%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP068-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 07:22:15 AM UTC 2026
% Result : Unsatisfiable 31.02s 5.13s
% Output : CNFRefutation 31.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 5
% Syntax : Number of clauses : 85 ( 80 unt; 0 nHn; 12 RR)
% Number of literals : 93 ( 92 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 164 ( 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,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ) ).
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(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
inference(clausification,[status(esa)],[prove_these_axioms]) ).
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(X1,X0) = divide(X1,inverse(X0)),
inference(demodulation,[status(thm)],[c1,c2]) ).
cnf(d3,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c2,d1]) ).
cnf(d4,plain,
multiply(X0,identity) = divide(X0,identity),
inference(superposition,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
inverse(inverse(X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[d2,c2]) ).
cnf(d7,plain,
identity = inverse(identity),
inference(superposition,[status(thm)],[c2,c3]) ).
cnf(d8,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(d9,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)],[d8,c2]) ).
cnf(d10,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)],[d9,c2]) ).
cnf(d11,plain,
divide(divide(divide(inverse(X0),X1),divide(identity,X1)),divide(divide(divide(identity,X2),X3),divide(X0,X3))) = X2,
inference(demodulation,[status(thm)],[d10,d7]) ).
cnf(d12,plain,
divide(divide(divide(inverse(X1),X0),inverse(X0)),divide(divide(divide(identity,X2),X3),divide(X1,X3))) = X2,
inference(demodulation,[status(thm)],[d11,c2]) ).
cnf(d13,plain,
divide(multiply(divide(inverse(X0),X1),X1),divide(divide(divide(identity,X2),X3),divide(X0,X3))) = X2,
inference(demodulation,[status(thm)],[d12,d2]) ).
cnf(d14,plain,
divide(multiply(divide(inverse(X1),X2),X2),divide(divide(inverse(X0),X3),divide(X1,X3))) = X0,
inference(demodulation,[status(thm)],[d13,c2]) ).
cnf(d15,plain,
divide(multiply(divide(inverse(inverse(X0)),X2),X2),identity) = X0,
inference(superposition,[status(thm)],[c3,d14]) ).
cnf(d16,plain,
multiply(divide(inverse(inverse(X0)),X1),X1) = X0,
inference(demodulation,[status(thm)],[d15,d1]) ).
cnf(d17,plain,
multiply(divide(multiply(identity,X0),X1),X1) = X0,
inference(demodulation,[status(thm)],[d16,d6]) ).
cnf(d18,plain,
X0 = divide(multiply(identity,X0),identity),
inference(superposition,[status(thm)],[d17,d5]) ).
cnf(d19,plain,
X0 = multiply(identity,X0),
inference(demodulation,[status(thm)],[d18,d1]) ).
cnf(d20,plain,
identity = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[d2,c3]) ).
cnf(d21,plain,
( identity != identity
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2 ),
inference(demodulation,[status(thm)],[c4,d20]) ).
cnf(d22,plain,
identity = multiply(multiply(identity,X0),inverse(X0)),
inference(superposition,[status(thm)],[d6,d20]) ).
cnf(d23,plain,
identity = multiply(identity,inverse(identity)),
inference(superposition,[status(thm)],[d5,d22]) ).
cnf(d24,plain,
identity = multiply(identity,identity),
inference(demodulation,[status(thm)],[d23,d7]) ).
cnf(d25,plain,
identity = identity,
inference(demodulation,[status(thm)],[d24,d5]) ).
cnf(d26,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2 ),
inference(resolution,[status(thm)],[d25,d21]) ).
cnf(d27,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(demodulation,[status(thm)],[d26,d19]) ).
cnf(d28,plain,
multiply(divide(X0,X1),X1) = X0,
inference(demodulation,[status(thm)],[d17,d19]) ).
cnf(d29,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d6,d19]) ).
cnf(d30,plain,
divide(X1,divide(identity,divide(divide(identity,X1),divide(identity,X0)))) = X0,
inference(superposition,[status(thm)],[c3,d0]) ).
cnf(d31,plain,
divide(X0,inverse(divide(divide(identity,X0),divide(identity,X1)))) = X1,
inference(demodulation,[status(thm)],[d30,c2]) ).
cnf(d32,plain,
multiply(X0,divide(divide(identity,X0),divide(identity,X1))) = X1,
inference(demodulation,[status(thm)],[d31,d2]) ).
cnf(d33,plain,
multiply(X0,divide(inverse(X0),divide(identity,X1))) = X1,
inference(demodulation,[status(thm)],[d32,c2]) ).
cnf(d34,plain,
multiply(X1,divide(inverse(X1),inverse(X0))) = X0,
inference(demodulation,[status(thm)],[d33,c2]) ).
cnf(d35,plain,
multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[d34,d2]) ).
cnf(d36,plain,
multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(superposition,[status(thm)],[d35,d35]) ).
cnf(d37,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d36,d29]) ).
cnf(d38,plain,
multiply(X1,inverse(X0)) = divide(X1,multiply(identity,X0)),
inference(superposition,[status(thm)],[d6,d2]) ).
cnf(d39,plain,
multiply(X1,inverse(X0)) = divide(X1,X0),
inference(demodulation,[status(thm)],[d38,d19]) ).
cnf(d40,plain,
divide(X0,X1) = multiply(X0,inverse(X1)),
inference(superposition,[status(thm)],[d39,d37]) ).
cnf(d41,plain,
divide(X1,inverse(X0)) = multiply(X1,X0),
inference(superposition,[status(thm)],[d29,d40]) ).
cnf(d42,plain,
divide(X0,divide(divide(divide(identity,X1),divide(identity,X0)),identity)) = X1,
inference(superposition,[status(thm)],[c3,d0]) ).
cnf(d43,plain,
divide(X1,divide(divide(identity,X0),divide(identity,X1))) = X0,
inference(demodulation,[status(thm)],[d42,d1]) ).
cnf(d44,plain,
divide(X1,divide(inverse(X0),divide(identity,X1))) = X0,
inference(demodulation,[status(thm)],[d43,c2]) ).
cnf(d45,plain,
divide(X0,divide(inverse(X1),inverse(X0))) = X1,
inference(demodulation,[status(thm)],[d44,c2]) ).
cnf(d46,plain,
divide(X1,multiply(inverse(X0),X1)) = X0,
inference(demodulation,[status(thm)],[d45,d2]) ).
cnf(d47,plain,
divide(X1,multiply(X0,X1)) = inverse(X0),
inference(superposition,[status(thm)],[d29,d46]) ).
cnf(d48,plain,
divide(X1,X0) = inverse(divide(X0,X1)),
inference(superposition,[status(thm)],[d28,d47]) ).
cnf(d49,plain,
divide(inverse(X1),X0) = inverse(multiply(X0,X1)),
inference(superposition,[status(thm)],[d2,d48]) ).
cnf(d50,plain,
divide(X2,divide(inverse(X1),X0)) = multiply(X2,multiply(X0,X1)),
inference(superposition,[status(thm)],[d49,d41]) ).
cnf(d51,plain,
X0 = divide(divide(X0,inverse(X1)),X1),
inference(superposition,[status(thm)],[d28,d39]) ).
cnf(d52,plain,
X0 = divide(multiply(X0,X1),X1),
inference(demodulation,[status(thm)],[d51,d2]) ).
cnf(d53,plain,
multiply(X2,divide(X0,X1)) = divide(X2,divide(X1,X0)),
inference(superposition,[status(thm)],[d48,d2]) ).
cnf(d54,plain,
X0 = divide(divide(X0,divide(X2,X1)),divide(X1,X2)),
inference(superposition,[status(thm)],[d53,d52]) ).
cnf(d55,plain,
X2 = divide(divide(X2,multiply(X0,X1)),divide(inverse(X1),X0)),
inference(superposition,[status(thm)],[d2,d54]) ).
cnf(d56,plain,
X0 = multiply(divide(X0,multiply(X1,X2)),multiply(X1,X2)),
inference(demodulation,[status(thm)],[d55,d50]) ).
cnf(d57,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d56,d28]) ).
cnf(d58,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(resolution,[status(thm)],[d57,d27]) ).
cnf(d59,plain,
divide(multiply(divide(identity,X0),X0),divide(divide(inverse(X1),X2),divide(identity,X2))) = X1,
inference(superposition,[status(thm)],[d3,d14]) ).
cnf(d60,plain,
divide(identity,divide(divide(inverse(X1),X2),divide(identity,X2))) = X1,
inference(demodulation,[status(thm)],[d59,d28]) ).
cnf(d61,plain,
inverse(divide(divide(inverse(X0),X1),divide(identity,X1))) = X0,
inference(demodulation,[status(thm)],[d60,c2]) ).
cnf(d62,plain,
divide(divide(identity,X1),divide(inverse(X0),X1)) = X0,
inference(demodulation,[status(thm)],[d61,d48]) ).
cnf(d63,plain,
divide(inverse(X0),divide(inverse(X1),X0)) = X1,
inference(demodulation,[status(thm)],[d62,c2]) ).
cnf(d64,plain,
divide(divide(X1,X0),divide(inverse(X2),divide(X0,X1))) = X2,
inference(superposition,[status(thm)],[d48,d63]) ).
cnf(d65,plain,
multiply(identity,X0) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c2,d2]) ).
cnf(d66,plain,
divide(multiply(divide(inverse(X1),X2),X2),divide(divide(multiply(identity,X0),X3),divide(X1,X3))) = inverse(X0),
inference(superposition,[status(thm)],[d65,d14]) ).
cnf(d67,plain,
divide(inverse(X0),divide(divide(multiply(identity,X2),X3),divide(X0,X3))) = inverse(X2),
inference(demodulation,[status(thm)],[d66,d28]) ).
cnf(d68,plain,
divide(inverse(X1),divide(divide(X0,X2),divide(X1,X2))) = inverse(X0),
inference(demodulation,[status(thm)],[d67,d19]) ).
cnf(d69,plain,
divide(divide(divide(X0,X2),divide(X1,X2)),inverse(X1)) = X0,
inference(superposition,[status(thm)],[d68,d64]) ).
cnf(d70,plain,
multiply(divide(divide(X0,X1),divide(X2,X1)),X2) = X0,
inference(demodulation,[status(thm)],[d69,d2]) ).
cnf(d71,plain,
multiply(divide(X0,divide(X2,X1)),X2) = multiply(X0,X1),
inference(superposition,[status(thm)],[d52,d70]) ).
cnf(d72,plain,
multiply(divide(X2,inverse(X1)),X0) = multiply(X2,multiply(X1,X0)),
inference(superposition,[status(thm)],[d47,d71]) ).
cnf(d73,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(demodulation,[status(thm)],[d72,d2]) ).
cnf(d74,plain,
$false,
inference(resolution,[status(thm)],[d73,d58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP068-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 14:20:32 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 31.02/5.13 % SZS status Unsatisfiable for theBenchmark.p
% 31.02/5.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------