%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : HAL003+3 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Jul 24 06:30:29 PM UTC 2025
% Result : Theorem 6.95s 1.19s
% Output : CNFRefutation 6.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 9 unt; 0 def)
% Number of atoms : 53 ( 6 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 50 ( 21 ~; 20 |; 5 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 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 : 24 ( 0 sgn 8 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(g_surjection,plain,
surjection(g),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',g_surjection) ).
fof(g_surjection_negated,plain,
~ surjection(g),
inference(negate_conjecture,[status(cth)],[g_surjection]) ).
cnf(58,plain,
~ surjection(g),
inference(cnf,[status(esa)],[g_surjection_negated]) ).
cnf(l0,plain,
~ surjection(g),
inference(instantiation,[status(thm)],[58]) ).
fof(properties_for_surjection,plain,
! [Morphism,Dom,Cod] :
( ( morphism(Morphism,Dom,Cod)
& ! [ElCod] :
( element(ElCod,Cod)
=> ? [ElDom] :
( element(ElDom,Dom)
& apply(Morphism,ElDom) = ElCod ) ) )
=> surjection(Morphism) ),
file('Axioms/HAL001+0.ax',properties_for_surjection) ).
cnf(9,plain,
( ~ morphism(X0,X1,X2)
| element(sK4(X0,X1,X2),X2)
| surjection(X0) ),
inference(cnf,[status(esa)],[properties_for_surjection]) ).
cnf(l1,plain,
( ~ morphism(g,b,e)
| element(sK4(g,b,e),e)
| surjection(g) ),
inference(instantiation,[status(thm)],[9]) ).
fof(g_morphism,plain,
morphism(g,b,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',g_morphism) ).
cnf(32,plain,
morphism(g,b,e),
inference(cnf,[status(esa)],[g_morphism]) ).
cnf(l2,plain,
morphism(g,b,e),
inference(instantiation,[status(thm)],[32]) ).
fof(lemma12,plain,
! [E] :
( element(E,e)
=> ? [B1,B2] :
( element(B1,b)
& element(B2,b)
& apply(g,subtract(b,B1,B2)) = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma12) ).
cnf(57,plain,
( ~ element(X0,e)
| apply(g,subtract(b,sK16(X0),sK17(X0))) = X0 ),
inference(cnf,[status(esa)],[lemma12]) ).
cnf(l3,plain,
( ~ element(sK4(g,b,e),e)
| apply(g,subtract(b,sK16(sK4(g,b,e)),sK17(sK4(g,b,e)))) = sK4(g,b,e) ),
inference(instantiation,[status(thm)],[57]) ).
cnf(10,plain,
( ~ morphism(X0,X1,X2)
| ~ element(X3,X1)
| apply(X0,X3) != sK4(X0,X1,X2)
| surjection(X0) ),
inference(cnf,[status(esa)],[properties_for_surjection]) ).
cnf(l17,plain,
( ~ morphism(g,b,e)
| ~ element(subtract(b,sK16(sK4(g,b,e)),sK17(sK4(g,b,e))),b)
| apply(g,subtract(b,sK16(sK4(g,b,e)),sK17(sK4(g,b,e)))) != sK4(g,b,e)
| surjection(g) ),
inference(instantiation,[status(thm)],[10]) ).
fof(subtract_in_domain,plain,
! [Dom,El1,El2] :
( ( element(El1,Dom)
& element(El2,Dom) )
=> element(subtract(Dom,El1,El2),Dom) ),
file('Axioms/HAL001+0.ax',subtract_in_domain) ).
cnf(23,plain,
( ~ element(X0,X1)
| ~ element(X2,X1)
| element(subtract(X1,X0,X2),X1) ),
inference(cnf,[status(esa)],[subtract_in_domain]) ).
cnf(l60,plain,
( ~ element(sK16(sK4(g,b,e)),b)
| ~ element(sK17(sK4(g,b,e)),b)
| element(subtract(b,sK16(sK4(g,b,e)),sK17(sK4(g,b,e))),b) ),
inference(instantiation,[status(thm)],[23]) ).
cnf(l64,plain,
morphism(g,b,e),
inference(instantiation,[status(thm)],[32]) ).
cnf(56,plain,
( ~ element(X0,e)
| element(sK17(X0),b) ),
inference(cnf,[status(esa)],[lemma12]) ).
cnf(l99,plain,
( ~ element(sK4(g,b,e),e)
| element(sK17(sK4(g,b,e)),b) ),
inference(instantiation,[status(thm)],[56]) ).
cnf(55,plain,
( ~ element(X0,e)
| element(sK16(X0),b) ),
inference(cnf,[status(esa)],[lemma12]) ).
cnf(l78,plain,
( ~ element(sK4(g,b,e),e)
| element(sK16(sK4(g,b,e)),b) ),
inference(instantiation,[status(thm)],[55]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l3,l17,l60,l64,l99,l78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : HAL003+3 : TPTP v9.0.0. Released v2.6.0.
% 0.08/0.09 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.29 % Computer : n019.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Sun Jul 20 17:29:34 EDT 2025
% 0.09/0.29 % CPUTime :
% 0.09/0.29 % launching worker at depth: 4
% 0.09/0.29 % launching worker at depth: 1
% 0.09/0.29 % launching worker at depth: 2
% 0.09/0.29 % launching worker at depth: 5
% 0.09/0.29 % launching worker at depth: 6
% 0.09/0.29 % launching worker at depth: 3
% 0.09/0.29 % launching worker at depth: 7
% 0.09/0.29 % launching worker at depth: 8
% 0.09/0.30 % launching worker at depth: 9
% 0.14/0.32 % launching worker at depth: 10
% 0.14/0.34 % launching worker at depth: 11
% 2.00/0.62 % launching worker at depth: 12
% 6.95/1.19 % SZS status Theorem for theBenchmark
% 6.95/1.19 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------