%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP613-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/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 07:24:09 AM UTC 2026
% Result : Unsatisfiable 24.28s 5.06s
% Output : CNFRefutation 24.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of clauses : 42 ( 42 unt; 0 nHn; 5 RR)
% Number of literals : 42 ( 41 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 99 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
'double$udivide'(inverse('double$udivide'(inverse('double$udivide'(X0,inverse(X1))),X2)),'double$udivide'(X0,X2)) = X1 ).
cnf(multiply,axiom,
multiply(X0,X1) = inverse('double$udivide'(X1,X0)) ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ).
cnf(c0,plain,
'double$udivide'(inverse('double$udivide'(inverse('double$udivide'(X0,inverse(X1))),X2)),'double$udivide'(X0,X2)) = X1,
inference(clausification,[status(esa)],[single_axiom]) ).
cnf(c1,plain,
multiply(X0,X1) = inverse('double$udivide'(X1,X0)),
inference(clausification,[status(esa)],[multiply]) ).
cnf(c2,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(clausification,[status(esa)],[prove_these_axioms_1]) ).
cnf(d0,plain,
'double$udivide'(multiply(X2,inverse('double$udivide'(X0,inverse(X1)))),'double$udivide'(X0,X2)) = X1,
inference(demodulation,[status(thm)],[c0,c1]) ).
cnf(d1,plain,
'double$udivide'(multiply(X2,multiply(inverse(X1),X0)),'double$udivide'(X0,X2)) = X1,
inference(demodulation,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
'double$udivide'(multiply('double$udivide'(X2,X0),multiply(inverse(X3),multiply(X0,multiply(inverse(X1),X2)))),X1) = X3,
inference(superposition,[status(thm)],[d1,d1]) ).
cnf(d3,plain,
multiply('double$udivide'(X2,X0),multiply(X0,multiply(inverse(X1),X2))) = inverse(X1),
inference(superposition,[status(thm)],[d1,c1]) ).
cnf(d4,plain,
multiply(X1,multiply('double$udivide'(X2,X0),multiply(inverse(X3),multiply(X0,multiply(inverse(X1),X2))))) = inverse(X3),
inference(superposition,[status(thm)],[d1,d3]) ).
cnf(d5,plain,
'double$udivide'(multiply('double$udivide'(multiply(X2,multiply(inverse(inverse(X0)),X1)),'double$udivide'(X1,X2)),inverse(X3)),X3) = X0,
inference(superposition,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
'double$udivide'(multiply(inverse(X1),inverse(X3)),X3) = X1,
inference(demodulation,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
multiply('double$udivide'(X2,X3),multiply(X3,multiply(multiply(X1,X0),X2))) = inverse('double$udivide'(X0,X1)),
inference(superposition,[status(thm)],[c1,d3]) ).
cnf(d8,plain,
multiply('double$udivide'(X2,X3),multiply(X3,multiply(multiply(X1,X0),X2))) = multiply(X1,X0),
inference(demodulation,[status(thm)],[d7,c1]) ).
cnf(d9,plain,
multiply('double$udivide'(multiply(inverse(X3),X0),'double$udivide'(X0,multiply(X1,X2))),inverse(X3)) = multiply(X1,X2),
inference(superposition,[status(thm)],[d3,d8]) ).
cnf(d10,plain,
'double$udivide'(multiply(X2,X3),'double$udivide'(multiply(multiply(X2,X3),X0),'double$udivide'(X0,inverse(X1)))) = X1,
inference(superposition,[status(thm)],[d8,d1]) ).
cnf(d11,plain,
multiply(X1,multiply(inverse(X0),inverse(X1))) = inverse(X0),
inference(superposition,[status(thm)],[d6,c1]) ).
cnf(d12,plain,
'double$udivide'(inverse(X1),'double$udivide'(inverse(X0),X0)) = X1,
inference(superposition,[status(thm)],[d11,d1]) ).
cnf(d13,plain,
'double$udivide'(multiply(X1,X0),'double$udivide'(inverse(X2),X2)) = 'double$udivide'(X0,X1),
inference(superposition,[status(thm)],[c1,d12]) ).
cnf(d14,plain,
'double$udivide'(multiply(X0,X1),'double$udivide'(inverse(inverse(X2)),multiply(X0,X1))) = X2,
inference(superposition,[status(thm)],[d13,d10]) ).
cnf(d15,plain,
multiply(X1,inverse(X0)) = multiply(inverse(X0),inverse(inverse(X1))),
inference(superposition,[status(thm)],[d14,d9]) ).
cnf(d16,plain,
'double$udivide'(multiply(X1,inverse(X0)),inverse(X1)) = X0,
inference(superposition,[status(thm)],[d15,d6]) ).
cnf(d17,plain,
inverse(inverse(X0)) = X0,
inference(superposition,[status(thm)],[d16,d6]) ).
cnf(d18,plain,
multiply(X0,inverse(X1)) = multiply(inverse(X1),X0),
inference(demodulation,[status(thm)],[d15,d17]) ).
cnf(d19,plain,
multiply(a1,inverse(a1)) != multiply(inverse(b1),b1),
inference(demodulation,[status(thm)],[c2,d18]) ).
cnf(d20,plain,
multiply(a1,inverse(a1)) != multiply(b1,inverse(b1)),
inference(demodulation,[status(thm)],[d19,d18]) ).
cnf(d21,plain,
'double$udivide'(inverse(X2),'double$udivide'(multiply(inverse(X2),X0),'double$udivide'(X0,inverse(X1)))) = X1,
inference(superposition,[status(thm)],[d3,d1]) ).
cnf(d22,plain,
'double$udivide'(inverse(X2),'double$udivide'(multiply(inverse(X2),X3),'double$udivide'(X3,multiply(X1,X0)))) = 'double$udivide'(X0,X1),
inference(superposition,[status(thm)],[c1,d21]) ).
cnf(d23,plain,
'double$udivide'(inverse(X0),X1) = 'double$udivide'(inverse(inverse(X1)),inverse(X0)),
inference(superposition,[status(thm)],[d14,d22]) ).
cnf(d24,plain,
'double$udivide'(multiply(inverse(X2),multiply(X1,X0)),'double$udivide'(X0,X1)) = X2,
inference(superposition,[status(thm)],[c1,d6]) ).
cnf(d25,plain,
'double$udivide'(inverse(X1),'double$udivide'(inverse(inverse(X0)),inverse(X1))) = X0,
inference(superposition,[status(thm)],[d11,d24]) ).
cnf(d26,plain,
'double$udivide'(inverse(X1),'double$udivide'(inverse(X1),X0)) = X0,
inference(demodulation,[status(thm)],[d25,d23]) ).
cnf(d27,plain,
X1 = 'double$udivide'(multiply(inverse(X1),inverse(X0)),X0),
inference(superposition,[status(thm)],[d1,d13]) ).
cnf(d28,plain,
X2 = 'double$udivide'(multiply(inverse(X2),multiply(X1,X0)),'double$udivide'(X0,X1)),
inference(superposition,[status(thm)],[c1,d27]) ).
cnf(d29,plain,
'double$udivide'(multiply(X1,inverse(X1)),inverse(X0)) = X0,
inference(superposition,[status(thm)],[d13,d24]) ).
cnf(d30,plain,
multiply(inverse(X1),multiply(X0,inverse(X0))) = inverse(X1),
inference(superposition,[status(thm)],[d29,c1]) ).
cnf(d31,plain,
X0 = 'double$udivide'(inverse(X0),'double$udivide'(inverse(X1),X1)),
inference(superposition,[status(thm)],[d30,d28]) ).
cnf(d32,plain,
'double$udivide'(inverse(X0),X0) = 'double$udivide'(inverse(X1),X1),
inference(superposition,[status(thm)],[d31,d26]) ).
cnf(d33,plain,
multiply(X0,inverse(X0)) = inverse('double$udivide'(inverse(X1),X1)),
inference(superposition,[status(thm)],[d32,c1]) ).
cnf(d34,plain,
multiply(X1,inverse(X1)) = multiply(X0,inverse(X0)),
inference(demodulation,[status(thm)],[d33,c1]) ).
cnf(d35,plain,
$false,
inference(resolution,[status(thm)],[d34,d20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP613-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n001.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 15:07:57 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.28/5.06 % SZS status Unsatisfiable for theBenchmark.p
% 24.28/5.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------