%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP351-1 : 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 : n003.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 07:23:37 AM UTC 2026
% Result : Unsatisfiable 211.28s 30.71s
% Output : CNFRefutation 211.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 19
% Syntax : Number of clauses : 174 ( 49 unt; 102 nHn; 136 RR)
% Number of literals : 454 ( 453 equ; 177 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 : 69 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this_1,negated_conjecture,
( multiply('sk$uc6','sk$uc7') = 'sk$uc5'
| multiply('sk$uc6','sk$uc5') = 'sk$uc7' ) ).
cnf(prove_this_6,negated_conjecture,
( multiply('sk$uc6','sk$uc7') = 'sk$uc5'
| multiply('sk$uc1','sk$uc7') = 'sk$uc6' ) ).
cnf(prove_this_7,negated_conjecture,
( multiply('sk$uc3','sk$uc6') = 'sk$uc7'
| multiply('sk$uc1','sk$uc7') = 'sk$uc6' ) ).
cnf(prove_this_8,negated_conjecture,
( inverse('sk$uc3') = 'sk$uc6'
| multiply('sk$uc1','sk$uc7') = 'sk$uc6' ) ).
cnf(prove_this_9,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc5'
| multiply('sk$uc1','sk$uc7') = 'sk$uc6' ) ).
cnf(prove_this_10,negated_conjecture,
( multiply('sk$uc4','sk$uc6') = 'sk$uc5'
| multiply('sk$uc1','sk$uc7') = 'sk$uc6' ) ).
cnf(prove_this_11,negated_conjecture,
( multiply('sk$uc6','sk$uc7') = 'sk$uc5'
| inverse('sk$uc1') = 'sk$uc7' ) ).
cnf(prove_this_12,negated_conjecture,
( multiply('sk$uc3','sk$uc6') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7' ) ).
cnf(prove_this_13,negated_conjecture,
( inverse('sk$uc3') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc7' ) ).
cnf(prove_this_14,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc5'
| inverse('sk$uc1') = 'sk$uc7' ) ).
cnf(prove_this_15,negated_conjecture,
( multiply('sk$uc4','sk$uc6') = 'sk$uc5'
| inverse('sk$uc1') = 'sk$uc7' ) ).
cnf(prove_this_17,negated_conjecture,
( multiply('sk$uc3','sk$uc6') = 'sk$uc7'
| multiply('sk$uc2','sk$uc6') = 'sk$uc5' ) ).
cnf(prove_this_18,negated_conjecture,
( inverse('sk$uc3') = 'sk$uc6'
| multiply('sk$uc2','sk$uc6') = 'sk$uc5' ) ).
cnf(prove_this_22,negated_conjecture,
( multiply('sk$uc3','sk$uc6') = 'sk$uc7'
| inverse('sk$uc2') = 'sk$uc6' ) ).
cnf(prove_this_23,negated_conjecture,
( inverse('sk$uc3') = 'sk$uc6'
| inverse('sk$uc2') = 'sk$uc6' ) ).
cnf(prove_this_26,negated_conjecture,
( multiply(X3,'sk$uc6') != 'sk$uc5'
| inverse(X3) != 'sk$uc5'
| inverse(X2) != 'sk$uc6'
| multiply(X2,'sk$uc6') != 'sk$uc7'
| multiply('sk$uc6','sk$uc7') != 'sk$uc5'
| inverse(X1) != 'sk$uc6'
| multiply(X1,'sk$uc6') != 'sk$uc5'
| inverse(X0) != 'sk$uc7'
| multiply(X0,'sk$uc7') != 'sk$uc6'
| multiply('sk$uc6','sk$uc5') != 'sk$uc7' ) ).
cnf(left_identity,axiom,
multiply(identity,X0) = X0 ).
cnf(left_inverse,axiom,
multiply(inverse(X0),X0) = identity ).
cnf(associativity,axiom,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)) ).
cnf(c0,plain,
( multiply('sk$uc6','sk$uc7') = 'sk$uc5'
| multiply('sk$uc6','sk$uc5') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_1]) ).
cnf(c5,plain,
( multiply('sk$uc6','sk$uc7') = 'sk$uc5'
| multiply('sk$uc1','sk$uc7') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_6]) ).
cnf(c6,plain,
( multiply('sk$uc3','sk$uc6') = 'sk$uc7'
| multiply('sk$uc1','sk$uc7') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_7]) ).
cnf(c7,plain,
( inverse('sk$uc3') = 'sk$uc6'
| multiply('sk$uc1','sk$uc7') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_8]) ).
cnf(c8,plain,
( inverse('sk$uc4') = 'sk$uc5'
| multiply('sk$uc1','sk$uc7') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_9]) ).
cnf(c9,plain,
( multiply('sk$uc4','sk$uc6') = 'sk$uc5'
| multiply('sk$uc1','sk$uc7') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_10]) ).
cnf(c10,plain,
( multiply('sk$uc6','sk$uc7') = 'sk$uc5'
| inverse('sk$uc1') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_11]) ).
cnf(c11,plain,
( multiply('sk$uc3','sk$uc6') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_12]) ).
cnf(c12,plain,
( inverse('sk$uc3') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_13]) ).
cnf(c13,plain,
( inverse('sk$uc4') = 'sk$uc5'
| inverse('sk$uc1') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_14]) ).
cnf(c14,plain,
( multiply('sk$uc4','sk$uc6') = 'sk$uc5'
| inverse('sk$uc1') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_15]) ).
cnf(c16,plain,
( multiply('sk$uc3','sk$uc6') = 'sk$uc7'
| multiply('sk$uc2','sk$uc6') = 'sk$uc5' ),
inference(clausification,[status(esa)],[prove_this_17]) ).
cnf(c17,plain,
( inverse('sk$uc3') = 'sk$uc6'
| multiply('sk$uc2','sk$uc6') = 'sk$uc5' ),
inference(clausification,[status(esa)],[prove_this_18]) ).
cnf(c21,plain,
( multiply('sk$uc3','sk$uc6') = 'sk$uc7'
| inverse('sk$uc2') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_22]) ).
cnf(c22,plain,
( inverse('sk$uc3') = 'sk$uc6'
| inverse('sk$uc2') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_23]) ).
cnf(c25,plain,
( multiply(X2,'sk$uc6') != 'sk$uc5'
| inverse(X1) != 'sk$uc6'
| multiply('sk$uc6','sk$uc5') != 'sk$uc7'
| multiply(X3,'sk$uc7') != 'sk$uc6'
| multiply('sk$uc6','sk$uc7') != 'sk$uc5'
| inverse(X0) != 'sk$uc5'
| inverse(X3) != 'sk$uc7'
| inverse(X2) != 'sk$uc6'
| multiply(X1,'sk$uc6') != 'sk$uc7'
| multiply(X0,'sk$uc6') != 'sk$uc5' ),
inference(clausification,[status(esa)],[prove_this_26]) ).
cnf(c26,plain,
multiply(identity,X0) = X0,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c27,plain,
multiply(inverse(X0),X0) = identity,
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c28,plain,
multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(clausification,[status(esa)],[associativity]) ).
cnf(d0,plain,
multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c27,c28]) ).
cnf(d1,plain,
multiply(inverse(X1),multiply(X1,X0)) = X0,
inference(demodulation,[status(thm)],[d0,c26]) ).
cnf(d2,plain,
multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[d1,d1]) ).
cnf(d3,plain,
multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[d2,c27]) ).
cnf(d4,plain,
multiply(identity,multiply(X0,X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c26,c28]) ).
cnf(d5,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d4,c26]) ).
cnf(d6,plain,
X0 = multiply(identity,X0),
inference(superposition,[status(thm)],[c26,d5]) ).
cnf(d7,plain,
multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
multiply(inverse(inverse(identity)),X0) = X0,
inference(superposition,[status(thm)],[d7,d1]) ).
cnf(d9,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[d8,c27]) ).
cnf(d10,plain,
multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c27,d1]) ).
cnf(d11,plain,
X0 = multiply(inverse(inverse(X0)),identity),
inference(superposition,[status(thm)],[d10,d5]) ).
cnf(d12,plain,
X0 = multiply(X0,identity),
inference(demodulation,[status(thm)],[d11,d2]) ).
cnf(d13,plain,
multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[d10,d2]) ).
cnf(d14,plain,
multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d2,d13]) ).
cnf(d15,plain,
X0 = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d14,d12]) ).
cnf(d16,plain,
multiply(inverse(X0),identity) = inverse(X0),
inference(superposition,[status(thm)],[d3,d1]) ).
cnf(d17,plain,
inverse(X0) = inverse(X0),
inference(demodulation,[status(thm)],[d16,d12]) ).
cnf(d18,plain,
( inverse('sk$uc1') = 'sk$uc7'
| 'sk$uc5' = inverse('sk$uc4') ),
inference(superposition,[status(thm)],[c13,d17]) ).
cnf(d19,plain,
( inverse('sk$uc1') = 'sk$uc7'
| 'sk$uc3' = inverse('sk$uc6') ),
inference(superposition,[status(thm)],[c12,d15]) ).
cnf(d20,plain,
inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[status(thm)],[d12,d2]) ).
cnf(d21,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d20,d12]) ).
cnf(d22,plain,
( inverse('sk$uc1') = 'sk$uc7'
| inverse('sk$uc5') = 'sk$uc4' ),
inference(superposition,[status(thm)],[c13,d21]) ).
cnf(d23,plain,
( inverse('sk$uc1') = 'sk$uc7'
| multiply('sk$uc6','sk$uc3') = identity ),
inference(superposition,[status(thm)],[c12,c27]) ).
cnf(d24,plain,
( inverse('sk$uc1') = 'sk$uc7'
| multiply('sk$uc6',multiply('sk$uc3',X0)) = multiply(identity,X0) ),
inference(superposition,[status(thm)],[d23,c28]) ).
cnf(d25,plain,
( inverse('sk$uc1') = 'sk$uc7'
| multiply('sk$uc6',multiply('sk$uc3',X0)) = X0 ),
inference(demodulation,[status(thm)],[d24,c26]) ).
cnf(d26,plain,
( inverse('sk$uc1') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7'
| multiply('sk$uc6','sk$uc7') = 'sk$uc6' ),
inference(superposition,[status(thm)],[c11,d25]) ).
cnf(d27,plain,
( inverse('sk$uc1') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7'
| 'sk$uc6' = 'sk$uc5' ),
inference(superposition,[status(thm)],[d26,c10]) ).
cnf(d28,plain,
( inverse('sk$uc1') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7'
| inverse('sk$uc6') = 'sk$uc4' ),
inference(superposition,[status(thm)],[d27,d22]) ).
cnf(d29,plain,
( inverse('sk$uc1') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7'
| 'sk$uc3' = 'sk$uc4' ),
inference(superposition,[status(thm)],[d28,d19]) ).
cnf(d30,plain,
( inverse('sk$uc1') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7'
| 'sk$uc5' = inverse('sk$uc3') ),
inference(superposition,[status(thm)],[d29,d18]) ).
cnf(d31,plain,
( inverse('sk$uc1') = 'sk$uc7'
| 'sk$uc3' = inverse('sk$uc5') ),
inference(superposition,[status(thm)],[d30,d15]) ).
cnf(d32,plain,
( inverse('sk$uc1') = 'sk$uc7'
| 'sk$uc5' = multiply('sk$uc4','sk$uc6') ),
inference(superposition,[status(thm)],[c14,d5]) ).
cnf(d33,plain,
( inverse('sk$uc1') = 'sk$uc7'
| multiply('sk$uc4','sk$uc6') = identity ),
inference(superposition,[status(thm)],[d28,c27]) ).
cnf(d34,plain,
( inverse('sk$uc1') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7'
| 'sk$uc5' = identity ),
inference(superposition,[status(thm)],[d33,d32]) ).
cnf(d35,plain,
( inverse('sk$uc1') = 'sk$uc7'
| inverse('sk$uc5') = identity ),
inference(superposition,[status(thm)],[d34,d9]) ).
cnf(d36,plain,
( inverse('sk$uc1') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7'
| 'sk$uc3' = identity ),
inference(superposition,[status(thm)],[d35,d31]) ).
cnf(d37,plain,
( inverse('sk$uc1') = 'sk$uc7'
| inverse('sk$uc3') = identity ),
inference(superposition,[status(thm)],[d36,d9]) ).
cnf(d38,plain,
( inverse('sk$uc1') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7'
| identity = 'sk$uc6' ),
inference(superposition,[status(thm)],[d37,c12]) ).
cnf(d39,plain,
( identity = 'sk$uc6'
| multiply('sk$uc1','sk$uc7') = identity ),
inference(superposition,[status(thm)],[d38,d3]) ).
cnf(d40,plain,
( identity = 'sk$uc6'
| inverse('sk$uc3') = 'sk$uc6'
| identity = 'sk$uc6' ),
inference(superposition,[status(thm)],[d39,c7]) ).
cnf(d41,plain,
( identity = 'sk$uc6'
| inverse('sk$uc4') = 'sk$uc5'
| identity = 'sk$uc6' ),
inference(superposition,[status(thm)],[d39,c8]) ).
cnf(d42,plain,
( identity = 'sk$uc6'
| 'sk$uc5' = inverse('sk$uc4') ),
inference(superposition,[status(thm)],[d41,d17]) ).
cnf(d43,plain,
( identity = 'sk$uc6'
| inverse('sk$uc6') = 'sk$uc3' ),
inference(superposition,[status(thm)],[d40,d21]) ).
cnf(d44,plain,
( identity = 'sk$uc6'
| inverse('sk$uc5') = 'sk$uc4' ),
inference(superposition,[status(thm)],[d41,d21]) ).
cnf(d45,plain,
( multiply('sk$uc1','sk$uc7') = 'sk$uc6'
| 'sk$uc5' = multiply('sk$uc6','sk$uc7') ),
inference(superposition,[status(thm)],[c5,d5]) ).
cnf(d46,plain,
( identity = 'sk$uc6'
| 'sk$uc5' = multiply('sk$uc6','sk$uc7')
| identity = 'sk$uc6' ),
inference(superposition,[status(thm)],[d39,d45]) ).
cnf(d47,plain,
( identity = 'sk$uc6'
| multiply('sk$uc6','sk$uc7') = 'sk$uc5' ),
inference(superposition,[status(thm)],[d46,d5]) ).
cnf(d48,plain,
( multiply('sk$uc1','sk$uc7') = 'sk$uc6'
| 'sk$uc7' = multiply('sk$uc3','sk$uc6') ),
inference(superposition,[status(thm)],[c6,d5]) ).
cnf(d49,plain,
( identity = 'sk$uc6'
| 'sk$uc7' = multiply('sk$uc3','sk$uc6')
| identity = 'sk$uc6' ),
inference(superposition,[status(thm)],[d39,d48]) ).
cnf(d50,plain,
( identity = 'sk$uc6'
| multiply('sk$uc3','sk$uc6') = identity ),
inference(superposition,[status(thm)],[d40,d3]) ).
cnf(d51,plain,
( identity = 'sk$uc6'
| identity = 'sk$uc6'
| 'sk$uc7' = identity ),
inference(superposition,[status(thm)],[d50,d49]) ).
cnf(d52,plain,
( identity = 'sk$uc6'
| multiply(X0,'sk$uc7') = X0 ),
inference(superposition,[status(thm)],[d51,d13]) ).
cnf(d53,plain,
( identity = 'sk$uc6'
| identity = 'sk$uc6'
| 'sk$uc6' = 'sk$uc5' ),
inference(superposition,[status(thm)],[d52,d47]) ).
cnf(d54,plain,
( identity = 'sk$uc6'
| identity = 'sk$uc6'
| inverse('sk$uc6') = 'sk$uc4' ),
inference(superposition,[status(thm)],[d53,d44]) ).
cnf(d55,plain,
( identity = 'sk$uc6'
| identity = 'sk$uc6'
| 'sk$uc4' = 'sk$uc3' ),
inference(superposition,[status(thm)],[d54,d43]) ).
cnf(d56,plain,
( identity = 'sk$uc6'
| identity = 'sk$uc6'
| 'sk$uc5' = inverse('sk$uc3') ),
inference(superposition,[status(thm)],[d55,d42]) ).
cnf(d57,plain,
( identity = 'sk$uc6'
| 'sk$uc3' = inverse('sk$uc5') ),
inference(superposition,[status(thm)],[d56,d15]) ).
cnf(d58,plain,
( multiply('sk$uc1','sk$uc7') = 'sk$uc6'
| 'sk$uc5' = multiply('sk$uc4','sk$uc6') ),
inference(superposition,[status(thm)],[c9,d5]) ).
cnf(d59,plain,
( identity = 'sk$uc6'
| 'sk$uc5' = multiply('sk$uc4','sk$uc6')
| identity = 'sk$uc6' ),
inference(superposition,[status(thm)],[d39,d58]) ).
cnf(d60,plain,
identity = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[c27,d5]) ).
cnf(d61,plain,
identity = multiply(X0,inverse(X0)),
inference(superposition,[status(thm)],[d2,d60]) ).
cnf(d62,plain,
( identity = 'sk$uc6'
| identity = multiply('sk$uc4','sk$uc5') ),
inference(superposition,[status(thm)],[d41,d61]) ).
cnf(d63,plain,
( identity = 'sk$uc6'
| identity = 'sk$uc6'
| identity = multiply('sk$uc4','sk$uc6') ),
inference(superposition,[status(thm)],[d53,d62]) ).
cnf(d64,plain,
( identity = 'sk$uc6'
| identity = 'sk$uc6'
| 'sk$uc5' = identity ),
inference(superposition,[status(thm)],[d63,d59]) ).
cnf(d65,plain,
( identity = 'sk$uc6'
| inverse('sk$uc5') = identity ),
inference(superposition,[status(thm)],[d64,d9]) ).
cnf(d66,plain,
( identity = 'sk$uc6'
| identity = 'sk$uc6'
| 'sk$uc3' = identity ),
inference(superposition,[status(thm)],[d65,d57]) ).
cnf(d67,plain,
( identity = 'sk$uc6'
| inverse('sk$uc3') = identity ),
inference(superposition,[status(thm)],[d66,d9]) ).
cnf(d68,plain,
( identity = 'sk$uc6'
| identity = 'sk$uc6'
| identity = 'sk$uc6' ),
inference(superposition,[status(thm)],[d67,d40]) ).
cnf(d69,plain,
X0 = multiply('sk$uc6',X0),
inference(demodulation,[status(thm)],[d6,d68]) ).
cnf(d70,plain,
( multiply('sk$uc6','sk$uc7') = 'sk$uc5'
| 'sk$uc7' = multiply('sk$uc6','sk$uc5') ),
inference(superposition,[status(thm)],[c0,d5]) ).
cnf(d71,plain,
( 'sk$uc7' = multiply('sk$uc6','sk$uc5')
| 'sk$uc7' = 'sk$uc5' ),
inference(demodulation,[status(thm)],[d70,d69]) ).
cnf(d72,plain,
( 'sk$uc7' = 'sk$uc5'
| 'sk$uc7' = 'sk$uc5' ),
inference(demodulation,[status(thm)],[d71,d69]) ).
cnf(d73,plain,
( inverse(X2) != 'sk$uc6'
| inverse(X1) != 'sk$uc7'
| inverse(X0) != 'sk$uc6'
| inverse(inverse('sk$uc6')) != 'sk$uc5'
| multiply('sk$uc6','sk$uc7') != 'sk$uc5'
| multiply('sk$uc6','sk$uc5') != 'sk$uc7'
| multiply(X2,'sk$uc6') != 'sk$uc7'
| multiply(X1,'sk$uc7') != 'sk$uc6'
| multiply(X0,'sk$uc6') != 'sk$uc5'
| identity != 'sk$uc5' ),
inference(superposition,[status(thm)],[c27,c25]) ).
cnf(d74,plain,
( identity != 'sk$uc5'
| inverse(inverse('sk$uc6')) != 'sk$uc5'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc7'
| inverse(inverse('sk$uc6')) != 'sk$uc6'
| multiply('sk$uc6','sk$uc7') != 'sk$uc5'
| multiply('sk$uc6','sk$uc5') != 'sk$uc7'
| multiply(X1,'sk$uc6') != 'sk$uc5'
| multiply(X0,'sk$uc7') != 'sk$uc6'
| identity != 'sk$uc7' ),
inference(superposition,[status(thm)],[c27,d73]) ).
cnf(d75,plain,
( identity != 'sk$uc7'
| identity != 'sk$uc5'
| inverse(inverse('sk$uc6')) != 'sk$uc5'
| inverse(inverse('sk$uc6')) != 'sk$uc6'
| inverse(X0) != 'sk$uc7'
| inverse(inverse('sk$uc6')) != 'sk$uc6'
| multiply('sk$uc6','sk$uc7') != 'sk$uc5'
| multiply('sk$uc6','sk$uc5') != 'sk$uc7'
| multiply(X0,'sk$uc7') != 'sk$uc6'
| identity != 'sk$uc5' ),
inference(superposition,[status(thm)],[c27,d74]) ).
cnf(d76,plain,
( identity != 'sk$uc7'
| identity != 'sk$uc5'
| inverse(inverse('sk$uc6')) != 'sk$uc5'
| 'sk$uc6' != 'sk$uc6'
| inverse(X0) != 'sk$uc7'
| multiply('sk$uc6','sk$uc7') != 'sk$uc5'
| multiply('sk$uc6','sk$uc5') != 'sk$uc7'
| multiply(X0,'sk$uc7') != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d75,d21]) ).
cnf(d77,plain,
( identity != 'sk$uc7'
| identity != 'sk$uc5'
| 'sk$uc6' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc6'
| inverse(X0) != 'sk$uc7'
| multiply('sk$uc6','sk$uc7') != 'sk$uc5'
| multiply('sk$uc6','sk$uc5') != 'sk$uc7'
| multiply(X0,'sk$uc7') != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d76,d21]) ).
cnf(d78,plain,
( identity != 'sk$uc7'
| identity != 'sk$uc5'
| 'sk$uc6' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc6'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| multiply('sk$uc6','sk$uc7') != 'sk$uc5'
| multiply('sk$uc6','sk$uc5') != 'sk$uc7'
| identity != 'sk$uc6' ),
inference(superposition,[status(thm)],[c27,d77]) ).
cnf(d79,plain,
( identity != 'sk$uc7'
| identity != 'sk$uc5'
| identity != 'sk$uc6'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| 'sk$uc6' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc6'
| multiply('sk$uc6','sk$uc7') != 'sk$uc5'
| 'sk$uc5' != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d78,d69]) ).
cnf(d80,plain,
( identity != 'sk$uc7'
| identity != 'sk$uc5'
| identity != 'sk$uc6'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| 'sk$uc6' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc6'
| multiply('sk$uc6','sk$uc7') != 'sk$uc5'
| 'sk$uc5' != 'sk$uc5' ),
inference(demodulation,[status(thm)],[d79,d72]) ).
cnf(d81,plain,
( identity != 'sk$uc7'
| identity != 'sk$uc5'
| identity != 'sk$uc6'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| 'sk$uc6' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc7' != 'sk$uc5'
| 'sk$uc5' != 'sk$uc5' ),
inference(demodulation,[status(thm)],[d80,d69]) ).
cnf(d82,plain,
( identity != 'sk$uc7'
| identity != 'sk$uc5'
| identity != 'sk$uc6'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| 'sk$uc6' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc5' != 'sk$uc5'
| 'sk$uc5' != 'sk$uc5' ),
inference(demodulation,[status(thm)],[d81,d72]) ).
cnf(d83,plain,
( identity != 'sk$uc7'
| identity != 'sk$uc5'
| identity != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc6' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc5' != 'sk$uc5'
| 'sk$uc5' != 'sk$uc5' ),
inference(demodulation,[status(thm)],[d82,d21]) ).
cnf(d84,plain,
( identity != 'sk$uc7'
| identity != 'sk$uc5'
| identity != 'sk$uc6'
| 'sk$uc5' != 'sk$uc7'
| 'sk$uc6' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc5' != 'sk$uc5'
| 'sk$uc5' != 'sk$uc5' ),
inference(demodulation,[status(thm)],[d83,d72]) ).
cnf(d85,plain,
( identity != 'sk$uc7'
| identity != 'sk$uc5'
| identity != 'sk$uc6'
| 'sk$uc5' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc5' != 'sk$uc5'
| 'sk$uc5' != 'sk$uc5' ),
inference(demodulation,[status(thm)],[d84,d72]) ).
cnf(d86,plain,
( identity != 'sk$uc7'
| identity != 'sk$uc5'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc5' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc5' != 'sk$uc5'
| 'sk$uc5' != 'sk$uc5' ),
inference(demodulation,[status(thm)],[d85,d68]) ).
cnf(d87,plain,
( identity != 'sk$uc7'
| 'sk$uc6' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc5' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc5' != 'sk$uc5'
| 'sk$uc5' != 'sk$uc5' ),
inference(demodulation,[status(thm)],[d86,d68]) ).
cnf(d88,plain,
( 'sk$uc6' != 'sk$uc7'
| 'sk$uc6' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc5' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc5' != 'sk$uc5'
| 'sk$uc5' != 'sk$uc5' ),
inference(demodulation,[status(thm)],[d87,d68]) ).
cnf(d89,plain,
( 'sk$uc6' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc5' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc5' != 'sk$uc5'
| 'sk$uc5' != 'sk$uc5' ),
inference(demodulation,[status(thm)],[d88,d72]) ).
cnf(d90,plain,
identity = inverse(identity),
inference(superposition,[status(thm)],[d8,d60]) ).
cnf(d91,plain,
'sk$uc6' = inverse(identity),
inference(demodulation,[status(thm)],[d90,d68]) ).
cnf(d92,plain,
'sk$uc6' = inverse('sk$uc6'),
inference(demodulation,[status(thm)],[d91,d68]) ).
cnf(d93,plain,
X1 = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[status(thm)],[d1,d5]) ).
cnf(d94,plain,
( 'sk$uc7' = multiply('sk$uc6','sk$uc5')
| 'sk$uc7' = multiply(inverse('sk$uc6'),'sk$uc5') ),
inference(superposition,[status(thm)],[d70,d93]) ).
cnf(d95,plain,
( 'sk$uc7' = multiply('sk$uc6','sk$uc5')
| 'sk$uc7' = multiply('sk$uc6','sk$uc5') ),
inference(demodulation,[status(thm)],[d94,d92]) ).
cnf(d96,plain,
'sk$uc5' = multiply('sk$uc6','sk$uc5'),
inference(demodulation,[status(thm)],[d95,d72]) ).
cnf(d97,plain,
'sk$uc5' = 'sk$uc5',
inference(demodulation,[status(thm)],[d96,d69]) ).
cnf(d98,plain,
( 'sk$uc6' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc5' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc5' != 'sk$uc5' ),
inference(resolution,[status(thm)],[d97,d89]) ).
cnf(d99,plain,
'sk$uc6' = multiply(X0,inverse(X0)),
inference(demodulation,[status(thm)],[d61,d68]) ).
cnf(d100,plain,
'sk$uc6' = multiply('sk$uc6','sk$uc6'),
inference(superposition,[status(thm)],[d92,d99]) ).
cnf(d101,plain,
'sk$uc6' = 'sk$uc6',
inference(demodulation,[status(thm)],[d100,d69]) ).
cnf(d102,plain,
( 'sk$uc5' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc5' ),
inference(resolution,[status(thm)],[d101,d98]) ).
cnf(d103,plain,
( inverse('sk$uc2') = 'sk$uc6'
| multiply('sk$uc3','sk$uc6') = identity ),
inference(superposition,[status(thm)],[c22,d3]) ).
cnf(d104,plain,
( inverse('sk$uc2') = 'sk$uc6'
| inverse('sk$uc2') = 'sk$uc6'
| identity = 'sk$uc7' ),
inference(superposition,[status(thm)],[d103,c21]) ).
cnf(d105,plain,
( identity = 'sk$uc7'
| inverse('sk$uc6') = 'sk$uc2' ),
inference(superposition,[status(thm)],[d104,d21]) ).
cnf(d106,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[d9,c27]) ).
cnf(d107,plain,
identity = identity,
inference(demodulation,[status(thm)],[d106,c26]) ).
cnf(d108,plain,
( identity = 'sk$uc6'
| identity = 'sk$uc7' ),
inference(superposition,[status(thm)],[d51,d107]) ).
cnf(d109,plain,
( identity = 'sk$uc7'
| inverse('sk$uc6') = identity ),
inference(superposition,[status(thm)],[d108,d9]) ).
cnf(d110,plain,
( identity = 'sk$uc7'
| identity = 'sk$uc7'
| identity = 'sk$uc2' ),
inference(superposition,[status(thm)],[d109,d105]) ).
cnf(d111,plain,
( identity = 'sk$uc2'
| 'sk$uc6' = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d110,d68]) ).
cnf(d112,plain,
( 'sk$uc6' = 'sk$uc2'
| 'sk$uc6' = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d111,d68]) ).
cnf(d113,plain,
( 'sk$uc6' = 'sk$uc2'
| 'sk$uc6' = 'sk$uc5' ),
inference(demodulation,[status(thm)],[d112,d72]) ).
cnf(d114,plain,
( 'sk$uc6' = 'sk$uc2'
| 'sk$uc5' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc6' ),
inference(superposition,[status(thm)],[d113,d102]) ).
cnf(d115,plain,
( 'sk$uc6' = 'sk$uc2'
| 'sk$uc6' != 'sk$uc6' ),
inference(resolution,[status(thm)],[d97,d114]) ).
cnf(d116,plain,
'sk$uc6' = 'sk$uc2',
inference(resolution,[status(thm)],[d101,d115]) ).
cnf(d117,plain,
multiply(X0,'sk$uc6') = X0,
inference(demodulation,[status(thm)],[d13,d68]) ).
cnf(d118,plain,
( inverse('sk$uc3') = 'sk$uc6'
| 'sk$uc2' = 'sk$uc5' ),
inference(demodulation,[status(thm)],[c17,d117]) ).
cnf(d119,plain,
( 'sk$uc2' = 'sk$uc5'
| inverse('sk$uc6') = 'sk$uc3' ),
inference(superposition,[status(thm)],[d118,d21]) ).
cnf(d120,plain,
( 'sk$uc2' = 'sk$uc5'
| 'sk$uc6' = 'sk$uc3' ),
inference(demodulation,[status(thm)],[d119,d92]) ).
cnf(d121,plain,
multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d122,plain,
multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[status(thm)],[c28,d1]) ).
cnf(d123,plain,
multiply(inverse(multiply(X2,X0)),multiply(X2,X1)) = multiply(inverse(X0),X1),
inference(superposition,[status(thm)],[d121,d122]) ).
cnf(d124,plain,
( multiply('sk$uc2','sk$uc6') = 'sk$uc5'
| multiply(inverse(multiply(X0,'sk$uc3')),multiply(X0,'sk$uc7')) = 'sk$uc6' ),
inference(superposition,[status(thm)],[c16,d122]) ).
cnf(d125,plain,
( multiply('sk$uc2','sk$uc6') = 'sk$uc5'
| multiply(inverse('sk$uc3'),'sk$uc7') = 'sk$uc6' ),
inference(demodulation,[status(thm)],[d124,d123]) ).
cnf(d126,plain,
( multiply('sk$uc2','sk$uc6') = 'sk$uc5'
| multiply(inverse('sk$uc3'),'sk$uc5') = 'sk$uc6' ),
inference(demodulation,[status(thm)],[d125,d72]) ).
cnf(d127,plain,
( 'sk$uc2' = 'sk$uc5'
| multiply(inverse('sk$uc3'),'sk$uc5') = 'sk$uc6' ),
inference(demodulation,[status(thm)],[d126,d117]) ).
cnf(d128,plain,
( 'sk$uc2' = 'sk$uc5'
| multiply('sk$uc3','sk$uc6') = 'sk$uc5' ),
inference(superposition,[status(thm)],[d127,d121]) ).
cnf(d129,plain,
( 'sk$uc2' = 'sk$uc5'
| 'sk$uc3' = 'sk$uc5' ),
inference(demodulation,[status(thm)],[d128,d117]) ).
cnf(d130,plain,
( 'sk$uc2' = 'sk$uc5'
| 'sk$uc2' = 'sk$uc5'
| 'sk$uc6' = 'sk$uc5' ),
inference(superposition,[status(thm)],[d129,d120]) ).
cnf(d131,plain,
( 'sk$uc6' = 'sk$uc5'
| 'sk$uc6' = 'sk$uc5' ),
inference(demodulation,[status(thm)],[d130,d116]) ).
cnf(d132,plain,
'sk$uc5' != 'sk$uc5',
inference(resolution,[status(thm)],[d131,d102]) ).
cnf(d133,plain,
'sk$uc6' != 'sk$uc5',
inference(demodulation,[status(thm)],[d132,d131]) ).
cnf(d134,plain,
'sk$uc6' != 'sk$uc6',
inference(demodulation,[status(thm)],[d133,d131]) ).
cnf(d135,plain,
$false,
inference(resolution,[status(thm)],[d101,d134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP351-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.46 % Computer : n003.cluster.edu
% 0.21/0.46 % Model : x86_64 x86_64
% 0.21/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.46 % Memory : 8046.5625MB
% 0.21/0.46 % OS : Linux 6.8.0-71-generic
% 0.21/0.46 % CPULimit : 300
% 0.21/0.46 % WCLimit : 300
% 0.21/0.46 % DateTime : Fri Sep 25 14:49:22 UTC 2026
% 0.21/0.46 % CPUTime :
% 0.21/0.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 211.28/30.71 % SZS status Unsatisfiable for theBenchmark.p
% 211.28/30.71 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------