%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP222-1 : 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 : n010.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 07:23:26 AM UTC 2026
% Result : Unsatisfiable 68.63s 15.78s
% Output : CNFRefutation 68.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 18
% Syntax : Number of clauses : 119 ( 34 unt; 60 nHn; 96 RR)
% Number of literals : 339 ( 338 equ; 168 neg)
% Maximal clause size : 9 ( 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 : 65 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this_2,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7' ) ).
cnf(prove_this_3,negated_conjecture,
( inverse('sk$uc5') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7' ) ).
cnf(prove_this_4,negated_conjecture,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7' ) ).
cnf(prove_this_6,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc1','sk$uc6') = 'sk$uc7' ) ).
cnf(prove_this_7,negated_conjecture,
( inverse('sk$uc5') = 'sk$uc7'
| multiply('sk$uc1','sk$uc6') = 'sk$uc7' ) ).
cnf(prove_this_8,negated_conjecture,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| multiply('sk$uc1','sk$uc6') = 'sk$uc7' ) ).
cnf(prove_this_9,negated_conjecture,
( multiply('sk$uc4','sk$uc7') = 'sk$uc6'
| multiply('sk$uc2','sk$uc3') = 'sk$uc6' ) ).
cnf(prove_this_10,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc2','sk$uc3') = 'sk$uc6' ) ).
cnf(prove_this_12,negated_conjecture,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| multiply('sk$uc2','sk$uc3') = 'sk$uc6' ) ).
cnf(prove_this_13,negated_conjecture,
( multiply('sk$uc4','sk$uc7') = 'sk$uc6'
| inverse('sk$uc2') = 'sk$uc3' ) ).
cnf(prove_this_14,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc2') = 'sk$uc3' ) ).
cnf(prove_this_16,negated_conjecture,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| inverse('sk$uc2') = 'sk$uc3' ) ).
cnf(prove_this_18,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc3','sk$uc7') = 'sk$uc6' ) ).
cnf(prove_this_20,negated_conjecture,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| multiply('sk$uc3','sk$uc7') = 'sk$uc6' ) ).
cnf(prove_this_21,negated_conjecture,
( multiply(X4,'sk$uc6') != 'sk$uc7'
| inverse(X4) != 'sk$uc7'
| inverse(X3) != 'sk$uc7'
| multiply(X3,'sk$uc7') != 'sk$uc6'
| multiply(X2,'sk$uc7') != 'sk$uc6'
| inverse(X1) != X2
| multiply(X1,X2) != 'sk$uc6'
| multiply(X0,'sk$uc6') != 'sk$uc7'
| inverse(X0) != 'sk$uc7' ) ).
cnf(left_identity,axiom,
multiply(identity,X0) = X0 ).
cnf(left_inverse,axiom,
multiply(inverse(X0),X0) = identity ).
cnf(associativity,axiom,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)) ).
cnf(c1,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_2]) ).
cnf(c2,plain,
( inverse('sk$uc5') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_3]) ).
cnf(c3,plain,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_4]) ).
cnf(c5,plain,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc1','sk$uc6') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_6]) ).
cnf(c6,plain,
( inverse('sk$uc5') = 'sk$uc7'
| multiply('sk$uc1','sk$uc6') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_7]) ).
cnf(c7,plain,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| multiply('sk$uc1','sk$uc6') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_8]) ).
cnf(c8,plain,
( multiply('sk$uc4','sk$uc7') = 'sk$uc6'
| multiply('sk$uc2','sk$uc3') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_9]) ).
cnf(c9,plain,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc2','sk$uc3') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_10]) ).
cnf(c11,plain,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| multiply('sk$uc2','sk$uc3') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_12]) ).
cnf(c12,plain,
( multiply('sk$uc4','sk$uc7') = 'sk$uc6'
| inverse('sk$uc2') = 'sk$uc3' ),
inference(clausification,[status(esa)],[prove_this_13]) ).
cnf(c13,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc2') = 'sk$uc3' ),
inference(clausification,[status(esa)],[prove_this_14]) ).
cnf(c15,plain,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| inverse('sk$uc2') = 'sk$uc3' ),
inference(clausification,[status(esa)],[prove_this_16]) ).
cnf(c17,plain,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc3','sk$uc7') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_18]) ).
cnf(c19,plain,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| multiply('sk$uc3','sk$uc7') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_20]) ).
cnf(c20,plain,
( multiply(X3,'sk$uc7') != 'sk$uc6'
| inverse(X4) != 'sk$uc7'
| multiply(X4,'sk$uc6') != 'sk$uc7'
| inverse(X3) != 'sk$uc7'
| inverse(X2) != 'sk$uc7'
| multiply(X2,'sk$uc6') != 'sk$uc7'
| inverse(X0) != X1
| multiply(X1,'sk$uc7') != 'sk$uc6'
| multiply(X0,X1) != 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_21]) ).
cnf(c21,plain,
multiply(identity,X0) = X0,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c22,plain,
multiply(inverse(X0),X0) = identity,
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c23,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(clausification,[status(esa)],[associativity]) ).
cnf(d0,plain,
multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[status(thm)],[c22,c23]) ).
cnf(d1,plain,
X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(demodulation,[status(thm)],[d0,c21]) ).
cnf(d2,plain,
multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(superposition,[status(thm)],[d1,d1]) ).
cnf(d3,plain,
multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[d2,c22]) ).
cnf(d4,plain,
multiply(X0,X1) = multiply(identity,multiply(X0,X1)),
inference(superposition,[status(thm)],[c21,c23]) ).
cnf(d5,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d4,c21]) ).
cnf(d6,plain,
( inverse('sk$uc4') = 'sk$uc7'
| 'sk$uc6' = multiply('sk$uc2','sk$uc3') ),
inference(superposition,[status(thm)],[c9,d5]) ).
cnf(d7,plain,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc2','sk$uc3') = identity ),
inference(superposition,[status(thm)],[c13,d3]) ).
cnf(d8,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| 'sk$uc6' = identity ),
inference(superposition,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
( 'sk$uc6' = identity
| multiply('sk$uc4','sk$uc7') = identity ),
inference(superposition,[status(thm)],[d8,d3]) ).
cnf(d10,plain,
( multiply('sk$uc4','sk$uc7') = 'sk$uc6'
| 'sk$uc6' = multiply('sk$uc2','sk$uc3') ),
inference(superposition,[status(thm)],[c8,d5]) ).
cnf(d11,plain,
( inverse('sk$uc2') = 'sk$uc3'
| 'sk$uc6' = multiply('sk$uc4','sk$uc7') ),
inference(superposition,[status(thm)],[c12,d5]) ).
cnf(d12,plain,
( 'sk$uc6' = identity
| inverse('sk$uc2') = 'sk$uc3'
| 'sk$uc6' = identity ),
inference(superposition,[status(thm)],[d9,d11]) ).
cnf(d13,plain,
( 'sk$uc6' = identity
| multiply('sk$uc2','sk$uc3') = identity ),
inference(superposition,[status(thm)],[d12,d3]) ).
cnf(d14,plain,
( 'sk$uc6' = identity
| multiply('sk$uc4','sk$uc7') = 'sk$uc6'
| 'sk$uc6' = identity ),
inference(superposition,[status(thm)],[d13,d10]) ).
cnf(d15,plain,
( 'sk$uc6' = identity
| 'sk$uc6' = identity
| 'sk$uc6' = identity ),
inference(superposition,[status(thm)],[d14,d9]) ).
cnf(d16,plain,
identity = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[c22,d5]) ).
cnf(d17,plain,
X0 = multiply(inverse(inverse(X0)),identity),
inference(superposition,[status(thm)],[d16,d1]) ).
cnf(d18,plain,
multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[d17,d5]) ).
cnf(d19,plain,
multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[d18,d2]) ).
cnf(d20,plain,
multiply(X0,'sk$uc6') = X0,
inference(demodulation,[status(thm)],[d19,d15]) ).
cnf(d21,plain,
multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d19,d2]) ).
cnf(d22,plain,
X0 = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d21,d19]) ).
cnf(d23,plain,
( multiply(X2,X3) != 'sk$uc6'
| multiply(X3,'sk$uc7') != 'sk$uc6'
| multiply(X1,'sk$uc6') != 'sk$uc7'
| multiply(X1,'sk$uc6') != 'sk$uc7'
| multiply(X0,'sk$uc7') != 'sk$uc6'
| inverse(X2) != X3
| inverse(X1) != 'sk$uc7'
| inverse(X0) != 'sk$uc7' ),
inference(factoring,[status(thm)],[c20]) ).
cnf(d24,plain,
( multiply(X2,'sk$uc6') != 'sk$uc7'
| multiply(X0,X1) != 'sk$uc6'
| multiply(X1,'sk$uc7') != 'sk$uc6'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse(X2) != 'sk$uc7'
| inverse(X0) != X1
| identity != 'sk$uc6' ),
inference(superposition,[status(thm)],[c22,d23]) ).
cnf(d25,plain,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| identity != 'sk$uc6'
| multiply('sk$uc3','sk$uc7') != 'sk$uc6'
| multiply(X0,'sk$uc6') != 'sk$uc7'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse('sk$uc2') != 'sk$uc3'
| inverse(X0) != 'sk$uc7'
| 'sk$uc6' != 'sk$uc6' ),
inference(superposition,[status(thm)],[c11,d24]) ).
cnf(d26,plain,
( identity != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| multiply('sk$uc3','sk$uc7') != 'sk$uc6'
| multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| multiply(X0,'sk$uc6') != 'sk$uc7'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse(X0) != 'sk$uc7'
| multiply('sk$uc5','sk$uc6') = 'sk$uc7' ),
inference(resolution,[status(thm)],[c15,d25]) ).
cnf(d27,plain,
( identity != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| multiply(X0,'sk$uc6') != 'sk$uc7'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse(X0) != 'sk$uc7'
| multiply('sk$uc5','sk$uc6') = 'sk$uc7' ),
inference(resolution,[status(thm)],[c19,d26]) ).
cnf(d28,plain,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| identity != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse('sk$uc1') != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7' ),
inference(superposition,[status(thm)],[c7,d27]) ).
cnf(d29,plain,
( identity != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc1') != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d28,d22]) ).
cnf(d30,plain,
( identity != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc5' = 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc1') != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d29,d20]) ).
cnf(d31,plain,
( 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc5' = 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc1') != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d30,d15]) ).
cnf(d32,plain,
multiply('sk$uc6',X0) = X0,
inference(demodulation,[status(thm)],[c21,d15]) ).
cnf(d33,plain,
multiply(inverse(X0),X0) = 'sk$uc6',
inference(demodulation,[status(thm)],[c22,d15]) ).
cnf(d34,plain,
X0 = multiply(inverse(identity),X0),
inference(superposition,[status(thm)],[c21,d1]) ).
cnf(d35,plain,
X0 = multiply(inverse(inverse(identity)),X0),
inference(superposition,[status(thm)],[d34,d1]) ).
cnf(d36,plain,
identity = inverse(identity),
inference(superposition,[status(thm)],[d35,d16]) ).
cnf(d37,plain,
'sk$uc6' = inverse(identity),
inference(demodulation,[status(thm)],[d36,d15]) ).
cnf(d38,plain,
'sk$uc6' = inverse('sk$uc6'),
inference(demodulation,[status(thm)],[d37,d15]) ).
cnf(d39,plain,
multiply('sk$uc6','sk$uc6') = 'sk$uc6',
inference(superposition,[status(thm)],[d38,d33]) ).
cnf(d40,plain,
'sk$uc6' = 'sk$uc6',
inference(demodulation,[status(thm)],[d39,d32]) ).
cnf(d41,plain,
( 'sk$uc6' != 'sk$uc6'
| 'sk$uc5' = 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc1') != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7' ),
inference(resolution,[status(thm)],[d40,d31]) ).
cnf(d42,plain,
( 'sk$uc5' = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7' ),
inference(demodulation,[status(thm)],[c3,d20]) ).
cnf(d43,plain,
( 'sk$uc5' = 'sk$uc7'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc5' = 'sk$uc7' ),
inference(resolution,[status(thm)],[d42,d41]) ).
cnf(d44,plain,
( 'sk$uc5' = 'sk$uc7'
| 'sk$uc7' != 'sk$uc7' ),
inference(equality_resolution,[status(thm)],[d43]) ).
cnf(d45,plain,
'sk$uc5' = 'sk$uc7',
inference(equality_resolution,[status(thm)],[d44]) ).
cnf(d46,plain,
( inverse('sk$uc4') = 'sk$uc7'
| identity != 'sk$uc6'
| multiply('sk$uc3','sk$uc7') != 'sk$uc6'
| multiply(X0,'sk$uc6') != 'sk$uc7'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse('sk$uc2') != 'sk$uc3'
| inverse(X0) != 'sk$uc7'
| 'sk$uc6' != 'sk$uc6' ),
inference(superposition,[status(thm)],[c9,d24]) ).
cnf(d47,plain,
( identity != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| multiply('sk$uc3','sk$uc7') != 'sk$uc6'
| multiply(X0,'sk$uc6') != 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse(X0) != 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7' ),
inference(resolution,[status(thm)],[c13,d46]) ).
cnf(d48,plain,
( identity != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| multiply(X0,'sk$uc6') != 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse(X0) != 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7' ),
inference(resolution,[status(thm)],[c17,d47]) ).
cnf(d49,plain,
( inverse('sk$uc4') = 'sk$uc7'
| 'sk$uc7' = multiply('sk$uc1','sk$uc6') ),
inference(superposition,[status(thm)],[c5,d5]) ).
cnf(d50,plain,
( inverse('sk$uc4') = 'sk$uc7'
| identity != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| inverse('sk$uc4') = 'sk$uc7'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse('sk$uc1') != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7' ),
inference(superposition,[status(thm)],[d49,d48]) ).
cnf(d51,plain,
( identity != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc1') != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d50,d22]) ).
cnf(d52,plain,
( 'sk$uc6' != 'sk$uc6'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc1') != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d51,d15]) ).
cnf(d53,plain,
( 'sk$uc6' != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc1') != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7' ),
inference(resolution,[status(thm)],[d40,d52]) ).
cnf(d54,plain,
( 'sk$uc6' != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7' ),
inference(resolution,[status(thm)],[c1,d53]) ).
cnf(d55,plain,
( 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7' ),
inference(equality_resolution,[status(thm)],[d54]) ).
cnf(d56,plain,
inverse('sk$uc4') = 'sk$uc7',
inference(equality_resolution,[status(thm)],[d55]) ).
cnf(d57,plain,
'sk$uc4' = inverse('sk$uc7'),
inference(superposition,[status(thm)],[d56,d22]) ).
cnf(d58,plain,
( inverse('sk$uc5') = 'sk$uc7'
| 'sk$uc1' = inverse('sk$uc7') ),
inference(superposition,[status(thm)],[c2,d22]) ).
cnf(d59,plain,
( 'sk$uc1' = inverse('sk$uc7')
| 'sk$uc5' = inverse('sk$uc7') ),
inference(superposition,[status(thm)],[d58,d22]) ).
cnf(d60,plain,
( 'sk$uc5' = inverse('sk$uc7')
| 'sk$uc1' = 'sk$uc4' ),
inference(demodulation,[status(thm)],[d59,d57]) ).
cnf(d61,plain,
( 'sk$uc5' = 'sk$uc4'
| 'sk$uc1' = 'sk$uc4' ),
inference(demodulation,[status(thm)],[d60,d57]) ).
cnf(d62,plain,
( 'sk$uc7' = 'sk$uc4'
| 'sk$uc1' = 'sk$uc4' ),
inference(demodulation,[status(thm)],[d61,d45]) ).
cnf(d63,plain,
( 'sk$uc1' = 'sk$uc7'
| inverse('sk$uc5') = 'sk$uc7' ),
inference(demodulation,[status(thm)],[c6,d20]) ).
cnf(d64,plain,
( 'sk$uc1' = 'sk$uc7'
| 'sk$uc5' = inverse('sk$uc7') ),
inference(superposition,[status(thm)],[d63,d22]) ).
cnf(d65,plain,
( 'sk$uc1' = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7' ),
inference(demodulation,[status(thm)],[c5,d20]) ).
cnf(d66,plain,
( 'sk$uc1' = 'sk$uc7'
| 'sk$uc4' = inverse('sk$uc7') ),
inference(superposition,[status(thm)],[d65,d22]) ).
cnf(d67,plain,
( 'sk$uc1' = 'sk$uc7'
| 'sk$uc1' = 'sk$uc7'
| 'sk$uc5' = 'sk$uc4' ),
inference(superposition,[status(thm)],[d66,d64]) ).
cnf(d68,plain,
( 'sk$uc7' = 'sk$uc4'
| 'sk$uc1' = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d67,d45]) ).
cnf(d69,plain,
( 'sk$uc7' = 'sk$uc4'
| 'sk$uc7' = 'sk$uc4'
| 'sk$uc7' = 'sk$uc4' ),
inference(superposition,[status(thm)],[d68,d62]) ).
cnf(d70,plain,
inverse('sk$uc7') = 'sk$uc7',
inference(demodulation,[status(thm)],[d56,d69]) ).
cnf(d71,plain,
( identity != 'sk$uc6'
| multiply(X0,'sk$uc7') != 'sk$uc6'
| multiply(X1,'sk$uc6') != 'sk$uc7'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse(inverse(X0)) != X0
| inverse(X1) != 'sk$uc7'
| identity != 'sk$uc6' ),
inference(superposition,[status(thm)],[c22,d24]) ).
cnf(d72,plain,
( identity != 'sk$uc6'
| multiply(X0,'sk$uc6') != 'sk$uc7'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse(inverse(inverse('sk$uc7'))) != inverse('sk$uc7')
| inverse(X0) != 'sk$uc7'
| identity != 'sk$uc6' ),
inference(superposition,[status(thm)],[d16,d71]) ).
cnf(d73,plain,
( identity != 'sk$uc6'
| multiply(X0,'sk$uc6') != 'sk$uc7'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse('sk$uc7') != inverse('sk$uc7')
| inverse(X0) != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d72,d22]) ).
cnf(d74,plain,
( identity != 'sk$uc6'
| multiply(X0,'sk$uc6') != 'sk$uc7'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| 'sk$uc7' != inverse('sk$uc7')
| inverse(X0) != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d73,d70]) ).
cnf(d75,plain,
( identity != 'sk$uc6'
| multiply(X0,'sk$uc6') != 'sk$uc7'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| inverse(X0) != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d74,d70]) ).
cnf(d76,plain,
( identity != 'sk$uc6'
| multiply(X0,'sk$uc6') != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| inverse(X0) != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d75,d22]) ).
cnf(d77,plain,
( identity != 'sk$uc6'
| X0 != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| inverse(X0) != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d76,d20]) ).
cnf(d78,plain,
( 'sk$uc6' != 'sk$uc6'
| X0 != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| inverse(X0) != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d77,d15]) ).
cnf(d79,plain,
( X0 != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| inverse(X0) != 'sk$uc7' ),
inference(resolution,[status(thm)],[d40,d78]) ).
cnf(d80,plain,
'sk$uc7' = inverse('sk$uc7'),
inference(demodulation,[status(thm)],[d57,d69]) ).
cnf(d81,plain,
( 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7' ),
inference(superposition,[status(thm)],[d80,d79]) ).
cnf(d82,plain,
$false,
inference(equality_resolution,[status(thm)],[d81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP222-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n010.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 14:39:29 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 68.63/15.78 % SZS status Unsatisfiable for theBenchmark.p
% 68.63/15.78 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------