%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP292-1 : 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 : n005.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 07:23:32 AM UTC 2026
% Result : Unsatisfiable 68.76s 9.92s
% Output : CNFRefutation 68.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 9
% Syntax : Number of clauses : 75 ( 35 unt; 21 nHn; 46 RR)
% Number of literals : 205 ( 204 equ; 124 neg)
% Maximal clause size : 9 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this_1,negated_conjecture,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| multiply('sk$uc7','sk$uc6') = 'sk$uc5' ) ).
cnf(prove_this_6,negated_conjecture,
( multiply('sk$uc3','sk$uc4') = 'sk$uc6'
| multiply('sk$uc1','sk$uc7') = 'sk$uc6' ) ).
cnf(prove_this_7,negated_conjecture,
( inverse('sk$uc3') = 'sk$uc4'
| multiply('sk$uc1','sk$uc7') = 'sk$uc6' ) ).
cnf(prove_this_10,negated_conjecture,
( multiply('sk$uc3','sk$uc4') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc7' ) ).
cnf(prove_this_11,negated_conjecture,
( inverse('sk$uc3') = 'sk$uc4'
| inverse('sk$uc1') = 'sk$uc7' ) ).
cnf(prove_this_21,negated_conjecture,
( multiply(X3,'sk$uc5') != 'sk$uc6'
| inverse(X2) != X3
| multiply(X2,X3) != 'sk$uc6'
| multiply('sk$uc5','sk$uc6') != 'sk$uc7'
| inverse(X1) != 'sk$uc5'
| multiply(X1,'sk$uc5') != 'sk$uc6'
| inverse(X0) != 'sk$uc7'
| multiply(X0,'sk$uc7') != 'sk$uc6'
| multiply('sk$uc7','sk$uc6') != 'sk$uc5' ) ).
cnf(left_identity,axiom,
multiply(identity,X0) = X0 ).
cnf(left_inverse,axiom,
multiply(inverse(X0),X0) = identity ).
cnf(associativity,axiom,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)) ).
cnf(c0,plain,
( multiply('sk$uc5','sk$uc6') = 'sk$uc7'
| multiply('sk$uc7','sk$uc6') = 'sk$uc5' ),
inference(clausification,[status(esa)],[prove_this_1]) ).
cnf(c5,plain,
( multiply('sk$uc3','sk$uc4') = 'sk$uc6'
| multiply('sk$uc1','sk$uc7') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_6]) ).
cnf(c6,plain,
( inverse('sk$uc3') = 'sk$uc4'
| multiply('sk$uc1','sk$uc7') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_7]) ).
cnf(c9,plain,
( multiply('sk$uc3','sk$uc4') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_10]) ).
cnf(c10,plain,
( inverse('sk$uc3') = 'sk$uc4'
| inverse('sk$uc1') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_11]) ).
cnf(c20,plain,
( multiply(X1,'sk$uc5') != 'sk$uc6'
| multiply(X2,'sk$uc5') != 'sk$uc6'
| multiply('sk$uc7','sk$uc6') != 'sk$uc5'
| multiply('sk$uc5','sk$uc6') != 'sk$uc7'
| multiply(X3,'sk$uc7') != 'sk$uc6'
| inverse(X0) != X1
| inverse(X3) != 'sk$uc7'
| inverse(X2) != 'sk$uc5'
| multiply(X0,X1) != 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_21]) ).
cnf(c21,plain,
multiply(identity,X0) = X0,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c22,plain,
multiply(inverse(X0),X0) = identity,
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c23,plain,
multiply(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)],[c22,c23]) ).
cnf(d1,plain,
multiply(inverse(X1),multiply(X1,X0)) = X0,
inference(demodulation,[status(thm)],[d0,c21]) ).
cnf(d2,plain,
multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[d1,d1]) ).
cnf(d3,plain,
multiply(identity,multiply(X0,X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c21,c23]) ).
cnf(d4,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d3,c21]) ).
cnf(d5,plain,
identity = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[c22,d4]) ).
cnf(d6,plain,
multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[status(thm)],[d7,d2]) ).
cnf(d9,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
identity = multiply(X0,inverse(X0)),
inference(superposition,[status(thm)],[d2,d5]) ).
cnf(d11,plain,
multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[d2,c22]) ).
cnf(d12,plain,
( inverse('sk$uc1') = 'sk$uc7'
| multiply('sk$uc3','sk$uc4') = identity ),
inference(superposition,[status(thm)],[c10,d11]) ).
cnf(d13,plain,
( inverse('sk$uc1') = 'sk$uc7'
| inverse('sk$uc1') = 'sk$uc7'
| identity = 'sk$uc6' ),
inference(superposition,[status(thm)],[d12,c9]) ).
cnf(d14,plain,
( identity = 'sk$uc6'
| identity = multiply('sk$uc1','sk$uc7') ),
inference(superposition,[status(thm)],[d13,d10]) ).
cnf(d15,plain,
( identity = 'sk$uc6'
| inverse('sk$uc3') = 'sk$uc4'
| identity = 'sk$uc6' ),
inference(superposition,[status(thm)],[d14,c6]) ).
cnf(d16,plain,
( identity = 'sk$uc6'
| identity = multiply('sk$uc3','sk$uc4') ),
inference(superposition,[status(thm)],[d15,d10]) ).
cnf(d17,plain,
( multiply('sk$uc1','sk$uc7') = 'sk$uc6'
| 'sk$uc6' = multiply('sk$uc3','sk$uc4') ),
inference(superposition,[status(thm)],[c5,d4]) ).
cnf(d18,plain,
( identity = 'sk$uc6'
| 'sk$uc6' = multiply('sk$uc3','sk$uc4')
| identity = 'sk$uc6' ),
inference(superposition,[status(thm)],[d14,d17]) ).
cnf(d19,plain,
( identity = 'sk$uc6'
| identity = 'sk$uc6'
| identity = 'sk$uc6' ),
inference(superposition,[status(thm)],[d18,d16]) ).
cnf(d20,plain,
X0 = multiply(inverse(inverse(X0)),identity),
inference(superposition,[status(thm)],[d6,d4]) ).
cnf(d21,plain,
X0 = multiply(X0,identity),
inference(demodulation,[status(thm)],[d20,d2]) ).
cnf(d22,plain,
X0 = multiply(X0,'sk$uc6'),
inference(demodulation,[status(thm)],[d21,d19]) ).
cnf(d23,plain,
( multiply('sk$uc7','sk$uc6') = 'sk$uc5'
| 'sk$uc7' = multiply('sk$uc5','sk$uc6') ),
inference(superposition,[status(thm)],[c0,d4]) ).
cnf(d24,plain,
( 'sk$uc7' = multiply('sk$uc5','sk$uc6')
| 'sk$uc7' = 'sk$uc5' ),
inference(demodulation,[status(thm)],[d23,d22]) ).
cnf(d25,plain,
( 'sk$uc7' = 'sk$uc5'
| 'sk$uc7' = 'sk$uc5' ),
inference(demodulation,[status(thm)],[d24,d22]) ).
cnf(d26,plain,
( inverse(X2) != 'sk$uc7'
| inverse(X1) != 'sk$uc5'
| inverse(X0) != inverse('sk$uc5')
| multiply('sk$uc7','sk$uc6') != 'sk$uc5'
| multiply('sk$uc5','sk$uc6') != 'sk$uc7'
| multiply(X2,'sk$uc7') != 'sk$uc6'
| multiply(X1,'sk$uc5') != 'sk$uc6'
| multiply(X0,inverse('sk$uc5')) != 'sk$uc6'
| identity != 'sk$uc6' ),
inference(superposition,[status(thm)],[c22,c20]) ).
cnf(d27,plain,
( identity != 'sk$uc6'
| inverse(X1) != inverse('sk$uc5')
| inverse(X0) != 'sk$uc5'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| multiply('sk$uc7','sk$uc6') != 'sk$uc5'
| multiply('sk$uc5','sk$uc6') != 'sk$uc7'
| multiply(X1,inverse('sk$uc5')) != 'sk$uc6'
| multiply(X0,'sk$uc5') != 'sk$uc6'
| identity != 'sk$uc6' ),
inference(superposition,[status(thm)],[d5,d26]) ).
cnf(d28,plain,
( identity != 'sk$uc6'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse(X0) != 'sk$uc5'
| inverse(inverse(inverse('sk$uc5'))) != inverse('sk$uc5')
| multiply('sk$uc7','sk$uc6') != 'sk$uc5'
| multiply('sk$uc5','sk$uc6') != 'sk$uc7'
| multiply(X0,'sk$uc5') != 'sk$uc6'
| identity != 'sk$uc6' ),
inference(superposition,[status(thm)],[d5,d27]) ).
cnf(d29,plain,
( identity != 'sk$uc6'
| inverse(inverse(inverse('sk$uc5'))) != inverse('sk$uc5')
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse(X0) != 'sk$uc5'
| multiply('sk$uc7','sk$uc6') != 'sk$uc5'
| 'sk$uc5' != 'sk$uc7'
| multiply(X0,'sk$uc5') != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d28,d22]) ).
cnf(d30,plain,
( identity != 'sk$uc6'
| inverse(inverse(inverse('sk$uc5'))) != inverse('sk$uc5')
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse(X0) != 'sk$uc5'
| multiply('sk$uc7','sk$uc6') != 'sk$uc5'
| 'sk$uc5' != 'sk$uc5'
| multiply(X0,'sk$uc5') != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d29,d25]) ).
cnf(d31,plain,
( identity != 'sk$uc6'
| inverse(inverse(inverse('sk$uc5'))) != inverse('sk$uc5')
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse(X0) != 'sk$uc5'
| 'sk$uc7' != 'sk$uc5'
| 'sk$uc5' != 'sk$uc5'
| multiply(X0,'sk$uc5') != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d30,d22]) ).
cnf(d32,plain,
( identity != 'sk$uc6'
| inverse(inverse(inverse('sk$uc5'))) != inverse('sk$uc5')
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse(X0) != 'sk$uc5'
| 'sk$uc5' != 'sk$uc5'
| 'sk$uc5' != 'sk$uc5'
| multiply(X0,'sk$uc5') != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d31,d25]) ).
cnf(d33,plain,
( identity != 'sk$uc6'
| inverse(inverse(inverse('sk$uc5'))) != inverse('sk$uc5')
| 'sk$uc7' != 'sk$uc7'
| inverse(X0) != 'sk$uc5'
| 'sk$uc5' != 'sk$uc5'
| 'sk$uc5' != 'sk$uc5'
| multiply(X0,'sk$uc5') != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d32,d9]) ).
cnf(d34,plain,
( identity != 'sk$uc6'
| inverse(inverse(inverse('sk$uc5'))) != inverse('sk$uc5')
| 'sk$uc5' != 'sk$uc7'
| inverse(X0) != 'sk$uc5'
| 'sk$uc5' != 'sk$uc5'
| 'sk$uc5' != 'sk$uc5'
| multiply(X0,'sk$uc5') != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d33,d25]) ).
cnf(d35,plain,
( identity != 'sk$uc6'
| inverse(inverse(inverse('sk$uc5'))) != inverse('sk$uc5')
| 'sk$uc5' != 'sk$uc5'
| inverse(X0) != 'sk$uc5'
| 'sk$uc5' != 'sk$uc5'
| 'sk$uc5' != 'sk$uc5'
| multiply(X0,'sk$uc5') != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d34,d25]) ).
cnf(d36,plain,
( identity != 'sk$uc6'
| inverse('sk$uc5') != inverse('sk$uc5')
| 'sk$uc5' != 'sk$uc5'
| inverse(X0) != 'sk$uc5'
| 'sk$uc5' != 'sk$uc5'
| 'sk$uc5' != 'sk$uc5'
| multiply(X0,'sk$uc5') != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d35,d9]) ).
cnf(d37,plain,
( 'sk$uc6' != 'sk$uc6'
| inverse('sk$uc5') != inverse('sk$uc5')
| 'sk$uc5' != 'sk$uc5'
| inverse(X0) != 'sk$uc5'
| 'sk$uc5' != 'sk$uc5'
| 'sk$uc5' != 'sk$uc5'
| multiply(X0,'sk$uc5') != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d36,d19]) ).
cnf(d38,plain,
X1 = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[status(thm)],[d1,d4]) ).
cnf(d39,plain,
inverse(X0) = multiply(inverse(X0),identity),
inference(superposition,[status(thm)],[d11,d38]) ).
cnf(d40,plain,
inverse(X0) = inverse(X0),
inference(demodulation,[status(thm)],[d39,d7]) ).
cnf(d41,plain,
( 'sk$uc6' != 'sk$uc6'
| 'sk$uc5' != 'sk$uc5'
| inverse(X0) != 'sk$uc5'
| 'sk$uc5' != 'sk$uc5'
| 'sk$uc5' != 'sk$uc5'
| multiply(X0,'sk$uc5') != 'sk$uc6' ),
inference(resolution,[status(thm)],[d40,d37]) ).
cnf(d42,plain,
X0 = multiply(identity,X0),
inference(superposition,[status(thm)],[c21,d4]) ).
cnf(d43,plain,
X0 = multiply('sk$uc6',X0),
inference(demodulation,[status(thm)],[d42,d19]) ).
cnf(d44,plain,
multiply(inverse(X0),X0) = 'sk$uc6',
inference(demodulation,[status(thm)],[c22,d19]) ).
cnf(d45,plain,
multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c21,d1]) ).
cnf(d46,plain,
multiply(inverse(inverse(identity)),X0) = X0,
inference(superposition,[status(thm)],[d45,d1]) ).
cnf(d47,plain,
identity = inverse(identity),
inference(superposition,[status(thm)],[d46,d5]) ).
cnf(d48,plain,
'sk$uc6' = inverse(identity),
inference(demodulation,[status(thm)],[d47,d19]) ).
cnf(d49,plain,
'sk$uc6' = inverse('sk$uc6'),
inference(demodulation,[status(thm)],[d48,d19]) ).
cnf(d50,plain,
multiply('sk$uc6','sk$uc6') = 'sk$uc6',
inference(superposition,[status(thm)],[d49,d44]) ).
cnf(d51,plain,
'sk$uc6' = 'sk$uc6',
inference(demodulation,[status(thm)],[d50,d43]) ).
cnf(d52,plain,
( inverse(X0) != 'sk$uc5'
| 'sk$uc5' != 'sk$uc5'
| multiply(X0,'sk$uc5') != 'sk$uc6' ),
inference(resolution,[status(thm)],[d51,d41]) ).
cnf(d53,plain,
( inverse(inverse('sk$uc5')) != 'sk$uc5'
| 'sk$uc5' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc6' ),
inference(superposition,[status(thm)],[d44,d52]) ).
cnf(d54,plain,
( 'sk$uc5' != 'sk$uc5'
| 'sk$uc6' != 'sk$uc6'
| 'sk$uc5' != 'sk$uc5' ),
inference(demodulation,[status(thm)],[d53,d9]) ).
cnf(d55,plain,
( 'sk$uc5' != 'sk$uc5'
| 'sk$uc5' != 'sk$uc5' ),
inference(resolution,[status(thm)],[d51,d54]) ).
cnf(d56,plain,
$false,
inference(equality_resolution,[status(thm)],[d55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP292-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.38 % Computer : n005.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Fri Sep 25 14:43:32 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 68.76/9.92 % SZS status Unsatisfiable for theBenchmark.p
% 68.76/9.92 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------