%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP214-1 : 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 07:23:26 AM UTC 2026
% Result : Unsatisfiable 27.87s 9.39s
% Output : CNFRefutation 27.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 8
% Syntax : Number of clauses : 64 ( 36 unt; 16 nHn; 36 RR)
% Number of literals : 132 ( 131 equ; 62 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 71 ( 16 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this_3,negated_conjecture,
( multiply('sk$uc4','sk$uc5') = 'sk$uc6'
| multiply('sk$uc1','sk$uc7') = 'sk$uc6' ) ).
cnf(prove_this_4,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc5'
| multiply('sk$uc1','sk$uc7') = 'sk$uc6' ) ).
cnf(prove_this_7,negated_conjecture,
( multiply('sk$uc4','sk$uc5') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc7' ) ).
cnf(prove_this_8,negated_conjecture,
( inverse('sk$uc4') = 'sk$uc5'
| inverse('sk$uc1') = 'sk$uc7' ) ).
cnf(prove_this_13,negated_conjecture,
( inverse(X4) != X3
| multiply(X4,X3) != 'sk$uc6'
| inverse(X2) != 'sk$uc7'
| multiply(X2,'sk$uc7') != X3
| multiply('sk$uc7',X1) != 'sk$uc6'
| inverse(X0) != 'sk$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(c2,plain,
( multiply('sk$uc4','sk$uc5') = 'sk$uc6'
| multiply('sk$uc1','sk$uc7') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_3]) ).
cnf(c3,plain,
( inverse('sk$uc4') = 'sk$uc5'
| multiply('sk$uc1','sk$uc7') = 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_4]) ).
cnf(c6,plain,
( multiply('sk$uc4','sk$uc5') = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_7]) ).
cnf(c7,plain,
( inverse('sk$uc4') = 'sk$uc5'
| inverse('sk$uc1') = 'sk$uc7' ),
inference(clausification,[status(esa)],[prove_this_8]) ).
cnf(c12,plain,
( inverse(X4) != X3
| inverse(X2) != 'sk$uc7'
| multiply(X4,X3) != 'sk$uc6'
| inverse(X1) != 'sk$uc7'
| multiply(X2,'sk$uc7') != X3
| multiply(X1,'sk$uc7') != 'sk$uc6'
| multiply('sk$uc7',X0) != 'sk$uc6' ),
inference(clausification,[status(esa)],[prove_this_13]) ).
cnf(c13,plain,
multiply(identity,X0) = X0,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c14,plain,
multiply(inverse(X0),X0) = identity,
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c15,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)],[c13,c15]) ).
cnf(d1,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d0,c13]) ).
cnf(d2,plain,
identity = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[c14,d1]) ).
cnf(d3,plain,
multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c14,c15]) ).
cnf(d4,plain,
multiply(inverse(X1),multiply(X1,X0)) = X0,
inference(demodulation,[status(thm)],[d3,c13]) ).
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,c14]) ).
cnf(d8,plain,
( inverse('sk$uc4') = 'sk$uc5'
| multiply('sk$uc1','sk$uc7') = identity ),
inference(superposition,[status(thm)],[c7,d7]) ).
cnf(d9,plain,
( inverse('sk$uc4') = 'sk$uc5'
| inverse('sk$uc4') = 'sk$uc5'
| identity = 'sk$uc6' ),
inference(superposition,[status(thm)],[d8,c3]) ).
cnf(d10,plain,
( identity = 'sk$uc6'
| identity = multiply('sk$uc4','sk$uc5') ),
inference(superposition,[status(thm)],[d9,d6]) ).
cnf(d11,plain,
( identity = 'sk$uc6'
| inverse('sk$uc1') = 'sk$uc7'
| identity = 'sk$uc6' ),
inference(superposition,[status(thm)],[d10,c6]) ).
cnf(d12,plain,
( identity = 'sk$uc6'
| identity = multiply('sk$uc1','sk$uc7') ),
inference(superposition,[status(thm)],[d11,d6]) ).
cnf(d13,plain,
( multiply('sk$uc4','sk$uc5') = 'sk$uc6'
| 'sk$uc6' = multiply('sk$uc1','sk$uc7') ),
inference(superposition,[status(thm)],[c2,d1]) ).
cnf(d14,plain,
( identity = 'sk$uc6'
| 'sk$uc6' = multiply('sk$uc1','sk$uc7')
| identity = 'sk$uc6' ),
inference(superposition,[status(thm)],[d10,d13]) ).
cnf(d15,plain,
( identity = 'sk$uc6'
| identity = 'sk$uc6'
| identity = 'sk$uc6' ),
inference(superposition,[status(thm)],[d14,d12]) ).
cnf(d16,plain,
multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[d2,d4]) ).
cnf(d17,plain,
X0 = multiply(inverse(inverse(X0)),identity),
inference(superposition,[status(thm)],[d16,d1]) ).
cnf(d18,plain,
X0 = multiply(X0,identity),
inference(demodulation,[status(thm)],[d17,d5]) ).
cnf(d19,plain,
inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[status(thm)],[d18,d5]) ).
cnf(d20,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d19,d18]) ).
cnf(d21,plain,
( inverse(X2) != X1
| inverse(X0) != 'sk$uc7'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| multiply('sk$uc7',X3) != 'sk$uc6'
| multiply(X2,X1) != 'sk$uc6'
| multiply(X0,'sk$uc7') != X1
| identity != 'sk$uc6' ),
inference(superposition,[status(thm)],[c14,c12]) ).
cnf(d22,plain,
( identity != 'sk$uc6'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse(X1) != 'sk$uc7'
| inverse(inverse(X0)) != X0
| multiply('sk$uc7',X2) != 'sk$uc6'
| multiply(X1,'sk$uc7') != X0
| identity != 'sk$uc6' ),
inference(superposition,[status(thm)],[d2,d21]) ).
cnf(d23,plain,
( identity != 'sk$uc6'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| inverse(inverse(multiply(X1,'sk$uc7'))) != multiply(X1,'sk$uc7')
| inverse(X1) != 'sk$uc7'
| multiply('sk$uc7',X0) != 'sk$uc6' ),
inference(equality_resolution,[status(thm)],[d22]) ).
cnf(d24,plain,
( identity != 'sk$uc6'
| inverse(inverse('sk$uc7')) != 'sk$uc7'
| multiply(X0,'sk$uc7') != multiply(X0,'sk$uc7')
| inverse(X0) != 'sk$uc7'
| multiply('sk$uc7',X1) != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d23,d20]) ).
cnf(d25,plain,
( identity != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| multiply(X1,'sk$uc7') != multiply(X1,'sk$uc7')
| inverse(X1) != 'sk$uc7'
| multiply('sk$uc7',X0) != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d24,d20]) ).
cnf(d26,plain,
( 'sk$uc6' != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| multiply(X1,'sk$uc7') != multiply(X1,'sk$uc7')
| inverse(X1) != 'sk$uc7'
| multiply('sk$uc7',X0) != 'sk$uc6' ),
inference(demodulation,[status(thm)],[d25,d15]) ).
cnf(d27,plain,
( 'sk$uc6' != 'sk$uc6'
| 'sk$uc7' != 'sk$uc7'
| inverse(X1) != 'sk$uc7'
| multiply('sk$uc7',X0) != 'sk$uc6' ),
inference(resolution,[status(thm)],[d1,d26]) ).
cnf(d28,plain,
multiply('sk$uc6',X0) = X0,
inference(demodulation,[status(thm)],[c13,d15]) ).
cnf(d29,plain,
'sk$uc6' = multiply(X0,inverse(X0)),
inference(demodulation,[status(thm)],[d6,d15]) ).
cnf(d30,plain,
X0 = multiply(identity,X0),
inference(superposition,[status(thm)],[c13,d1]) ).
cnf(d31,plain,
multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[d30,d4]) ).
cnf(d32,plain,
multiply(inverse(inverse(identity)),X0) = X0,
inference(superposition,[status(thm)],[d31,d4]) ).
cnf(d33,plain,
identity = inverse(identity),
inference(superposition,[status(thm)],[d32,d2]) ).
cnf(d34,plain,
'sk$uc6' = inverse(identity),
inference(demodulation,[status(thm)],[d33,d15]) ).
cnf(d35,plain,
'sk$uc6' = inverse('sk$uc6'),
inference(demodulation,[status(thm)],[d34,d15]) ).
cnf(d36,plain,
'sk$uc6' = multiply('sk$uc6','sk$uc6'),
inference(superposition,[status(thm)],[d35,d29]) ).
cnf(d37,plain,
'sk$uc6' = 'sk$uc6',
inference(demodulation,[status(thm)],[d36,d28]) ).
cnf(d38,plain,
( inverse(X1) != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| multiply('sk$uc7',X0) != 'sk$uc6' ),
inference(resolution,[status(thm)],[d37,d27]) ).
cnf(d39,plain,
multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = 'sk$uc6',
inference(superposition,[status(thm)],[d29,c15]) ).
cnf(d40,plain,
( inverse(X1) != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7'
| 'sk$uc6' != 'sk$uc6' ),
inference(superposition,[status(thm)],[d39,d38]) ).
cnf(d41,plain,
( inverse(X0) != 'sk$uc7'
| 'sk$uc7' != 'sk$uc7' ),
inference(resolution,[status(thm)],[d37,d40]) ).
cnf(d42,plain,
inverse(X0) != 'sk$uc7',
inference(equality_resolution,[status(thm)],[d41]) ).
cnf(d43,plain,
multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[d16,d5]) ).
cnf(d44,plain,
multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d5,d43]) ).
cnf(d45,plain,
X0 = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d44,d18]) ).
cnf(d46,plain,
X0 != 'sk$uc7',
inference(superposition,[status(thm)],[d45,d42]) ).
cnf(d47,plain,
$false,
inference(equality_resolution,[status(thm)],[d46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP214-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/1.19 % Computer : n005.cluster.edu
% 0.10/1.19 % Model : x86_64 x86_64
% 0.10/1.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/1.19 % Memory : 8046.5625MB
% 0.10/1.19 % OS : Linux 6.8.0-71-generic
% 0.10/1.19 % CPULimit : 300
% 0.10/1.19 % WCLimit : 300
% 0.10/1.20 % DateTime : Fri Sep 25 14:38:33 UTC 2026
% 0.15/1.20 % CPUTime :
% 0.15/1.20 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 27.87/9.39 % SZS status Unsatisfiable for theBenchmark.p
% 27.87/9.39 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------