%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP547-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 07:24:00 AM UTC 2026
% Result : Unsatisfiable 36.08s 5.03s
% Output : CNFRefutation 36.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of clauses : 56 ( 56 unt; 0 nHn; 5 RR)
% Number of literals : 56 ( 55 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 110 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(divide(identity,divide(X0,X1)),divide(divide(X1,X2),X0)) = X2 ).
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_3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ).
cnf(c0,plain,
divide(divide(identity,divide(X0,X1)),divide(divide(X1,X2),X0)) = X2,
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)),
inference(clausification,[status(esa)],[prove_these_axioms_3]) ).
cnf(d0,plain,
multiply(X1,X0) = divide(X1,inverse(X0)),
inference(demodulation,[status(thm)],[c1,c2]) ).
cnf(d1,plain,
divide(divide(identity,divide(X1,X0)),divide(identity,X1)) = X0,
inference(superposition,[status(thm)],[c3,c0]) ).
cnf(d2,plain,
divide(inverse(divide(X0,X1)),divide(identity,X0)) = X1,
inference(demodulation,[status(thm)],[d1,c2]) ).
cnf(d3,plain,
divide(inverse(divide(X0,X1)),inverse(X0)) = X1,
inference(demodulation,[status(thm)],[d2,c2]) ).
cnf(d4,plain,
multiply(inverse(divide(X0,X1)),X0) = X1,
inference(demodulation,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
identity = inverse(identity),
inference(superposition,[status(thm)],[c2,c3]) ).
cnf(d6,plain,
divide(divide(identity,identity),divide(divide(X0,X1),X0)) = X1,
inference(superposition,[status(thm)],[c3,c0]) ).
cnf(d7,plain,
divide(inverse(identity),divide(divide(X0,X1),X0)) = X1,
inference(demodulation,[status(thm)],[d6,c2]) ).
cnf(d8,plain,
divide(identity,divide(divide(X0,X1),X0)) = X1,
inference(demodulation,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
inverse(divide(divide(X0,X1),X0)) = X1,
inference(demodulation,[status(thm)],[d8,c2]) ).
cnf(d10,plain,
multiply(X1,divide(X0,X1)) = X0,
inference(superposition,[status(thm)],[d9,d4]) ).
cnf(d11,plain,
multiply(inverse(X1),multiply(X0,X1)) = X0,
inference(superposition,[status(thm)],[d0,d10]) ).
cnf(d12,plain,
inverse(divide(identity,X0)) = X0,
inference(superposition,[status(thm)],[c3,d9]) ).
cnf(d13,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d12,c2]) ).
cnf(d14,plain,
multiply(identity,X0) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c2,d0]) ).
cnf(d15,plain,
multiply(identity,X0) = X0,
inference(demodulation,[status(thm)],[d14,d13]) ).
cnf(d16,plain,
X0 = divide(X0,identity),
inference(superposition,[status(thm)],[d10,d15]) ).
cnf(d17,plain,
inverse(inverse(X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[d0,c2]) ).
cnf(d18,plain,
X0 = multiply(identity,X0),
inference(demodulation,[status(thm)],[d17,d13]) ).
cnf(d19,plain,
divide(divide(identity,divide(divide(X0,X1),X0)),identity) = X1,
inference(superposition,[status(thm)],[c3,c0]) ).
cnf(d20,plain,
divide(inverse(divide(divide(X0,X1),X0)),identity) = X1,
inference(demodulation,[status(thm)],[d19,c2]) ).
cnf(d21,plain,
divide(X1,identity) = X1,
inference(demodulation,[status(thm)],[d20,d9]) ).
cnf(d22,plain,
divide(divide(identity,divide(divide(divide(X1,X2),X0),identity)),X2) = divide(X0,X1),
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d23,plain,
divide(inverse(divide(divide(divide(X0,X1),X2),identity)),X1) = divide(X2,X0),
inference(demodulation,[status(thm)],[d22,c2]) ).
cnf(d24,plain,
divide(inverse(divide(divide(divide(X2,X0),X3),identity)),X1) = divide(X3,inverse(divide(divide(divide(X0,X1),X2),identity))),
inference(superposition,[status(thm)],[d23,d23]) ).
cnf(d25,plain,
divide(inverse(divide(divide(X0,X1),X2)),X3) = divide(X2,inverse(divide(divide(divide(X1,X3),X0),identity))),
inference(demodulation,[status(thm)],[d24,d21]) ).
cnf(d26,plain,
divide(inverse(divide(divide(X3,X1),X0)),X2) = multiply(X0,divide(divide(divide(X1,X2),X3),identity)),
inference(demodulation,[status(thm)],[d25,d0]) ).
cnf(d27,plain,
divide(inverse(divide(divide(X2,X0),X3)),X1) = multiply(X3,divide(divide(X0,X1),X2)),
inference(demodulation,[status(thm)],[d26,d21]) ).
cnf(d28,plain,
divide(inverse(divide(divide(inverse(X0),X1),identity)),X0) = divide(X1,identity),
inference(superposition,[status(thm)],[c2,d23]) ).
cnf(d29,plain,
multiply(identity,divide(divide(X1,X0),inverse(X0))) = divide(X1,identity),
inference(demodulation,[status(thm)],[d28,d27]) ).
cnf(d30,plain,
divide(divide(X0,X1),inverse(X1)) = divide(X0,identity),
inference(demodulation,[status(thm)],[d29,d18]) ).
cnf(d31,plain,
multiply(divide(X0,X1),X1) = divide(X0,identity),
inference(demodulation,[status(thm)],[d30,d0]) ).
cnf(d32,plain,
multiply(divide(X0,X1),X1) = X0,
inference(demodulation,[status(thm)],[d31,d16]) ).
cnf(d33,plain,
multiply(inverse(X1),X0) = divide(X0,X1),
inference(superposition,[status(thm)],[d32,d11]) ).
cnf(d34,plain,
divide(multiply(X1,X0),X0) = X1,
inference(demodulation,[status(thm)],[d11,d33]) ).
cnf(d35,plain,
multiply(X1,X0) = multiply(X0,X1),
inference(superposition,[status(thm)],[d34,d10]) ).
cnf(d36,plain,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(demodulation,[status(thm)],[c4,d35]) ).
cnf(d37,plain,
divide(inverse(divide(divide(multiply(X0,X1),X2),identity)),inverse(X1)) = divide(X2,X0),
inference(superposition,[status(thm)],[d0,d23]) ).
cnf(d38,plain,
multiply(identity,divide(divide(X2,inverse(X1)),multiply(X0,X1))) = divide(X2,X0),
inference(demodulation,[status(thm)],[d37,d27]) ).
cnf(d39,plain,
divide(divide(X0,inverse(X1)),multiply(X2,X1)) = divide(X0,X2),
inference(demodulation,[status(thm)],[d38,d18]) ).
cnf(d40,plain,
divide(multiply(X0,X1),multiply(X2,X1)) = divide(X0,X2),
inference(demodulation,[status(thm)],[d39,d0]) ).
cnf(d41,plain,
multiply(multiply(X2,X1),divide(X0,X2)) = multiply(X0,X1),
inference(superposition,[status(thm)],[d40,d10]) ).
cnf(d42,plain,
multiply(multiply(X1,X2),X0) = multiply(multiply(X0,X1),X2),
inference(superposition,[status(thm)],[d34,d41]) ).
cnf(d43,plain,
multiply(X2,multiply(X0,X1)) = multiply(multiply(X2,X0),X1),
inference(superposition,[status(thm)],[d42,d35]) ).
cnf(d44,plain,
multiply(X2,multiply(X0,X1)) = multiply(X0,multiply(X1,X2)),
inference(superposition,[status(thm)],[d43,d35]) ).
cnf(d45,plain,
$false,
inference(resolution,[status(thm)],[d44,d36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP547-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n007.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 14:57:23 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 36.08/5.03 % SZS status Unsatisfiable for theBenchmark.p
% 36.08/5.03 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------