%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP108-1 : 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 : n006.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 07:22:21 AM UTC 2026
% Result : Unsatisfiable 3.54s 21.25s
% Output : CNFRefutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 3
% Syntax : Number of clauses : 98 ( 87 unt; 0 nHn; 13 RR)
% Number of literals : 121 ( 120 equ; 35 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 : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 257 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
inverse('double$udivide'(inverse('double$udivide'(X0,inverse('double$udivide'(X1,'double$udivide'(X0,X2))))),X2)) = X1 ).
cnf(multiply,axiom,
multiply(X0,X1) = inverse('double$udivide'(X1,X0)) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ) ).
cnf(c0,plain,
inverse('double$udivide'(inverse('double$udivide'(X0,inverse('double$udivide'(X1,'double$udivide'(X0,X2))))),X2)) = X1,
inference(clausification,[status(esa)],[single_axiom]) ).
cnf(c1,plain,
multiply(X0,X1) = inverse('double$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,
multiply(X2,inverse('double$udivide'(X0,inverse('double$udivide'(X1,'double$udivide'(X0,X2)))))) = X1,
inference(demodulation,[status(thm)],[c0,c1]) ).
cnf(d1,plain,
multiply(X2,multiply(inverse('double$udivide'(X1,'double$udivide'(X0,X2))),X0)) = X1,
inference(demodulation,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
multiply(X2,multiply(multiply('double$udivide'(X1,X2),X0),X1)) = X0,
inference(demodulation,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
multiply(X1,multiply(X3,X0)) = multiply(multiply('double$udivide'(X2,'double$udivide'(X0,X1)),X3),X2),
inference(superposition,[status(thm)],[d2,d2]) ).
cnf(d4,plain,
multiply('double$udivide'(X1,X2),multiply(X2,multiply(X3,X1))) = X3,
inference(superposition,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
multiply('double$udivide'(multiply(X2,X0),'double$udivide'(X0,X1)),X2) = X1,
inference(superposition,[status(thm)],[d4,d4]) ).
cnf(d6,plain,
multiply('double$udivide'(multiply(X1,multiply(X2,X0)),X3),multiply(X3,X2)) = 'double$udivide'(X0,X1),
inference(superposition,[status(thm)],[d4,d4]) ).
cnf(d7,plain,
'double$udivide'(X1,multiply('double$udivide'(multiply(X0,X1),X2),X0)) = X2,
inference(superposition,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
'double$udivide'(multiply(X1,X2),'double$udivide'(X2,multiply(X0,X1))) = X0,
inference(superposition,[status(thm)],[d6,d7]) ).
cnf(d9,plain,
multiply('double$udivide'(X1,multiply(X2,X0)),multiply(X0,X1)) = inverse(X2),
inference(superposition,[status(thm)],[d8,c1]) ).
cnf(d10,plain,
multiply('double$udivide'(X1,multiply('double$udivide'(multiply(X0,X1),'double$udivide'(X2,X3)),X4)),multiply(X3,multiply(X4,X2))) = X0,
inference(superposition,[status(thm)],[d3,d4]) ).
cnf(d11,plain,
X2 = inverse('double$udivide'(multiply(X2,multiply(X0,X1)),'double$udivide'(X1,X0))),
inference(superposition,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
X0 = multiply('double$udivide'(X2,X1),multiply(X0,multiply(X1,X2))),
inference(demodulation,[status(thm)],[d11,c1]) ).
cnf(d13,plain,
'double$udivide'(X0,X1) = multiply('double$udivide'(multiply(X1,X0),X2),X2),
inference(superposition,[status(thm)],[d12,d12]) ).
cnf(d14,plain,
'double$udivide'(X1,'double$udivide'(X1,X0)) = X0,
inference(superposition,[status(thm)],[d13,d7]) ).
cnf(d15,plain,
multiply(X1,multiply(X2,X0)) = multiply(multiply(X1,X2),X0),
inference(superposition,[status(thm)],[d14,d3]) ).
cnf(d16,plain,
multiply(multiply('double$udivide'(multiply(X1,X0),X2),X1),X0) = inverse(X2),
inference(superposition,[status(thm)],[d7,c1]) ).
cnf(d17,plain,
multiply('double$udivide'(X1,X0),X1) = inverse(X0),
inference(superposition,[status(thm)],[d13,d16]) ).
cnf(d18,plain,
'double$udivide'(X1,X0) = inverse(multiply(X0,X1)),
inference(superposition,[status(thm)],[d17,d13]) ).
cnf(d19,plain,
multiply(X2,multiply(multiply('double$udivide'(X1,X2),multiply(X3,X0)),X1)) = multiply(X3,X0),
inference(superposition,[status(thm)],[d4,d3]) ).
cnf(d20,plain,
multiply(X2,X3) = multiply(X2,X3),
inference(demodulation,[status(thm)],[d19,d2]) ).
cnf(d21,plain,
X2 = multiply(X0,multiply(multiply('double$udivide'(X1,X0),X2),X1)),
inference(superposition,[status(thm)],[d2,d20]) ).
cnf(d22,plain,
X0 = multiply(X1,multiply(inverse(X1),X0)),
inference(superposition,[status(thm)],[d17,d21]) ).
cnf(d23,plain,
X0 = multiply('double$udivide'(X1,inverse(X0)),X1),
inference(superposition,[status(thm)],[d22,d12]) ).
cnf(d24,plain,
X1 = inverse(inverse(X1)),
inference(demodulation,[status(thm)],[d23,d17]) ).
cnf(d25,plain,
X2 = multiply('double$udivide'(X0,X1),multiply(X1,multiply(X2,X0))),
inference(superposition,[status(thm)],[d4,d20]) ).
cnf(d26,plain,
X2 = multiply('double$udivide'(X0,'double$udivide'(X0,multiply(X1,X2))),inverse(X1)),
inference(superposition,[status(thm)],[d9,d25]) ).
cnf(d27,plain,
X2 = multiply(multiply(X1,X2),inverse(X1)),
inference(demodulation,[status(thm)],[d26,d14]) ).
cnf(d28,plain,
inverse(X0) = multiply(X1,inverse(multiply(X0,X1))),
inference(superposition,[status(thm)],[d27,d27]) ).
cnf(d29,plain,
inverse(X0) = multiply(X1,'double$udivide'(X1,X0)),
inference(demodulation,[status(thm)],[d28,d18]) ).
cnf(d30,plain,
X2 = multiply('double$udivide'(multiply(X0,X1),'double$udivide'(X1,X2)),X0),
inference(superposition,[status(thm)],[d5,d20]) ).
cnf(d31,plain,
X2 = 'double$udivide'(X1,multiply('double$udivide'(multiply(X0,X1),X2),X0)),
inference(superposition,[status(thm)],[d6,d30]) ).
cnf(d32,plain,
X0 = 'double$udivide'(X1,'double$udivide'(X1,X0)),
inference(superposition,[status(thm)],[d13,d31]) ).
cnf(d33,plain,
inverse('double$udivide'(X0,X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[d32,d29]) ).
cnf(d34,plain,
'double$udivide'(X0,X1) = inverse(multiply(X0,X1)),
inference(superposition,[status(thm)],[d33,d24]) ).
cnf(d35,plain,
'double$udivide'(X1,X0) = 'double$udivide'(X0,X1),
inference(superposition,[status(thm)],[d34,d18]) ).
cnf(d36,plain,
'double$udivide'(X0,'double$udivide'(X1,X0)) = X1,
inference(superposition,[status(thm)],[d35,d14]) ).
cnf(d37,plain,
inverse(X2) = multiply(multiply('double$udivide'(multiply(X0,X1),X2),X0),X1),
inference(superposition,[status(thm)],[d16,d20]) ).
cnf(d38,plain,
inverse('double$udivide'(X1,X2)) = multiply(X2,X1),
inference(superposition,[status(thm)],[d30,d37]) ).
cnf(d39,plain,
multiply(X0,X1) = multiply(X1,X0),
inference(superposition,[status(thm)],[d33,d38]) ).
cnf(d40,plain,
'double$udivide'(X0,X1) = multiply('double$udivide'(multiply(X2,X0),X1),X2),
inference(superposition,[status(thm)],[d4,d12]) ).
cnf(d41,plain,
'double$udivide'(X1,X2) = multiply(X0,'double$udivide'(multiply(X0,X1),X2)),
inference(demodulation,[status(thm)],[d40,d39]) ).
cnf(d42,plain,
multiply('double$udivide'(multiply(X2,multiply(X0,X1)),X3),X2) = 'double$udivide'(X1,multiply(X3,X0)),
inference(superposition,[status(thm)],[d31,d31]) ).
cnf(d43,plain,
multiply(X0,'double$udivide'(multiply(X0,multiply(X1,X2)),X3)) = 'double$udivide'(X2,multiply(X3,X1)),
inference(demodulation,[status(thm)],[d42,d39]) ).
cnf(d44,plain,
'double$udivide'(multiply(X1,X2),X3) = 'double$udivide'(X2,multiply(X3,X1)),
inference(demodulation,[status(thm)],[d43,d41]) ).
cnf(d45,plain,
multiply(X0,'double$udivide'(X0,X1)) = inverse(X1),
inference(superposition,[status(thm)],[d29,d20]) ).
cnf(d46,plain,
multiply(X0,'double$udivide'(X1,X0)) = inverse(X1),
inference(superposition,[status(thm)],[d35,d45]) ).
cnf(d47,plain,
'double$udivide'('double$udivide'(X2,X0),'double$udivide'(multiply(X3,X1),multiply(X4,'double$udivide'(multiply(X0,multiply(X1,X2)),X3)))) = X4,
inference(superposition,[status(thm)],[d6,d8]) ).
cnf(d48,plain,
'double$udivide'('double$udivide'(X4,X3),'double$udivide'(X1,multiply(multiply(X2,'double$udivide'(multiply(X3,multiply(X1,X4)),X0)),X0))) = X2,
inference(demodulation,[status(thm)],[d47,d44]) ).
cnf(d49,plain,
'double$udivide'('double$udivide'(X3,X1),'double$udivide'(X2,multiply(X0,multiply('double$udivide'(multiply(X1,multiply(X2,X3)),X4),X4)))) = X0,
inference(demodulation,[status(thm)],[d48,d15]) ).
cnf(d50,plain,
'double$udivide'('double$udivide'(X2,X0),'double$udivide'(X1,multiply(X4,multiply(X3,'double$udivide'(multiply(X0,multiply(X1,X2)),X3))))) = X4,
inference(demodulation,[status(thm)],[d49,d39]) ).
cnf(d51,plain,
'double$udivide'('double$udivide'(X3,X1),'double$udivide'(X2,multiply(X4,inverse(multiply(X1,multiply(X2,X3)))))) = X4,
inference(demodulation,[status(thm)],[d50,d46]) ).
cnf(d52,plain,
'double$udivide'('double$udivide'(X2,X0),'double$udivide'(X1,multiply(X3,'double$udivide'(multiply(X1,X2),X0)))) = X3,
inference(demodulation,[status(thm)],[d51,d18]) ).
cnf(d53,plain,
'double$udivide'('double$udivide'(X1,X2),'double$udivide'(X0,multiply(X3,'double$udivide'(X1,multiply(X2,X0))))) = X3,
inference(demodulation,[status(thm)],[d52,d44]) ).
cnf(d54,plain,
multiply('double$udivide'(X0,X4),multiply(X4,multiply(X2,multiply(X3,X1)))) = multiply('double$udivide'(X0,'double$udivide'(X1,X2)),X3),
inference(superposition,[status(thm)],[d3,d4]) ).
cnf(d55,plain,
X2 = multiply('double$udivide'(multiply(X0,X1),'double$udivide'(X1,X2)),X0),
inference(superposition,[status(thm)],[d54,d12]) ).
cnf(d56,plain,
X2 = multiply(X0,'double$udivide'(multiply(X0,X1),'double$udivide'(X1,X2))),
inference(demodulation,[status(thm)],[d55,d39]) ).
cnf(d57,plain,
'double$udivide'(X1,X0) = multiply(X2,'double$udivide'(multiply(X2,X0),X1)),
inference(superposition,[status(thm)],[d36,d56]) ).
cnf(d58,plain,
'double$udivide'(X2,X1) = multiply(X0,'double$udivide'(X1,multiply(X2,X0))),
inference(demodulation,[status(thm)],[d57,d44]) ).
cnf(d59,plain,
'double$udivide'('double$udivide'(X1,X2),'double$udivide'(X0,'double$udivide'(X2,X1))) = X0,
inference(superposition,[status(thm)],[d58,d53]) ).
cnf(d60,plain,
'double$udivide'('double$udivide'(X0,X1),X2) = 'double$udivide'(X2,'double$udivide'(X1,X0)),
inference(superposition,[status(thm)],[d59,d14]) ).
cnf(d61,plain,
'double$udivide'(X0,X1) = multiply(inverse(X1),inverse(X0)),
inference(superposition,[status(thm)],[d29,d27]) ).
cnf(d62,plain,
'double$udivide'('double$udivide'(X0,X1),X2) = multiply(inverse(X2),multiply(X0,X1)),
inference(superposition,[status(thm)],[d33,d61]) ).
cnf(d63,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(resolution,[status(thm)],[d39,c2]) ).
cnf(d64,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(a1,inverse(a1)) != multiply(inverse(b1),b1) ),
inference(demodulation,[status(thm)],[d63,d39]) ).
cnf(d65,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(a1,inverse(a1)) != multiply(b1,inverse(b1)) ),
inference(demodulation,[status(thm)],[d64,d39]) ).
cnf(d66,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(inverse(b2),multiply(b2,a2)) != a2
| multiply(a1,inverse(a1)) != multiply(b1,inverse(b1)) ),
inference(demodulation,[status(thm)],[d65,d15]) ).
cnf(d67,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| 'double$udivide'('double$udivide'(b2,a2),b2) != a2
| multiply(a1,inverse(a1)) != multiply(b1,inverse(b1)) ),
inference(demodulation,[status(thm)],[d66,d62]) ).
cnf(d68,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| 'double$udivide'(b2,'double$udivide'(a2,b2)) != a2
| multiply(a1,inverse(a1)) != multiply(b1,inverse(b1)) ),
inference(demodulation,[status(thm)],[d67,d60]) ).
cnf(d69,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2
| multiply(a1,inverse(a1)) != multiply(b1,inverse(b1)) ),
inference(demodulation,[status(thm)],[d68,d36]) ).
cnf(d70,plain,
( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| a2 != a2
| multiply(a1,inverse(a1)) != multiply(b1,inverse(b1)) ),
inference(demodulation,[status(thm)],[d69,d15]) ).
cnf(d71,plain,
multiply(X1,multiply(inverse(X1),X0)) = X0,
inference(superposition,[status(thm)],[d17,d2]) ).
cnf(d72,plain,
multiply(X2,multiply(X1,X0)) = multiply(X1,multiply(X2,X0)),
inference(superposition,[status(thm)],[d12,d21]) ).
cnf(d73,plain,
multiply(X0,multiply(X1,inverse(X0))) = X1,
inference(superposition,[status(thm)],[d39,d71]) ).
cnf(d74,plain,
multiply(X1,multiply(X0,inverse(X0))) = X1,
inference(superposition,[status(thm)],[d73,d72]) ).
cnf(d75,plain,
multiply(X0,inverse(X0)) = multiply(X1,inverse(X1)),
inference(superposition,[status(thm)],[d74,d71]) ).
cnf(d76,plain,
( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(resolution,[status(thm)],[d75,d70]) ).
cnf(d77,plain,
X4 = 'double$udivide'(multiply(X3,X1),multiply('double$udivide'('double$udivide'(X2,X0),X4),'double$udivide'(multiply(X0,multiply(X1,X2)),X3))),
inference(superposition,[status(thm)],[d6,d31]) ).
cnf(d78,plain,
X4 = 'double$udivide'(X1,multiply(multiply('double$udivide'('double$udivide'(X2,X3),X4),'double$udivide'(multiply(X3,multiply(X1,X2)),X0)),X0)),
inference(demodulation,[status(thm)],[d77,d44]) ).
cnf(d79,plain,
X2 = 'double$udivide'(X3,multiply('double$udivide'('double$udivide'(X0,X1),X2),multiply('double$udivide'(multiply(X1,multiply(X3,X0)),X4),X4))),
inference(demodulation,[status(thm)],[d78,d15]) ).
cnf(d80,plain,
X4 = 'double$udivide'(X1,multiply('double$udivide'('double$udivide'(X2,X0),X4),multiply(X3,'double$udivide'(multiply(X0,multiply(X1,X2)),X3)))),
inference(demodulation,[status(thm)],[d79,d39]) ).
cnf(d81,plain,
X4 = 'double$udivide'(X2,multiply('double$udivide'('double$udivide'(X3,X1),X4),inverse(multiply(X1,multiply(X2,X3))))),
inference(demodulation,[status(thm)],[d80,d46]) ).
cnf(d82,plain,
X3 = 'double$udivide'(X1,multiply('double$udivide'('double$udivide'(X2,X0),X3),'double$udivide'(multiply(X1,X2),X0))),
inference(demodulation,[status(thm)],[d81,d18]) ).
cnf(d83,plain,
X3 = 'double$udivide'(X0,multiply('double$udivide'('double$udivide'(X1,X2),X3),'double$udivide'(X1,multiply(X2,X0)))),
inference(demodulation,[status(thm)],[d82,d44]) ).
cnf(d84,plain,
'double$udivide'(X0,X1) = multiply('double$udivide'(multiply(X2,X0),X1),X2),
inference(superposition,[status(thm)],[d14,d30]) ).
cnf(d85,plain,
'double$udivide'(X1,X2) = multiply(X0,'double$udivide'(multiply(X0,X1),X2)),
inference(demodulation,[status(thm)],[d84,d39]) ).
cnf(d86,plain,
'double$udivide'(X1,X2) = multiply(X0,'double$udivide'(X1,multiply(X2,X0))),
inference(demodulation,[status(thm)],[d85,d44]) ).
cnf(d87,plain,
X2 = 'double$udivide'('double$udivide'('double$udivide'(X0,X1),X2),'double$udivide'(X0,X1)),
inference(superposition,[status(thm)],[d86,d83]) ).
cnf(d88,plain,
X2 = 'double$udivide'('double$udivide'(X0,X1),'double$udivide'('double$udivide'(X0,X1),X2)),
inference(demodulation,[status(thm)],[d87,d35]) ).
cnf(d89,plain,
X2 = X2,
inference(demodulation,[status(thm)],[d88,d14]) ).
cnf(d90,plain,
a2 != a2,
inference(resolution,[status(thm)],[d89,d76]) ).
cnf(d91,plain,
$false,
inference(equality_resolution,[status(thm)],[d90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP108-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.33 % Computer : n006.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 25 14:22:26 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.54/21.25 % SZS status Unsatisfiable for theBenchmark.p
% 3.54/21.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------