%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP265-1 : 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 159.75s 27.22s
% Output : CNFRefutation 159.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 17
% Syntax : Number of clauses : 159 ( 51 unt; 69 nHn; 105 RR)
% Number of literals : 547 ( 546 equ; 330 neg)
% Maximal clause size : 11 ( 3 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 176 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this_1,negated_conjecture,
( multiply('sk$uc3','sk$uc9') = 'sk$uc8'
| multiply('sk$uc1','sk$uc9') = 'sk$uc8' ) ).
cnf(prove_this_2,negated_conjecture,
( inverse('sk$uc3') = 'sk$uc9'
| multiply('sk$uc1','sk$uc9') = 'sk$uc8' ) ).
cnf(prove_this_10,negated_conjecture,
( multiply('sk$uc4','sk$uc7') = 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc9' ) ).
cnf(prove_this_11,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc9' ) ).
cnf(prove_this_12,negated_conjecture,
( multiply('sk$uc7','sk$uc6') = 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc9' ) ).
cnf(prove_this_13,negated_conjecture,
( multiply('sk$uc5','sk$uc7') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc9' ) ).
cnf(prove_this_14,negated_conjecture,
( inverse('sk$uc5') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc9' ) ).
cnf(prove_this_19,negated_conjecture,
( multiply('sk$uc7','sk$uc6') = 'sk$uc8'
| multiply('sk$uc2','sk$uc8') = 'sk$uc7' ) ).
cnf(prove_this_20,negated_conjecture,
( multiply('sk$uc5','sk$uc7') = 'sk$uc6'
| multiply('sk$uc2','sk$uc8') = 'sk$uc7' ) ).
cnf(prove_this_21,negated_conjecture,
( inverse('sk$uc5') = 'sk$uc7'
| multiply('sk$uc2','sk$uc8') = 'sk$uc7' ) ).
cnf(prove_this_26,negated_conjecture,
( multiply('sk$uc7','sk$uc6') = 'sk$uc8'
| inverse('sk$uc2') = 'sk$uc8' ) ).
cnf(prove_this_27,negated_conjecture,
( multiply('sk$uc5','sk$uc7') = 'sk$uc6'
| inverse('sk$uc2') = 'sk$uc8' ) ).
cnf(prove_this_28,negated_conjecture,
( inverse('sk$uc5') = 'sk$uc7'
| inverse('sk$uc2') = 'sk$uc8' ) ).
cnf(prove_this_29,negated_conjecture,
( inverse(X5) != 'sk$uc7'
| multiply(X5,'sk$uc7') != X4
| multiply('sk$uc7',X4) != 'sk$uc8'
| inverse(X3) != 'sk$uc7'
| multiply(X3,'sk$uc7') != 'sk$uc8'
| inverse(X2) != 'sk$uc9'
| multiply(X2,'sk$uc9') != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| multiply(X1,'sk$uc8') != 'sk$uc7'
| inverse(X0) != 'sk$uc9'
| multiply(X0,'sk$uc9') != 'sk$uc8' ) ).
cnf(left_identity,axiom,
multiply(identity,X0) = X0 ).
cnf(left_inverse,axiom,
multiply(inverse(X0),X0) = identity ).
cnf(associativity,axiom,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)) ).
cnf(c0,plain,
( multiply('sk$uc3','sk$uc9') = 'sk$uc8'
| multiply('sk$uc1','sk$uc9') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_1]) ).
cnf(c1,plain,
( inverse('sk$uc3') = 'sk$uc9'
| multiply('sk$uc1','sk$uc9') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_2]) ).
cnf(c9,plain,
( multiply('sk$uc4','sk$uc7') = 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc9' ),
inference(clausification,[status(esa)],[prove_this_10]) ).
cnf(c10,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc9' ),
inference(clausification,[status(esa)],[prove_this_11]) ).
cnf(c11,plain,
( multiply('sk$uc7','sk$uc6') = 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc9' ),
inference(clausification,[status(esa)],[prove_this_12]) ).
cnf(c12,plain,
( multiply('sk$uc5','sk$uc7') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc9' ),
inference(clausification,[status(esa)],[prove_this_13]) ).
cnf(c13,plain,
( inverse('sk$uc5') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc9' ),
inference(clausification,[status(esa)],[prove_this_14]) ).
cnf(c18,plain,
( multiply('sk$uc7','sk$uc6') = 'sk$uc8'
| multiply('sk$uc2','sk$uc8') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_19]) ).
cnf(c19,plain,
( multiply('sk$uc5','sk$uc7') = 'sk$uc6'
| multiply('sk$uc2','sk$uc8') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_20]) ).
cnf(c20,plain,
( inverse('sk$uc5') = 'sk$uc7'
| multiply('sk$uc2','sk$uc8') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_21]) ).
cnf(c25,plain,
( multiply('sk$uc7','sk$uc6') = 'sk$uc8'
| inverse('sk$uc2') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_26]) ).
cnf(c26,plain,
( multiply('sk$uc5','sk$uc7') = 'sk$uc6'
| inverse('sk$uc2') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_27]) ).
cnf(c27,plain,
( inverse('sk$uc5') = 'sk$uc7'
| inverse('sk$uc2') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_28]) ).
cnf(c28,plain,
( multiply(X5,'sk$uc7') != 'sk$uc8'
| inverse(X4) != 'sk$uc9'
| inverse(X3) != 'sk$uc9'
| inverse(X5) != 'sk$uc7'
| multiply('sk$uc7',X2) != 'sk$uc8'
| multiply(X4,'sk$uc9') != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| multiply(X3,'sk$uc9') != 'sk$uc8'
| multiply(X1,'sk$uc7') != X2
| inverse(X1) != 'sk$uc7'
| multiply(X0,'sk$uc8') != 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_29]) ).
cnf(c29,plain,
multiply(identity,X0) = X0,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c30,plain,
multiply(inverse(X0),X0) = identity,
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c31,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(clausification,[status(esa)],[associativity]) ).
cnf(d0,plain,
multiply(X0,X1) = multiply(identity,multiply(X0,X1)),
inference(superposition,[status(thm)],[c29,c31]) ).
cnf(d1,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d0,c29]) ).
cnf(d2,plain,
identity = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[c30,d1]) ).
cnf(d3,plain,
multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[status(thm)],[c30,c31]) ).
cnf(d4,plain,
X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(demodulation,[status(thm)],[d3,c29]) ).
cnf(d5,plain,
multiply(X0,X1) = multiply(inverse(inverse(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,
( inverse('sk$uc1') = 'sk$uc9'
| identity = multiply('sk$uc4','sk$uc7') ),
inference(superposition,[status(thm)],[c10,d6]) ).
cnf(d8,plain,
( inverse('sk$uc1') = 'sk$uc9'
| inverse('sk$uc1') = 'sk$uc9'
| identity = 'sk$uc8' ),
inference(superposition,[status(thm)],[d7,c9]) ).
cnf(d9,plain,
( identity = 'sk$uc8'
| identity = multiply('sk$uc1','sk$uc9') ),
inference(superposition,[status(thm)],[d8,d6]) ).
cnf(d10,plain,
( identity = 'sk$uc8'
| inverse('sk$uc3') = 'sk$uc9'
| identity = 'sk$uc8' ),
inference(superposition,[status(thm)],[d9,c1]) ).
cnf(d11,plain,
( identity = 'sk$uc8'
| identity = multiply('sk$uc3','sk$uc9') ),
inference(superposition,[status(thm)],[d10,d6]) ).
cnf(d12,plain,
( identity = 'sk$uc8'
| multiply('sk$uc1','sk$uc9') = 'sk$uc8'
| identity = 'sk$uc8' ),
inference(superposition,[status(thm)],[d11,c0]) ).
cnf(d13,plain,
( identity = 'sk$uc8'
| identity = 'sk$uc8'
| identity = 'sk$uc8' ),
inference(superposition,[status(thm)],[d12,d9]) ).
cnf(d14,plain,
X0 = multiply(inverse(identity),X0),
inference(superposition,[status(thm)],[c29,d4]) ).
cnf(d15,plain,
X0 = multiply(inverse(inverse(identity)),X0),
inference(superposition,[status(thm)],[d14,d4]) ).
cnf(d16,plain,
identity = inverse(identity),
inference(superposition,[status(thm)],[d15,d2]) ).
cnf(d17,plain,
'sk$uc8' = inverse(identity),
inference(demodulation,[status(thm)],[d16,d13]) ).
cnf(d18,plain,
'sk$uc8' = inverse('sk$uc8'),
inference(demodulation,[status(thm)],[d17,d13]) ).
cnf(d19,plain,
X0 = multiply(inverse(inverse(X0)),identity),
inference(superposition,[status(thm)],[d2,d4]) ).
cnf(d20,plain,
X0 = multiply(X0,identity),
inference(demodulation,[status(thm)],[d19,d5]) ).
cnf(d21,plain,
multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d20,d5]) ).
cnf(d22,plain,
X0 = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d21,d20]) ).
cnf(d23,plain,
( inverse('sk$uc2') = 'sk$uc8'
| multiply('sk$uc7','sk$uc5') = identity ),
inference(superposition,[status(thm)],[c27,c30]) ).
cnf(d24,plain,
( inverse('sk$uc2') = 'sk$uc8'
| multiply(identity,X0) = multiply('sk$uc7',multiply('sk$uc5',X0)) ),
inference(superposition,[status(thm)],[d23,c31]) ).
cnf(d25,plain,
( inverse('sk$uc2') = 'sk$uc8'
| X0 = multiply('sk$uc7',multiply('sk$uc5',X0)) ),
inference(demodulation,[status(thm)],[d24,c29]) ).
cnf(d26,plain,
( inverse('sk$uc2') = 'sk$uc8'
| inverse('sk$uc2') = 'sk$uc8'
| 'sk$uc7' = multiply('sk$uc7','sk$uc6') ),
inference(superposition,[status(thm)],[c26,d25]) ).
cnf(d27,plain,
( inverse('sk$uc2') = 'sk$uc8'
| inverse('sk$uc2') = 'sk$uc8'
| 'sk$uc7' = 'sk$uc8' ),
inference(superposition,[status(thm)],[d26,c25]) ).
cnf(d28,plain,
( 'sk$uc7' = 'sk$uc8'
| 'sk$uc2' = inverse('sk$uc8') ),
inference(superposition,[status(thm)],[d27,d22]) ).
cnf(d29,plain,
( 'sk$uc2' = 'sk$uc8'
| 'sk$uc7' = 'sk$uc8' ),
inference(demodulation,[status(thm)],[d28,d18]) ).
cnf(d30,plain,
X0 = multiply(X0,'sk$uc8'),
inference(demodulation,[status(thm)],[d20,d13]) ).
cnf(d31,plain,
multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(superposition,[status(thm)],[d4,d1]) ).
cnf(d32,plain,
multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[d5,d31]) ).
cnf(d33,plain,
( multiply('sk$uc7','sk$uc6') = 'sk$uc8'
| 'sk$uc8' = multiply(inverse('sk$uc2'),'sk$uc7') ),
inference(superposition,[status(thm)],[c18,d4]) ).
cnf(d34,plain,
( multiply('sk$uc7','sk$uc6') = 'sk$uc8'
| multiply('sk$uc2','sk$uc8') = 'sk$uc7' ),
inference(superposition,[status(thm)],[d33,d32]) ).
cnf(d35,plain,
( 'sk$uc2' = 'sk$uc7'
| multiply('sk$uc7','sk$uc6') = 'sk$uc8' ),
inference(demodulation,[status(thm)],[d34,d30]) ).
cnf(d36,plain,
( multiply('sk$uc2','sk$uc8') = 'sk$uc7'
| 'sk$uc7' = multiply(inverse('sk$uc5'),'sk$uc6') ),
inference(superposition,[status(thm)],[c19,d4]) ).
cnf(d37,plain,
( multiply('sk$uc2','sk$uc8') = 'sk$uc7'
| 'sk$uc7' = multiply(inverse('sk$uc5'),'sk$uc6') ),
inference(superposition,[status(thm)],[d36,d1]) ).
cnf(d38,plain,
( 'sk$uc7' = multiply(inverse('sk$uc5'),'sk$uc6')
| 'sk$uc2' = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d37,d30]) ).
cnf(d39,plain,
( inverse('sk$uc5') = 'sk$uc7'
| 'sk$uc8' = multiply(inverse('sk$uc2'),'sk$uc7') ),
inference(superposition,[status(thm)],[c20,d4]) ).
cnf(d40,plain,
( inverse('sk$uc5') = 'sk$uc7'
| multiply('sk$uc2','sk$uc8') = 'sk$uc7' ),
inference(superposition,[status(thm)],[d39,d32]) ).
cnf(d41,plain,
( inverse('sk$uc5') = 'sk$uc7'
| 'sk$uc2' = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d40,d30]) ).
cnf(d42,plain,
( 'sk$uc2' = 'sk$uc7'
| 'sk$uc2' = 'sk$uc7'
| 'sk$uc7' = multiply('sk$uc7','sk$uc6') ),
inference(superposition,[status(thm)],[d41,d38]) ).
cnf(d43,plain,
( 'sk$uc2' = 'sk$uc7'
| 'sk$uc2' = 'sk$uc7'
| 'sk$uc7' = 'sk$uc8' ),
inference(superposition,[status(thm)],[d42,d35]) ).
cnf(d44,plain,
( 'sk$uc7' = 'sk$uc8'
| 'sk$uc7' = 'sk$uc8'
| 'sk$uc7' = 'sk$uc8' ),
inference(superposition,[status(thm)],[d43,d29]) ).
cnf(d45,plain,
( inverse(X3) != 'sk$uc7'
| inverse(X2) != 'sk$uc7'
| inverse(X0) != 'sk$uc9'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc9'
| multiply('sk$uc7',X4) != 'sk$uc8'
| multiply(X3,'sk$uc7') != X4
| multiply(X2,'sk$uc7') != 'sk$uc8'
| multiply(X1,'sk$uc8') != 'sk$uc7'
| multiply(X0,'sk$uc9') != 'sk$uc8' ),
inference(factoring,[status(thm)],[c28]) ).
cnf(d46,plain,
( inverse('sk$uc1') = 'sk$uc9'
| inverse(X3) != 'sk$uc9'
| inverse(X2) != 'sk$uc8'
| inverse(X1) != 'sk$uc7'
| inverse(X0) != 'sk$uc7'
| multiply(X3,'sk$uc9') != 'sk$uc8'
| multiply(X2,'sk$uc8') != 'sk$uc7'
| multiply(X1,'sk$uc7') != 'sk$uc8'
| multiply(X0,'sk$uc7') != 'sk$uc6'
| 'sk$uc8' != 'sk$uc8' ),
inference(superposition,[status(thm)],[c11,d45]) ).
cnf(d47,plain,
( inverse('sk$uc1') = 'sk$uc9'
| inverse(identity) != 'sk$uc7'
| inverse(X2) != 'sk$uc7'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc9'
| 'sk$uc8' != 'sk$uc8'
| multiply(X2,'sk$uc7') != 'sk$uc8'
| multiply(X1,'sk$uc8') != 'sk$uc7'
| multiply(X0,'sk$uc9') != 'sk$uc8'
| 'sk$uc7' != 'sk$uc6' ),
inference(superposition,[status(thm)],[c29,d46]) ).
cnf(d48,plain,
( 'sk$uc7' != 'sk$uc6'
| identity != 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc9'
| inverse(X2) != 'sk$uc9'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| multiply(X2,'sk$uc9') != 'sk$uc8'
| multiply(X1,'sk$uc8') != 'sk$uc7'
| multiply(X0,'sk$uc7') != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d47,d16]) ).
cnf(d49,plain,
( 'sk$uc7' != 'sk$uc6'
| identity != 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc9'
| inverse(X1) != 'sk$uc9'
| inverse(X0) != 'sk$uc8'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| multiply(X1,'sk$uc9') != 'sk$uc8'
| multiply(X0,'sk$uc8') != 'sk$uc7'
| identity != 'sk$uc8' ),
inference(superposition,[status(thm)],[d2,d48]) ).
cnf(d50,plain,
( identity != 'sk$uc7'
| identity != 'sk$uc8'
| 'sk$uc7' != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc9'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc9'
| 'sk$uc8' != 'sk$uc8'
| multiply(X1,'sk$uc8') != 'sk$uc7'
| multiply(X0,'sk$uc9') != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d49,d22]) ).
cnf(d51,plain,
( identity != 'sk$uc7'
| 'sk$uc7' != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc9'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc9'
| 'sk$uc8' != 'sk$uc8'
| multiply(X1,'sk$uc8') != 'sk$uc7'
| multiply(X0,'sk$uc9') != 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc9' ),
inference(resolution,[status(thm)],[d8,d50]) ).
cnf(d52,plain,
( identity != 'sk$uc7'
| 'sk$uc7' != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc9'
| inverse(inverse('sk$uc9')) != 'sk$uc9'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| multiply(X0,'sk$uc8') != 'sk$uc7'
| identity != 'sk$uc8' ),
inference(superposition,[status(thm)],[d2,d51]) ).
cnf(d53,plain,
( identity != 'sk$uc7'
| identity != 'sk$uc8'
| 'sk$uc7' != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| inverse(inverse('sk$uc9')) != 'sk$uc9'
| inverse('sk$uc1') = 'sk$uc9'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d52,d30]) ).
cnf(d54,plain,
( identity != 'sk$uc7'
| identity != 'sk$uc8'
| 'sk$uc7' != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| inverse(inverse('sk$uc9')) != 'sk$uc9'
| inverse('sk$uc1') = 'sk$uc9'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d53,d44]) ).
cnf(d55,plain,
( identity != 'sk$uc7'
| identity != 'sk$uc8'
| 'sk$uc7' != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc9' != 'sk$uc9'
| inverse('sk$uc1') = 'sk$uc9'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d54,d22]) ).
cnf(d56,plain,
( identity != 'sk$uc7'
| identity != 'sk$uc8'
| 'sk$uc7' != 'sk$uc6'
| 'sk$uc8' != 'sk$uc7'
| 'sk$uc9' != 'sk$uc9'
| inverse('sk$uc1') = 'sk$uc9'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d55,d44]) ).
cnf(d57,plain,
( identity != 'sk$uc7'
| identity != 'sk$uc8'
| 'sk$uc7' != 'sk$uc6'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc9' != 'sk$uc9'
| inverse('sk$uc1') = 'sk$uc9'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d56,d44]) ).
cnf(d58,plain,
( identity != 'sk$uc7'
| identity != 'sk$uc8'
| 'sk$uc8' != 'sk$uc6'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc9' != 'sk$uc9'
| inverse('sk$uc1') = 'sk$uc9'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d57,d44]) ).
cnf(d59,plain,
( identity != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc6'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc9' != 'sk$uc9'
| inverse('sk$uc1') = 'sk$uc9'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d58,d13]) ).
cnf(d60,plain,
( 'sk$uc8' != 'sk$uc7'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc6'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc9' != 'sk$uc9'
| inverse('sk$uc1') = 'sk$uc9'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d59,d13]) ).
cnf(d61,plain,
( 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc6'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc9' != 'sk$uc9'
| inverse('sk$uc1') = 'sk$uc9'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d60,d44]) ).
cnf(d62,plain,
multiply('sk$uc8',X0) = X0,
inference(demodulation,[status(thm)],[c29,d13]) ).
cnf(d63,plain,
'sk$uc8' = multiply(inverse(X0),X0),
inference(demodulation,[status(thm)],[d2,d13]) ).
cnf(d64,plain,
'sk$uc8' = multiply('sk$uc8','sk$uc8'),
inference(superposition,[status(thm)],[d18,d63]) ).
cnf(d65,plain,
'sk$uc8' = 'sk$uc8',
inference(demodulation,[status(thm)],[d64,d62]) ).
cnf(d66,plain,
( 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc6'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc9' != 'sk$uc9'
| inverse('sk$uc1') = 'sk$uc9'
| inverse(X0) != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(resolution,[status(thm)],[d65,d61]) ).
cnf(d67,plain,
( inverse('sk$uc1') = 'sk$uc9'
| identity = multiply('sk$uc5','sk$uc7') ),
inference(superposition,[status(thm)],[c13,d6]) ).
cnf(d68,plain,
( inverse('sk$uc1') = 'sk$uc9'
| inverse('sk$uc1') = 'sk$uc9'
| identity = 'sk$uc6' ),
inference(superposition,[status(thm)],[d67,c12]) ).
cnf(d69,plain,
( 'sk$uc8' = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc9' ),
inference(demodulation,[status(thm)],[d68,d13]) ).
cnf(d70,plain,
( inverse('sk$uc1') = 'sk$uc9'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc9' != 'sk$uc9'
| X0 != 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc9' ),
inference(resolution,[status(thm)],[d69,d66]) ).
cnf(d71,plain,
( inverse('sk$uc1') = 'sk$uc9'
| multiply('sk$uc8',X0) = multiply('sk$uc7',multiply('sk$uc6',X0)) ),
inference(superposition,[status(thm)],[c11,c31]) ).
cnf(d72,plain,
( inverse('sk$uc1') = 'sk$uc9'
| multiply('sk$uc7',multiply('sk$uc6',X0)) = multiply('sk$uc8',X0) ),
inference(superposition,[status(thm)],[d71,d1]) ).
cnf(d73,plain,
( inverse('sk$uc1') = 'sk$uc9'
| multiply('sk$uc7','sk$uc5') = identity ),
inference(superposition,[status(thm)],[c13,c30]) ).
cnf(d74,plain,
( inverse('sk$uc1') = 'sk$uc9'
| multiply(identity,X0) = multiply('sk$uc7',multiply('sk$uc5',X0)) ),
inference(superposition,[status(thm)],[d73,c31]) ).
cnf(d75,plain,
( inverse('sk$uc1') = 'sk$uc9'
| X0 = multiply('sk$uc7',multiply('sk$uc5',X0)) ),
inference(demodulation,[status(thm)],[d74,c29]) ).
cnf(d76,plain,
( inverse('sk$uc1') = 'sk$uc9'
| multiply('sk$uc6',X0) = multiply('sk$uc5',multiply('sk$uc7',X0)) ),
inference(superposition,[status(thm)],[c12,c31]) ).
cnf(d77,plain,
( inverse('sk$uc1') = 'sk$uc9'
| inverse('sk$uc1') = 'sk$uc9'
| multiply('sk$uc7',X0) = multiply('sk$uc7',multiply('sk$uc6',X0)) ),
inference(superposition,[status(thm)],[d76,d75]) ).
cnf(d78,plain,
( inverse('sk$uc1') = 'sk$uc9'
| inverse('sk$uc1') = 'sk$uc9'
| multiply('sk$uc7',X0) = multiply('sk$uc8',X0) ),
inference(superposition,[status(thm)],[d77,d72]) ).
cnf(d79,plain,
( inverse('sk$uc1') = 'sk$uc9'
| multiply('sk$uc8',X0) = multiply('sk$uc8',X0) ),
inference(demodulation,[status(thm)],[d78,d44]) ).
cnf(d80,plain,
( inverse('sk$uc1') = 'sk$uc9'
| X0 = multiply('sk$uc8',X0) ),
inference(demodulation,[status(thm)],[d79,d62]) ).
cnf(d81,plain,
( inverse('sk$uc1') = 'sk$uc9'
| X0 = X0 ),
inference(demodulation,[status(thm)],[d80,d62]) ).
cnf(d82,plain,
( inverse('sk$uc1') = 'sk$uc9'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc9' ),
inference(resolution,[status(thm)],[d81,d70]) ).
cnf(d83,plain,
( inverse('sk$uc1') = 'sk$uc9'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8' ),
inference(superposition,[status(thm)],[d18,d82]) ).
cnf(d84,plain,
inverse('sk$uc1') = 'sk$uc9',
inference(resolution,[status(thm)],[d65,d83]) ).
cnf(d85,plain,
( inverse(X3) != 'sk$uc9'
| inverse(X2) != 'sk$uc8'
| inverse(X1) != 'sk$uc7'
| inverse(X0) != 'sk$uc7'
| multiply(X3,'sk$uc9') != 'sk$uc8'
| multiply(X2,'sk$uc8') != 'sk$uc7'
| multiply(X1,'sk$uc7') != 'sk$uc8'
| multiply(X0,'sk$uc7') != identity
| 'sk$uc7' != 'sk$uc8' ),
inference(superposition,[status(thm)],[d20,d45]) ).
cnf(d86,plain,
( 'sk$uc7' != 'sk$uc8'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse(X2) != 'sk$uc7'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc9'
| multiply(X2,'sk$uc7') != 'sk$uc8'
| multiply(X1,'sk$uc8') != 'sk$uc7'
| multiply(X0,'sk$uc9') != 'sk$uc8'
| identity != identity ),
inference(superposition,[status(thm)],[d2,d85]) ).
cnf(d87,plain,
( identity != identity
| 'sk$uc7' != 'sk$uc8'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse(X2) != 'sk$uc9'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc7'
| multiply(X2,'sk$uc9') != 'sk$uc8'
| multiply(X1,'sk$uc8') != 'sk$uc7'
| multiply(X0,'sk$uc8') != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d86,d44]) ).
cnf(d88,plain,
( identity != identity
| 'sk$uc7' != 'sk$uc8'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse(X2) != 'sk$uc9'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc7'
| multiply(X2,'sk$uc9') != 'sk$uc8'
| multiply(X1,'sk$uc8') != 'sk$uc7'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d87,d30]) ).
cnf(d89,plain,
( identity != identity
| 'sk$uc7' != 'sk$uc8'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse(X2) != 'sk$uc9'
| inverse(X0) != 'sk$uc8'
| inverse(X1) != 'sk$uc7'
| multiply(X2,'sk$uc9') != 'sk$uc8'
| X0 != 'sk$uc7'
| X1 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d88,d30]) ).
cnf(d90,plain,
( identity != identity
| 'sk$uc7' != 'sk$uc8'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse(X2) != 'sk$uc9'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc7'
| multiply(X2,'sk$uc9') != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d89,d44]) ).
cnf(d91,plain,
( identity != identity
| 'sk$uc7' != 'sk$uc8'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse(X2) != 'sk$uc9'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| multiply(X2,'sk$uc9') != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d90,d44]) ).
cnf(d92,plain,
( identity != identity
| 'sk$uc7' != 'sk$uc8'
| 'sk$uc7' != 'sk$uc7'
| inverse(X2) != 'sk$uc9'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| multiply(X2,'sk$uc9') != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d91,d22]) ).
cnf(d93,plain,
( identity != identity
| 'sk$uc7' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc7'
| inverse(X2) != 'sk$uc9'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| multiply(X2,'sk$uc9') != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d92,d44]) ).
cnf(d94,plain,
( identity != identity
| 'sk$uc7' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| inverse(X2) != 'sk$uc9'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| multiply(X2,'sk$uc9') != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d93,d44]) ).
cnf(d95,plain,
( identity != identity
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| inverse(X2) != 'sk$uc9'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| multiply(X2,'sk$uc9') != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d94,d44]) ).
cnf(d96,plain,
( 'sk$uc8' != identity
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| inverse(X2) != 'sk$uc9'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| multiply(X2,'sk$uc9') != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d95,d13]) ).
cnf(d97,plain,
( 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| inverse(X2) != 'sk$uc9'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| multiply(X2,'sk$uc9') != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d96,d13]) ).
cnf(d98,plain,
( 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| inverse(X2) != 'sk$uc9'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| multiply(X2,'sk$uc9') != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(resolution,[status(thm)],[d65,d97]) ).
cnf(d99,plain,
'sk$uc8' = multiply(X0,inverse(X0)),
inference(demodulation,[status(thm)],[d6,d13]) ).
cnf(d100,plain,
'sk$uc8' = multiply('sk$uc1','sk$uc9'),
inference(superposition,[status(thm)],[d84,d99]) ).
cnf(d101,plain,
( inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| inverse('sk$uc1') != 'sk$uc9'
| 'sk$uc8' != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8' ),
inference(superposition,[status(thm)],[d100,d98]) ).
cnf(d102,plain,
( inverse('sk$uc1') != 'sk$uc9'
| inverse(X0) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(factoring,[status(thm)],[d101]) ).
cnf(d103,plain,
( 'sk$uc9' != 'sk$uc9'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d102,d84]) ).
cnf(d104,plain,
X2 = multiply(X0,multiply(X1,multiply(inverse(multiply(X0,X1)),X2))),
inference(superposition,[status(thm)],[d32,c31]) ).
cnf(d105,plain,
multiply(X1,multiply(inverse(multiply(X0,X1)),X2)) = multiply(inverse(X0),X2),
inference(superposition,[status(thm)],[d104,d4]) ).
cnf(d106,plain,
X2 = multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))),
inference(superposition,[status(thm)],[c31,d4]) ).
cnf(d107,plain,
multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[d5,c30]) ).
cnf(d108,plain,
inverse(X0) = multiply(inverse(multiply(X1,X0)),multiply(X1,identity)),
inference(superposition,[status(thm)],[d107,d106]) ).
cnf(d109,plain,
inverse(X0) = multiply(inverse(multiply(X1,X0)),multiply(X1,'sk$uc8')),
inference(demodulation,[status(thm)],[d108,d13]) ).
cnf(d110,plain,
inverse(X1) = multiply(inverse(multiply(X0,X1)),X0),
inference(demodulation,[status(thm)],[d109,d30]) ).
cnf(d111,plain,
inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
inference(superposition,[status(thm)],[d31,d110]) ).
cnf(d112,plain,
inverse(multiply('sk$uc1',X0)) = multiply(inverse(X0),'sk$uc9'),
inference(superposition,[status(thm)],[d84,d111]) ).
cnf(d113,plain,
X1 = multiply(X0,multiply(inverse(X0),X1)),
inference(superposition,[status(thm)],[d5,d4]) ).
cnf(d114,plain,
X0 = multiply('sk$uc1',multiply('sk$uc9',X0)),
inference(superposition,[status(thm)],[d84,d113]) ).
cnf(d115,plain,
X3 = multiply(X2,multiply(X0,multiply(X1,multiply(inverse(multiply(X2,multiply(X0,X1))),X3)))),
inference(superposition,[status(thm)],[c31,d104]) ).
cnf(d116,plain,
multiply(X0,multiply(inverse(multiply('sk$uc1',multiply('sk$uc9',X0))),X1)) = X1,
inference(superposition,[status(thm)],[d115,d114]) ).
cnf(d117,plain,
multiply(X0,multiply(multiply(inverse(multiply('sk$uc9',X0)),'sk$uc9'),X1)) = X1,
inference(demodulation,[status(thm)],[d116,d112]) ).
cnf(d118,plain,
multiply(X0,multiply(inverse(multiply('sk$uc9',X0)),multiply('sk$uc9',X1))) = X1,
inference(demodulation,[status(thm)],[d117,c31]) ).
cnf(d119,plain,
multiply(inverse('sk$uc9'),multiply('sk$uc9',X1)) = X1,
inference(demodulation,[status(thm)],[d118,d105]) ).
cnf(d120,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d119,d31]) ).
cnf(d121,plain,
( 'sk$uc9' != 'sk$uc9'
| inverse(X0) != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(resolution,[status(thm)],[d120,d103]) ).
cnf(d122,plain,
( 'sk$uc9' != 'sk$uc9'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8' ),
inference(superposition,[status(thm)],[d18,d121]) ).
cnf(d123,plain,
'sk$uc8' != 'sk$uc8',
inference(resolution,[status(thm)],[d120,d122]) ).
cnf(d124,plain,
$false,
inference(equality_resolution,[status(thm)],[d123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP265-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 14:42:14 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 159.75/27.22 % SZS status Unsatisfiable for theBenchmark.p
% 159.75/27.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------