%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP063-1 : 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 : n008.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 07:22:14 AM UTC 2026
% Result : Unsatisfiable 46.13s 10.58s
% Output : CNFRefutation 46.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of clauses : 67 ( 63 unt; 0 nHn; 6 RR)
% Number of literals : 74 ( 73 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 140 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(X0,divide(divide(divide(divide(X0,X0),X1),X2),divide(divide(divide(X0,X0),X0),X2))) = X1 ).
cnf(multiply,axiom,
multiply(X0,X1) = divide(X0,divide(divide(X2,X2),X1)) ).
cnf(inverse,axiom,
inverse(X0) = divide(divide(X1,X1),X0) ).
cnf(prove_these_axioms,negated_conjecture,
( 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(X0,divide(divide(divide(divide(X0,X0),X1),X2),divide(divide(divide(X0,X0),X0),X2))) = X1,
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,
( multiply(a3,multiply(b3,c3)) != multiply(multiply(a3,b3),c3)
| multiply(inverse(b1),b1) != multiply(inverse(a1),a1)
| multiply(multiply(inverse(b2),b2),a2) != a2 ),
inference(clausification,[status(esa)],[prove_these_axioms]) ).
cnf(d0,plain,
divide(X2,inverse(X1)) = multiply(X2,X1),
inference(demodulation,[status(thm)],[c1,c2]) ).
cnf(d1,plain,
divide(multiply(inverse(X0),X0),X1) = inverse(X1),
inference(superposition,[status(thm)],[d0,c2]) ).
cnf(d2,plain,
divide(X0,divide(divide(inverse(X1),X2),divide(divide(divide(X0,X0),X0),X2))) = X1,
inference(demodulation,[status(thm)],[c0,c2]) ).
cnf(d3,plain,
divide(X0,divide(divide(inverse(X1),X2),divide(inverse(X0),X2))) = X1,
inference(demodulation,[status(thm)],[d2,c2]) ).
cnf(d4,plain,
divide(X1,inverse(divide(inverse(X1),inverse(X0)))) = X0,
inference(superposition,[status(thm)],[c2,d3]) ).
cnf(d5,plain,
multiply(X0,divide(inverse(X0),inverse(X1))) = X1,
inference(demodulation,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(superposition,[status(thm)],[d6,d6]) ).
cnf(d8,plain,
divide(multiply(X0,inverse(X0)),X1) = inverse(X1),
inference(superposition,[status(thm)],[d7,d1]) ).
cnf(d9,plain,
divide(X2,divide(X1,divide(inverse(X2),inverse(divide(inverse(inverse(X0)),inverse(X1)))))) = X0,
inference(superposition,[status(thm)],[d4,d3]) ).
cnf(d10,plain,
divide(X0,divide(X2,multiply(inverse(X0),divide(inverse(inverse(X1)),inverse(X2))))) = X1,
inference(demodulation,[status(thm)],[d9,d0]) ).
cnf(d11,plain,
divide(X2,divide(X1,multiply(inverse(X2),multiply(inverse(inverse(X0)),X1)))) = X0,
inference(demodulation,[status(thm)],[d10,d0]) ).
cnf(d12,plain,
divide(X2,divide(X1,multiply(inverse(X2),multiply(X0,X1)))) = X0,
inference(demodulation,[status(thm)],[d11,d7]) ).
cnf(d13,plain,
divide(X0,divide(divide(inverse(X3),divide(divide(inverse(X1),X2),divide(inverse(inverse(X0)),X2))),X1)) = X3,
inference(superposition,[status(thm)],[d3,d3]) ).
cnf(d14,plain,
divide(X0,divide(X1,X1)) = X0,
inference(superposition,[status(thm)],[d3,d13]) ).
cnf(d15,plain,
divide(X1,multiply(inverse(X0),X0)) = X1,
inference(superposition,[status(thm)],[d0,d14]) ).
cnf(d16,plain,
divide(multiply(X1,X0),X0) = X1,
inference(superposition,[status(thm)],[d15,d12]) ).
cnf(d17,plain,
X0 = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d16,d8]) ).
cnf(d18,plain,
inverse(inverse(X1)) = multiply(multiply(inverse(X0),X0),X1),
inference(superposition,[status(thm)],[d1,d0]) ).
cnf(d19,plain,
X0 = multiply(multiply(inverse(X1),X1),X0),
inference(demodulation,[status(thm)],[d18,d17]) ).
cnf(d20,plain,
( multiply(a3,multiply(b3,c3)) != multiply(multiply(a3,b3),c3)
| multiply(inverse(b1),b1) != multiply(inverse(a1),a1)
| a2 != a2 ),
inference(demodulation,[status(thm)],[c3,d19]) ).
cnf(d21,plain,
divide(X0,X0) = inverse(divide(X1,X1)),
inference(superposition,[status(thm)],[d14,c2]) ).
cnf(d22,plain,
divide(X2,X2) = divide(X1,X1),
inference(superposition,[status(thm)],[d21,d21]) ).
cnf(d23,plain,
divide(X1,X1) = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[d22,d0]) ).
cnf(d24,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(superposition,[status(thm)],[d23,d23]) ).
cnf(d25,plain,
( a2 != a2
| multiply(a3,multiply(b3,c3)) != multiply(multiply(a3,b3),c3) ),
inference(resolution,[status(thm)],[d24,d20]) ).
cnf(d26,plain,
divide(inverse(divide(X0,X0)),X1) = inverse(X1),
inference(superposition,[status(thm)],[c2,c2]) ).
cnf(d27,plain,
X1 = inverse(inverse(divide(inverse(inverse(divide(X0,X0))),inverse(X1)))),
inference(superposition,[status(thm)],[d4,d26]) ).
cnf(d28,plain,
X1 = divide(inverse(inverse(divide(X0,X0))),inverse(X1)),
inference(demodulation,[status(thm)],[d27,d17]) ).
cnf(d29,plain,
X1 = multiply(inverse(inverse(divide(X0,X0))),X1),
inference(demodulation,[status(thm)],[d28,d0]) ).
cnf(d30,plain,
X1 = multiply(divide(X0,X0),X1),
inference(demodulation,[status(thm)],[d29,d17]) ).
cnf(d31,plain,
multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(superposition,[status(thm)],[d7,d6]) ).
cnf(d32,plain,
multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[d31,d31]) ).
cnf(d33,plain,
X1 = multiply(X0,multiply(inverse(X0),X1)),
inference(superposition,[status(thm)],[d31,d32]) ).
cnf(d34,plain,
X1 = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[status(thm)],[d32,d33]) ).
cnf(d35,plain,
divide(X1,multiply(X0,X1)) = inverse(X0),
inference(superposition,[status(thm)],[d34,d16]) ).
cnf(d36,plain,
divide(X1,X0) = multiply(X1,inverse(X0)),
inference(superposition,[status(thm)],[d17,d0]) ).
cnf(d37,plain,
multiply(multiply(X0,inverse(X1)),X1) = X0,
inference(superposition,[status(thm)],[d0,d16]) ).
cnf(d38,plain,
multiply(divide(X0,X1),X1) = X0,
inference(demodulation,[status(thm)],[d37,d36]) ).
cnf(d39,plain,
divide(X1,X0) = inverse(divide(X0,X1)),
inference(superposition,[status(thm)],[d38,d35]) ).
cnf(d40,plain,
divide(inverse(X1),X0) = inverse(multiply(X0,X1)),
inference(superposition,[status(thm)],[d0,d39]) ).
cnf(d41,plain,
inverse(divide(divide(inverse(X1),X2),divide(inverse(divide(X0,X0)),X2))) = X1,
inference(superposition,[status(thm)],[c2,d3]) ).
cnf(d42,plain,
inverse(divide(divide(inverse(X2),X1),inverse(X1))) = X2,
inference(demodulation,[status(thm)],[d41,d26]) ).
cnf(d43,plain,
inverse(multiply(divide(inverse(X0),X1),X1)) = X0,
inference(demodulation,[status(thm)],[d42,d0]) ).
cnf(d44,plain,
inverse(multiply(inverse(X1),X1)) = divide(X0,X0),
inference(superposition,[status(thm)],[d26,d43]) ).
cnf(d45,plain,
multiply(inverse(multiply(inverse(X1),X1)),X0) = X0,
inference(superposition,[status(thm)],[d44,d38]) ).
cnf(d46,plain,
multiply(divide(inverse(X0),inverse(X0)),X1) = X1,
inference(demodulation,[status(thm)],[d45,d40]) ).
cnf(d47,plain,
X1 = X1,
inference(demodulation,[status(thm)],[d46,d30]) ).
cnf(d48,plain,
multiply(a3,multiply(b3,c3)) != multiply(multiply(a3,b3),c3),
inference(resolution,[status(thm)],[d47,d25]) ).
cnf(d49,plain,
divide(X2,divide(inverse(X1),X0)) = multiply(X2,multiply(X0,X1)),
inference(superposition,[status(thm)],[d40,d0]) ).
cnf(d50,plain,
divide(X0,divide(divide(inverse(X2),inverse(divide(inverse(inverse(X0)),inverse(X1)))),X1)) = X2,
inference(superposition,[status(thm)],[d4,d3]) ).
cnf(d51,plain,
divide(X1,divide(multiply(inverse(X0),divide(inverse(inverse(X1)),inverse(X2))),X2)) = X0,
inference(demodulation,[status(thm)],[d50,d0]) ).
cnf(d52,plain,
divide(X0,divide(multiply(inverse(X2),multiply(inverse(inverse(X0)),X1)),X1)) = X2,
inference(demodulation,[status(thm)],[d51,d0]) ).
cnf(d53,plain,
divide(X0,divide(multiply(inverse(X2),multiply(X0,X1)),X1)) = X2,
inference(demodulation,[status(thm)],[d52,d7]) ).
cnf(d54,plain,
X1 = multiply(inverse(divide(X0,X1)),X0),
inference(superposition,[status(thm)],[d38,d34]) ).
cnf(d55,plain,
inverse(X1) = multiply(inverse(multiply(X0,X1)),X0),
inference(superposition,[status(thm)],[d0,d54]) ).
cnf(d56,plain,
divide(X0,divide(inverse(X2),X1)) = multiply(multiply(X0,X1),X2),
inference(superposition,[status(thm)],[d55,d53]) ).
cnf(d57,plain,
multiply(X0,multiply(X2,X1)) = multiply(multiply(X0,X2),X1),
inference(demodulation,[status(thm)],[d56,d49]) ).
cnf(d58,plain,
$false,
inference(resolution,[status(thm)],[d57,d48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP063-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n008.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Fri Sep 25 14:21:39 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 46.13/10.58 % SZS status Unsatisfiable for theBenchmark.p
% 46.13/10.58 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------