%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP268-1 : 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 : n009.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 07:23:30 AM UTC 2026
% Result : Unsatisfiable 12.07s 11.27s
% Output : CNFRefutation 12.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 12
% Syntax : Number of clauses : 108 ( 38 unt; 49 nHn; 77 RR)
% Number of literals : 310 ( 309 equ; 161 neg)
% Maximal clause size : 10 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this_7,negated_conjecture,
( multiply('sk$uc5','sk$uc8') = 'sk$uc7'
| multiply('sk$uc2','sk$uc6') = 'sk$uc7' ) ).
cnf(prove_this_8,negated_conjecture,
( inverse('sk$uc5') = 'sk$uc8'
| multiply('sk$uc2','sk$uc6') = 'sk$uc7' ) ).
cnf(prove_this_10,negated_conjecture,
( multiply('sk$uc5','sk$uc8') = 'sk$uc7'
| inverse('sk$uc2') = 'sk$uc6' ) ).
cnf(prove_this_11,negated_conjecture,
( inverse('sk$uc5') = 'sk$uc8'
| inverse('sk$uc2') = 'sk$uc6' ) ).
cnf(prove_this_12,negated_conjecture,
( inverse('sk$uc6') = 'sk$uc7'
| inverse('sk$uc2') = 'sk$uc6' ) ).
cnf(prove_this_15,negated_conjecture,
( inverse('sk$uc6') = 'sk$uc7'
| multiply('sk$uc6','sk$uc4') = 'sk$uc7' ) ).
cnf(prove_this_18,negated_conjecture,
( inverse('sk$uc6') = 'sk$uc7'
| multiply('sk$uc3','sk$uc6') = 'sk$uc4' ) ).
cnf(prove_this_21,negated_conjecture,
( inverse('sk$uc6') = 'sk$uc7'
| inverse('sk$uc3') = 'sk$uc6' ) ).
cnf(prove_this_22,negated_conjecture,
( inverse('sk$uc6') != 'sk$uc7'
| inverse(X4) != 'sk$uc8'
| multiply(X4,'sk$uc8') != 'sk$uc7'
| inverse(X3) != 'sk$uc6'
| multiply(X3,'sk$uc6') != X2
| multiply('sk$uc6',X2) != 'sk$uc7'
| inverse(X1) != 'sk$uc6'
| multiply(X1,'sk$uc6') != 'sk$uc7'
| inverse(X0) != 'sk$uc8'
| multiply(X0,'sk$uc8') != 'sk$uc7' ) ).
cnf(left_identity,axiom,
multiply(identity,X0) = X0 ).
cnf(left_inverse,axiom,
multiply(inverse(X0),X0) = identity ).
cnf(associativity,axiom,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)) ).
cnf(c6,plain,
( multiply('sk$uc5','sk$uc8') = 'sk$uc7'
| multiply('sk$uc2','sk$uc6') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_7]) ).
cnf(c7,plain,
( inverse('sk$uc5') = 'sk$uc8'
| multiply('sk$uc2','sk$uc6') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_8]) ).
cnf(c9,plain,
( multiply('sk$uc5','sk$uc8') = 'sk$uc7'
| inverse('sk$uc2') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_10]) ).
cnf(c10,plain,
( inverse('sk$uc5') = 'sk$uc8'
| inverse('sk$uc2') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_11]) ).
cnf(c11,plain,
( inverse('sk$uc6') = 'sk$uc7'
| inverse('sk$uc2') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_12]) ).
cnf(c14,plain,
( inverse('sk$uc6') = 'sk$uc7'
| multiply('sk$uc6','sk$uc4') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_15]) ).
cnf(c17,plain,
( inverse('sk$uc6') = 'sk$uc7'
| multiply('sk$uc3','sk$uc6') = 'sk$uc4' ),
inference(clausification,[status(esa)],[prove_this_18]) ).
cnf(c20,plain,
( inverse('sk$uc6') = 'sk$uc7'
| inverse('sk$uc3') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_21]) ).
cnf(c21,plain,
( multiply(X1,'sk$uc6') != X4
| inverse('sk$uc6') != 'sk$uc7'
| inverse(X2) != 'sk$uc8'
| multiply(X3,'sk$uc6') != 'sk$uc7'
| inverse(X0) != 'sk$uc8'
| multiply('sk$uc6',X4) != 'sk$uc7'
| inverse(X3) != 'sk$uc6'
| multiply(X2,'sk$uc8') != 'sk$uc7'
| inverse(X1) != 'sk$uc6'
| multiply(X0,'sk$uc8') != 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_22]) ).
cnf(c22,plain,
multiply(identity,X0) = X0,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c23,plain,
multiply(inverse(X0),X0) = identity,
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c24,plain,
multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(clausification,[status(esa)],[associativity]) ).
cnf(d0,plain,
multiply(identity,multiply(X0,X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c22,c24]) ).
cnf(d1,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d0,c22]) ).
cnf(d2,plain,
identity = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[c23,d1]) ).
cnf(d3,plain,
multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c23,c24]) ).
cnf(d4,plain,
multiply(inverse(X1),multiply(X1,X0)) = X0,
inference(demodulation,[status(thm)],[d3,c22]) ).
cnf(d5,plain,
multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[d4,d4]) ).
cnf(d6,plain,
identity = multiply(X0,inverse(X0)),
inference(superposition,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[d5,c23]) ).
cnf(d8,plain,
( inverse('sk$uc2') = 'sk$uc6'
| multiply('sk$uc5','sk$uc8') = identity ),
inference(superposition,[status(thm)],[c10,d7]) ).
cnf(d9,plain,
( inverse('sk$uc2') = 'sk$uc6'
| inverse('sk$uc2') = 'sk$uc6'
| identity = 'sk$uc7' ),
inference(superposition,[status(thm)],[d8,c9]) ).
cnf(d10,plain,
( identity = 'sk$uc7'
| identity = multiply('sk$uc2','sk$uc6') ),
inference(superposition,[status(thm)],[d9,d6]) ).
cnf(d11,plain,
( identity = 'sk$uc7'
| inverse('sk$uc5') = 'sk$uc8'
| identity = 'sk$uc7' ),
inference(superposition,[status(thm)],[d10,c7]) ).
cnf(d12,plain,
( identity = 'sk$uc7'
| identity = multiply('sk$uc5','sk$uc8') ),
inference(superposition,[status(thm)],[d11,d6]) ).
cnf(d13,plain,
( multiply('sk$uc2','sk$uc6') = 'sk$uc7'
| 'sk$uc7' = multiply('sk$uc5','sk$uc8') ),
inference(superposition,[status(thm)],[c6,d1]) ).
cnf(d14,plain,
( identity = 'sk$uc7'
| 'sk$uc7' = multiply('sk$uc5','sk$uc8')
| identity = 'sk$uc7' ),
inference(superposition,[status(thm)],[d10,d13]) ).
cnf(d15,plain,
( identity = 'sk$uc7'
| identity = 'sk$uc7'
| identity = 'sk$uc7' ),
inference(superposition,[status(thm)],[d14,d12]) ).
cnf(d16,plain,
multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[d2,d4]) ).
cnf(d17,plain,
multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[d16,d5]) ).
cnf(d18,plain,
multiply(X0,'sk$uc7') = X0,
inference(demodulation,[status(thm)],[d17,d15]) ).
cnf(d19,plain,
X0 = multiply(identity,X0),
inference(superposition,[status(thm)],[c22,d1]) ).
cnf(d20,plain,
multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[d19,d4]) ).
cnf(d21,plain,
multiply(inverse(inverse(identity)),X0) = X0,
inference(superposition,[status(thm)],[d20,d4]) ).
cnf(d22,plain,
identity = inverse(identity),
inference(superposition,[status(thm)],[d21,d2]) ).
cnf(d23,plain,
'sk$uc7' = inverse(identity),
inference(demodulation,[status(thm)],[d22,d15]) ).
cnf(d24,plain,
'sk$uc7' = inverse('sk$uc7'),
inference(demodulation,[status(thm)],[d23,d15]) ).
cnf(d25,plain,
X0 = multiply(inverse(inverse(X0)),identity),
inference(superposition,[status(thm)],[d16,d1]) ).
cnf(d26,plain,
X0 = multiply(X0,identity),
inference(demodulation,[status(thm)],[d25,d5]) ).
cnf(d27,plain,
multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d5,d17]) ).
cnf(d28,plain,
X0 = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d27,d26]) ).
cnf(d29,plain,
( inverse('sk$uc2') = 'sk$uc6'
| 'sk$uc6' = inverse('sk$uc7') ),
inference(superposition,[status(thm)],[c11,d28]) ).
cnf(d30,plain,
( 'sk$uc6' = inverse('sk$uc7')
| multiply('sk$uc6',multiply('sk$uc2',X0)) = X0 ),
inference(superposition,[status(thm)],[d29,d4]) ).
cnf(d31,plain,
( 'sk$uc6' = 'sk$uc7'
| multiply('sk$uc6',multiply('sk$uc2',X0)) = X0 ),
inference(demodulation,[status(thm)],[d30,d24]) ).
cnf(d32,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[d21,c23]) ).
cnf(d33,plain,
( inverse('sk$uc2') = 'sk$uc6'
| 'sk$uc7' = multiply('sk$uc5','sk$uc8') ),
inference(superposition,[status(thm)],[c9,d1]) ).
cnf(d34,plain,
( inverse('sk$uc2') = 'sk$uc6'
| inverse('sk$uc2') = 'sk$uc6'
| 'sk$uc7' = identity ),
inference(superposition,[status(thm)],[d8,d33]) ).
cnf(d35,plain,
( inverse('sk$uc2') = 'sk$uc6'
| inverse('sk$uc7') = identity ),
inference(superposition,[status(thm)],[d34,d32]) ).
cnf(d36,plain,
inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[status(thm)],[d26,d5]) ).
cnf(d37,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d36,d26]) ).
cnf(d38,plain,
( inverse('sk$uc2') = 'sk$uc6'
| inverse('sk$uc7') = 'sk$uc6' ),
inference(superposition,[status(thm)],[c11,d37]) ).
cnf(d39,plain,
( inverse('sk$uc2') = 'sk$uc6'
| inverse('sk$uc2') = 'sk$uc6'
| 'sk$uc6' = identity ),
inference(superposition,[status(thm)],[d38,d35]) ).
cnf(d40,plain,
( 'sk$uc6' = identity
| multiply('sk$uc2','sk$uc6') = identity ),
inference(superposition,[status(thm)],[d39,d7]) ).
cnf(d41,plain,
( 'sk$uc6' = identity
| multiply('sk$uc2','sk$uc6') = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d40,d15]) ).
cnf(d42,plain,
( 'sk$uc6' = 'sk$uc7'
| multiply('sk$uc2','sk$uc6') = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d41,d15]) ).
cnf(d43,plain,
( 'sk$uc6' = 'sk$uc7'
| 'sk$uc6' = 'sk$uc7'
| multiply('sk$uc6','sk$uc7') = 'sk$uc6' ),
inference(superposition,[status(thm)],[d42,d31]) ).
cnf(d44,plain,
( 'sk$uc6' = 'sk$uc7'
| 'sk$uc6' = 'sk$uc6' ),
inference(demodulation,[status(thm)],[d43,d18]) ).
cnf(d45,plain,
( inverse('sk$uc6') = 'sk$uc7'
| 'sk$uc7' = multiply('sk$uc6','sk$uc4') ),
inference(superposition,[status(thm)],[c14,d1]) ).
cnf(d46,plain,
multiply('sk$uc7',X0) = X0,
inference(demodulation,[status(thm)],[c22,d15]) ).
cnf(d47,plain,
( inverse('sk$uc3') = 'sk$uc6'
| multiply('sk$uc7','sk$uc6') = identity ),
inference(superposition,[status(thm)],[c20,c23]) ).
cnf(d48,plain,
( inverse('sk$uc3') = 'sk$uc6'
| identity = multiply('sk$uc7','sk$uc6') ),
inference(superposition,[status(thm)],[d47,d1]) ).
cnf(d49,plain,
( identity = multiply('sk$uc7','sk$uc6')
| multiply('sk$uc6',multiply('sk$uc3',X0)) = X0 ),
inference(superposition,[status(thm)],[d48,d4]) ).
cnf(d50,plain,
( inverse('sk$uc6') = 'sk$uc7'
| identity = multiply('sk$uc7','sk$uc6')
| multiply('sk$uc6','sk$uc4') = 'sk$uc6' ),
inference(superposition,[status(thm)],[c17,d49]) ).
cnf(d51,plain,
( 'sk$uc7' = multiply('sk$uc7','sk$uc6')
| inverse('sk$uc6') = 'sk$uc7'
| multiply('sk$uc6','sk$uc4') = 'sk$uc6' ),
inference(demodulation,[status(thm)],[d50,d15]) ).
cnf(d52,plain,
( 'sk$uc7' = 'sk$uc6'
| inverse('sk$uc6') = 'sk$uc7'
| multiply('sk$uc6','sk$uc4') = 'sk$uc6' ),
inference(demodulation,[status(thm)],[d51,d46]) ).
cnf(d53,plain,
( 'sk$uc7' = 'sk$uc6'
| inverse('sk$uc6') = 'sk$uc7'
| inverse('sk$uc6') = 'sk$uc7'
| 'sk$uc7' = 'sk$uc6' ),
inference(superposition,[status(thm)],[d52,d45]) ).
cnf(d54,plain,
( inverse('sk$uc6') = 'sk$uc7'
| 'sk$uc6' = 'sk$uc7'
| 'sk$uc6' = 'sk$uc7' ),
inference(superposition,[status(thm)],[d53,d44]) ).
cnf(d55,plain,
( 'sk$uc6' = 'sk$uc7'
| 'sk$uc6' = inverse('sk$uc7') ),
inference(superposition,[status(thm)],[d54,d28]) ).
cnf(d56,plain,
( 'sk$uc6' = 'sk$uc7'
| 'sk$uc6' = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d55,d24]) ).
cnf(d57,plain,
( 'sk$uc6' = 'sk$uc7'
| 'sk$uc6' = 'sk$uc7'
| 'sk$uc6' = 'sk$uc7' ),
inference(superposition,[status(thm)],[d56,d44]) ).
cnf(d58,plain,
( inverse('sk$uc6') != 'sk$uc7'
| inverse(X3) != 'sk$uc8'
| inverse(X2) != 'sk$uc6'
| inverse(X1) != 'sk$uc8'
| inverse(inverse('sk$uc6')) != 'sk$uc6'
| multiply('sk$uc6',X0) != 'sk$uc7'
| multiply(X3,'sk$uc8') != 'sk$uc7'
| multiply(X2,'sk$uc6') != 'sk$uc7'
| multiply(X1,'sk$uc8') != 'sk$uc7'
| identity != X0 ),
inference(superposition,[status(thm)],[c23,c21]) ).
cnf(d59,plain,
( identity != X2
| inverse('sk$uc6') != 'sk$uc7'
| inverse(inverse('sk$uc6')) != 'sk$uc6'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc6'
| inverse(inverse('sk$uc8')) != 'sk$uc8'
| multiply('sk$uc6',X2) != 'sk$uc7'
| multiply(X1,'sk$uc8') != 'sk$uc7'
| multiply(X0,'sk$uc6') != 'sk$uc7'
| identity != 'sk$uc7' ),
inference(superposition,[status(thm)],[c23,d58]) ).
cnf(d60,plain,
( identity != 'sk$uc7'
| identity != X1
| inverse('sk$uc6') != 'sk$uc7'
| inverse(inverse('sk$uc6')) != 'sk$uc6'
| inverse(inverse('sk$uc8')) != 'sk$uc8'
| inverse(X0) != 'sk$uc6'
| inverse(inverse('sk$uc8')) != 'sk$uc8'
| multiply('sk$uc6',X1) != 'sk$uc7'
| multiply(X0,'sk$uc6') != 'sk$uc7'
| identity != 'sk$uc7' ),
inference(superposition,[status(thm)],[d2,d59]) ).
cnf(d61,plain,
( identity != 'sk$uc7'
| identity != X1
| inverse('sk$uc6') != 'sk$uc7'
| inverse(inverse('sk$uc6')) != 'sk$uc6'
| 'sk$uc8' != 'sk$uc8'
| inverse(X0) != 'sk$uc6'
| multiply('sk$uc6',X1) != 'sk$uc7'
| multiply(X0,'sk$uc6') != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d60,d37]) ).
cnf(d62,plain,
( identity != 'sk$uc7'
| identity != X1
| inverse('sk$uc6') != 'sk$uc7'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc8' != 'sk$uc8'
| inverse(X0) != 'sk$uc6'
| multiply('sk$uc6',X1) != 'sk$uc7'
| multiply(X0,'sk$uc6') != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d61,d37]) ).
cnf(d63,plain,
( identity != 'sk$uc7'
| identity != X0
| inverse('sk$uc6') != 'sk$uc7'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc8' != 'sk$uc8'
| inverse(inverse('sk$uc6')) != 'sk$uc6'
| multiply('sk$uc6',X0) != 'sk$uc7'
| identity != 'sk$uc7' ),
inference(superposition,[status(thm)],[d2,d62]) ).
cnf(d64,plain,
( identity != 'sk$uc7'
| identity != X0
| 'sk$uc6' != 'sk$uc6'
| inverse('sk$uc6') != 'sk$uc7'
| inverse(inverse('sk$uc6')) != 'sk$uc6'
| 'sk$uc8' != 'sk$uc8'
| multiply('sk$uc7',X0) != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d63,d57]) ).
cnf(d65,plain,
( identity != 'sk$uc7'
| identity != X0
| 'sk$uc6' != 'sk$uc6'
| inverse('sk$uc6') != 'sk$uc7'
| inverse(inverse('sk$uc6')) != 'sk$uc6'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d64,d46]) ).
cnf(d66,plain,
( identity != 'sk$uc7'
| identity != X0
| 'sk$uc6' != 'sk$uc6'
| inverse('sk$uc6') != 'sk$uc7'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d65,d37]) ).
cnf(d67,plain,
( identity != 'sk$uc7'
| identity != X0
| 'sk$uc6' != 'sk$uc6'
| inverse('sk$uc6') != 'sk$uc7'
| 'sk$uc7' != 'sk$uc6'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d66,d57]) ).
cnf(d68,plain,
( identity != 'sk$uc7'
| identity != X0
| 'sk$uc6' != 'sk$uc6'
| inverse('sk$uc6') != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d67,d57]) ).
cnf(d69,plain,
( identity != 'sk$uc7'
| identity != X0
| 'sk$uc6' != 'sk$uc6'
| inverse('sk$uc7') != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d68,d57]) ).
cnf(d70,plain,
( identity != 'sk$uc7'
| identity != X0
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d69,d24]) ).
cnf(d71,plain,
( identity != 'sk$uc7'
| identity != X0
| 'sk$uc7' != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d70,d57]) ).
cnf(d72,plain,
( identity != 'sk$uc7'
| identity != X0
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d71,d57]) ).
cnf(d73,plain,
( identity != 'sk$uc7'
| 'sk$uc7' != X0
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d72,d15]) ).
cnf(d74,plain,
( 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != X0
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d73,d15]) ).
cnf(d75,plain,
'sk$uc7' = multiply(X0,inverse(X0)),
inference(demodulation,[status(thm)],[d6,d15]) ).
cnf(d76,plain,
inverse('sk$uc7') = identity,
inference(demodulation,[status(thm)],[d32,d15]) ).
cnf(d77,plain,
inverse('sk$uc7') = 'sk$uc7',
inference(demodulation,[status(thm)],[d76,d15]) ).
cnf(d78,plain,
'sk$uc7' = multiply('sk$uc7','sk$uc7'),
inference(superposition,[status(thm)],[d77,d75]) ).
cnf(d79,plain,
'sk$uc7' = 'sk$uc7',
inference(demodulation,[status(thm)],[d78,d46]) ).
cnf(d80,plain,
( 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != X0
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc7' ),
inference(resolution,[status(thm)],[d79,d74]) ).
cnf(d81,plain,
( 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8' ),
inference(equality_resolution,[status(thm)],[d80]) ).
cnf(d82,plain,
'sk$uc8' != 'sk$uc8',
inference(resolution,[status(thm)],[d79,d81]) ).
cnf(d83,plain,
$false,
inference(equality_resolution,[status(thm)],[d82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP268-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 14:41:59 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.07/11.27 % SZS status Unsatisfiable for theBenchmark.p
% 12.07/11.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------