%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP098-1 : 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 : n004.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 07:22:19 AM UTC 2026
% Result : Unsatisfiable 59.98s 16.63s
% Output : CNFRefutation 59.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of clauses : 62 ( 53 unt; 0 nHn; 11 RR)
% Number of literals : 81 ( 80 equ; 29 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 137 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(divide(divide(X0,inverse(X1)),X2),divide(X0,X2)) = X1 ).
cnf(multiply,axiom,
multiply(X0,X1) = divide(X0,inverse(X1)) ).
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(divide(X0,inverse(X1)),X2),divide(X0,X2)) = X1,
inference(clausification,[status(esa)],[single_axiom]) ).
cnf(c1,plain,
multiply(X0,X1) = divide(X0,inverse(X1)),
inference(clausification,[status(esa)],[multiply]) ).
cnf(c2,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,
divide(divide(multiply(X0,X1),X2),divide(X0,X2)) = X1,
inference(demodulation,[status(thm)],[c0,c1]) ).
cnf(d1,plain,
divide(multiply(multiply(X0,X1),X2),divide(X0,inverse(X2))) = X1,
inference(superposition,[status(thm)],[c1,d0]) ).
cnf(d2,plain,
divide(multiply(multiply(X0,X2),X1),multiply(X0,X1)) = X2,
inference(demodulation,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
divide(X1,divide(multiply(X0,X1),multiply(X0,X2))) = X2,
inference(superposition,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
divide(divide(multiply(divide(multiply(X0,X1),X2),X3),divide(X0,X2)),X1) = X3,
inference(superposition,[status(thm)],[d0,d0]) ).
cnf(d5,plain,
multiply(divide(multiply(divide(multiply(X0,inverse(X1)),X2),X3),divide(X0,X2)),X1) = X3,
inference(superposition,[status(thm)],[d4,c1]) ).
cnf(d6,plain,
divide(divide(X3,divide(divide(multiply(X0,inverse(X1)),X2),divide(X0,X2))),X3) = X1,
inference(superposition,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
divide(divide(X3,inverse(X1)),X3) = X1,
inference(demodulation,[status(thm)],[d6,d0]) ).
cnf(d8,plain,
divide(multiply(X0,X1),X0) = X1,
inference(demodulation,[status(thm)],[d7,c1]) ).
cnf(d9,plain,
divide(X1,divide(X0,X0)) = X1,
inference(superposition,[status(thm)],[d8,d0]) ).
cnf(d10,plain,
X1 = divide(multiply(X0,X1),X0),
inference(superposition,[status(thm)],[d0,d9]) ).
cnf(d11,plain,
multiply(multiply(inverse(X0),X1),X0) = X1,
inference(superposition,[status(thm)],[d8,c1]) ).
cnf(d12,plain,
X0 = divide(X1,multiply(inverse(X0),X1)),
inference(superposition,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
divide(X1,X0) = multiply(inverse(X0),X1),
inference(superposition,[status(thm)],[d12,d3]) ).
cnf(d14,plain,
multiply(divide(X1,X0),X0) = X1,
inference(demodulation,[status(thm)],[d11,d13]) ).
cnf(d15,plain,
multiply(X1,X0) = multiply(X0,X1),
inference(superposition,[status(thm)],[d8,d14]) ).
cnf(d16,plain,
X1 = multiply(multiply(inverse(X0),X1),X0),
inference(superposition,[status(thm)],[c1,d10]) ).
cnf(d17,plain,
X1 = multiply(divide(X1,X0),X0),
inference(demodulation,[status(thm)],[d16,d13]) ).
cnf(d18,plain,
multiply(multiply(X0,X1),X2) = multiply(X1,multiply(X0,X2)),
inference(superposition,[status(thm)],[d2,d17]) ).
cnf(d19,plain,
divide(X1,multiply(inverse(X0),X1)) = X0,
inference(superposition,[status(thm)],[d11,d8]) ).
cnf(d20,plain,
divide(X1,divide(X1,X0)) = X0,
inference(demodulation,[status(thm)],[d19,d13]) ).
cnf(d21,plain,
X0 = multiply(X1,divide(X0,X1)),
inference(superposition,[status(thm)],[d20,d17]) ).
cnf(d22,plain,
divide(X3,divide(X0,divide(multiply(X2,multiply(X0,X1)),multiply(X2,X3)))) = X1,
inference(superposition,[status(thm)],[d3,d0]) ).
cnf(d23,plain,
X0 = divide(X1,divide(X1,X0)),
inference(demodulation,[status(thm)],[d12,d13]) ).
cnf(d24,plain,
divide(multiply(X1,multiply(X0,X2)),multiply(X1,X0)) = X2,
inference(superposition,[status(thm)],[d23,d22]) ).
cnf(d25,plain,
multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(superposition,[status(thm)],[d24,d21]) ).
cnf(d26,plain,
multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(X0,X2)),
inference(superposition,[status(thm)],[d25,d18]) ).
cnf(d27,plain,
multiply(X1,multiply(X0,X2)) = multiply(multiply(X0,X1),X2),
inference(superposition,[status(thm)],[d2,d14]) ).
cnf(d28,plain,
multiply(divide(X0,X0),X1) = X1,
inference(superposition,[status(thm)],[d9,d8]) ).
cnf(d29,plain,
multiply(multiply(inverse(X0),X0),X1) = X1,
inference(superposition,[status(thm)],[c1,d28]) ).
cnf(d30,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(resolution,[status(thm)],[d29,c2]) ).
cnf(d31,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| divide(a1,a1) != multiply(inverse(b1),b1) ),
inference(demodulation,[status(thm)],[d30,d13]) ).
cnf(d32,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| divide(a1,a1) != divide(b1,b1) ),
inference(demodulation,[status(thm)],[d31,d13]) ).
cnf(d33,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(b3,multiply(a3,c3)) != multiply(a3,multiply(b3,c3))
| divide(a1,a1) != divide(b1,b1) ),
inference(demodulation,[status(thm)],[d32,d27]) ).
cnf(d34,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| divide(a1,a1) != divide(b1,b1) ),
inference(demodulation,[status(thm)],[d33,d26]) ).
cnf(d35,plain,
( multiply(a4,b4) != multiply(a4,b4)
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| divide(a1,a1) != divide(b1,b1) ),
inference(demodulation,[status(thm)],[d34,d15]) ).
cnf(d36,plain,
X1 = divide(X1,divide(X0,X0)),
inference(superposition,[status(thm)],[d28,d10]) ).
cnf(d37,plain,
divide(X1,X1) = divide(X0,X0),
inference(superposition,[status(thm)],[d36,d23]) ).
cnf(d38,plain,
( multiply(a4,b4) != multiply(a4,b4)
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)) ),
inference(resolution,[status(thm)],[d37,d35]) ).
cnf(d39,plain,
divide(X1,X0) = multiply(X1,inverse(X0)),
inference(superposition,[status(thm)],[d15,d13]) ).
cnf(d40,plain,
divide(inverse(X1),X0) = divide(inverse(X0),X1),
inference(superposition,[status(thm)],[d39,d13]) ).
cnf(d41,plain,
divide(multiply(X1,X0),multiply(X1,X2)) = divide(X0,X2),
inference(superposition,[status(thm)],[d3,d23]) ).
cnf(d42,plain,
divide(divide(multiply(X0,X3),divide(multiply(X1,X0),multiply(X1,X2))),X2) = X3,
inference(superposition,[status(thm)],[d3,d0]) ).
cnf(d43,plain,
multiply(divide(multiply(X0,X1),divide(multiply(X2,X0),multiply(X2,inverse(X3)))),X3) = X1,
inference(superposition,[status(thm)],[d42,c1]) ).
cnf(d44,plain,
divide(divide(X1,divide(multiply(X4,divide(multiply(X0,X1),divide(multiply(X2,X0),multiply(X2,inverse(X3))))),multiply(X4,X5))),X5) = X3,
inference(superposition,[status(thm)],[d43,d42]) ).
cnf(d45,plain,
divide(divide(X2,divide(divide(multiply(X1,X2),divide(multiply(X3,X1),multiply(X3,inverse(X4)))),X5)),X5) = X4,
inference(demodulation,[status(thm)],[d44,d41]) ).
cnf(d46,plain,
divide(divide(X3,divide(divide(multiply(X1,X3),divide(X1,inverse(X2))),X4)),X4) = X2,
inference(demodulation,[status(thm)],[d45,d41]) ).
cnf(d47,plain,
divide(divide(X2,divide(divide(multiply(X0,X2),multiply(X0,X1)),X3)),X3) = X1,
inference(demodulation,[status(thm)],[d46,c1]) ).
cnf(d48,plain,
divide(divide(X1,divide(divide(X1,X2),X3)),X3) = X2,
inference(demodulation,[status(thm)],[d47,d41]) ).
cnf(d49,plain,
divide(X0,multiply(X0,X1)) = inverse(X1),
inference(superposition,[status(thm)],[c1,d20]) ).
cnf(d50,plain,
divide(inverse(X0),divide(X1,X0)) = inverse(X1),
inference(superposition,[status(thm)],[d13,d49]) ).
cnf(d51,plain,
divide(inverse(divide(inverse(X0),X1)),X0) = X1,
inference(superposition,[status(thm)],[d50,d48]) ).
cnf(d52,plain,
divide(inverse(X0),divide(inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[d51,d40]) ).
cnf(d53,plain,
X1 = X1,
inference(demodulation,[status(thm)],[d52,d23]) ).
cnf(d54,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(resolution,[status(thm)],[d53,d38]) ).
cnf(d55,plain,
$false,
inference(equality_resolution,[status(thm)],[d54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP098-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n004.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Fri Sep 25 14:22:06 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 59.98/16.63 % SZS status Unsatisfiable for theBenchmark.p
% 59.98/16.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------