%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP585-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 07:24:05 AM UTC 2026
% Result : Unsatisfiable 10.50s 2.37s
% Output : CNFRefutation 10.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of clauses : 22 ( 22 unt; 0 nHn; 3 RR)
% Number of literals : 22 ( 21 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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 : 46 ( 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$udivide'(X1,X0)) ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ).
cnf(c0,plain,
'double$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(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(clausification,[status(esa)],[prove_these_axioms_1]) ).
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,
'double$udivide'(multiply(inverse(X0),X1),multiply(inverse(X1),multiply(inverse(X2),X0))) = X2,
inference(superposition,[status(thm)],[d4,d1]) ).
cnf(d8,plain,
'double$udivide'(multiply(inverse(X0),X0),inverse(X1)) = X1,
inference(superposition,[status(thm)],[d5,d7]) ).
cnf(d9,plain,
multiply(inverse(multiply(inverse(X1),X0)),inverse(X1)) = inverse(X0),
inference(superposition,[status(thm)],[d5,d5]) ).
cnf(d10,plain,
multiply(inverse(inverse(X0)),inverse(X1)) = inverse(multiply(inverse(X0),X1)),
inference(superposition,[status(thm)],[d9,d5]) ).
cnf(d11,plain,
'double$udivide'(inverse(multiply(inverse(X0),X0)),inverse(X1)) = X1,
inference(superposition,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
multiply(inverse(multiply(inverse(X0),X0)),X1) = X1,
inference(superposition,[status(thm)],[d11,d6]) ).
cnf(d13,plain,
'double$udivide'(X1,inverse(X1)) = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[d12,d4]) ).
cnf(d14,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(superposition,[status(thm)],[d13,d13]) ).
cnf(d15,plain,
$false,
inference(resolution,[status(thm)],[d14,c2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP585-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.55 % Computer : n016.cluster.edu
% 0.12/0.55 % Model : x86_64 x86_64
% 0.12/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.55 % Memory : 8046.5625MB
% 0.12/0.55 % OS : Linux 6.8.0-71-generic
% 0.12/0.55 % CPULimit : 300
% 0.12/0.55 % WCLimit : 300
% 0.12/0.55 % DateTime : Fri Sep 25 15:06:00 UTC 2026
% 0.12/0.55 % CPUTime :
% 0.12/0.55 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.50/2.37 % SZS status Unsatisfiable for theBenchmark.p
% 10.50/2.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------