%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP329-1 : 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 : n020.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 07:23:36 AM UTC 2026
% Result : Unsatisfiable 116.96s 34.75s
% Output : CNFRefutation 116.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 21
% Syntax : Number of clauses : 160 ( 48 unt; 84 nHn; 119 RR)
% Number of literals : 513 ( 512 equ; 280 neg)
% Maximal clause size : 13 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 154 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this_1,negated_conjecture,
( inverse('sk$uc8') = 'sk$uc7'
| multiply('sk$uc8','sk$uc9') = 'sk$uc7' ) ).
cnf(prove_this_6,negated_conjecture,
( multiply('sk$uc6','sk$uc9') = 'sk$uc7'
| multiply('sk$uc8','sk$uc9') = 'sk$uc7' ) ).
cnf(prove_this_7,negated_conjecture,
( inverse('sk$uc6') = 'sk$uc9'
| multiply('sk$uc8','sk$uc9') = 'sk$uc7' ) ).
cnf(prove_this_8,negated_conjecture,
( inverse('sk$uc8') = 'sk$uc7'
| multiply('sk$uc1','sk$uc8') = 'sk$uc9' ) ).
cnf(prove_this_11,negated_conjecture,
( multiply('sk$uc5','sk$uc8') = 'sk$uc9'
| multiply('sk$uc1','sk$uc8') = 'sk$uc9' ) ).
cnf(prove_this_12,negated_conjecture,
( inverse('sk$uc5') = 'sk$uc8'
| multiply('sk$uc1','sk$uc8') = 'sk$uc9' ) ).
cnf(prove_this_14,negated_conjecture,
( inverse('sk$uc6') = 'sk$uc9'
| multiply('sk$uc1','sk$uc8') = 'sk$uc9' ) ).
cnf(prove_this_15,negated_conjecture,
( inverse('sk$uc8') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc8' ) ).
cnf(prove_this_18,negated_conjecture,
( multiply('sk$uc5','sk$uc8') = 'sk$uc9'
| inverse('sk$uc1') = 'sk$uc8' ) ).
cnf(prove_this_19,negated_conjecture,
( inverse('sk$uc5') = 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc8' ) ).
cnf(prove_this_21,negated_conjecture,
( inverse('sk$uc6') = 'sk$uc9'
| inverse('sk$uc1') = 'sk$uc8' ) ).
cnf(prove_this_27,negated_conjecture,
( multiply('sk$uc6','sk$uc9') = 'sk$uc7'
| multiply('sk$uc9','sk$uc3') = 'sk$uc8' ) ).
cnf(prove_this_28,negated_conjecture,
( inverse('sk$uc6') = 'sk$uc9'
| multiply('sk$uc9','sk$uc3') = 'sk$uc8' ) ).
cnf(prove_this_34,negated_conjecture,
( multiply('sk$uc6','sk$uc9') = 'sk$uc7'
| multiply('sk$uc2','sk$uc9') = 'sk$uc3' ) ).
cnf(prove_this_35,negated_conjecture,
( inverse('sk$uc6') = 'sk$uc9'
| multiply('sk$uc2','sk$uc9') = 'sk$uc3' ) ).
cnf(prove_this_41,negated_conjecture,
( multiply('sk$uc6','sk$uc9') = 'sk$uc7'
| inverse('sk$uc2') = 'sk$uc9' ) ).
cnf(prove_this_42,negated_conjecture,
( inverse('sk$uc6') = 'sk$uc9'
| inverse('sk$uc2') = 'sk$uc9' ) ).
cnf(prove_this_43,negated_conjecture,
( inverse(X5) != 'sk$uc9'
| multiply(X5,'sk$uc9') != 'sk$uc7'
| inverse(X4) != 'sk$uc8'
| multiply(X4,'sk$uc8') != 'sk$uc9'
| inverse(X3) != 'sk$uc8'
| multiply(X3,'sk$uc8') != 'sk$uc7'
| inverse('sk$uc8') != 'sk$uc7'
| inverse(X2) != 'sk$uc9'
| multiply(X2,'sk$uc9') != X1
| multiply('sk$uc9',X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| multiply(X0,'sk$uc8') != 'sk$uc9'
| multiply('sk$uc8','sk$uc9') != 'sk$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,
( inverse('sk$uc8') = 'sk$uc7'
| multiply('sk$uc8','sk$uc9') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_1]) ).
cnf(c5,plain,
( multiply('sk$uc6','sk$uc9') = 'sk$uc7'
| multiply('sk$uc8','sk$uc9') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_6]) ).
cnf(c6,plain,
( inverse('sk$uc6') = 'sk$uc9'
| multiply('sk$uc8','sk$uc9') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_7]) ).
cnf(c7,plain,
( inverse('sk$uc8') = 'sk$uc7'
| multiply('sk$uc1','sk$uc8') = 'sk$uc9' ),
inference(clausification,[status(esa)],[prove_this_8]) ).
cnf(c10,plain,
( multiply('sk$uc5','sk$uc8') = 'sk$uc9'
| multiply('sk$uc1','sk$uc8') = 'sk$uc9' ),
inference(clausification,[status(esa)],[prove_this_11]) ).
cnf(c11,plain,
( inverse('sk$uc5') = 'sk$uc8'
| multiply('sk$uc1','sk$uc8') = 'sk$uc9' ),
inference(clausification,[status(esa)],[prove_this_12]) ).
cnf(c13,plain,
( inverse('sk$uc6') = 'sk$uc9'
| multiply('sk$uc1','sk$uc8') = 'sk$uc9' ),
inference(clausification,[status(esa)],[prove_this_14]) ).
cnf(c14,plain,
( inverse('sk$uc8') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_15]) ).
cnf(c17,plain,
( multiply('sk$uc5','sk$uc8') = 'sk$uc9'
| inverse('sk$uc1') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_18]) ).
cnf(c18,plain,
( inverse('sk$uc5') = 'sk$uc8'
| inverse('sk$uc1') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_19]) ).
cnf(c20,plain,
( inverse('sk$uc6') = 'sk$uc9'
| inverse('sk$uc1') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_21]) ).
cnf(c26,plain,
( multiply('sk$uc6','sk$uc9') = 'sk$uc7'
| multiply('sk$uc9','sk$uc3') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_27]) ).
cnf(c27,plain,
( inverse('sk$uc6') = 'sk$uc9'
| multiply('sk$uc9','sk$uc3') = 'sk$uc8' ),
inference(clausification,[status(esa)],[prove_this_28]) ).
cnf(c33,plain,
( multiply('sk$uc6','sk$uc9') = 'sk$uc7'
| multiply('sk$uc2','sk$uc9') = 'sk$uc3' ),
inference(clausification,[status(esa)],[prove_this_34]) ).
cnf(c34,plain,
( inverse('sk$uc6') = 'sk$uc9'
| multiply('sk$uc2','sk$uc9') = 'sk$uc3' ),
inference(clausification,[status(esa)],[prove_this_35]) ).
cnf(c40,plain,
( multiply('sk$uc6','sk$uc9') = 'sk$uc7'
| inverse('sk$uc2') = 'sk$uc9' ),
inference(clausification,[status(esa)],[prove_this_41]) ).
cnf(c41,plain,
( inverse('sk$uc6') = 'sk$uc9'
| inverse('sk$uc2') = 'sk$uc9' ),
inference(clausification,[status(esa)],[prove_this_42]) ).
cnf(c42,plain,
( multiply(X2,'sk$uc8') != 'sk$uc9'
| multiply(X5,'sk$uc8') != 'sk$uc9'
| multiply(X0,'sk$uc9') != 'sk$uc7'
| inverse('sk$uc8') != 'sk$uc7'
| inverse(X3) != 'sk$uc9'
| inverse(X1) != 'sk$uc8'
| multiply('sk$uc9',X4) != 'sk$uc8'
| inverse(X5) != 'sk$uc8'
| multiply(X3,'sk$uc9') != X4
| multiply('sk$uc8','sk$uc9') != 'sk$uc7'
| inverse(X2) != 'sk$uc8'
| multiply(X1,'sk$uc8') != 'sk$uc7'
| inverse(X0) != 'sk$uc9' ),
inference(clausification,[status(esa)],[prove_this_43]) ).
cnf(c43,plain,
multiply(identity,X0) = X0,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c44,plain,
multiply(inverse(X0),X0) = identity,
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c45,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)],[c43,c45]) ).
cnf(d1,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d0,c43]) ).
cnf(d2,plain,
identity = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[c44,d1]) ).
cnf(d3,plain,
multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c44,c45]) ).
cnf(d4,plain,
multiply(inverse(X1),multiply(X1,X0)) = X0,
inference(demodulation,[status(thm)],[d3,c43]) ).
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,c44]) ).
cnf(d8,plain,
( inverse('sk$uc5') = 'sk$uc8'
| multiply('sk$uc1','sk$uc8') = identity ),
inference(superposition,[status(thm)],[c18,d7]) ).
cnf(d9,plain,
( inverse('sk$uc5') = 'sk$uc8'
| inverse('sk$uc5') = 'sk$uc8'
| identity = 'sk$uc9' ),
inference(superposition,[status(thm)],[d8,c11]) ).
cnf(d10,plain,
( identity = 'sk$uc9'
| identity = multiply('sk$uc5','sk$uc8') ),
inference(superposition,[status(thm)],[d9,d6]) ).
cnf(d11,plain,
( identity = 'sk$uc9'
| inverse('sk$uc1') = 'sk$uc8'
| identity = 'sk$uc9' ),
inference(superposition,[status(thm)],[d10,c17]) ).
cnf(d12,plain,
( identity = 'sk$uc9'
| identity = multiply('sk$uc1','sk$uc8') ),
inference(superposition,[status(thm)],[d11,d6]) ).
cnf(d13,plain,
( identity = 'sk$uc9'
| multiply('sk$uc5','sk$uc8') = 'sk$uc9'
| identity = 'sk$uc9' ),
inference(superposition,[status(thm)],[d12,c10]) ).
cnf(d14,plain,
( identity = 'sk$uc9'
| identity = 'sk$uc9'
| identity = 'sk$uc9' ),
inference(superposition,[status(thm)],[d13,d10]) ).
cnf(d15,plain,
X0 = multiply(identity,X0),
inference(superposition,[status(thm)],[c43,d1]) ).
cnf(d16,plain,
multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[d15,d4]) ).
cnf(d17,plain,
multiply(inverse(inverse(identity)),X0) = X0,
inference(superposition,[status(thm)],[d16,d4]) ).
cnf(d18,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[d17,c44]) ).
cnf(d19,plain,
inverse('sk$uc9') = identity,
inference(demodulation,[status(thm)],[d18,d14]) ).
cnf(d20,plain,
inverse('sk$uc9') = 'sk$uc9',
inference(demodulation,[status(thm)],[d19,d14]) ).
cnf(d21,plain,
multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[d2,d4]) ).
cnf(d22,plain,
multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[d21,d5]) ).
cnf(d23,plain,
inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[status(thm)],[d22,d5]) ).
cnf(d24,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d23,d22]) ).
cnf(d25,plain,
( inverse('sk$uc6') = 'sk$uc9'
| multiply('sk$uc9','sk$uc2') = identity ),
inference(superposition,[status(thm)],[c41,c44]) ).
cnf(d26,plain,
( inverse('sk$uc6') = 'sk$uc9'
| multiply('sk$uc9',multiply('sk$uc2',X0)) = multiply(identity,X0) ),
inference(superposition,[status(thm)],[d25,c45]) ).
cnf(d27,plain,
( inverse('sk$uc6') = 'sk$uc9'
| multiply('sk$uc9',multiply('sk$uc2',X0)) = X0 ),
inference(demodulation,[status(thm)],[d26,c43]) ).
cnf(d28,plain,
( inverse('sk$uc6') = 'sk$uc9'
| inverse('sk$uc6') = 'sk$uc9'
| multiply('sk$uc9','sk$uc3') = 'sk$uc9' ),
inference(superposition,[status(thm)],[c34,d27]) ).
cnf(d29,plain,
( inverse('sk$uc6') = 'sk$uc9'
| inverse('sk$uc6') = 'sk$uc9'
| 'sk$uc9' = 'sk$uc8' ),
inference(superposition,[status(thm)],[d28,c27]) ).
cnf(d30,plain,
( 'sk$uc9' = 'sk$uc8'
| inverse('sk$uc9') = 'sk$uc6' ),
inference(superposition,[status(thm)],[d29,d24]) ).
cnf(d31,plain,
( 'sk$uc9' = 'sk$uc6'
| 'sk$uc9' = 'sk$uc8' ),
inference(demodulation,[status(thm)],[d30,d20]) ).
cnf(d32,plain,
multiply(X0,'sk$uc9') = X0,
inference(demodulation,[status(thm)],[d22,d14]) ).
cnf(d33,plain,
( multiply('sk$uc2','sk$uc9') = 'sk$uc3'
| 'sk$uc6' = 'sk$uc7' ),
inference(demodulation,[status(thm)],[c33,d32]) ).
cnf(d34,plain,
( 'sk$uc2' = 'sk$uc3'
| 'sk$uc6' = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d33,d32]) ).
cnf(d35,plain,
multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d5,d22]) ).
cnf(d36,plain,
X0 = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d35,d22]) ).
cnf(d37,plain,
( inverse('sk$uc2') = 'sk$uc9'
| 'sk$uc6' = 'sk$uc7' ),
inference(demodulation,[status(thm)],[c40,d32]) ).
cnf(d38,plain,
( 'sk$uc6' = 'sk$uc7'
| 'sk$uc2' = inverse('sk$uc9') ),
inference(superposition,[status(thm)],[d37,d36]) ).
cnf(d39,plain,
( 'sk$uc2' = 'sk$uc9'
| 'sk$uc6' = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d38,d20]) ).
cnf(d40,plain,
( 'sk$uc6' = 'sk$uc7'
| 'sk$uc6' = 'sk$uc7'
| 'sk$uc9' = 'sk$uc3' ),
inference(superposition,[status(thm)],[d39,d34]) ).
cnf(d41,plain,
X0 = multiply('sk$uc9',X0),
inference(demodulation,[status(thm)],[d15,d14]) ).
cnf(d42,plain,
( multiply('sk$uc9','sk$uc3') = 'sk$uc8'
| multiply('sk$uc6',multiply('sk$uc9',X0)) = multiply('sk$uc7',X0) ),
inference(superposition,[status(thm)],[c26,c45]) ).
cnf(d43,plain,
( multiply('sk$uc9','sk$uc3') = 'sk$uc8'
| multiply('sk$uc6','sk$uc9') = multiply('sk$uc7',identity) ),
inference(superposition,[status(thm)],[d22,d42]) ).
cnf(d44,plain,
( multiply('sk$uc6','sk$uc9') = multiply('sk$uc7',identity)
| 'sk$uc3' = 'sk$uc8' ),
inference(demodulation,[status(thm)],[d43,d41]) ).
cnf(d45,plain,
( 'sk$uc6' = multiply('sk$uc7',identity)
| 'sk$uc3' = 'sk$uc8' ),
inference(demodulation,[status(thm)],[d44,d32]) ).
cnf(d46,plain,
( 'sk$uc6' = multiply('sk$uc7','sk$uc9')
| 'sk$uc3' = 'sk$uc8' ),
inference(demodulation,[status(thm)],[d45,d14]) ).
cnf(d47,plain,
( 'sk$uc6' = 'sk$uc7'
| 'sk$uc3' = 'sk$uc8' ),
inference(demodulation,[status(thm)],[d46,d32]) ).
cnf(d48,plain,
( 'sk$uc6' = 'sk$uc7'
| 'sk$uc6' = 'sk$uc7'
| 'sk$uc9' = 'sk$uc8' ),
inference(superposition,[status(thm)],[d47,d40]) ).
cnf(d49,plain,
( 'sk$uc9' = 'sk$uc8'
| 'sk$uc9' = 'sk$uc8'
| 'sk$uc9' = 'sk$uc7' ),
inference(superposition,[status(thm)],[d48,d31]) ).
cnf(d50,plain,
( inverse('sk$uc8') = 'sk$uc7'
| multiply('sk$uc8','sk$uc1') = identity ),
inference(superposition,[status(thm)],[c14,c44]) ).
cnf(d51,plain,
( inverse('sk$uc8') = 'sk$uc7'
| multiply('sk$uc8',multiply('sk$uc1',X0)) = multiply(identity,X0) ),
inference(superposition,[status(thm)],[d50,c45]) ).
cnf(d52,plain,
( inverse('sk$uc8') = 'sk$uc7'
| multiply('sk$uc8',multiply('sk$uc1',X0)) = X0 ),
inference(demodulation,[status(thm)],[d51,c43]) ).
cnf(d53,plain,
( inverse('sk$uc8') = 'sk$uc7'
| inverse('sk$uc8') = 'sk$uc7'
| multiply('sk$uc8','sk$uc9') = 'sk$uc8' ),
inference(superposition,[status(thm)],[c7,d52]) ).
cnf(d54,plain,
( inverse('sk$uc8') = 'sk$uc7'
| inverse('sk$uc8') = 'sk$uc7'
| 'sk$uc8' = 'sk$uc7' ),
inference(superposition,[status(thm)],[d53,c0]) ).
cnf(d55,plain,
( 'sk$uc8' = 'sk$uc7'
| inverse('sk$uc7') = 'sk$uc8' ),
inference(superposition,[status(thm)],[d54,d24]) ).
cnf(d56,plain,
multiply(inverse(X0),identity) = inverse(X0),
inference(superposition,[status(thm)],[d7,d4]) ).
cnf(d57,plain,
inverse(X0) = inverse(X0),
inference(demodulation,[status(thm)],[d56,d22]) ).
cnf(d58,plain,
( inverse('sk$uc6') = 'sk$uc9'
| multiply('sk$uc8','sk$uc1') = identity ),
inference(superposition,[status(thm)],[c20,c44]) ).
cnf(d59,plain,
( inverse('sk$uc6') = 'sk$uc9'
| multiply('sk$uc8',multiply('sk$uc1',X0)) = multiply(identity,X0) ),
inference(superposition,[status(thm)],[d58,c45]) ).
cnf(d60,plain,
( inverse('sk$uc6') = 'sk$uc9'
| multiply('sk$uc8',multiply('sk$uc1',X0)) = X0 ),
inference(demodulation,[status(thm)],[d59,c43]) ).
cnf(d61,plain,
( inverse('sk$uc6') = 'sk$uc9'
| 'sk$uc9' = multiply('sk$uc1','sk$uc8') ),
inference(superposition,[status(thm)],[c13,d1]) ).
cnf(d62,plain,
( inverse('sk$uc6') = 'sk$uc9'
| inverse('sk$uc6') = 'sk$uc9'
| multiply('sk$uc8','sk$uc9') = 'sk$uc8' ),
inference(superposition,[status(thm)],[d61,d60]) ).
cnf(d63,plain,
( inverse('sk$uc6') = 'sk$uc9'
| inverse('sk$uc6') = 'sk$uc9'
| 'sk$uc8' = 'sk$uc7' ),
inference(superposition,[status(thm)],[d62,c6]) ).
cnf(d64,plain,
( 'sk$uc8' = 'sk$uc7'
| 'sk$uc9' = inverse('sk$uc6') ),
inference(superposition,[status(thm)],[d63,d57]) ).
cnf(d65,plain,
( multiply('sk$uc6','sk$uc9') = 'sk$uc7'
| 'sk$uc8' = 'sk$uc7' ),
inference(demodulation,[status(thm)],[c5,d32]) ).
cnf(d66,plain,
( 'sk$uc6' = 'sk$uc7'
| 'sk$uc8' = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d65,d32]) ).
cnf(d67,plain,
( 'sk$uc8' = 'sk$uc7'
| 'sk$uc8' = 'sk$uc7'
| 'sk$uc9' = inverse('sk$uc7') ),
inference(superposition,[status(thm)],[d66,d64]) ).
cnf(d68,plain,
( 'sk$uc8' = 'sk$uc7'
| 'sk$uc8' = 'sk$uc7'
| 'sk$uc9' = 'sk$uc8' ),
inference(superposition,[status(thm)],[d67,d55]) ).
cnf(d69,plain,
( 'sk$uc9' = 'sk$uc8'
| 'sk$uc9' = 'sk$uc8'
| 'sk$uc9' = 'sk$uc8' ),
inference(superposition,[status(thm)],[d68,d49]) ).
cnf(d70,plain,
( 'sk$uc8' = 'sk$uc7'
| inverse('sk$uc9') = 'sk$uc6' ),
inference(superposition,[status(thm)],[d63,d24]) ).
cnf(d71,plain,
( 'sk$uc9' = 'sk$uc6'
| 'sk$uc8' = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d70,d20]) ).
cnf(d72,plain,
( 'sk$uc8' = 'sk$uc7'
| 'sk$uc8' = 'sk$uc7'
| 'sk$uc9' = 'sk$uc7' ),
inference(superposition,[status(thm)],[d66,d71]) ).
cnf(d73,plain,
( 'sk$uc8' = 'sk$uc7'
| 'sk$uc8' = 'sk$uc7' ),
inference(demodulation,[status(thm)],[d72,d69]) ).
cnf(d74,plain,
identity = inverse(identity),
inference(superposition,[status(thm)],[d17,d2]) ).
cnf(d75,plain,
'sk$uc9' = inverse(identity),
inference(demodulation,[status(thm)],[d74,d14]) ).
cnf(d76,plain,
'sk$uc9' = inverse('sk$uc9'),
inference(demodulation,[status(thm)],[d75,d14]) ).
cnf(d77,plain,
'sk$uc8' = inverse('sk$uc9'),
inference(demodulation,[status(thm)],[d76,d69]) ).
cnf(d78,plain,
'sk$uc8' = inverse('sk$uc8'),
inference(demodulation,[status(thm)],[d77,d69]) ).
cnf(d79,plain,
multiply('sk$uc9',X0) = X0,
inference(demodulation,[status(thm)],[c43,d14]) ).
cnf(d80,plain,
multiply('sk$uc8',X0) = X0,
inference(demodulation,[status(thm)],[d79,d69]) ).
cnf(d81,plain,
multiply(X0,'sk$uc8') = X0,
inference(demodulation,[status(thm)],[d32,d69]) ).
cnf(d82,plain,
identity = 'sk$uc8',
inference(demodulation,[status(thm)],[d14,d69]) ).
cnf(d83,plain,
( inverse('sk$uc8') != 'sk$uc7'
| inverse(X1) != 'sk$uc8'
| inverse(X4) != 'sk$uc8'
| inverse(X2) != 'sk$uc9'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc9'
| multiply('sk$uc9',X3) != 'sk$uc8'
| multiply('sk$uc8','sk$uc9') != 'sk$uc7'
| multiply(X4,'sk$uc8') != 'sk$uc7'
| multiply(X2,'sk$uc9') != X3
| multiply(X1,'sk$uc8') != 'sk$uc9'
| multiply(X0,'sk$uc9') != 'sk$uc7' ),
inference(factoring,[status(thm)],[c42]) ).
cnf(d84,plain,
X0 = multiply(inverse(inverse(X0)),identity),
inference(superposition,[status(thm)],[d21,d1]) ).
cnf(d85,plain,
X0 = multiply(X0,identity),
inference(demodulation,[status(thm)],[d84,d5]) ).
cnf(d86,plain,
( inverse('sk$uc8') != 'sk$uc7'
| inverse(X3) != 'sk$uc9'
| inverse(X2) != 'sk$uc8'
| inverse(X1) != 'sk$uc9'
| inverse(X0) != 'sk$uc8'
| multiply('sk$uc8','sk$uc9') != 'sk$uc7'
| multiply(X3,'sk$uc9') != 'sk$uc7'
| multiply(X2,'sk$uc8') != 'sk$uc9'
| multiply(X1,'sk$uc9') != identity
| multiply(X0,'sk$uc8') != 'sk$uc7'
| 'sk$uc9' != 'sk$uc8' ),
inference(superposition,[status(thm)],[d85,d83]) ).
cnf(d87,plain,
( inverse('sk$uc8') != 'sk$uc7'
| inverse(X3) != 'sk$uc8'
| inverse(X2) != 'sk$uc9'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc9'
| 'sk$uc9' != 'sk$uc8'
| multiply('sk$uc8','sk$uc9') != 'sk$uc7'
| multiply(X3,'sk$uc8') != 'sk$uc7'
| multiply(X2,'sk$uc9') != identity
| multiply(X1,'sk$uc8') != 'sk$uc9'
| multiply(X0,'sk$uc8') != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d86,d69]) ).
cnf(d88,plain,
( inverse('sk$uc8') != 'sk$uc7'
| inverse(X3) != 'sk$uc8'
| inverse(X2) != 'sk$uc9'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc9'
| 'sk$uc9' != 'sk$uc8'
| multiply('sk$uc8','sk$uc9') != 'sk$uc7'
| multiply(X3,'sk$uc8') != 'sk$uc7'
| multiply(X2,'sk$uc9') != identity
| multiply(X1,'sk$uc8') != 'sk$uc9'
| X0 != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d87,d81]) ).
cnf(d89,plain,
( inverse('sk$uc8') != 'sk$uc7'
| inverse(X3) != 'sk$uc8'
| inverse(X2) != 'sk$uc9'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc9'
| 'sk$uc9' != 'sk$uc8'
| multiply('sk$uc8','sk$uc9') != 'sk$uc7'
| multiply(X3,'sk$uc8') != 'sk$uc7'
| multiply(X2,'sk$uc9') != identity
| multiply(X1,'sk$uc8') != 'sk$uc9'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d88,d73]) ).
cnf(d90,plain,
( inverse('sk$uc8') != 'sk$uc7'
| inverse(X3) != 'sk$uc8'
| inverse(X2) != 'sk$uc9'
| inverse(X0) != 'sk$uc8'
| inverse(X1) != 'sk$uc9'
| 'sk$uc9' != 'sk$uc8'
| multiply('sk$uc8','sk$uc9') != 'sk$uc7'
| multiply(X3,'sk$uc8') != 'sk$uc7'
| multiply(X2,'sk$uc9') != identity
| X0 != 'sk$uc9'
| X1 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d89,d81]) ).
cnf(d91,plain,
( inverse('sk$uc8') != 'sk$uc7'
| inverse(X3) != 'sk$uc8'
| inverse(X2) != 'sk$uc9'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc9'
| 'sk$uc9' != 'sk$uc8'
| multiply('sk$uc8','sk$uc9') != 'sk$uc7'
| multiply(X3,'sk$uc8') != 'sk$uc7'
| multiply(X2,'sk$uc9') != identity
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d90,d69]) ).
cnf(d92,plain,
( inverse('sk$uc8') != 'sk$uc7'
| inverse(X3) != 'sk$uc8'
| inverse(X2) != 'sk$uc9'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc9'
| 'sk$uc9' != 'sk$uc8'
| multiply('sk$uc8','sk$uc9') != 'sk$uc7'
| multiply(X3,'sk$uc8') != 'sk$uc7'
| multiply(X2,'sk$uc8') != identity
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d91,d69]) ).
cnf(d93,plain,
( inverse('sk$uc8') != 'sk$uc7'
| inverse(X3) != 'sk$uc8'
| inverse(X0) != 'sk$uc9'
| inverse(X2) != 'sk$uc8'
| inverse(X1) != 'sk$uc9'
| 'sk$uc9' != 'sk$uc8'
| multiply('sk$uc8','sk$uc9') != 'sk$uc7'
| multiply(X3,'sk$uc8') != 'sk$uc7'
| X0 != identity
| X2 != 'sk$uc8'
| X1 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d92,d81]) ).
cnf(d94,plain,
( inverse('sk$uc8') != 'sk$uc7'
| inverse(X3) != 'sk$uc8'
| inverse(X2) != 'sk$uc9'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc9'
| 'sk$uc9' != 'sk$uc8'
| multiply('sk$uc8','sk$uc9') != 'sk$uc7'
| multiply(X3,'sk$uc8') != 'sk$uc7'
| X2 != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d93,d82]) ).
cnf(d95,plain,
( inverse('sk$uc8') != 'sk$uc7'
| inverse(X0) != 'sk$uc8'
| inverse(X3) != 'sk$uc9'
| inverse(X2) != 'sk$uc8'
| inverse(X1) != 'sk$uc9'
| 'sk$uc9' != 'sk$uc8'
| multiply('sk$uc8','sk$uc9') != 'sk$uc7'
| X0 != 'sk$uc7'
| X3 != 'sk$uc8'
| X2 != 'sk$uc8'
| X1 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d94,d81]) ).
cnf(d96,plain,
( inverse('sk$uc8') != 'sk$uc7'
| inverse(X3) != 'sk$uc8'
| inverse(X2) != 'sk$uc9'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc9'
| 'sk$uc9' != 'sk$uc8'
| multiply('sk$uc8','sk$uc9') != 'sk$uc7'
| X3 != 'sk$uc8'
| X2 != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d95,d73]) ).
cnf(d97,plain,
( inverse('sk$uc8') != 'sk$uc7'
| inverse(X3) != 'sk$uc8'
| inverse(X2) != 'sk$uc9'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc9'
| 'sk$uc9' != 'sk$uc8'
| 'sk$uc9' != 'sk$uc7'
| X3 != 'sk$uc8'
| X2 != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d96,d80]) ).
cnf(d98,plain,
( inverse('sk$uc8') != 'sk$uc7'
| inverse(X3) != 'sk$uc8'
| inverse(X2) != 'sk$uc9'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc9'
| 'sk$uc9' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc7'
| X3 != 'sk$uc8'
| X2 != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d97,d69]) ).
cnf(d99,plain,
( inverse('sk$uc8') != 'sk$uc7'
| inverse(X3) != 'sk$uc8'
| inverse(X2) != 'sk$uc9'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc9'
| 'sk$uc9' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X3 != 'sk$uc8'
| X2 != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d98,d73]) ).
cnf(d100,plain,
( inverse('sk$uc8') != 'sk$uc7'
| inverse(X3) != 'sk$uc8'
| inverse(X2) != 'sk$uc9'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc9'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X3 != 'sk$uc8'
| X2 != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d99,d69]) ).
cnf(d101,plain,
( inverse('sk$uc8') != 'sk$uc7'
| inverse(X3) != 'sk$uc8'
| inverse(X2) != 'sk$uc9'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X3 != 'sk$uc8'
| X2 != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d100,d69]) ).
cnf(d102,plain,
( inverse('sk$uc8') != 'sk$uc7'
| inverse(X3) != 'sk$uc8'
| inverse(X2) != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X3 != 'sk$uc8'
| X2 != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d101,d69]) ).
cnf(d103,plain,
( 'sk$uc8' != 'sk$uc7'
| inverse(X3) != 'sk$uc8'
| inverse(X2) != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X3 != 'sk$uc8'
| X2 != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d102,d78]) ).
cnf(d104,plain,
( 'sk$uc8' != 'sk$uc8'
| inverse(X3) != 'sk$uc8'
| inverse(X2) != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X3 != 'sk$uc8'
| X2 != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(demodulation,[status(thm)],[d103,d73]) ).
cnf(d105,plain,
'sk$uc9' = multiply(X0,inverse(X0)),
inference(demodulation,[status(thm)],[d6,d14]) ).
cnf(d106,plain,
'sk$uc8' = multiply(X0,inverse(X0)),
inference(demodulation,[status(thm)],[d105,d69]) ).
cnf(d107,plain,
inverse('sk$uc8') = 'sk$uc9',
inference(demodulation,[status(thm)],[d20,d69]) ).
cnf(d108,plain,
inverse('sk$uc8') = 'sk$uc8',
inference(demodulation,[status(thm)],[d107,d69]) ).
cnf(d109,plain,
'sk$uc8' = multiply('sk$uc8','sk$uc8'),
inference(superposition,[status(thm)],[d108,d106]) ).
cnf(d110,plain,
'sk$uc8' = 'sk$uc8',
inference(demodulation,[status(thm)],[d109,d80]) ).
cnf(d111,plain,
( 'sk$uc8' != 'sk$uc8'
| inverse(X3) != 'sk$uc8'
| inverse(X2) != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X3 != 'sk$uc8'
| X2 != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(resolution,[status(thm)],[d110,d104]) ).
cnf(d112,plain,
( inverse(X2) != 'sk$uc8'
| inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X2 != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8' ),
inference(superposition,[status(thm)],[d108,d111]) ).
cnf(d113,plain,
( inverse(X1) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X1 != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(factoring,[status(thm)],[d112]) ).
cnf(d114,plain,
( inverse(X0) != 'sk$uc8'
| inverse(X0) != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(factoring,[status(thm)],[d113]) ).
cnf(d115,plain,
( inverse(X0) != 'sk$uc8'
| X0 != 'sk$uc8' ),
inference(resolution,[status(thm)],[d110,d114]) ).
cnf(d116,plain,
( 'sk$uc8' != 'sk$uc8'
| 'sk$uc8' != 'sk$uc8' ),
inference(superposition,[status(thm)],[d108,d115]) ).
cnf(d117,plain,
$false,
inference(resolution,[status(thm)],[d110,d116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP329-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n020.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 14:46:34 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 116.96/34.75 % SZS status Unsatisfiable for theBenchmark.p
% 116.96/34.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------