%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP253-1 : 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 07:23:29 AM UTC 2026
% Result : Unsatisfiable 72.96s 18.17s
% Output : CNFRefutation 72.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 10
% Syntax : Number of clauses : 92 ( 38 unt; 36 nHn; 58 RR)
% Number of literals : 226 ( 225 equ; 112 neg)
% Maximal clause size : 9 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 75 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this_1,negated_conjecture,
( multiply('sk$uc4','sk$uc7') = 'sk$uc6'
| multiply('sk$uc1','sk$uc7') = 'sk$uc6' ) ).
cnf(prove_this_2,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc1','sk$uc7') = 'sk$uc6' ) ).
cnf(prove_this_4,negated_conjecture,
( multiply('sk$uc4','sk$uc7') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc7' ) ).
cnf(prove_this_5,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7' ) ).
cnf(prove_this_9,negated_conjecture,
( inverse('sk$uc5') = 'sk$uc6'
| multiply('sk$uc2','sk$uc6') = 'sk$uc5' ) ).
cnf(prove_this_12,negated_conjecture,
( inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc2') = 'sk$uc6' ) ).
cnf(prove_this_19,negated_conjecture,
( inverse('sk$uc5') != 'sk$uc6'
| inverse(X3) != 'sk$uc7'
| multiply(X3,'sk$uc7') != 'sk$uc6'
| multiply(X2,'sk$uc5') != 'sk$uc6'
| inverse(X2) != 'sk$uc6'
| inverse(X1) != 'sk$uc6'
| multiply(X1,'sk$uc6') != 'sk$uc5'
| inverse(X0) != 'sk$uc7'
| multiply(X0,'sk$uc7') != 'sk$uc6' ) ).
cnf(left_identity,axiom,
multiply(identity,X0) = X0 ).
cnf(left_inverse,axiom,
multiply(inverse(X0),X0) = identity ).
cnf(associativity,axiom,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)) ).
cnf(c0,plain,
( multiply('sk$uc4','sk$uc7') = 'sk$uc6'
| multiply('sk$uc1','sk$uc7') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_1]) ).
cnf(c1,plain,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc1','sk$uc7') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_2]) ).
cnf(c3,plain,
( multiply('sk$uc4','sk$uc7') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_4]) ).
cnf(c4,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_5]) ).
cnf(c8,plain,
( inverse('sk$uc5') = 'sk$uc6'
| multiply('sk$uc2','sk$uc6') = 'sk$uc5' ),
inference(clausification,[status(esa)],[prove_this_9]) ).
cnf(c11,plain,
( inverse('sk$uc5') = 'sk$uc6'
| inverse('sk$uc2') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_12]) ).
cnf(c18,plain,
( multiply(X3,'sk$uc6') != 'sk$uc5'
| inverse(X1) != 'sk$uc6'
| inverse(X3) != 'sk$uc6'
| inverse('sk$uc5') != 'sk$uc6'
| inverse(X0) != 'sk$uc7'
| multiply(X2,'sk$uc7') != 'sk$uc6'
| inverse(X2) != 'sk$uc7'
| multiply(X1,'sk$uc5') != 'sk$uc6'
| multiply(X0,'sk$uc7') != 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_19]) ).
cnf(c19,plain,
multiply(identity,X0) = X0,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c20,plain,
multiply(inverse(X0),X0) = identity,
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c21,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)],[c19,c21]) ).
cnf(d1,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d0,c19]) ).
cnf(d2,plain,
identity = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[c20,d1]) ).
cnf(d3,plain,
multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c20,c21]) ).
cnf(d4,plain,
multiply(inverse(X1),multiply(X1,X0)) = X0,
inference(demodulation,[status(thm)],[d3,c19]) ).
cnf(d5,plain,
X0 = multiply(identity,X0),
inference(superposition,[status(thm)],[c19,d1]) ).
cnf(d6,plain,
multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
multiply(inverse(inverse(identity)),X0) = X0,
inference(superposition,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
identity = inverse(identity),
inference(superposition,[status(thm)],[d7,d2]) ).
cnf(d9,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[d8,c20]) ).
cnf(d10,plain,
identity = identity,
inference(demodulation,[status(thm)],[d9,c19]) ).
cnf(d11,plain,
( multiply('sk$uc4','sk$uc7') = 'sk$uc6'
| 'sk$uc6' = multiply('sk$uc1','sk$uc7') ),
inference(superposition,[status(thm)],[c0,d1]) ).
cnf(d12,plain,
multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[d4,d4]) ).
cnf(d13,plain,
multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[d12,c20]) ).
cnf(d14,plain,
( inverse('sk$uc4') = 'sk$uc7'
| multiply('sk$uc1','sk$uc7') = identity ),
inference(superposition,[status(thm)],[c4,d13]) ).
cnf(d15,plain,
( inverse('sk$uc4') = 'sk$uc7'
| inverse('sk$uc4') = 'sk$uc7'
| identity = 'sk$uc6' ),
inference(superposition,[status(thm)],[d14,c1]) ).
cnf(d16,plain,
( identity = 'sk$uc6'
| multiply('sk$uc4','sk$uc7') = identity ),
inference(superposition,[status(thm)],[d15,d13]) ).
cnf(d17,plain,
( identity = 'sk$uc6'
| 'sk$uc6' = multiply('sk$uc1','sk$uc7')
| identity = 'sk$uc6' ),
inference(superposition,[status(thm)],[d16,d11]) ).
cnf(d18,plain,
( identity = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc7'
| identity = 'sk$uc6' ),
inference(superposition,[status(thm)],[d16,c3]) ).
cnf(d19,plain,
( identity = 'sk$uc6'
| multiply('sk$uc1','sk$uc7') = identity ),
inference(superposition,[status(thm)],[d18,d13]) ).
cnf(d20,plain,
( identity = 'sk$uc6'
| identity = 'sk$uc6'
| 'sk$uc6' = identity ),
inference(superposition,[status(thm)],[d19,d17]) ).
cnf(d21,plain,
( identity = 'sk$uc6'
| identity = 'sk$uc6' ),
inference(superposition,[status(thm)],[d20,d10]) ).
cnf(d22,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[d7,c20]) ).
cnf(d23,plain,
inverse('sk$uc6') = identity,
inference(demodulation,[status(thm)],[d22,d21]) ).
cnf(d24,plain,
inverse('sk$uc6') = 'sk$uc6',
inference(demodulation,[status(thm)],[d23,d21]) ).
cnf(d25,plain,
multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c20,d4]) ).
cnf(d26,plain,
multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[d25,d12]) ).
cnf(d27,plain,
multiply(X0,'sk$uc6') = X0,
inference(demodulation,[status(thm)],[d26,d21]) ).
cnf(d28,plain,
multiply('sk$uc6',X0) = X0,
inference(demodulation,[status(thm)],[c19,d21]) ).
cnf(d29,plain,
( inverse('sk$uc2') = 'sk$uc6'
| multiply('sk$uc6','sk$uc5') = identity ),
inference(superposition,[status(thm)],[c11,c20]) ).
cnf(d30,plain,
( inverse('sk$uc2') = 'sk$uc6'
| identity = multiply('sk$uc6','sk$uc5') ),
inference(superposition,[status(thm)],[d29,d1]) ).
cnf(d31,plain,
( identity = multiply('sk$uc6','sk$uc5')
| multiply(inverse('sk$uc6'),X0) = multiply('sk$uc2',X0) ),
inference(superposition,[status(thm)],[d30,d12]) ).
cnf(d32,plain,
( identity = multiply('sk$uc6','sk$uc5')
| multiply('sk$uc6',X0) = multiply('sk$uc2',X0) ),
inference(demodulation,[status(thm)],[d31,d24]) ).
cnf(d33,plain,
( identity = multiply('sk$uc6','sk$uc5')
| X0 = multiply('sk$uc2',X0) ),
inference(demodulation,[status(thm)],[d32,d28]) ).
cnf(d34,plain,
( 'sk$uc6' = multiply('sk$uc6','sk$uc5')
| X0 = multiply('sk$uc2',X0) ),
inference(demodulation,[status(thm)],[d33,d21]) ).
cnf(d35,plain,
( 'sk$uc6' = 'sk$uc5'
| X0 = multiply('sk$uc2',X0) ),
inference(demodulation,[status(thm)],[d34,d28]) ).
cnf(d36,plain,
X0 = multiply(inverse(inverse(X0)),identity),
inference(superposition,[status(thm)],[d25,d1]) ).
cnf(d37,plain,
X0 = multiply(X0,identity),
inference(demodulation,[status(thm)],[d36,d12]) ).
cnf(d38,plain,
inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[status(thm)],[d37,d12]) ).
cnf(d39,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d38,d37]) ).
cnf(d40,plain,
X1 = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[status(thm)],[d4,d1]) ).
cnf(d41,plain,
identity = multiply(inverse(inverse(inverse(X0))),X0),
inference(superposition,[status(thm)],[d25,d40]) ).
cnf(d42,plain,
( inverse('sk$uc5') = 'sk$uc6'
| 'sk$uc5' = multiply('sk$uc2','sk$uc6') ),
inference(superposition,[status(thm)],[c8,d1]) ).
cnf(d43,plain,
( 'sk$uc5' = multiply('sk$uc2','sk$uc6')
| identity = multiply(inverse(inverse('sk$uc6')),'sk$uc5') ),
inference(superposition,[status(thm)],[d42,d41]) ).
cnf(d44,plain,
( identity = multiply(inverse(inverse('sk$uc6')),'sk$uc5')
| 'sk$uc5' = 'sk$uc2' ),
inference(demodulation,[status(thm)],[d43,d27]) ).
cnf(d45,plain,
( 'sk$uc6' = multiply(inverse(inverse('sk$uc6')),'sk$uc5')
| 'sk$uc5' = 'sk$uc2' ),
inference(demodulation,[status(thm)],[d44,d21]) ).
cnf(d46,plain,
( 'sk$uc6' = multiply('sk$uc6','sk$uc5')
| 'sk$uc5' = 'sk$uc2' ),
inference(demodulation,[status(thm)],[d45,d39]) ).
cnf(d47,plain,
( 'sk$uc6' = 'sk$uc5'
| 'sk$uc5' = 'sk$uc2' ),
inference(demodulation,[status(thm)],[d46,d28]) ).
cnf(d48,plain,
( 'sk$uc6' = 'sk$uc5'
| 'sk$uc6' = 'sk$uc5'
| X0 = multiply('sk$uc5',X0) ),
inference(superposition,[status(thm)],[d47,d35]) ).
cnf(d49,plain,
( 'sk$uc6' = 'sk$uc5'
| 'sk$uc6' = 'sk$uc5' ),
inference(superposition,[status(thm)],[d48,d27]) ).
cnf(d50,plain,
( inverse('sk$uc5') != 'sk$uc6'
| inverse(X2) != 'sk$uc7'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| multiply(X2,'sk$uc7') != 'sk$uc6'
| multiply(X1,'sk$uc5') != 'sk$uc6'
| multiply(X0,'sk$uc6') != 'sk$uc5'
| identity != 'sk$uc6' ),
inference(superposition,[status(thm)],[c20,c18]) ).
cnf(d51,plain,
multiply(inverse(inverse(inverse(X0))),X0) = identity,
inference(superposition,[status(thm)],[d25,d4]) ).
cnf(d52,plain,
( identity != 'sk$uc6'
| inverse('sk$uc5') != 'sk$uc6'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| inverse(inverse(inverse(inverse('sk$uc7')))) != 'sk$uc7'
| multiply(X1,'sk$uc6') != 'sk$uc5'
| multiply(X0,'sk$uc5') != 'sk$uc6'
| identity != 'sk$uc6' ),
inference(superposition,[status(thm)],[d51,d50]) ).
cnf(d53,plain,
( identity != 'sk$uc6'
| inverse('sk$uc5') != 'sk$uc6'
| inverse(inverse(inverse(inverse('sk$uc7')))) != 'sk$uc7'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| multiply(X1,'sk$uc5') != 'sk$uc6'
| X0 != 'sk$uc5' ),
inference(demodulation,[status(thm)],[d52,d27]) ).
cnf(d54,plain,
( identity != 'sk$uc6'
| inverse('sk$uc5') != 'sk$uc6'
| inverse(inverse(inverse(inverse('sk$uc7')))) != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| multiply(X1,'sk$uc5') != 'sk$uc6'
| X0 != 'sk$uc5' ),
inference(demodulation,[status(thm)],[d53,d39]) ).
cnf(d55,plain,
( identity != 'sk$uc6'
| inverse('sk$uc5') != 'sk$uc6'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| multiply(X1,'sk$uc5') != 'sk$uc6'
| X0 != 'sk$uc5' ),
inference(demodulation,[status(thm)],[d54,d39]) ).
cnf(d56,plain,
( identity != 'sk$uc6'
| inverse('sk$uc5') != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| multiply(X1,'sk$uc5') != 'sk$uc6'
| X0 != 'sk$uc5' ),
inference(demodulation,[status(thm)],[d55,d39]) ).
cnf(d57,plain,
( 'sk$uc6' != 'sk$uc6'
| inverse('sk$uc5') != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| multiply(X1,'sk$uc5') != 'sk$uc6'
| X0 != 'sk$uc5' ),
inference(demodulation,[status(thm)],[d56,d21]) ).
cnf(d58,plain,
multiply(X0,inverse(X0)) = 'sk$uc6',
inference(demodulation,[status(thm)],[d13,d21]) ).
cnf(d59,plain,
multiply('sk$uc6','sk$uc6') = 'sk$uc6',
inference(superposition,[status(thm)],[d24,d58]) ).
cnf(d60,plain,
'sk$uc6' = 'sk$uc6',
inference(demodulation,[status(thm)],[d59,d28]) ).
cnf(d61,plain,
( inverse('sk$uc5') != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| inverse(X1) != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| multiply(X1,'sk$uc5') != 'sk$uc6'
| X0 != 'sk$uc5' ),
inference(resolution,[status(thm)],[d60,d57]) ).
cnf(d62,plain,
( inverse('sk$uc5') != 'sk$uc6'
| inverse('sk$uc5') != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| multiply(X0,'sk$uc5') != 'sk$uc6' ),
inference(equality_resolution,[status(thm)],[d61]) ).
cnf(d63,plain,
( inverse('sk$uc5') != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| multiply(X0,'sk$uc6') != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d62,d49]) ).
cnf(d64,plain,
( inverse('sk$uc5') != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| X0 != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d63,d27]) ).
cnf(d65,plain,
( inverse('sk$uc6') != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| X0 != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d64,d49]) ).
cnf(d66,plain,
( 'sk$uc6' != 'sk$uc6'
| inverse(X0) != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| X0 != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d65,d24]) ).
cnf(d67,plain,
( inverse(X0) != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| X0 != 'sk$uc6' ),
inference(resolution,[status(thm)],[d60,d66]) ).
cnf(d68,plain,
( inverse('sk$uc6') != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7' ),
inference(equality_resolution,[status(thm)],[d67]) ).
cnf(d69,plain,
( 'sk$uc6' != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7' ),
inference(demodulation,[status(thm)],[d68,d24]) ).
cnf(d70,plain,
'sk$uc7' != 'sk$uc7',
inference(resolution,[status(thm)],[d60,d69]) ).
cnf(d71,plain,
$false,
inference(equality_resolution,[status(thm)],[d70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP253-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.34 % Computer : n003.cluster.edu
% 0.05/0.34 % Model : x86_64 x86_64
% 0.05/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.34 % Memory : 8046.5625MB
% 0.05/0.34 % OS : Linux 6.8.0-71-generic
% 0.05/0.34 % CPULimit : 300
% 0.05/0.34 % WCLimit : 300
% 0.05/0.34 % DateTime : Fri Sep 25 14:42:37 UTC 2026
% 0.05/0.34 % CPUTime :
% 0.05/0.34 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 72.96/18.17 % SZS status Unsatisfiable for theBenchmark.p
% 72.96/18.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------