%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP091-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 67.35s 19.02s
% Output : CNFRefutation 67.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of clauses : 87 ( 78 unt; 0 nHn; 11 RR)
% Number of literals : 109 ( 108 equ; 32 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 8 ( 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 : 204 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(divide(X0,divide(divide(X0,X1),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,divide(divide(X0,X1),X2)),X1) = X2,
inference(clausification,[status(esa)],[single_axiom]) ).
cnf(c1,plain,
divide(X0,divide(divide(X1,X1),X2)) = multiply(X0,X2),
inference(clausification,[status(esa)],[multiply]) ).
cnf(c2,plain,
divide(divide(X0,X0),X1) = inverse(X1),
inference(clausification,[status(esa)],[inverse]) ).
cnf(c3,plain,
divide(X0,X0) = identity,
inference(clausification,[status(esa)],[identity]) ).
cnf(c4,plain,
( multiply(b4,a4) != multiply(a4,b4)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(b1),b1) != multiply(inverse(a1),a1)
| multiply(a3,multiply(b3,c3)) != multiply(multiply(a3,b3),c3) ),
inference(clausification,[status(esa)],[prove_these_axioms]) ).
cnf(d0,plain,
divide(identity,X1) = inverse(X1),
inference(demodulation,[status(thm)],[c2,c3]) ).
cnf(d1,plain,
divide(X1,divide(identity,X2)) = multiply(X1,X2),
inference(demodulation,[status(thm)],[c1,c3]) ).
cnf(d2,plain,
divide(X1,inverse(X0)) = multiply(X1,X0),
inference(demodulation,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
divide(divide(X0,divide(multiply(X0,X1),X2)),inverse(X1)) = X2,
inference(superposition,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
multiply(divide(X0,divide(multiply(X0,X1),X2)),X1) = X2,
inference(demodulation,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
divide(divide(X0,divide(identity,X1)),X0) = X1,
inference(superposition,[status(thm)],[c3,c0]) ).
cnf(d6,plain,
divide(divide(X1,inverse(X0)),X1) = X0,
inference(demodulation,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
divide(multiply(X0,X1),X0) = X1,
inference(demodulation,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
multiply(divide(X0,X1),X1) = X0,
inference(superposition,[status(thm)],[d7,d4]) ).
cnf(d9,plain,
multiply(X1,X0) = multiply(X0,X1),
inference(superposition,[status(thm)],[d7,d8]) ).
cnf(d10,plain,
multiply(inverse(X0),X0) = identity,
inference(superposition,[status(thm)],[d2,c3]) ).
cnf(d11,plain,
( multiply(a3,multiply(b3,c3)) != multiply(multiply(a3,b3),c3)
| multiply(b4,a4) != multiply(a4,b4)
| multiply(inverse(b1),b1) != multiply(inverse(a1),a1)
| multiply(identity,a2) != a2 ),
inference(demodulation,[status(thm)],[c4,d10]) ).
cnf(d12,plain,
( multiply(a3,multiply(b3,c3)) != multiply(multiply(a3,b3),c3)
| multiply(b4,a4) != multiply(a4,b4)
| identity != multiply(inverse(a1),a1)
| multiply(identity,a2) != a2 ),
inference(demodulation,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
( multiply(a3,multiply(b3,c3)) != multiply(multiply(a3,b3),c3)
| multiply(b4,a4) != multiply(a4,b4)
| identity != identity
| multiply(identity,a2) != a2 ),
inference(demodulation,[status(thm)],[d12,d10]) ).
cnf(d14,plain,
divide(divide(X0,identity),X1) = divide(X0,X1),
inference(superposition,[status(thm)],[c3,c0]) ).
cnf(d15,plain,
divide(divide(X0,divide(X0,X1)),identity) = X1,
inference(superposition,[status(thm)],[d14,c0]) ).
cnf(d16,plain,
divide(divide(X0,X2),divide(divide(X0,X1),X2)) = X1,
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d17,plain,
divide(X1,identity) = X1,
inference(superposition,[status(thm)],[d16,d15]) ).
cnf(d18,plain,
multiply(identity,X0) = X0,
inference(superposition,[status(thm)],[d17,d7]) ).
cnf(d19,plain,
( multiply(a3,multiply(b3,c3)) != multiply(multiply(a3,b3),c3)
| multiply(b4,a4) != multiply(a4,b4)
| identity != identity ),
inference(resolution,[status(thm)],[d18,d13]) ).
cnf(d20,plain,
( identity != identity
| multiply(a3,multiply(b3,c3)) != multiply(multiply(a3,b3),c3)
| multiply(b4,a4) != multiply(b4,a4) ),
inference(demodulation,[status(thm)],[d19,d9]) ).
cnf(d21,plain,
( identity != identity
| multiply(a3,multiply(b3,c3)) != multiply(c3,multiply(a3,b3))
| multiply(b4,a4) != multiply(b4,a4) ),
inference(demodulation,[status(thm)],[d20,d9]) ).
cnf(d22,plain,
divide(divide(divide(X0,divide(divide(X0,X1),X2)),divide(X2,X3)),X1) = X3,
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d23,plain,
divide(divide(divide(X0,X2),divide(divide(divide(X0,X2),X1),X3)),X1) = X3,
inference(superposition,[status(thm)],[d16,d22]) ).
cnf(d24,plain,
X3 = X3,
inference(demodulation,[status(thm)],[d23,c0]) ).
cnf(d25,plain,
( identity != identity
| multiply(a3,multiply(b3,c3)) != multiply(c3,multiply(a3,b3)) ),
inference(resolution,[status(thm)],[d24,d21]) ).
cnf(d26,plain,
multiply(X2,X1) = divide(X0,divide(divide(X0,X1),X2)),
inference(superposition,[status(thm)],[c0,d8]) ).
cnf(d27,plain,
divide(divide(divide(X0,X1),X3),divide(X2,X3)) = divide(divide(X0,X2),X1),
inference(superposition,[status(thm)],[d16,d16]) ).
cnf(d28,plain,
divide(divide(divide(X0,X3),X1),X2) = divide(divide(divide(X0,X1),X2),X3),
inference(superposition,[status(thm)],[d27,d22]) ).
cnf(d29,plain,
divide(X1,X2) = divide(divide(X0,divide(divide(X0,identity),X1)),X2),
inference(superposition,[status(thm)],[c0,d14]) ).
cnf(d30,plain,
divide(X1,X2) = divide(divide(X0,divide(X0,X1)),X2),
inference(demodulation,[status(thm)],[d29,d17]) ).
cnf(d31,plain,
divide(divide(X0,X2),divide(X1,X2)) = divide(X0,X1),
inference(superposition,[status(thm)],[d30,d16]) ).
cnf(d32,plain,
divide(divide(X2,X3),divide(X4,X3)) = divide(divide(divide(X0,divide(divide(X0,X1),X2)),X4),X1),
inference(superposition,[status(thm)],[c0,d27]) ).
cnf(d33,plain,
divide(X0,X2) = divide(divide(divide(X3,divide(divide(X3,X4),X0)),X2),X4),
inference(demodulation,[status(thm)],[d32,d31]) ).
cnf(d34,plain,
divide(X2,X3) = divide(divide(divide(X0,X3),X1),divide(divide(X0,X1),X2)),
inference(demodulation,[status(thm)],[d33,d28]) ).
cnf(d35,plain,
divide(X2,divide(divide(divide(X0,divide(divide(X0,X1),X2)),X3),X1)) = X3,
inference(superposition,[status(thm)],[c0,d16]) ).
cnf(d36,plain,
divide(X2,divide(X5,X1)) = divide(divide(divide(X3,divide(divide(X3,X4),divide(X0,divide(divide(X0,X1),X2)))),X5),X4),
inference(superposition,[status(thm)],[d35,d35]) ).
cnf(d37,plain,
divide(X4,divide(X5,X3)) = divide(divide(divide(X0,X5),X1),divide(divide(X0,X1),divide(X2,divide(divide(X2,X3),X4)))),
inference(demodulation,[status(thm)],[d36,d28]) ).
cnf(d38,plain,
divide(X5,divide(X1,X4)) = divide(divide(X3,divide(divide(X3,X4),X5)),X1),
inference(demodulation,[status(thm)],[d37,d34]) ).
cnf(d39,plain,
divide(X2,divide(X3,X1)) = divide(multiply(X2,X1),X3),
inference(demodulation,[status(thm)],[d38,d26]) ).
cnf(d40,plain,
multiply(divide(X0,identity),X1) = divide(X0,inverse(X1)),
inference(superposition,[status(thm)],[d2,d14]) ).
cnf(d41,plain,
multiply(X0,X1) = divide(X0,inverse(X1)),
inference(demodulation,[status(thm)],[d40,d17]) ).
cnf(d42,plain,
X3 = multiply(divide(divide(X0,divide(divide(X0,inverse(X1)),X2)),divide(X2,X3)),X1),
inference(superposition,[status(thm)],[d22,d2]) ).
cnf(d43,plain,
X3 = multiply(X1,divide(divide(X0,divide(divide(X0,inverse(X1)),X2)),divide(X2,X3))),
inference(demodulation,[status(thm)],[d42,d9]) ).
cnf(d44,plain,
X2 = multiply(X1,divide(divide(X0,divide(multiply(X0,X1),X3)),divide(X3,X2))),
inference(demodulation,[status(thm)],[d43,d41]) ).
cnf(d45,plain,
divide(multiply(X0,X1),X2) = multiply(X1,divide(X0,X2)),
inference(superposition,[status(thm)],[d31,d44]) ).
cnf(d46,plain,
divide(X0,divide(X2,X1)) = multiply(X1,divide(X0,X2)),
inference(demodulation,[status(thm)],[d45,d39]) ).
cnf(d47,plain,
divide(X0,divide(X0,identity)) = identity,
inference(superposition,[status(thm)],[d14,c3]) ).
cnf(d48,plain,
divide(divide(X0,identity),X1) = divide(divide(X0,X1),identity),
inference(superposition,[status(thm)],[d47,c0]) ).
cnf(d49,plain,
divide(X0,X1) = divide(divide(X0,X1),identity),
inference(demodulation,[status(thm)],[d48,d17]) ).
cnf(d50,plain,
divide(X0,X1) = divide(X0,X1),
inference(demodulation,[status(thm)],[d49,d17]) ).
cnf(d51,plain,
X0 = divide(X0,identity),
inference(superposition,[status(thm)],[d17,d50]) ).
cnf(d52,plain,
X1 = divide(X0,divide(divide(X0,X1),identity)),
inference(superposition,[status(thm)],[d16,d14]) ).
cnf(d53,plain,
X1 = divide(X0,divide(X0,X1)),
inference(demodulation,[status(thm)],[d52,d51]) ).
cnf(d54,plain,
multiply(divide(X1,divide(multiply(divide(X0,divide(X0,X1)),X2),X3)),X2) = X3,
inference(superposition,[status(thm)],[d30,d4]) ).
cnf(d55,plain,
multiply(X2,divide(X0,divide(multiply(divide(X1,divide(X1,X0)),X2),X3))) = X3,
inference(demodulation,[status(thm)],[d54,d9]) ).
cnf(d56,plain,
multiply(X2,divide(X1,divide(multiply(X1,X2),X3))) = X3,
inference(demodulation,[status(thm)],[d55,d53]) ).
cnf(d57,plain,
divide(identity,X1) = divide(divide(X0,X1),X0),
inference(superposition,[status(thm)],[c3,d22]) ).
cnf(d58,plain,
inverse(X0) = divide(divide(X1,X0),X1),
inference(demodulation,[status(thm)],[d57,d0]) ).
cnf(d59,plain,
inverse(X0) = divide(X1,multiply(X0,X1)),
inference(superposition,[status(thm)],[d7,d58]) ).
cnf(d60,plain,
multiply(X1,divide(X0,inverse(X2))) = multiply(X2,multiply(X0,X1)),
inference(superposition,[status(thm)],[d59,d56]) ).
cnf(d61,plain,
divide(X1,divide(inverse(X2),X0)) = multiply(X2,multiply(X1,X0)),
inference(demodulation,[status(thm)],[d60,d46]) ).
cnf(d62,plain,
divide(X1,divide(divide(multiply(X0,X1),X2),X0)) = X2,
inference(superposition,[status(thm)],[d7,d16]) ).
cnf(d63,plain,
inverse(X1) = divide(X0,multiply(X0,X1)),
inference(superposition,[status(thm)],[d2,d53]) ).
cnf(d64,plain,
divide(X1,divide(inverse(X2),X0)) = multiply(multiply(X0,X1),X2),
inference(superposition,[status(thm)],[d63,d62]) ).
cnf(d65,plain,
multiply(multiply(X2,X0),X1) = multiply(X1,multiply(X0,X2)),
inference(superposition,[status(thm)],[d64,d61]) ).
cnf(d66,plain,
divide(X1,divide(inverse(X2),X0)) = multiply(X2,multiply(X0,X1)),
inference(superposition,[status(thm)],[d59,d62]) ).
cnf(d67,plain,
multiply(multiply(inverse(X0),X1),X0) = X1,
inference(superposition,[status(thm)],[d2,d7]) ).
cnf(d68,plain,
multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[d67,d9]) ).
cnf(d69,plain,
multiply(X1,divide(X0,X1)) = X0,
inference(superposition,[status(thm)],[d53,d8]) ).
cnf(d70,plain,
multiply(X0,X1) = divide(X1,inverse(X0)),
inference(superposition,[status(thm)],[d69,d68]) ).
cnf(d71,plain,
inverse(multiply(X0,X1)) = divide(inverse(X1),X0),
inference(superposition,[status(thm)],[d63,d58]) ).
cnf(d72,plain,
multiply(multiply(X0,X1),X2) = divide(X2,divide(inverse(X1),X0)),
inference(superposition,[status(thm)],[d71,d70]) ).
cnf(d73,plain,
multiply(multiply(X2,X1),X0) = multiply(X1,multiply(X2,X0)),
inference(demodulation,[status(thm)],[d72,d66]) ).
cnf(d74,plain,
multiply(X1,multiply(X0,X2)) = multiply(X2,multiply(X1,X0)),
inference(superposition,[status(thm)],[d73,d65]) ).
cnf(d75,plain,
identity != identity,
inference(resolution,[status(thm)],[d74,d25]) ).
cnf(d76,plain,
$false,
inference(resolution,[status(thm)],[d24,d75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP091-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.34 % Computer : n013.cluster.edu
% 0.06/0.34 % Model : x86_64 x86_64
% 0.06/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.34 % Memory : 8046.5625MB
% 0.06/0.34 % OS : Linux 6.8.0-71-generic
% 0.06/0.34 % CPULimit : 300
% 0.06/0.35 % WCLimit : 300
% 0.06/0.35 % DateTime : Fri Sep 25 14:21:21 UTC 2026
% 0.06/0.35 % CPUTime :
% 0.06/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 67.35/19.02 % SZS status Unsatisfiable for theBenchmark.p
% 67.35/19.02 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------