7',X0) ),
inference(demodulation,[status(thm)],[d87,d18]) ).
cnf(d89,plain,
( inverse('sk$uc4') = 'sk$uc8'
| inverse('sk$uc4') = 'sk$uc8'
| multiply('sk$uc7','sk$uc1') = 'sk$uc7' ),
inference(superposition,[status(thm)],[d88,d82]) ).
cnf(d90,plain,
( inverse('sk$uc4') = 'sk$uc8'
| inverse('sk$uc4') = 'sk$uc8'
| multiply('sk$uc2','sk$uc7') = 'sk$uc1' ),
inference(superposition,[status(thm)],[d89,d78]) ).
cnf(d91,plain,
( inverse('sk$uc4') = 'sk$uc8'
| inverse('sk$uc4') = 'sk$uc8'
| identity = 'sk$uc1' ),
inference(superposition,[status(thm)],[d90,d77]) ).
cnf(d92,plain,
( identity = 'sk$uc1'
| identity = multiply('sk$uc8','sk$uc4') ),
inference(superposition,[status(thm)],[d91,d5]) ).
cnf(d93,plain,
( identity = 'sk$uc1'
| identity = multiply('sk$uc7','sk$uc4') ),
inference(demodulation,[status(thm)],[d92,d57]) ).
cnf(d94,plain,
( multiply('sk$uc4','sk$uc7') = 'sk$uc8'
| multiply('sk$uc1',multiply('sk$uc8',X0)) = multiply('sk$uc7',X0) ),
inference(superposition,[status(thm)],[c2,c28]) ).
cnf(d95,plain,
( 'sk$uc8' = identity
| identity = multiply('sk$uc8','sk$uc4') ),
inference(superposition,[status(thm)],[d60,d5]) ).
cnf(d96,plain,
( 'sk$uc8' = identity
| multiply('sk$uc4','sk$uc7') = 'sk$uc8'
| multiply('sk$uc1',identity) = multiply('sk$uc7','sk$uc4') ),
inference(superposition,[status(thm)],[d95,d94]) ).
cnf(d97,plain,
( 'sk$uc8' = identity
| multiply('sk$uc1',identity) = multiply('sk$uc7','sk$uc4')
| multiply('sk$uc4','sk$uc7') = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d96,d57]) ).
cnf(d98,plain,
( 'sk$uc8' = identity
| 'sk$uc1' = multiply('sk$uc7','sk$uc4')
| multiply('sk$uc4','sk$uc7') = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d97,d7]) ).
cnf(d99,plain,
( 'sk$uc7' = identity
| 'sk$uc1' = multiply('sk$uc7','sk$uc4')
| multiply('sk$uc4','sk$uc7') = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d98,d57]) ).
cnf(d100,plain,
( 'sk$uc7' = identity
| 'sk$uc1' = multiply('sk$uc7','sk$uc4')
| 'sk$uc7' = identity
| 'sk$uc7' = identity ),
inference(superposition,[status(thm)],[d99,d63]) ).
cnf(d101,plain,
( 'sk$uc7' = identity
| identity = 'sk$uc1'
| identity = 'sk$uc1' ),
inference(superposition,[status(thm)],[d100,d93]) ).
cnf(d102,plain,
( 'sk$uc7' = identity
| inverse('sk$uc1') = identity ),
inference(superposition,[status(thm)],[d101,d41]) ).
cnf(d103,plain,
( 'sk$uc7' = identity
| 'sk$uc7' = identity
| 'sk$uc7' = identity ),
inference(superposition,[status(thm)],[d102,d76]) ).
cnf(d104,plain,
inverse('sk$uc7') = identity,
inference(demodulation,[status(thm)],[d41,d103]) ).
cnf(d105,plain,
inverse('sk$uc7') = 'sk$uc7',
inference(demodulation,[status(thm)],[d104,d103]) ).
cnf(d106,plain,
X0 = multiply(inverse(inverse(X0)),identity),
inference(superposition,[status(thm)],[d6,d4]) ).
cnf(d107,plain,
X0 = multiply(X0,identity),
inference(demodulation,[status(thm)],[d106,d2]) ).
cnf(d108,plain,
X0 = multiply(X0,'sk$uc7'),
inference(demodulation,[status(thm)],[d107,d103]) ).
cnf(d109,plain,
multiply('sk$uc7','sk$uc7') = 'sk$uc6',
inference(demodulation,[status(thm)],[c0,d57]) ).
cnf(d110,plain,
'sk$uc7' = 'sk$uc6',
inference(demodulation,[status(thm)],[d109,d108]) ).
cnf(d111,plain,
( inverse(X4) != 'sk$uc7'
| inverse(X3) != 'sk$uc8'
| inverse(X2) != 'sk$uc8'
| inverse(X1) != 'sk$uc7'
| inverse(X0) != 'sk$uc7'
| 'sk$uc6' != 'sk$uc6'
| multiply(X4,'sk$uc6') != 'sk$uc7'
| multiply(X3,'sk$uc7') != 'sk$uc8'
| multiply(X2,'sk$uc8') != 'sk$uc7'
| multiply(X1,'sk$uc7') != 'sk$uc8'
| multiply(X0,'sk$uc7') != 'sk$uc6' ),
inference(demodulation,[status(thm)],[c25,c0]) ).
cnf(d112,plain,
( inverse(X3) != 'sk$uc7'
| inverse(X2) != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc7'
| inverse(identity) != 'sk$uc7'
| 'sk$uc6' != 'sk$uc6'
| multiply(X3,'sk$uc6') != 'sk$uc7'
| multiply(X2,'sk$uc7') != 'sk$uc8'
| multiply(X1,'sk$uc8') != 'sk$uc7'
| multiply(X0,'sk$uc7') != 'sk$uc8'
| 'sk$uc7' != 'sk$uc6' ),
inference(superposition,[status(thm)],[c26,d111]) ).
cnf(d113,plain,
( identity != 'sk$uc7'
| inverse(X3) != 'sk$uc7'
| inverse(X2) != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc7'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc7' != 'sk$uc6'
| multiply(X3,'sk$uc7') != 'sk$uc8'
| multiply(X2,'sk$uc8') != 'sk$uc7'
| multiply(X1,'sk$uc7') != 'sk$uc8'
| multiply(X0,'sk$uc6') != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d112,d41]) ).
cnf(d114,plain,
( identity != 'sk$uc7'
| inverse(X2) != 'sk$uc7'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| inverse(identity) != 'sk$uc7'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc7' != 'sk$uc6'
| multiply(X2,'sk$uc7') != 'sk$uc8'
| multiply(X1,'sk$uc8') != 'sk$uc7'
| multiply(X0,'sk$uc7') != 'sk$uc8'
| 'sk$uc6' != 'sk$uc7' ),
inference(superposition,[status(thm)],[d33,d113]) ).
cnf(d115,plain,
( identity != 'sk$uc7'
| identity != 'sk$uc7'
| inverse(X2) != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc7'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc6'
| multiply(X2,'sk$uc7') != 'sk$uc8'
| multiply(X1,'sk$uc8') != 'sk$uc7'
| multiply(X0,'sk$uc7') != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d114,d41]) ).
cnf(d116,plain,
multiply('sk$uc7','sk$uc8') = multiply('sk$uc6',identity),
inference(superposition,[status(thm)],[d7,d18]) ).
cnf(d117,plain,
'sk$uc6' = multiply('sk$uc6',identity),
inference(demodulation,[status(thm)],[d116,c0]) ).
cnf(d118,plain,
'sk$uc6' = 'sk$uc6',
inference(demodulation,[status(thm)],[d117,d7]) ).
cnf(d119,plain,
( identity != 'sk$uc7'
| identity != 'sk$uc7'
| inverse(X2) != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc7'
| 'sk$uc6' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc6'
| multiply(X2,'sk$uc7') != 'sk$uc8'
| multiply(X1,'sk$uc8') != 'sk$uc7'
| multiply(X0,'sk$uc7') != 'sk$uc8' ),
inference(resolution,[status(thm)],[d118,d115]) ).
cnf(d120,plain,
( identity != 'sk$uc7'
| inverse(identity) != 'sk$uc7'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc6' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc6'
| multiply(X1,'sk$uc8') != 'sk$uc7'
| multiply(X0,'sk$uc7') != 'sk$uc8'
| 'sk$uc7' != 'sk$uc8' ),
inference(superposition,[status(thm)],[d33,d119]) ).
cnf(d121,plain,
( identity != 'sk$uc7'
| inverse(identity) != 'sk$uc7'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc6' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc6'
| 'sk$uc7' != 'sk$uc8'
| multiply(X1,'sk$uc7') != 'sk$uc8'
| multiply(X0,'sk$uc7') != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d120,d57]) ).
cnf(d122,plain,
( identity != 'sk$uc7'
| inverse(identity) != 'sk$uc7'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc6' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc6'
| 'sk$uc7' != 'sk$uc8'
| multiply(X1,'sk$uc7') != 'sk$uc8'
| X0 != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d121,d108]) ).
cnf(d123,plain,
( identity != 'sk$uc7'
| inverse(identity) != 'sk$uc7'
| inverse(X0) != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| 'sk$uc6' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc6'
| 'sk$uc7' != 'sk$uc8'
| X0 != 'sk$uc8'
| X1 != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d122,d108]) ).
cnf(d124,plain,
( identity != 'sk$uc7'
| inverse(identity) != 'sk$uc7'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc6' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc6'
| 'sk$uc7' != 'sk$uc8'
| X1 != 'sk$uc7'
| X0 != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d123,d57]) ).
cnf(d125,plain,
( identity != 'sk$uc7'
| inverse(identity) != 'sk$uc7'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc6' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| X1 != 'sk$uc7'
| X0 != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d124,d57]) ).
cnf(d126,plain,
( identity != 'sk$uc7'
| inverse(identity) != 'sk$uc7'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc6' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| X1 != 'sk$uc7'
| X0 != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d125,d110]) ).
cnf(d127,plain,
( identity != 'sk$uc7'
| inverse(identity) != 'sk$uc7'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| X1 != 'sk$uc7'
| X0 != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d126,d110]) ).
cnf(d128,plain,
( identity != 'sk$uc7'
| inverse(identity) != 'sk$uc7'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| X1 != 'sk$uc7'
| X0 != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d127,d57]) ).
cnf(d129,plain,
( identity != 'sk$uc7'
| inverse(identity) != 'sk$uc7'
| inverse(X1) != 'sk$uc7'
| inverse(X0) != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| X1 != 'sk$uc7'
| X0 != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d128,d57]) ).
cnf(d130,plain,
( identity != 'sk$uc7'
| inverse('sk$uc7') != 'sk$uc7'
| inverse(X1) != 'sk$uc7'
| inverse(X0) != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| X1 != 'sk$uc7'
| X0 != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d129,d103]) ).
cnf(d131,plain,
( identity != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| inverse(X1) != 'sk$uc7'
| inverse(X0) != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| X1 != 'sk$uc7'
| X0 != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d130,d105]) ).
cnf(d132,plain,
( 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| inverse(X1) != 'sk$uc7'
| inverse(X0) != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| X1 != 'sk$uc7'
| X0 != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d131,d103]) ).
cnf(d133,plain,
X0 = multiply('sk$uc7',X0),
inference(demodulation,[status(thm)],[d33,d103]) ).
cnf(d134,plain,
multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[status(thm)],[c28,d1]) ).
cnf(d135,plain,
multiply('sk$uc7',identity) = multiply('sk$uc6',inverse('sk$uc8')),
inference(superposition,[status(thm)],[d9,d18]) ).
cnf(d136,plain,
'sk$uc7' = multiply('sk$uc6',inverse('sk$uc8')),
inference(demodulation,[status(thm)],[d135,d7]) ).
cnf(d137,plain,
inverse('sk$uc8') = multiply(inverse('sk$uc6'),'sk$uc7'),
inference(superposition,[status(thm)],[d136,d8]) ).
cnf(d138,plain,
multiply(inverse(inverse('sk$uc8')),multiply(inverse('sk$uc6'),multiply('sk$uc7',X0))) = X0,
inference(superposition,[status(thm)],[d137,d134]) ).
cnf(d139,plain,
multiply('sk$uc8',multiply(inverse('sk$uc6'),multiply('sk$uc7',X0))) = X0,
inference(demodulation,[status(thm)],[d138,d15]) ).
cnf(d140,plain,
multiply('sk$uc7',multiply(inverse('sk$uc6'),multiply('sk$uc7',X0))) = X0,
inference(demodulation,[status(thm)],[d139,d57]) ).
cnf(d141,plain,
multiply(inverse('sk$uc6'),multiply('sk$uc7',X0)) = X0,
inference(demodulation,[status(thm)],[d140,d133]) ).
cnf(d142,plain,
multiply(inverse('sk$uc7'),multiply('sk$uc7',X0)) = X0,
inference(demodulation,[status(thm)],[d141,d110]) ).
cnf(d143,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d142,d8]) ).
cnf(d144,plain,
( 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| inverse(X1) != 'sk$uc7'
| inverse(X0) != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| X1 != 'sk$uc7'
| X0 != 'sk$uc7' ),
inference(resolution,[status(thm)],[d143,d132]) ).
cnf(d145,plain,
( inverse(X0) != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| X0 != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7' ),
inference(superposition,[status(thm)],[d105,d144]) ).
cnf(d146,plain,
( inverse(X0) != 'sk$uc7'
| X0 != 'sk$uc7' ),
inference(resolution,[status(thm)],[d143,d145]) ).
cnf(d147,plain,
( 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7' ),
inference(superposition,[status(thm)],[d105,d146]) ).
cnf(d148,plain,
$false,
inference(resolution,[status(thm)],[d143,d147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP314-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/20.86 % CPULimit : 300
% 0.12/20.86 % WCLimit : 300
% 0.12/20.86 % DateTime : Fri Sep 25 14:45:13 UTC 2026
% 0.12/20.87 % CPUTime :
% 0.12/20.87 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 146.20/45.18 % SZS status Unsatisfiable for theBenchmark.p
% 146.20/45.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------