%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET734+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 08:33:09 AM UTC 2026
% Result : Theorem 68.42s 17.61s
% Output : CNFRefutation 68.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 3 unt; 0 def)
% Number of atoms : 58 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 62 ( 23 ~; 23 |; 8 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-5 aty)
% Number of variables : 54 ( 0 sgn 22 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(compose_function,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( member(X6,X4)
& member(X5,X2) )
=> ( apply('compose$ufunction'(X0,X1,X2,X3,X4),X5,X6)
<=> ? [X7] :
( apply(X0,X7,X6)
& apply(X1,X5,X7)
& member(X7,X3) ) ) ) ).
fof(identity,axiom,
! [X0,X1] :
( identity(X0,X1)
<=> ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ) ).
fof(surjective,axiom,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
<=> ! [X3] :
( member(X3,X2)
=> ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) ) ) ) ).
fof(thII25,conjecture,
! [X0,X1,X2,X3] :
( ( identity('compose$ufunction'(X1,X0,X3,X2,X3),X3)
& maps(X0,X3,X2)
& maps(X1,X2,X3) )
=> surjective(X1,X2,X3) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( identity('compose$ufunction'(X1,X0,X3,X2,X3),X3)
& maps(X0,X3,X2)
& maps(X1,X2,X3) )
=> surjective(X1,X2,X3) ),
inference(negate_conjecture,[status(cth)],[thII25]) ).
cnf(c52,plain,
( member(sK67(X4,X5,X6,X2,X0),X6)
| ~ apply('compose$ufunction'(X4,X5,X3,X6,X1),X2,X0)
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[compose_function]) ).
cnf(c53,plain,
( apply(X4,sK67(X4,X5,X6,X2,X0),X0)
| ~ apply('compose$ufunction'(X4,X5,X3,X6,X1),X2,X0)
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[compose_function]) ).
cnf(c64,plain,
( apply(X0,X2,X2)
| ~ member(X2,X1)
| ~ identity(X0,X1) ),
inference(clausification,[status(esa)],[identity]) ).
cnf(c77,plain,
( member(sK99(X0,X1,X2),X2)
| surjective(X0,X1,X2) ),
inference(clausification,[status(esa)],[surjective]) ).
cnf(c78,plain,
( ~ apply(X0,X3,sK99(X0,X1,X2))
| ~ member(X3,X1)
| surjective(X0,X1,X2) ),
inference(clausification,[status(esa)],[surjective]) ).
cnf(c143,plain,
identity('compose$ufunction'(sK183,sK182,sK185,sK184,sK185),sK185),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c145,plain,
~ surjective(sK183,sK184,sK185),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( apply('compose$ufunction'(sK183,sK182,sK185,sK184,sK185),X0,X0)
| ~ member(X0,sK185) ),
inference(resolution,[status(thm)],[c64,c143]) ).
cnf(d1,plain,
( member(sK67(sK183,sK182,sK184,X0,X0),sK184)
| ~ member(X0,sK185)
| ~ member(X0,sK185)
| ~ member(X0,sK185) ),
inference(resolution,[status(thm)],[d0,c52]) ).
cnf(d2,plain,
( apply(sK183,sK67(sK183,sK182,sK184,X0,X0),X0)
| ~ member(X0,sK185)
| ~ member(X0,sK185)
| ~ member(X0,sK185) ),
inference(resolution,[status(thm)],[d0,c53]) ).
cnf(d3,plain,
( surjective(sK183,X0,X1)
| ~ member(sK67(sK183,sK182,sK184,sK99(sK183,X0,X1),sK99(sK183,X0,X1)),X0)
| ~ member(sK99(sK183,X0,X1),sK185) ),
inference(resolution,[status(thm)],[d2,c78]) ).
cnf(d4,plain,
( ~ member(sK99(sK183,sK184,X0),sK185)
| surjective(sK183,sK184,X0)
| ~ member(sK99(sK183,sK184,X0),sK185) ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( surjective(sK183,sK184,sK185)
| surjective(sK183,sK184,sK185) ),
inference(resolution,[status(thm)],[d4,c77]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[c145,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET734+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 08:11:09 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 68.42/17.61 % SZS status Theorem for theBenchmark.p
% 68.42/17.61 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------