%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP092-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 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 07:22:18 AM UTC 2026
% Result : Unsatisfiable 68.00s 17.91s
% Output : CNFRefutation 68.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of clauses : 97 ( 85 unt; 0 nHn; 18 RR)
% Number of literals : 123 ( 122 equ; 39 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 186 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(divide(X0,X1),divide(divide(X0,X2),X1)) = X2 ).
cnf(multiply,axiom,
multiply(X0,X1) = divide(X0,divide(divide(X2,X2),X1)) ).
cnf(inverse,axiom,
inverse(X0) = divide(divide(X1,X1),X0) ).
cnf(identity,axiom,
identity = divide(X0,X0) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ) ).
cnf(c0,plain,
divide(divide(X0,X1),divide(divide(X0,X2),X1)) = X2,
inference(clausification,[status(esa)],[single_axiom]) ).
cnf(c1,plain,
multiply(X0,X1) = divide(X0,divide(divide(X2,X2),X1)),
inference(clausification,[status(esa)],[multiply]) ).
cnf(c2,plain,
inverse(X0) = divide(divide(X1,X1),X0),
inference(clausification,[status(esa)],[inverse]) ).
cnf(c3,plain,
identity = divide(X0,X0),
inference(clausification,[status(esa)],[identity]) ).
cnf(c4,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(clausification,[status(esa)],[prove_these_axioms]) ).
cnf(d0,plain,
inverse(X1) = divide(identity,X1),
inference(demodulation,[status(thm)],[c2,c3]) ).
cnf(d1,plain,
multiply(X1,X2) = divide(X1,divide(identity,X2)),
inference(demodulation,[status(thm)],[c1,c3]) ).
cnf(d2,plain,
multiply(X1,X0) = divide(X1,inverse(X0)),
inference(demodulation,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
divide(identity,divide(divide(X0,X1),X0)) = X1,
inference(superposition,[status(thm)],[c3,c0]) ).
cnf(d4,plain,
inverse(divide(divide(X0,X1),X0)) = X1,
inference(demodulation,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
inverse(divide(identity,X0)) = X0,
inference(superposition,[status(thm)],[c3,d4]) ).
cnf(d6,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
inverse(X1) = divide(divide(X0,X1),X0),
inference(superposition,[status(thm)],[d4,d6]) ).
cnf(d8,plain,
inverse(divide(inverse(X0),identity)) = X0,
inference(superposition,[status(thm)],[d0,d4]) ).
cnf(d9,plain,
inverse(X0) = divide(inverse(X0),identity),
inference(superposition,[status(thm)],[d8,d6]) ).
cnf(d10,plain,
inverse(inverse(X0)) = divide(X0,identity),
inference(superposition,[status(thm)],[d6,d9]) ).
cnf(d11,plain,
X0 = divide(X0,identity),
inference(demodulation,[status(thm)],[d10,d6]) ).
cnf(d12,plain,
divide(divide(X0,divide(X0,X1)),identity) = X1,
inference(superposition,[status(thm)],[c3,c0]) ).
cnf(d13,plain,
divide(X0,divide(X0,X1)) = X1,
inference(demodulation,[status(thm)],[d12,d11]) ).
cnf(d14,plain,
inverse(divide(X0,X1)) = divide(X1,X0),
inference(superposition,[status(thm)],[d13,d7]) ).
cnf(d15,plain,
multiply(X2,divide(X0,X1)) = divide(X2,divide(X1,X0)),
inference(superposition,[status(thm)],[d14,d2]) ).
cnf(d16,plain,
divide(divide(X0,X1),divide(identity,X1)) = X0,
inference(superposition,[status(thm)],[c3,c0]) ).
cnf(d17,plain,
divide(divide(X1,X0),inverse(X0)) = X1,
inference(demodulation,[status(thm)],[d16,d0]) ).
cnf(d18,plain,
multiply(divide(X0,X1),X1) = X0,
inference(demodulation,[status(thm)],[d17,d2]) ).
cnf(d19,plain,
multiply(X1,divide(X0,X1)) = X0,
inference(superposition,[status(thm)],[d13,d18]) ).
cnf(d20,plain,
divide(divide(divide(X0,X1),X3),divide(X2,X3)) = divide(divide(X0,X2),X1),
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d21,plain,
X3 = divide(divide(X0,divide(divide(X0,X1),X3)),X1),
inference(superposition,[status(thm)],[c0,d20]) ).
cnf(d22,plain,
multiply(X1,X2) = divide(X0,divide(divide(X0,X1),X2)),
inference(superposition,[status(thm)],[d21,d19]) ).
cnf(d23,plain,
multiply(X1,X2) = multiply(X0,divide(X2,divide(X0,X1))),
inference(demodulation,[status(thm)],[d22,d15]) ).
cnf(d24,plain,
multiply(X2,X0) = multiply(X1,multiply(X0,divide(X2,X1))),
inference(demodulation,[status(thm)],[d23,d15]) ).
cnf(d25,plain,
multiply(X1,inverse(X0)) = divide(X1,X0),
inference(superposition,[status(thm)],[d6,d2]) ).
cnf(d26,plain,
divide(divide(X0,divide(divide(X0,X2),X1)),X2) = X1,
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d27,plain,
divide(divide(X0,inverse(X1)),X1) = X0,
inference(superposition,[status(thm)],[d7,d26]) ).
cnf(d28,plain,
divide(multiply(X0,X1),X1) = X0,
inference(demodulation,[status(thm)],[d27,d2]) ).
cnf(d29,plain,
multiply(X1,X0) = multiply(X0,X1),
inference(superposition,[status(thm)],[d28,d19]) ).
cnf(d30,plain,
X0 = divide(divide(X0,inverse(X1)),X1),
inference(superposition,[status(thm)],[d18,d25]) ).
cnf(d31,plain,
X0 = divide(multiply(X0,X1),X1),
inference(demodulation,[status(thm)],[d30,d2]) ).
cnf(d32,plain,
X0 = multiply(multiply(X0,inverse(X1)),X1),
inference(superposition,[status(thm)],[d2,d31]) ).
cnf(d33,plain,
X0 = multiply(X1,multiply(X0,inverse(X1))),
inference(demodulation,[status(thm)],[d32,d29]) ).
cnf(d34,plain,
X0 = multiply(X1,divide(X0,X1)),
inference(demodulation,[status(thm)],[d33,d25]) ).
cnf(d35,plain,
divide(X0,divide(divide(X0,X1),X2)) = multiply(X1,X2),
inference(superposition,[status(thm)],[d26,d34]) ).
cnf(d36,plain,
multiply(X0,divide(X2,divide(X0,X1))) = multiply(X1,X2),
inference(demodulation,[status(thm)],[d35,d15]) ).
cnf(d37,plain,
multiply(X1,multiply(X0,divide(X2,X1))) = multiply(X2,X0),
inference(demodulation,[status(thm)],[d36,d15]) ).
cnf(d38,plain,
divide(X0,multiply(X0,X1)) = inverse(X1),
inference(superposition,[status(thm)],[d2,d13]) ).
cnf(d39,plain,
divide(X0,inverse(X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[d38,d13]) ).
cnf(d40,plain,
inverse(divide(divide(X0,X2),X1)) = divide(X2,divide(X0,X1)),
inference(superposition,[status(thm)],[c0,d7]) ).
cnf(d41,plain,
divide(X2,divide(X0,X1)) = divide(X1,divide(X0,X2)),
inference(demodulation,[status(thm)],[d40,d14]) ).
cnf(d42,plain,
divide(divide(X0,X1),divide(X2,X1)) = divide(divide(X0,X2),identity),
inference(superposition,[status(thm)],[d11,d20]) ).
cnf(d43,plain,
divide(X1,divide(X2,divide(X0,X1))) = divide(divide(X0,X2),identity),
inference(demodulation,[status(thm)],[d42,d41]) ).
cnf(d44,plain,
divide(X2,divide(X1,divide(X0,X2))) = divide(X0,X1),
inference(demodulation,[status(thm)],[d43,d11]) ).
cnf(d45,plain,
divide(divide(multiply(X0,X1),X2),divide(X3,X2)) = divide(divide(X0,X3),inverse(X1)),
inference(superposition,[status(thm)],[d2,d20]) ).
cnf(d46,plain,
divide(X2,divide(X3,divide(multiply(X0,X1),X2))) = divide(divide(X0,X3),inverse(X1)),
inference(demodulation,[status(thm)],[d45,d41]) ).
cnf(d47,plain,
divide(multiply(X2,X3),X1) = divide(divide(X2,X1),inverse(X3)),
inference(demodulation,[status(thm)],[d46,d44]) ).
cnf(d48,plain,
divide(multiply(X0,X2),X1) = multiply(divide(X0,X1),X2),
inference(demodulation,[status(thm)],[d47,d39]) ).
cnf(d49,plain,
divide(multiply(X0,X1),divide(divide(X0,X2),inverse(X1))) = X2,
inference(superposition,[status(thm)],[d2,c0]) ).
cnf(d50,plain,
divide(multiply(X0,X2),multiply(divide(X0,X1),X2)) = X1,
inference(demodulation,[status(thm)],[d49,d2]) ).
cnf(d51,plain,
X0 = divide(X1,divide(X1,X0)),
inference(superposition,[status(thm)],[d19,d31]) ).
cnf(d52,plain,
divide(multiply(X0,X2),multiply(X1,X2)) = divide(X0,X1),
inference(superposition,[status(thm)],[d51,d50]) ).
cnf(d53,plain,
multiply(divide(X0,multiply(X2,X1)),X1) = divide(X0,X2),
inference(demodulation,[status(thm)],[d52,d48]) ).
cnf(d54,plain,
multiply(X2,divide(X0,multiply(X1,X2))) = divide(X0,X1),
inference(demodulation,[status(thm)],[d53,d29]) ).
cnf(d55,plain,
multiply(multiply(X2,X0),divide(X1,X2)) = multiply(X1,X0),
inference(superposition,[status(thm)],[d54,d37]) ).
cnf(d56,plain,
multiply(X2,multiply(X0,X1)) = multiply(X0,multiply(X2,X1)),
inference(superposition,[status(thm)],[d55,d24]) ).
cnf(d57,plain,
inverse(divide(X2,divide(X0,divide(divide(X0,X1),X2)))) = X1,
inference(superposition,[status(thm)],[d26,d4]) ).
cnf(d58,plain,
divide(divide(X1,divide(divide(X1,X2),X0)),X0) = X2,
inference(demodulation,[status(thm)],[d57,d14]) ).
cnf(d59,plain,
divide(X0,divide(divide(X0,X1),X2)) = multiply(X2,X1),
inference(superposition,[status(thm)],[d58,d34]) ).
cnf(d60,plain,
multiply(X0,divide(X2,divide(X0,X1))) = multiply(X2,X1),
inference(demodulation,[status(thm)],[d59,d15]) ).
cnf(d61,plain,
multiply(X1,multiply(X0,divide(X2,X1))) = multiply(X0,X2),
inference(demodulation,[status(thm)],[d60,d15]) ).
cnf(d62,plain,
multiply(multiply(X2,X0),divide(X1,X2)) = multiply(X0,X1),
inference(superposition,[status(thm)],[d54,d61]) ).
cnf(d63,plain,
multiply(X2,multiply(X0,X1)) = multiply(X0,multiply(X1,X2)),
inference(superposition,[status(thm)],[d62,d24]) ).
cnf(d64,plain,
multiply(X1,multiply(X2,X0)) = multiply(X1,multiply(X0,X2)),
inference(superposition,[status(thm)],[d63,d56]) ).
cnf(d65,plain,
inverse(inverse(X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[d2,d0]) ).
cnf(d66,plain,
X0 = multiply(identity,X0),
inference(demodulation,[status(thm)],[d65,d6]) ).
cnf(d67,plain,
identity = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[d2,c3]) ).
cnf(d68,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2 ),
inference(demodulation,[status(thm)],[c4,d67]) ).
cnf(d69,plain,
( multiply(a4,b4) != multiply(b4,a4)
| identity != multiply(inverse(b1),b1)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2 ),
inference(demodulation,[status(thm)],[d68,d67]) ).
cnf(d70,plain,
( multiply(a4,b4) != multiply(b4,a4)
| identity != identity
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2 ),
inference(demodulation,[status(thm)],[d69,d67]) ).
cnf(d71,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c3,d0]) ).
cnf(d72,plain,
inverse(divide(identity,identity)) = identity,
inference(superposition,[status(thm)],[d71,d8]) ).
cnf(d73,plain,
inverse(inverse(identity)) = identity,
inference(demodulation,[status(thm)],[d72,d0]) ).
cnf(d74,plain,
identity = identity,
inference(demodulation,[status(thm)],[d73,d6]) ).
cnf(d75,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2 ),
inference(resolution,[status(thm)],[d74,d70]) ).
cnf(d76,plain,
( multiply(a4,b4) != multiply(b4,a4)
| a2 != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(demodulation,[status(thm)],[d75,d66]) ).
cnf(d77,plain,
( a2 != a2
| multiply(a4,b4) != multiply(b4,a4)
| multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)) ),
inference(demodulation,[status(thm)],[d76,d29]) ).
cnf(d78,plain,
( a2 != a2
| multiply(a4,b4) != multiply(a4,b4)
| multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)) ),
inference(demodulation,[status(thm)],[d77,d29]) ).
cnf(d79,plain,
divide(inverse(X0),divide(divide(inverse(X0),X1),identity)) = X1,
inference(superposition,[status(thm)],[d9,c0]) ).
cnf(d80,plain,
divide(inverse(X0),divide(inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[d79,d11]) ).
cnf(d81,plain,
X1 = X1,
inference(demodulation,[status(thm)],[d80,d13]) ).
cnf(d82,plain,
( a2 != a2
| multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)) ),
inference(resolution,[status(thm)],[d81,d78]) ).
cnf(d83,plain,
( a2 != a2
| multiply(a3,multiply(c3,b3)) != multiply(a3,multiply(b3,c3)) ),
inference(demodulation,[status(thm)],[d82,d56]) ).
cnf(d84,plain,
( a2 != a2
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)) ),
inference(demodulation,[status(thm)],[d83,d64]) ).
cnf(d85,plain,
a2 != a2,
inference(resolution,[status(thm)],[d81,d84]) ).
cnf(d86,plain,
$false,
inference(equality_resolution,[status(thm)],[d85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP092-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n014.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Fri Sep 25 14:21:47 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 68.00/17.91 % SZS status Unsatisfiable for theBenchmark.p
% 68.00/17.91 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------