%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO447+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 07:15:14 AM UTC 2026
% Result : Theorem 186.86s 55.25s
% Output : CNFRefutation 186.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 9 unt; 0 def)
% Number of atoms : 25 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 10 ~; 4 |; 3 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(aORTHOGONALu_SYM,axiom,
! [X0,X1,X2] : s(bool,i(s(fun(cart(real,X0),bool),i(s(fun(cart(real,X0),fun(cart(real,X0),bool)),orthogonal),s(cart(real,X0),X1))),s(cart(real,X0),X2))) = s(bool,i(s(fun(cart(real,X0),bool),i(s(fun(cart(real,X0),fun(cart(real,X0),bool)),orthogonal),s(cart(real,X0),X2))),s(cart(real,X0),X1))) ).
fof(aORTHOGONALu_CLAUSESu_conjunct3,axiom,
! [X0,X1,X2,X3] :
( ( p(s(bool,i(s(fun(cart(real,X0),bool),i(s(fun(cart(real,X0),fun(cart(real,X0),bool)),orthogonal),s(cart(real,X0),X1))),s(cart(real,X0),X3))))
& p(s(bool,i(s(fun(cart(real,X0),bool),i(s(fun(cart(real,X0),fun(cart(real,X0),bool)),orthogonal),s(cart(real,X0),X1))),s(cart(real,X0),X2)))) )
=> p(s(bool,i(s(fun(cart(real,X0),bool),i(s(fun(cart(real,X0),fun(cart(real,X0),bool)),orthogonal),s(cart(real,X0),X1))),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(cart(real,X0),fun(cart(real,X0),cart(real,X0))),'vectoru$uadd'),s(cart(real,X0),X2))),s(cart(real,X0),X3)))))) ) ).
fof(aORTHOGONALu_CLAUSESu_conjunct8,conjecture,
! [X0,X1,X2,X3] :
( ( p(s(bool,i(s(fun(cart(real,X0),bool),i(s(fun(cart(real,X0),fun(cart(real,X0),bool)),orthogonal),s(cart(real,X0),X3))),s(cart(real,X0),X1))))
& p(s(bool,i(s(fun(cart(real,X0),bool),i(s(fun(cart(real,X0),fun(cart(real,X0),bool)),orthogonal),s(cart(real,X0),X2))),s(cart(real,X0),X1)))) )
=> p(s(bool,i(s(fun(cart(real,X0),bool),i(s(fun(cart(real,X0),fun(cart(real,X0),bool)),orthogonal),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(cart(real,X0),fun(cart(real,X0),cart(real,X0))),'vectoru$uadd'),s(cart(real,X0),X2))),s(cart(real,X0),X3))))),s(cart(real,X0),X1)))) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( p(s(bool,i(s(fun(cart(real,X0),bool),i(s(fun(cart(real,X0),fun(cart(real,X0),bool)),orthogonal),s(cart(real,X0),X3))),s(cart(real,X0),X1))))
& p(s(bool,i(s(fun(cart(real,X0),bool),i(s(fun(cart(real,X0),fun(cart(real,X0),bool)),orthogonal),s(cart(real,X0),X2))),s(cart(real,X0),X1)))) )
=> p(s(bool,i(s(fun(cart(real,X0),bool),i(s(fun(cart(real,X0),fun(cart(real,X0),bool)),orthogonal),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(cart(real,X0),fun(cart(real,X0),cart(real,X0))),'vectoru$uadd'),s(cart(real,X0),X2))),s(cart(real,X0),X3))))),s(cart(real,X0),X1)))) ),
inference(negate_conjecture,[status(cth)],[aORTHOGONALu_CLAUSESu_conjunct8]) ).
cnf(c533,plain,
s(bool,i(s(fun(cart(real,X0),bool),i(s(fun(cart(real,X0),fun(cart(real,X0),bool)),orthogonal),s(cart(real,X0),X1))),s(cart(real,X0),X2))) = s(bool,i(s(fun(cart(real,X0),bool),i(s(fun(cart(real,X0),fun(cart(real,X0),bool)),orthogonal),s(cart(real,X0),X2))),s(cart(real,X0),X1))),
inference(clausification,[status(esa)],[aORTHOGONALu_SYM]) ).
cnf(c543,plain,
( p(s(bool,i(s(fun(cart(real,X0),bool),i(s(fun(cart(real,X0),fun(cart(real,X0),bool)),orthogonal),s(cart(real,X0),X1))),s(cart(real,X0),i(s(fun(cart(real,X0),cart(real,X0)),i(s(fun(cart(real,X0),fun(cart(real,X0),cart(real,X0))),'vectoru$uadd'),s(cart(real,X0),X2))),s(cart(real,X0),X3))))))
| ~ p(s(bool,i(s(fun(cart(real,X0),bool),i(s(fun(cart(real,X0),fun(cart(real,X0),bool)),orthogonal),s(cart(real,X0),X1))),s(cart(real,X0),X3))))
| ~ p(s(bool,i(s(fun(cart(real,X0),bool),i(s(fun(cart(real,X0),fun(cart(real,X0),bool)),orthogonal),s(cart(real,X0),X1))),s(cart(real,X0),X2)))) ),
inference(clausification,[status(esa)],[aORTHOGONALu_CLAUSESu_conjunct3]) ).
cnf(c8502,plain,
p(s(bool,i(s(fun(cart(real,sK14049),bool),i(s(fun(cart(real,sK14049),fun(cart(real,sK14049),bool)),orthogonal),s(cart(real,sK14049),sK14051))),s(cart(real,sK14049),sK14050)))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c8503,plain,
p(s(bool,i(s(fun(cart(real,sK14049),bool),i(s(fun(cart(real,sK14049),fun(cart(real,sK14049),bool)),orthogonal),s(cart(real,sK14049),sK14052))),s(cart(real,sK14049),sK14050)))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c8504,plain,
~ p(s(bool,i(s(fun(cart(real,sK14049),bool),i(s(fun(cart(real,sK14049),fun(cart(real,sK14049),bool)),orthogonal),s(cart(real,sK14049),i(s(fun(cart(real,sK14049),cart(real,sK14049)),i(s(fun(cart(real,sK14049),fun(cart(real,sK14049),cart(real,sK14049))),'vectoru$uadd'),s(cart(real,sK14049),sK14051))),s(cart(real,sK14049),sK14052))))),s(cart(real,sK14049),sK14050)))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
~ p(s(bool,i(s(fun(cart(real,sK14049),bool),i(s(fun(cart(real,sK14049),fun(cart(real,sK14049),bool)),orthogonal),s(cart(real,sK14049),sK14050))),s(cart(real,sK14049),i(s(fun(cart(real,sK14049),cart(real,sK14049)),i(s(fun(cart(real,sK14049),fun(cart(real,sK14049),cart(real,sK14049))),'vectoru$uadd'),s(cart(real,sK14049),sK14051))),s(cart(real,sK14049),sK14052)))))),
inference(demodulation,[status(thm)],[c8504,c533]) ).
cnf(d1,plain,
( ~ p(s(bool,i(s(fun(cart(real,sK14049),bool),i(s(fun(cart(real,sK14049),fun(cart(real,sK14049),bool)),orthogonal),s(cart(real,sK14049),sK14050))),s(cart(real,sK14049),sK14051))))
| ~ p(s(bool,i(s(fun(cart(real,sK14049),bool),i(s(fun(cart(real,sK14049),fun(cart(real,sK14049),bool)),orthogonal),s(cart(real,sK14049),sK14050))),s(cart(real,sK14049),sK14052)))) ),
inference(resolution,[status(thm)],[c543,d0]) ).
cnf(d2,plain,
( ~ p(s(bool,i(s(fun(cart(real,sK14049),bool),i(s(fun(cart(real,sK14049),fun(cart(real,sK14049),bool)),orthogonal),s(cart(real,sK14049),sK14050))),s(cart(real,sK14049),sK14052))))
| ~ p(s(bool,i(s(fun(cart(real,sK14049),bool),i(s(fun(cart(real,sK14049),fun(cart(real,sK14049),bool)),orthogonal),s(cart(real,sK14049),sK14051))),s(cart(real,sK14049),sK14050)))) ),
inference(demodulation,[status(thm)],[d1,c533]) ).
cnf(d3,plain,
~ p(s(bool,i(s(fun(cart(real,sK14049),bool),i(s(fun(cart(real,sK14049),fun(cart(real,sK14049),bool)),orthogonal),s(cart(real,sK14049),sK14050))),s(cart(real,sK14049),sK14052)))),
inference(resolution,[status(thm)],[c8502,d2]) ).
cnf(d4,plain,
p(s(bool,i(s(fun(cart(real,sK14049),bool),i(s(fun(cart(real,sK14049),fun(cart(real,sK14049),bool)),orthogonal),s(cart(real,sK14049),sK14050))),s(cart(real,sK14049),sK14052)))),
inference(demodulation,[status(thm)],[c8503,c533]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[d4,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO447+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n026.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Fri Sep 25 13:29:41 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 186.86/55.25 % SZS status Theorem for theBenchmark.p
% 186.86/55.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------