%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : HAL003+3 : 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 : n005.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 07:31:32 AM UTC 2026
% Result : Theorem 39.54s 7.41s
% Output : CNFRefutation 39.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 7 unt; 0 def)
% Number of atoms : 61 ( 6 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 74 ( 36 ~; 29 |; 5 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 35 ( 0 sgn 8 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(g_morphism,axiom,
morphism(g,b,e) ).
fof(lemma12,axiom,
! [X0] :
( element(X0,e)
=> ? [X1,X2] :
( apply(g,subtract(b,X1,X2)) = X0
& element(X2,b)
& element(X1,b) ) ) ).
fof(properties_for_surjection,axiom,
! [X0,X1,X2] :
( ( ! [X3] :
( element(X3,X2)
=> ? [X4] :
( apply(X0,X4) = X3
& element(X4,X1) ) )
& morphism(X0,X1,X2) )
=> surjection(X0) ) ).
fof(subtract_in_domain,axiom,
! [X0,X1,X2] :
( ( element(X2,X0)
& element(X1,X0) )
=> element(subtract(X0,X1,X2),X0) ) ).
fof(g_surjection,conjecture,
surjection(g) ).
fof(negated_conjecture,negated_conjecture,
~ surjection(g),
inference(negate_conjecture,[status(cth)],[g_surjection]) ).
cnf(c5,plain,
morphism(g,b,e),
inference(clausification,[status(esa)],[g_morphism]) ).
cnf(c30,plain,
( element(sK10(X0),b)
| ~ element(X0,e) ),
inference(clausification,[status(esa)],[lemma12]) ).
cnf(c31,plain,
( element(sK11(X0),b)
| ~ element(X0,e) ),
inference(clausification,[status(esa)],[lemma12]) ).
cnf(c32,plain,
( apply(g,subtract(b,sK10(X0),sK11(X0))) = X0
| ~ element(X0,e) ),
inference(clausification,[status(esa)],[lemma12]) ).
cnf(c42,plain,
( surjection(X0)
| element(sK34(X0,X1,X2),X2)
| ~ morphism(X0,X1,X2) ),
inference(clausification,[status(esa)],[properties_for_surjection]) ).
cnf(c43,plain,
( surjection(X0)
| apply(X0,X3) != sK34(X0,X1,X2)
| ~ element(X3,X1)
| ~ morphism(X0,X1,X2) ),
inference(clausification,[status(esa)],[properties_for_surjection]) ).
cnf(c60,plain,
( element(subtract(X1,X0,X2),X1)
| ~ element(X2,X1)
| ~ element(X0,X1) ),
inference(clausification,[status(esa)],[subtract_in_domain]) ).
cnf(c64,plain,
~ surjection(g),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ element(X0,e)
| ~ element(subtract(b,sK10(X0),sK11(X0)),X1)
| surjection(g)
| ~ morphism(g,X1,X2)
| X0 != sK34(g,X1,X2) ),
inference(superposition,[status(thm)],[c32,c43]) ).
cnf(d1,plain,
( ~ element(subtract(b,sK10(X0),sK11(X0)),X1)
| ~ element(X0,e)
| ~ morphism(g,X1,X2)
| X0 != sK34(g,X1,X2) ),
inference(resolution,[status(thm)],[c64,d0]) ).
cnf(d2,plain,
( ~ element(subtract(b,sK10(sK34(g,X0,X1)),sK11(sK34(g,X0,X1))),X0)
| ~ element(sK34(g,X0,X1),e)
| ~ morphism(g,X0,X1) ),
inference(equality_resolution,[status(thm)],[d1]) ).
cnf(d3,plain,
( ~ element(sK11(sK34(g,b,X0)),b)
| ~ element(sK10(sK34(g,b,X0)),b)
| ~ element(sK34(g,b,X0),e)
| ~ morphism(g,b,X0) ),
inference(resolution,[status(thm)],[d2,c60]) ).
cnf(d4,plain,
( ~ element(sK34(g,b,X0),e)
| ~ element(sK34(g,b,X0),e)
| ~ element(sK10(sK34(g,b,X0)),b)
| ~ morphism(g,b,X0) ),
inference(resolution,[status(thm)],[d3,c31]) ).
cnf(d5,plain,
( ~ element(sK34(g,b,X0),e)
| ~ element(sK34(g,b,X0),e)
| ~ morphism(g,b,X0) ),
inference(resolution,[status(thm)],[d4,c30]) ).
cnf(d6,plain,
( surjection(g)
| ~ morphism(g,b,e)
| ~ morphism(g,b,e) ),
inference(resolution,[status(thm)],[d5,c42]) ).
cnf(d7,plain,
~ morphism(g,b,e),
inference(resolution,[status(thm)],[c64,d6]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[c5,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HAL003+3 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n005.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 : Fri Sep 25 15:53:47 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 39.54/7.41 % SZS status Theorem for theBenchmark.p
% 39.54/7.41 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------