%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP324-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:23:35 AM UTC 2026
% Result : Unsatisfiable 129.58s 19.14s
% Output : CNFRefutation 129.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 15
% Syntax : Number of clauses : 142 ( 37 unt; 75 nHn; 97 RR)
% Number of literals : 519 ( 518 equ; 322 neg)
% Maximal clause size : 12 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 126 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this_1,negated_conjecture,
( multiply('sk$uc8','sk$uc7') = 'sk$uc6'
| multiply('sk$uc7','sk$uc8') = 'sk$uc6' ) ).
cnf(prove_this_4,negated_conjecture,
( inverse('sk$uc8') = 'sk$uc6'
| multiply('sk$uc7','sk$uc8') = 'sk$uc6' ) ).
cnf(prove_this_10,negated_conjecture,
( inverse('sk$uc8') = 'sk$uc6'
| multiply('sk$uc1','sk$uc7') = 'sk$uc8' ) ).
cnf(prove_this_11,negated_conjecture,
( multiply('sk$uc5','sk$uc7') = 'sk$uc6'
| multiply('sk$uc1','sk$uc7') = 'sk$uc8' ) ).
cnf(prove_this_12,negated_conjecture,
( inverse('sk$uc5') = 'sk$uc7'
| multiply('sk$uc1','sk$uc7') = 'sk$uc8' ) ).
cnf(prove_this_16,negated_conjecture,
( inverse('sk$uc8') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc7' ) ).
cnf(prove_this_17,negated_conjecture,
( multiply('sk$uc5','sk$uc7') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc7' ) ).
cnf(prove_this_18,negated_conjecture,
( inverse('sk$uc5') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7' ) ).
cnf(prove_this_22,negated_conjecture,
( inverse('sk$uc8') = 'sk$uc6'
| multiply('sk$uc8','sk$uc3') = 'sk$uc7' ) ).
cnf(prove_this_28,negated_conjecture,
( inverse('sk$uc8') = 'sk$uc6'
| multiply('sk$uc2','sk$uc8') = 'sk$uc3' ) ).
cnf(prove_this_34,negated_conjecture,
( inverse('sk$uc8') = 'sk$uc6'
| inverse('sk$uc2') = 'sk$uc8' ) ).
cnf(prove_this_37,negated_conjecture,
( inverse(X4) != 'sk$uc7'
| multiply(X4,'sk$uc7') != 'sk$uc6'
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X3) != 'sk$uc8'
| multiply(X3,'sk$uc8') != 'sk$uc7'
| multiply('sk$uc8','sk$uc7') != 'sk$uc6'
| inverse(X2) != 'sk$uc8'
| multiply(X2,'sk$uc8') != X1
| multiply('sk$uc8',X1) != 'sk$uc7'
| inverse(X0) != 'sk$uc7'
| multiply(X0,'sk$uc7') != 'sk$uc8'
| multiply('sk$uc7','sk$uc8') != 'sk$uc6' ) ).
cnf(left_identity,axiom,
multiply(identity,X0) = X0 ).
cnf(left_inverse,axiom,
multiply(inverse(X0),X0) = identity ).
cnf(associativity,axiom,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)) ).
cnf(c0,plain,
( multiply('sk$uc8','sk$uc7') = 'sk$uc6'
| multiply('sk$uc7','sk$uc8') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_1]) ).
cnf(c3,plain,
( inverse('sk$uc8') = 'sk$uc6'
| multiply('sk$uc7','sk$uc8') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_4]) ).
cnf(c9,plain,
( inverse('sk$uc8') = 'sk$uc6'
| multiply('sk$uc1','sk$uc7') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_10]) ).
cnf(c10,plain,
( multiply('sk$uc5','sk$uc7') = 'sk$uc6'
| multiply('sk$uc1','sk$uc7') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_11]) ).
cnf(c11,plain,
( inverse('sk$uc5') = 'sk$uc7'
| multiply('sk$uc1','sk$uc7') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_12]) ).
cnf(c15,plain,
( inverse('sk$uc8') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_16]) ).
cnf(c16,plain,
( multiply('sk$uc5','sk$uc7') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_17]) ).
cnf(c17,plain,
( inverse('sk$uc5') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_18]) ).
cnf(c21,plain,
( inverse('sk$uc8') = 'sk$uc6'
| multiply('sk$uc8','sk$uc3') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_22]) ).
cnf(c27,plain,
( inverse('sk$uc8') = 'sk$uc6'
| multiply('sk$uc2','sk$uc8') = 'sk$uc3' ),
inference(clausification,[status(esa)],[prove_this_28]) ).
cnf(c33,plain,
( inverse('sk$uc8') = 'sk$uc6'
| inverse('sk$uc2') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_34]) ).
cnf(c36,plain,
( inverse(X0) != 'sk$uc7'
| inverse('sk$uc8') != 'sk$uc6'
| multiply('sk$uc7','sk$uc8') != 'sk$uc6'
| inverse(X4) != 'sk$uc8'
| inverse(X2) != 'sk$uc7'
| multiply('sk$uc8','sk$uc7') != 'sk$uc6'
| inverse(X3) != 'sk$uc8'
| multiply(X4,'sk$uc8') != 'sk$uc7'
| multiply(X3,'sk$uc8') != X1
| multiply(X2,'sk$uc7') != 'sk$uc6'
| multiply('sk$uc8',X1) != 'sk$uc7'
| multiply(X0,'sk$uc7') != 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_37]) ).
cnf(c37,plain,
multiply(identity,X0) = X0,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c38,plain,
multiply(inverse(X0),X0) = identity,
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c39,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)],[c38,c39]) ).
cnf(d1,plain,
multiply(inverse(X1),multiply(X1,X0)) = X0,
inference(demodulation,[status(thm)],[d0,c37]) ).
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)],[c37,c39]) ).
cnf(d4,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d3,c37]) ).
cnf(d5,plain,
multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c38,d1]) ).
cnf(d6,plain,
X0 = multiply(inverse(inverse(X0)),identity),
inference(superposition,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
X0 = multiply(X0,identity),
inference(demodulation,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[status(thm)],[d7,d2]) ).
cnf(d9,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[d2,c38]) ).
cnf(d11,plain,
( inverse('sk$uc1') = 'sk$uc7'
| inverse('sk$uc6') = 'sk$uc8' ),
inference(superposition,[status(thm)],[c15,d9]) ).
cnf(d12,plain,
X0 = multiply(identity,X0),
inference(superposition,[status(thm)],[c37,d4]) ).
cnf(d13,plain,
multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[d12,d1]) ).
cnf(d14,plain,
multiply(inverse(inverse(identity)),X0) = X0,
inference(superposition,[status(thm)],[d13,d1]) ).
cnf(d15,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[d14,c38]) ).
cnf(d16,plain,
( inverse('sk$uc1') = 'sk$uc7'
| 'sk$uc6' = multiply('sk$uc5','sk$uc7') ),
inference(superposition,[status(thm)],[c16,d4]) ).
cnf(d17,plain,
( inverse('sk$uc1') = 'sk$uc7'
| multiply('sk$uc5','sk$uc7') = identity ),
inference(superposition,[status(thm)],[c17,d10]) ).
cnf(d18,plain,
( inverse('sk$uc1') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7'
| 'sk$uc6' = identity ),
inference(superposition,[status(thm)],[d17,d16]) ).
cnf(d19,plain,
( inverse('sk$uc1') = 'sk$uc7'
| inverse('sk$uc6') = identity ),
inference(superposition,[status(thm)],[d18,d15]) ).
cnf(d20,plain,
( inverse('sk$uc1') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7'
| identity = 'sk$uc8' ),
inference(superposition,[status(thm)],[d19,d11]) ).
cnf(d21,plain,
( identity = 'sk$uc8'
| multiply('sk$uc1','sk$uc7') = identity ),
inference(superposition,[status(thm)],[d20,d10]) ).
cnf(d22,plain,
( identity = 'sk$uc8'
| inverse('sk$uc8') = 'sk$uc6'
| identity = 'sk$uc8' ),
inference(superposition,[status(thm)],[d21,c9]) ).
cnf(d23,plain,
( identity = 'sk$uc8'
| inverse('sk$uc6') = 'sk$uc8' ),
inference(superposition,[status(thm)],[d22,d9]) ).
cnf(d24,plain,
( multiply('sk$uc1','sk$uc7') = 'sk$uc8'
| 'sk$uc6' = multiply('sk$uc5','sk$uc7') ),
inference(superposition,[status(thm)],[c10,d4]) ).
cnf(d25,plain,
( identity = 'sk$uc8'
| 'sk$uc6' = multiply('sk$uc5','sk$uc7')
| identity = 'sk$uc8' ),
inference(superposition,[status(thm)],[d21,d24]) ).
cnf(d26,plain,
( identity = 'sk$uc8'
| inverse('sk$uc5') = 'sk$uc7'
| identity = 'sk$uc8' ),
inference(superposition,[status(thm)],[d21,c11]) ).
cnf(d27,plain,
( identity = 'sk$uc8'
| multiply('sk$uc5','sk$uc7') = identity ),
inference(superposition,[status(thm)],[d26,d10]) ).
cnf(d28,plain,
( identity = 'sk$uc8'
| identity = 'sk$uc8'
| 'sk$uc6' = identity ),
inference(superposition,[status(thm)],[d27,d25]) ).
cnf(d29,plain,
( identity = 'sk$uc8'
| inverse('sk$uc6') = identity ),
inference(superposition,[status(thm)],[d28,d15]) ).
cnf(d30,plain,
( identity = 'sk$uc8'
| identity = 'sk$uc8'
| identity = 'sk$uc8' ),
inference(superposition,[status(thm)],[d29,d23]) ).
cnf(d31,plain,
inverse('sk$uc8') = identity,
inference(demodulation,[status(thm)],[d15,d30]) ).
cnf(d32,plain,
inverse('sk$uc8') = 'sk$uc8',
inference(demodulation,[status(thm)],[d31,d30]) ).
cnf(d33,plain,
X1 = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[status(thm)],[d1,d4]) ).
cnf(d34,plain,
( inverse('sk$uc8') = 'sk$uc6'
| 'sk$uc6' = multiply('sk$uc7','sk$uc8') ),
inference(superposition,[status(thm)],[c3,d4]) ).
cnf(d35,plain,
( inverse('sk$uc8') = 'sk$uc6'
| 'sk$uc8' = multiply(inverse('sk$uc7'),'sk$uc6') ),
inference(superposition,[status(thm)],[d34,d33]) ).
cnf(d36,plain,
( 'sk$uc8' = 'sk$uc6'
| 'sk$uc8' = multiply(inverse('sk$uc7'),'sk$uc6') ),
inference(demodulation,[status(thm)],[d35,d32]) ).
cnf(d37,plain,
X0 = multiply(X0,'sk$uc8'),
inference(demodulation,[status(thm)],[d7,d30]) ).
cnf(d38,plain,
( inverse('sk$uc1') = 'sk$uc7'
| multiply('sk$uc6','sk$uc8') = identity ),
inference(superposition,[status(thm)],[c15,c38]) ).
cnf(d39,plain,
( inverse('sk$uc1') = 'sk$uc7'
| identity = multiply('sk$uc6','sk$uc8') ),
inference(superposition,[status(thm)],[d38,d4]) ).
cnf(d40,plain,
( identity = multiply('sk$uc6','sk$uc8')
| multiply(inverse('sk$uc7'),X0) = multiply('sk$uc1',X0) ),
inference(superposition,[status(thm)],[d39,d2]) ).
cnf(d41,plain,
( 'sk$uc8' = multiply('sk$uc6','sk$uc8')
| multiply(inverse('sk$uc7'),X0) = multiply('sk$uc1',X0) ),
inference(demodulation,[status(thm)],[d40,d30]) ).
cnf(d42,plain,
( 'sk$uc8' = 'sk$uc6'
| multiply(inverse('sk$uc7'),X0) = multiply('sk$uc1',X0) ),
inference(demodulation,[status(thm)],[d41,d37]) ).
cnf(d43,plain,
( 'sk$uc8' = 'sk$uc6'
| 'sk$uc8' = 'sk$uc6'
| 'sk$uc8' = multiply('sk$uc1','sk$uc6') ),
inference(superposition,[status(thm)],[d42,d36]) ).
cnf(d44,plain,
X0 = multiply('sk$uc8',X0),
inference(demodulation,[status(thm)],[d12,d30]) ).
cnf(d45,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(superposition,[status(thm)],[c39,d4]) ).
cnf(d46,plain,
( inverse('sk$uc8') = 'sk$uc6'
| 'sk$uc8' = multiply('sk$uc1','sk$uc7') ),
inference(superposition,[status(thm)],[c9,d4]) ).
cnf(d47,plain,
( inverse('sk$uc8') = 'sk$uc6'
| multiply('sk$uc8',X0) = multiply('sk$uc1',multiply('sk$uc7',X0)) ),
inference(superposition,[status(thm)],[d46,d45]) ).
cnf(d48,plain,
( inverse('sk$uc8') = 'sk$uc6'
| X0 = multiply('sk$uc1',multiply('sk$uc7',X0)) ),
inference(demodulation,[status(thm)],[d47,d44]) ).
cnf(d49,plain,
( 'sk$uc8' = 'sk$uc6'
| X0 = multiply('sk$uc1',multiply('sk$uc7',X0)) ),
inference(demodulation,[status(thm)],[d48,d32]) ).
cnf(d50,plain,
( inverse('sk$uc8') = 'sk$uc6'
| 'sk$uc7' = multiply('sk$uc8','sk$uc3') ),
inference(superposition,[status(thm)],[c21,d4]) ).
cnf(d51,plain,
( inverse('sk$uc8') = 'sk$uc6'
| multiply('sk$uc7',X0) = multiply('sk$uc8',multiply('sk$uc3',X0)) ),
inference(superposition,[status(thm)],[d50,d45]) ).
cnf(d52,plain,
( inverse('sk$uc8') = 'sk$uc6'
| multiply('sk$uc7',X0) = multiply('sk$uc3',X0) ),
inference(demodulation,[status(thm)],[d51,d44]) ).
cnf(d53,plain,
( 'sk$uc8' = 'sk$uc6'
| multiply('sk$uc7',X0) = multiply('sk$uc3',X0) ),
inference(demodulation,[status(thm)],[d52,d32]) ).
cnf(d54,plain,
( inverse('sk$uc2') = 'sk$uc8'
| multiply('sk$uc6','sk$uc8') = identity ),
inference(superposition,[status(thm)],[c33,c38]) ).
cnf(d55,plain,
( inverse('sk$uc2') = 'sk$uc8'
| identity = multiply('sk$uc6','sk$uc8') ),
inference(superposition,[status(thm)],[d54,d4]) ).
cnf(d56,plain,
( identity = multiply('sk$uc6','sk$uc8')
| X0 = multiply('sk$uc8',multiply('sk$uc2',X0)) ),
inference(superposition,[status(thm)],[d55,d33]) ).
cnf(d57,plain,
( identity = multiply('sk$uc6','sk$uc8')
| X0 = multiply('sk$uc2',X0) ),
inference(demodulation,[status(thm)],[d56,d44]) ).
cnf(d58,plain,
( 'sk$uc8' = multiply('sk$uc6','sk$uc8')
| X0 = multiply('sk$uc2',X0) ),
inference(demodulation,[status(thm)],[d57,d30]) ).
cnf(d59,plain,
( 'sk$uc8' = 'sk$uc6'
| X0 = multiply('sk$uc2',X0) ),
inference(demodulation,[status(thm)],[d58,d37]) ).
cnf(d60,plain,
( inverse('sk$uc8') = 'sk$uc6'
| multiply('sk$uc3',X0) = multiply('sk$uc2',multiply('sk$uc8',X0)) ),
inference(superposition,[status(thm)],[c27,d45]) ).
cnf(d61,plain,
( inverse('sk$uc8') = 'sk$uc6'
| multiply('sk$uc3',X0) = multiply('sk$uc2',X0) ),
inference(demodulation,[status(thm)],[d60,d44]) ).
cnf(d62,plain,
( 'sk$uc8' = 'sk$uc6'
| multiply('sk$uc3',X0) = multiply('sk$uc2',X0) ),
inference(demodulation,[status(thm)],[d61,d32]) ).
cnf(d63,plain,
( 'sk$uc8' = 'sk$uc6'
| 'sk$uc8' = 'sk$uc6'
| X0 = multiply('sk$uc3',X0) ),
inference(superposition,[status(thm)],[d62,d59]) ).
cnf(d64,plain,
( 'sk$uc8' = 'sk$uc6'
| 'sk$uc8' = 'sk$uc6'
| multiply('sk$uc7',X0) = X0 ),
inference(superposition,[status(thm)],[d63,d53]) ).
cnf(d65,plain,
( 'sk$uc8' = 'sk$uc6'
| 'sk$uc8' = 'sk$uc6'
| X0 = multiply('sk$uc1',X0) ),
inference(superposition,[status(thm)],[d64,d49]) ).
cnf(d66,plain,
( 'sk$uc8' = 'sk$uc6'
| 'sk$uc8' = 'sk$uc6'
| 'sk$uc8' = 'sk$uc6' ),
inference(superposition,[status(thm)],[d65,d43]) ).
cnf(d67,plain,
( multiply('sk$uc8','sk$uc7') = 'sk$uc6'
| 'sk$uc6' = multiply('sk$uc7','sk$uc8') ),
inference(superposition,[status(thm)],[c0,d4]) ).
cnf(d68,plain,
( 'sk$uc6' = multiply('sk$uc7','sk$uc8')
| multiply(inverse('sk$uc8'),'sk$uc6') = 'sk$uc7' ),
inference(superposition,[status(thm)],[d67,d1]) ).
cnf(d69,plain,
( 'sk$uc6' = multiply('sk$uc7','sk$uc8')
| multiply('sk$uc8','sk$uc6') = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d68,d32]) ).
cnf(d70,plain,
( 'sk$uc6' = multiply('sk$uc7','sk$uc8')
| 'sk$uc6' = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d69,d44]) ).
cnf(d71,plain,
( 'sk$uc6' = 'sk$uc7'
| 'sk$uc6' = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d70,d37]) ).
cnf(d72,plain,
( 'sk$uc6' = 'sk$uc7'
| 'sk$uc8' = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d71,d66]) ).
cnf(d73,plain,
( 'sk$uc8' = 'sk$uc7'
| 'sk$uc8' = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d72,d66]) ).
cnf(d74,plain,
( inverse('sk$uc8') != 'sk$uc6'
| inverse(X3) != 'sk$uc8'
| inverse(X2) != 'sk$uc7'
| inverse(X0) != 'sk$uc8'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| multiply('sk$uc8','sk$uc7') != 'sk$uc6'
| multiply('sk$uc8',X1) != 'sk$uc7'
| multiply('sk$uc7','sk$uc8') != 'sk$uc6'
| multiply(X3,'sk$uc8') != 'sk$uc7'
| multiply(X2,'sk$uc7') != 'sk$uc6'
| multiply(X0,'sk$uc8') != X1
| identity != 'sk$uc8' ),
inference(superposition,[status(thm)],[c38,c36]) ).
cnf(d75,plain,
( identity != 'sk$uc8'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc7'
| inverse(inverse(identity)) != 'sk$uc8'
| multiply('sk$uc8','sk$uc7') != 'sk$uc6'
| multiply('sk$uc8',X2) != 'sk$uc7'
| multiply('sk$uc7','sk$uc8') != 'sk$uc6'
| multiply(X1,'sk$uc8') != X2
| multiply(X0,'sk$uc7') != 'sk$uc6'
| 'sk$uc8' != 'sk$uc7' ),
inference(superposition,[status(thm)],[d13,d74]) ).
cnf(d76,plain,
( identity != 'sk$uc8'
| inverse(inverse(identity)) != 'sk$uc8'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X2) != 'sk$uc7'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc7'
| multiply('sk$uc8','sk$uc7') != 'sk$uc6'
| multiply('sk$uc8',X1) != 'sk$uc7'
| multiply('sk$uc7','sk$uc8') != 'sk$uc6'
| multiply(X2,'sk$uc7') != 'sk$uc6'
| multiply(X0,'sk$uc8') != X1 ),
inference(demodulation,[status(thm)],[d75,d9]) ).
cnf(d77,plain,
( identity != 'sk$uc8'
| identity != 'sk$uc8'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X2) != 'sk$uc7'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc7'
| multiply('sk$uc8','sk$uc7') != 'sk$uc6'
| multiply('sk$uc8',X1) != 'sk$uc7'
| multiply('sk$uc7','sk$uc8') != 'sk$uc6'
| multiply(X2,'sk$uc7') != 'sk$uc6'
| multiply(X0,'sk$uc8') != X1 ),
inference(demodulation,[status(thm)],[d76,d9]) ).
cnf(d78,plain,
( identity != 'sk$uc8'
| identity != 'sk$uc8'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X1) != 'sk$uc7'
| inverse(inverse('sk$uc8')) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc7'
| multiply('sk$uc8','sk$uc7') != 'sk$uc6'
| multiply('sk$uc8',X0) != 'sk$uc7'
| multiply('sk$uc7','sk$uc8') != 'sk$uc6'
| multiply(X1,'sk$uc7') != 'sk$uc6'
| identity != X0 ),
inference(superposition,[status(thm)],[c38,d77]) ).
cnf(d79,plain,
( identity != 'sk$uc8'
| identity != X1
| inverse(inverse('sk$uc8')) != 'sk$uc8'
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X0) != 'sk$uc7'
| 'sk$uc8' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| multiply('sk$uc8','sk$uc7') != 'sk$uc6'
| multiply('sk$uc8',X1) != 'sk$uc7'
| multiply('sk$uc7','sk$uc8') != 'sk$uc6'
| multiply(X0,'sk$uc8') != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d78,d73]) ).
cnf(d80,plain,
( identity != 'sk$uc8'
| identity != X1
| inverse(inverse('sk$uc8')) != 'sk$uc8'
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X0) != 'sk$uc7'
| 'sk$uc8' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| multiply('sk$uc8','sk$uc7') != 'sk$uc6'
| multiply('sk$uc8',X1) != 'sk$uc7'
| multiply('sk$uc7','sk$uc8') != 'sk$uc6'
| X0 != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d79,d37]) ).
cnf(d81,plain,
( identity != 'sk$uc8'
| identity != X1
| inverse(inverse('sk$uc8')) != 'sk$uc8'
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X0) != 'sk$uc7'
| 'sk$uc8' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| multiply('sk$uc8','sk$uc7') != 'sk$uc6'
| multiply('sk$uc8',X1) != 'sk$uc7'
| multiply('sk$uc7','sk$uc8') != 'sk$uc6'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d80,d66]) ).
cnf(d82,plain,
( identity != 'sk$uc8'
| identity != X1
| inverse(inverse('sk$uc8')) != 'sk$uc8'
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X0) != 'sk$uc7'
| 'sk$uc8' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| multiply('sk$uc8','sk$uc7') != 'sk$uc6'
| multiply('sk$uc8',X1) != 'sk$uc7'
| 'sk$uc7' != 'sk$uc6'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d81,d37]) ).
cnf(d83,plain,
( identity != 'sk$uc8'
| identity != X1
| inverse(inverse('sk$uc8')) != 'sk$uc8'
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X0) != 'sk$uc7'
| 'sk$uc8' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| multiply('sk$uc8','sk$uc7') != 'sk$uc6'
| multiply('sk$uc8',X1) != 'sk$uc7'
| 'sk$uc8' != 'sk$uc6'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d82,d73]) ).
cnf(d84,plain,
( identity != 'sk$uc8'
| identity != X1
| inverse(inverse('sk$uc8')) != 'sk$uc8'
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X0) != 'sk$uc7'
| 'sk$uc8' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| multiply('sk$uc8','sk$uc7') != 'sk$uc6'
| multiply('sk$uc8',X1) != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d83,d66]) ).
cnf(d85,plain,
( identity != 'sk$uc8'
| identity != X0
| inverse(inverse('sk$uc8')) != 'sk$uc8'
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X1) != 'sk$uc7'
| 'sk$uc8' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| multiply('sk$uc8','sk$uc7') != 'sk$uc6'
| X0 != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| X1 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d84,d44]) ).
cnf(d86,plain,
( identity != 'sk$uc8'
| identity != X1
| inverse(inverse('sk$uc8')) != 'sk$uc8'
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X0) != 'sk$uc7'
| 'sk$uc8' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| multiply('sk$uc8','sk$uc7') != 'sk$uc6'
| X1 != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d85,d73]) ).
cnf(d87,plain,
( identity != 'sk$uc8'
| identity != X1
| inverse(inverse('sk$uc8')) != 'sk$uc8'
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X0) != 'sk$uc7'
| 'sk$uc8' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc6'
| X1 != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d86,d44]) ).
cnf(d88,plain,
( identity != 'sk$uc8'
| identity != X1
| inverse(inverse('sk$uc8')) != 'sk$uc8'
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X0) != 'sk$uc7'
| 'sk$uc8' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc8' != 'sk$uc6'
| X1 != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d87,d73]) ).
cnf(d89,plain,
( identity != 'sk$uc8'
| identity != X1
| inverse(inverse('sk$uc8')) != 'sk$uc8'
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X0) != 'sk$uc7'
| 'sk$uc8' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| X1 != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d88,d66]) ).
cnf(d90,plain,
( identity != 'sk$uc8'
| identity != X1
| inverse(inverse('sk$uc8')) != 'sk$uc8'
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X0) != 'sk$uc7'
| 'sk$uc8' != 'sk$uc7'
| 'sk$uc8' != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| X1 != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d89,d73]) ).
cnf(d91,plain,
( identity != 'sk$uc8'
| identity != X1
| inverse(inverse('sk$uc8')) != 'sk$uc8'
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X0) != 'sk$uc7'
| 'sk$uc8' != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X1 != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d90,d73]) ).
cnf(d92,plain,
( identity != 'sk$uc8'
| identity != X1
| inverse(inverse('sk$uc8')) != 'sk$uc8'
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X0) != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X1 != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d91,d73]) ).
cnf(d93,plain,
( identity != 'sk$uc8'
| identity != X1
| inverse(inverse('sk$uc8')) != 'sk$uc8'
| inverse('sk$uc8') != 'sk$uc6'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X1 != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d92,d73]) ).
cnf(d94,plain,
( identity != 'sk$uc8'
| identity != X1
| inverse(inverse('sk$uc8')) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc6'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X1 != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d93,d32]) ).
cnf(d95,plain,
( identity != 'sk$uc8'
| identity != X1
| inverse(inverse('sk$uc8')) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X1 != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d94,d66]) ).
cnf(d96,plain,
( identity != 'sk$uc8'
| identity != X1
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X1 != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d95,d9]) ).
cnf(d97,plain,
( identity != 'sk$uc8'
| 'sk$uc8' != X1
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X1 != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d96,d30]) ).
cnf(d98,plain,
( 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != X1
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X1 != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d97,d30]) ).
cnf(d99,plain,
multiply(inverse(X0),X0) = 'sk$uc8',
inference(demodulation,[status(thm)],[c38,d30]) ).
cnf(d100,plain,
identity = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[c38,d4]) ).
cnf(d101,plain,
identity = inverse(identity),
inference(superposition,[status(thm)],[d14,d100]) ).
cnf(d102,plain,
'sk$uc8' = inverse(identity),
inference(demodulation,[status(thm)],[d101,d30]) ).
cnf(d103,plain,
'sk$uc8' = inverse('sk$uc8'),
inference(demodulation,[status(thm)],[d102,d30]) ).
cnf(d104,plain,
multiply('sk$uc8','sk$uc8') = 'sk$uc8',
inference(superposition,[status(thm)],[d103,d99]) ).
cnf(d105,plain,
'sk$uc8' = 'sk$uc8',
inference(demodulation,[status(thm)],[d104,d44]) ).
cnf(d106,plain,
( 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != X1
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(resolution,[status(thm)],[d105,d98]) ).
cnf(d107,plain,
( inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(equality_resolution,[status(thm)],[d106]) ).
cnf(d108,plain,
( inverse(X0) != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(resolution,[status(thm)],[d105,d107]) ).
cnf(d109,plain,
inverse('sk$uc8') != 'sk$uc8',
inference(equality_resolution,[status(thm)],[d108]) ).
cnf(d110,plain,
'sk$uc8' != 'sk$uc8',
inference(demodulation,[status(thm)],[d109,d32]) ).
cnf(d111,plain,
$false,
inference(resolution,[status(thm)],[d105,d110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP324-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n004.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 14:45:52 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 129.58/19.14 % SZS status Unsatisfiable for theBenchmark.p
% 129.58/19.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------