%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP011-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 07:22:05 AM UTC 2026
% Result : Unsatisfiable 18.56s 7.85s
% Output : CNFRefutation 18.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of clauses : 34 ( 34 unt; 0 nHn; 11 RR)
% Number of literals : 34 ( 33 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)) ).
cnf(left_identity,axiom,
multiply(identity,X0) = X0 ).
cnf(left_inverse,axiom,
multiply(inverse(X0),X0) = identity ).
cnf(product_equality,hypothesis,
multiply(b,c) = multiply(d,c) ).
cnf(prove_left_cancellation,negated_conjecture,
b != d ).
cnf(c0,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(clausification,[status(esa)],[associativity]) ).
cnf(c1,plain,
multiply(identity,X0) = X0,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c2,plain,
multiply(inverse(X0),X0) = identity,
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c3,plain,
multiply(b,c) = multiply(d,c),
inference(clausification,[status(esa)],[product_equality]) ).
cnf(c4,plain,
b != d,
inference(clausification,[status(esa)],[prove_left_cancellation]) ).
cnf(d0,plain,
multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[status(thm)],[c2,c0]) ).
cnf(d1,plain,
X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(demodulation,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(superposition,[status(thm)],[d1,d1]) ).
cnf(d3,plain,
X0 = multiply(inverse(inverse(X0)),identity),
inference(superposition,[status(thm)],[c2,d1]) ).
cnf(d4,plain,
X0 = multiply(X0,identity),
inference(demodulation,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
multiply(X0,X1) = multiply(identity,multiply(X0,X1)),
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(d6,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d5,c1]) ).
cnf(d7,plain,
multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(superposition,[status(thm)],[d1,d6]) ).
cnf(d8,plain,
multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[d2,d7]) ).
cnf(d9,plain,
multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[d2,c2]) ).
cnf(d10,plain,
multiply(multiply(b,c),X0) = multiply(d,multiply(c,X0)),
inference(superposition,[status(thm)],[c3,c0]) ).
cnf(d11,plain,
multiply(b,multiply(c,X0)) = multiply(d,multiply(c,X0)),
inference(demodulation,[status(thm)],[d10,c0]) ).
cnf(d12,plain,
multiply(c,X0) = multiply(inverse(d),multiply(b,multiply(c,X0))),
inference(superposition,[status(thm)],[d11,d1]) ).
cnf(d13,plain,
multiply(c,inverse(c)) = multiply(inverse(d),multiply(b,identity)),
inference(superposition,[status(thm)],[d9,d12]) ).
cnf(d14,plain,
identity = multiply(inverse(d),multiply(b,identity)),
inference(demodulation,[status(thm)],[d13,d9]) ).
cnf(d15,plain,
identity = multiply(inverse(d),b),
inference(demodulation,[status(thm)],[d14,d4]) ).
cnf(d16,plain,
multiply(d,identity) = b,
inference(superposition,[status(thm)],[d15,d8]) ).
cnf(d17,plain,
d = b,
inference(demodulation,[status(thm)],[d16,d4]) ).
cnf(d18,plain,
b != b,
inference(demodulation,[status(thm)],[c4,d17]) ).
cnf(d19,plain,
X2 = multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))),
inference(superposition,[status(thm)],[c0,d1]) ).
cnf(d20,plain,
X0 = multiply(inverse(multiply(b,c)),multiply(d,multiply(c,X0))),
inference(superposition,[status(thm)],[c3,d19]) ).
cnf(d21,plain,
X0 = multiply(inverse(multiply(b,c)),multiply(b,multiply(c,X0))),
inference(demodulation,[status(thm)],[d20,d11]) ).
cnf(d22,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d21,d19]) ).
cnf(d23,plain,
$false,
inference(resolution,[status(thm)],[d22,d18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP011-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/5.44 % Computer : n015.cluster.edu
% 0.17/5.44 % Model : x86_64 x86_64
% 0.17/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.44 % Memory : 8046.5625MB
% 0.17/5.44 % OS : Linux 6.8.0-71-generic
% 0.17/5.44 % CPULimit : 300
% 0.17/5.44 % WCLimit : 300
% 0.17/5.45 % DateTime : Fri Sep 25 14:19:32 UTC 2026
% 0.17/5.45 % CPUTime :
% 0.17/5.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.56/7.85 % SZS status Unsatisfiable for theBenchmark.p
% 18.56/7.85 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------