%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP461-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/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 07:23:49 AM UTC 2026
% Result : Unsatisfiable 11.27s 3.04s
% Output : CNFRefutation 11.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of clauses : 31 ( 31 unt; 0 nHn; 5 RR)
% Number of literals : 31 ( 30 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(X0,divide(divide(divide(identity,X1),X2),divide(divide(divide(X0,X0),X0),X2))) = X1 ).
cnf(multiply,axiom,
multiply(X0,X1) = divide(X0,divide(identity,X1)) ).
cnf(inverse,axiom,
inverse(X0) = divide(identity,X0) ).
cnf(identity,axiom,
identity = divide(X0,X0) ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(identity,a2) != a2 ).
cnf(c0,plain,
divide(X0,divide(divide(divide(identity,X1),X2),divide(divide(divide(X0,X0),X0),X2))) = X1,
inference(clausification,[status(esa)],[single_axiom]) ).
cnf(c1,plain,
multiply(X0,X1) = divide(X0,divide(identity,X1)),
inference(clausification,[status(esa)],[multiply]) ).
cnf(c2,plain,
inverse(X0) = divide(identity,X0),
inference(clausification,[status(esa)],[inverse]) ).
cnf(c3,plain,
identity = divide(X0,X0),
inference(clausification,[status(esa)],[identity]) ).
cnf(c4,plain,
multiply(identity,a2) != a2,
inference(clausification,[status(esa)],[prove_these_axioms_2]) ).
cnf(d0,plain,
divide(X0,divide(divide(divide(identity,X1),X2),divide(divide(identity,X0),X2))) = X1,
inference(demodulation,[status(thm)],[c0,c3]) ).
cnf(d1,plain,
divide(X0,identity) = X0,
inference(superposition,[status(thm)],[c3,d0]) ).
cnf(d2,plain,
multiply(X0,identity) = divide(X0,identity),
inference(superposition,[status(thm)],[c3,c1]) ).
cnf(d3,plain,
multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
multiply(X1,X0) = divide(X1,inverse(X0)),
inference(demodulation,[status(thm)],[c1,c2]) ).
cnf(d5,plain,
identity = inverse(identity),
inference(superposition,[status(thm)],[c2,c3]) ).
cnf(d6,plain,
divide(divide(divide(divide(identity,X0),X1),divide(divide(identity,identity),X1)),divide(divide(divide(identity,X2),X3),divide(X0,X3))) = X2,
inference(superposition,[status(thm)],[d0,d0]) ).
cnf(d7,plain,
divide(divide(divide(inverse(X0),X1),divide(divide(identity,identity),X1)),divide(divide(divide(identity,X2),X3),divide(X0,X3))) = X2,
inference(demodulation,[status(thm)],[d6,c2]) ).
cnf(d8,plain,
divide(divide(divide(inverse(X0),X1),divide(inverse(identity),X1)),divide(divide(divide(identity,X2),X3),divide(X0,X3))) = X2,
inference(demodulation,[status(thm)],[d7,c2]) ).
cnf(d9,plain,
divide(divide(divide(inverse(X0),X1),divide(identity,X1)),divide(divide(divide(identity,X2),X3),divide(X0,X3))) = X2,
inference(demodulation,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
divide(divide(divide(inverse(X1),X0),inverse(X0)),divide(divide(divide(identity,X2),X3),divide(X1,X3))) = X2,
inference(demodulation,[status(thm)],[d9,c2]) ).
cnf(d11,plain,
divide(divide(divide(inverse(X1),X2),inverse(X2)),divide(divide(inverse(X0),X3),divide(X1,X3))) = X0,
inference(demodulation,[status(thm)],[d10,c2]) ).
cnf(d12,plain,
divide(divide(inverse(X0),inverse(identity)),divide(divide(inverse(X1),X2),divide(X0,X2))) = X1,
inference(superposition,[status(thm)],[d1,d11]) ).
cnf(d13,plain,
divide(multiply(inverse(X0),identity),divide(divide(inverse(X1),X2),divide(X0,X2))) = X1,
inference(demodulation,[status(thm)],[d12,d4]) ).
cnf(d14,plain,
divide(inverse(X0),divide(divide(inverse(X1),X2),divide(X0,X2))) = X1,
inference(demodulation,[status(thm)],[d13,d3]) ).
cnf(d15,plain,
divide(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c3,d14]) ).
cnf(d16,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d15,d1]) ).
cnf(d17,plain,
inverse(inverse(X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[d4,c2]) ).
cnf(d18,plain,
X0 = multiply(identity,X0),
inference(demodulation,[status(thm)],[d17,d16]) ).
cnf(d19,plain,
a2 != a2,
inference(demodulation,[status(thm)],[c4,d18]) ).
cnf(d20,plain,
$false,
inference(equality_resolution,[status(thm)],[d19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP461-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n015.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 14:58:43 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.27/3.04 % SZS status Unsatisfiable for theBenchmark.p
% 11.27/3.04 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------