%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP104-1 : 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 : n001.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 07:22:20 AM UTC 2026
% Result : Unsatisfiable 75.56s 21.67s
% Output : CNFRefutation 75.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 3
% Syntax : Number of clauses : 85 ( 77 unt; 0 nHn; 12 RR)
% Number of literals : 102 ( 101 equ; 28 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 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 : 186 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
'double$udivide'(X0,inverse('double$udivide'(inverse('double$udivide'('double$udivide'(X0,X1),inverse(X2))),X1))) = X2 ).
cnf(multiply,axiom,
multiply(X0,X1) = inverse('double$udivide'(X1,X0)) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ) ).
cnf(c0,plain,
'double$udivide'(X0,inverse('double$udivide'(inverse('double$udivide'('double$udivide'(X0,X1),inverse(X2))),X1))) = X2,
inference(clausification,[status(esa)],[single_axiom]) ).
cnf(c1,plain,
multiply(X0,X1) = inverse('double$udivide'(X1,X0)),
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,
'double$udivide'(X0,multiply(X1,inverse('double$udivide'('double$udivide'(X0,X1),inverse(X2))))) = X2,
inference(demodulation,[status(thm)],[c0,c1]) ).
cnf(d1,plain,
'double$udivide'(X0,multiply(X1,multiply(inverse(X2),'double$udivide'(X0,X1)))) = X2,
inference(demodulation,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
'double$udivide'(X0,multiply(multiply(X1,multiply(inverse(X2),'double$udivide'(X0,X1))),multiply(inverse(X3),X2))) = X3,
inference(superposition,[status(thm)],[d1,d1]) ).
cnf(d3,plain,
multiply(multiply(X1,multiply(inverse(X2),'double$udivide'(X0,X1))),X0) = inverse(X2),
inference(superposition,[status(thm)],[d1,c1]) ).
cnf(d4,plain,
'double$udivide'(multiply(inverse(X2),X1),inverse(X1)) = X2,
inference(superposition,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
multiply(inverse(X1),multiply(inverse(X0),X1)) = inverse(X0),
inference(superposition,[status(thm)],[d4,c1]) ).
cnf(d6,plain,
'double$udivide'(inverse(X1),inverse(multiply(inverse(X1),X0))) = X0,
inference(superposition,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
multiply(inverse(X2),multiply(multiply(X1,X0),X2)) = inverse('double$udivide'(X0,X1)),
inference(superposition,[status(thm)],[c1,d5]) ).
cnf(d8,plain,
multiply(inverse(X2),multiply(multiply(X1,X0),X2)) = multiply(X1,X0),
inference(demodulation,[status(thm)],[d7,c1]) ).
cnf(d9,plain,
'double$udivide'(inverse(X0),inverse(multiply(X1,X2))) = multiply(multiply(X1,X2),X0),
inference(superposition,[status(thm)],[d8,d6]) ).
cnf(d10,plain,
multiply(multiply(inverse(X0),X1),X0) = X1,
inference(demodulation,[status(thm)],[d6,d9]) ).
cnf(d11,plain,
'double$udivide'(X2,multiply(X3,multiply(multiply(X1,X0),'double$udivide'(X2,X3)))) = 'double$udivide'(X0,X1),
inference(superposition,[status(thm)],[c1,d1]) ).
cnf(d12,plain,
'double$udivide'(X3,multiply(X4,multiply(inverse(X1),'double$udivide'(X3,X4)))) = 'double$udivide'(X2,multiply(X0,multiply(inverse(X1),'double$udivide'(X2,X0)))),
inference(superposition,[status(thm)],[d3,d11]) ).
cnf(d13,plain,
X2 = 'double$udivide'(X3,multiply(X4,multiply(inverse(X2),'double$udivide'(X3,X4)))),
inference(demodulation,[status(thm)],[d12,d1]) ).
cnf(d14,plain,
multiply(inverse(X1),'double$udivide'(X0,inverse(X0))) = inverse(X1),
inference(superposition,[status(thm)],[d10,d3]) ).
cnf(d15,plain,
multiply(inverse(X0),X0) = 'double$udivide'(X1,inverse(X1)),
inference(superposition,[status(thm)],[d14,d10]) ).
cnf(d16,plain,
multiply('double$udivide'(X1,inverse(X1)),X0) = X0,
inference(superposition,[status(thm)],[d15,d10]) ).
cnf(d17,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(superposition,[status(thm)],[d15,d16]) ).
cnf(d18,plain,
multiply(inverse(multiply(inverse(X1),X0)),inverse(X1)) = inverse(X0),
inference(superposition,[status(thm)],[d5,d5]) ).
cnf(d19,plain,
multiply(inverse(inverse(X0)),inverse(X1)) = inverse(multiply(inverse(X0),X1)),
inference(superposition,[status(thm)],[d18,d5]) ).
cnf(d20,plain,
multiply(inverse(multiply(inverse(X0),X0)),X1) = X1,
inference(superposition,[status(thm)],[d19,d17]) ).
cnf(d21,plain,
multiply(X1,multiply(inverse(X0),X0)) = X1,
inference(superposition,[status(thm)],[d20,d10]) ).
cnf(d22,plain,
multiply(X2,'double$udivide'(X1,inverse(X1))) = X2,
inference(superposition,[status(thm)],[d15,d21]) ).
cnf(d23,plain,
X0 = 'double$udivide'(X1,multiply(inverse(X1),inverse(X0))),
inference(superposition,[status(thm)],[d22,d13]) ).
cnf(d24,plain,
'double$udivide'(inverse(X0),multiply(inverse(multiply(inverse(X0),X1)),multiply(inverse(X2),X1))) = X2,
inference(superposition,[status(thm)],[d6,d1]) ).
cnf(d25,plain,
'double$udivide'(multiply(X1,X2),inverse(multiply(multiply(X1,X2),X0))) = X0,
inference(superposition,[status(thm)],[d8,d4]) ).
cnf(d26,plain,
'double$udivide'(multiply(inverse(X0),X0),inverse(X1)) = X1,
inference(superposition,[status(thm)],[d17,d25]) ).
cnf(d27,plain,
X1 = multiply(multiply(inverse(X0),X0),X1),
inference(superposition,[status(thm)],[d25,d26]) ).
cnf(d28,plain,
X1 = multiply(inverse(multiply(inverse(X0),X0)),X1),
inference(superposition,[status(thm)],[d19,d27]) ).
cnf(d29,plain,
'double$udivide'(inverse(X0),multiply(inverse(X1),X0)) = X1,
inference(superposition,[status(thm)],[d28,d24]) ).
cnf(d30,plain,
X0 = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d29,d23]) ).
cnf(d31,plain,
'double$udivide'(X0,X1) = inverse(multiply(X1,X0)),
inference(superposition,[status(thm)],[c1,d30]) ).
cnf(d32,plain,
multiply(inverse(multiply(inverse(X0),X1)),X1) = X0,
inference(superposition,[status(thm)],[d29,d24]) ).
cnf(d33,plain,
multiply('double$udivide'(X1,inverse(X0)),X1) = X0,
inference(demodulation,[status(thm)],[d32,d31]) ).
cnf(d34,plain,
multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[d4,d33]) ).
cnf(d35,plain,
multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(superposition,[status(thm)],[d30,d34]) ).
cnf(d36,plain,
multiply(X1,X0) = multiply(X0,X1),
inference(superposition,[status(thm)],[d35,d10]) ).
cnf(d37,plain,
'double$udivide'(X1,X0) = inverse(multiply(X1,X0)),
inference(superposition,[status(thm)],[d36,d31]) ).
cnf(d38,plain,
multiply(multiply(X0,X1),multiply('double$udivide'(X0,X1),X2)) = X2,
inference(superposition,[status(thm)],[d37,d34]) ).
cnf(d39,plain,
multiply(inverse(X0),multiply(X1,X0)) = X1,
inference(superposition,[status(thm)],[d36,d35]) ).
cnf(d40,plain,
multiply('double$udivide'(X1,X0),multiply(X2,multiply(X0,X1))) = X2,
inference(superposition,[status(thm)],[d31,d39]) ).
cnf(d41,plain,
multiply(multiply(X0,X1),X2) = multiply(X2,multiply(X1,X0)),
inference(superposition,[status(thm)],[d40,d38]) ).
cnf(d42,plain,
multiply(X2,multiply(X1,X0)) = multiply(X2,multiply(X0,X1)),
inference(superposition,[status(thm)],[d41,d36]) ).
cnf(d43,plain,
multiply(multiply(X2,multiply(multiply(X1,X0),'double$udivide'(X3,X2))),X3) = inverse('double$udivide'(X0,X1)),
inference(superposition,[status(thm)],[c1,d3]) ).
cnf(d44,plain,
multiply(multiply(X2,multiply(multiply(X1,X0),'double$udivide'(X3,X2))),X3) = multiply(X1,X0),
inference(demodulation,[status(thm)],[d43,c1]) ).
cnf(d45,plain,
multiply(multiply(X1,X2),X0) = multiply(inverse('double$udivide'(X0,X1)),X2),
inference(superposition,[status(thm)],[d10,d44]) ).
cnf(d46,plain,
multiply(multiply(X1,X2),X0) = multiply(multiply(X1,X0),X2),
inference(demodulation,[status(thm)],[d45,c1]) ).
cnf(d47,plain,
multiply(X2,multiply(X0,X1)) = multiply(multiply(X0,X2),X1),
inference(superposition,[status(thm)],[d46,d36]) ).
cnf(d48,plain,
multiply(multiply(X1,X0),X2) = multiply(multiply(X0,X2),X1),
inference(superposition,[status(thm)],[d36,d46]) ).
cnf(d49,plain,
multiply(X1,multiply(X0,X2)) = multiply(multiply(X1,X2),X0),
inference(demodulation,[status(thm)],[d48,d47]) ).
cnf(d50,plain,
multiply(X1,multiply(X0,X2)) = multiply(X0,multiply(X2,X1)),
inference(superposition,[status(thm)],[d49,d47]) ).
cnf(d51,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(resolution,[status(thm)],[d17,c2]) ).
cnf(d52,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a1,inverse(a1)) != multiply(inverse(b1),b1) ),
inference(demodulation,[status(thm)],[d51,d36]) ).
cnf(d53,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a1,inverse(a1)) != multiply(b1,inverse(b1)) ),
inference(demodulation,[status(thm)],[d52,d36]) ).
cnf(d54,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(b3,multiply(a3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(a1,inverse(a1)) != multiply(b1,inverse(b1)) ),
inference(demodulation,[status(thm)],[d53,d47]) ).
cnf(d55,plain,
( multiply(a4,b4) != multiply(a4,b4)
| multiply(b3,multiply(a3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(a1,inverse(a1)) != multiply(b1,inverse(b1)) ),
inference(demodulation,[status(thm)],[d54,d36]) ).
cnf(d56,plain,
'double$udivide'(X1,'double$udivide'(X1,X0)) = X0,
inference(superposition,[status(thm)],[d34,d1]) ).
cnf(d57,plain,
'double$udivide'(inverse(multiply(X0,X1)),X1) = X0,
inference(superposition,[status(thm)],[d35,d29]) ).
cnf(d58,plain,
'double$udivide'('double$udivide'(X1,X0),X1) = X0,
inference(demodulation,[status(thm)],[d57,d31]) ).
cnf(d59,plain,
X0 = 'double$udivide'(X1,'double$udivide'(X1,X0)),
inference(superposition,[status(thm)],[d34,d13]) ).
cnf(d60,plain,
'double$udivide'(X1,X0) = 'double$udivide'(X0,X1),
inference(superposition,[status(thm)],[d59,d58]) ).
cnf(d61,plain,
'double$udivide'(inverse(X0),inverse(inverse(X1))) = multiply(inverse(X1),X0),
inference(superposition,[status(thm)],[d5,d6]) ).
cnf(d62,plain,
'double$udivide'(multiply(X1,X0),inverse(inverse(X2))) = multiply(inverse(X2),'double$udivide'(X0,X1)),
inference(superposition,[status(thm)],[c1,d61]) ).
cnf(d63,plain,
'double$udivide'(multiply(X1,X2),X0) = multiply(inverse(X0),'double$udivide'(X2,X1)),
inference(demodulation,[status(thm)],[d62,d30]) ).
cnf(d64,plain,
'double$udivide'(multiply(inverse(X2),'double$udivide'(X0,X1)),multiply(X1,X0)) = X2,
inference(superposition,[status(thm)],[c1,d4]) ).
cnf(d65,plain,
'double$udivide'(multiply(multiply(X1,X0),X2),inverse(X2)) = 'double$udivide'(X0,X1),
inference(superposition,[status(thm)],[c1,d4]) ).
cnf(d66,plain,
'double$udivide'(multiply(inverse(X3),'double$udivide'(X1,X0)),multiply(inverse(X2),multiply(multiply(X0,X1),X2))) = X3,
inference(superposition,[status(thm)],[d65,d64]) ).
cnf(d67,plain,
'double$udivide'('double$udivide'(multiply(X2,X1),X0),multiply(inverse(X3),multiply(multiply(X2,X1),X3))) = X0,
inference(demodulation,[status(thm)],[d66,d63]) ).
cnf(d68,plain,
'double$udivide'('double$udivide'(multiply(X1,X2),X3),multiply(X1,X2)) = X3,
inference(demodulation,[status(thm)],[d67,d39]) ).
cnf(d69,plain,
'double$udivide'(multiply(X0,X1),'double$udivide'(multiply(X0,X1),X2)) = X2,
inference(demodulation,[status(thm)],[d68,d60]) ).
cnf(d70,plain,
X2 = X2,
inference(demodulation,[status(thm)],[d69,d56]) ).
cnf(d71,plain,
( multiply(b3,multiply(a3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(a1,inverse(a1)) != multiply(b1,inverse(b1)) ),
inference(resolution,[status(thm)],[d70,d55]) ).
cnf(d72,plain,
multiply(inverse(X2),X2) = multiply(inverse(X1),X1),
inference(superposition,[status(thm)],[d15,d15]) ).
cnf(d73,plain,
multiply(inverse(X1),X1) = multiply(X0,inverse(X0)),
inference(superposition,[status(thm)],[d30,d72]) ).
cnf(d74,plain,
multiply(X0,inverse(X0)) = multiply(X1,inverse(X1)),
inference(demodulation,[status(thm)],[d73,d36]) ).
cnf(d75,plain,
multiply(b3,multiply(a3,c3)) != multiply(a3,multiply(b3,c3)),
inference(resolution,[status(thm)],[d74,d71]) ).
cnf(d76,plain,
multiply(a3,multiply(c3,b3)) != multiply(a3,multiply(b3,c3)),
inference(demodulation,[status(thm)],[d75,d50]) ).
cnf(d77,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(demodulation,[status(thm)],[d76,d42]) ).
cnf(d78,plain,
$false,
inference(resolution,[status(thm)],[d70,d77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP104-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.42 % Computer : n001.cluster.edu
% 0.10/0.42 % Model : x86_64 x86_64
% 0.10/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.42 % Memory : 8046.5625MB
% 0.10/0.42 % OS : Linux 6.8.0-71-generic
% 0.10/0.42 % CPULimit : 300
% 0.10/0.42 % WCLimit : 300
% 0.10/0.42 % DateTime : Fri Sep 25 14:28:25 UTC 2026
% 0.10/0.42 % CPUTime :
% 0.10/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 75.56/21.67 % SZS status Unsatisfiable for theBenchmark.p
% 75.56/21.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------