%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : HAL003+3 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 : Thu Sep 24 08:42:26 AM UTC 2026
% Result : Theorem 25.24s 25.54s
% Output : Proof 25.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 55 ( 27 unt; 0 def)
% Number of atoms : 123 ( 15 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 113 ( 45 ~; 45 |; 19 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 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 : 61 ( 0 sgn 35 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(properties_for_surjection,axiom,
! [Morphism,Dom,Cod] :
( ( ! [ElCod] :
( element(ElCod,Cod)
=> ? [ElDom] :
( apply(Morphism,ElDom) = ElCod
& element(ElDom,Dom) ) )
& morphism(Morphism,Dom,Cod) )
=> surjection(Morphism) ),
file('HAL001+0.ax',properties_for_surjection) ).
fof(subtract_in_domain,axiom,
! [Dom,El1,El2] :
( ( element(El2,Dom)
& element(El1,Dom) )
=> element(subtract(Dom,El1,El2),Dom) ),
file('HAL001+0.ax',subtract_in_domain) ).
fof(g_morphism,axiom,
morphism(g,b,e),
file('theBenchmark.p',g_morphism) ).
fof(lemma12,axiom,
! [E] :
( element(E,e)
=> ? [B1,B2] :
( apply(g,subtract(b,B1,B2)) = E
& element(B2,b)
& element(B1,b) ) ),
file('theBenchmark.p',lemma12) ).
fof(g_surjection,conjecture,
surjection(g),
file('theBenchmark.p',g_surjection) ).
fof(f_5_1,plain,
! [Morphism,Dom,Cod] :
( surjection(Morphism)
| ? [ElCod] :
( ! [ElDom] :
( apply(Morphism,ElDom) != ElCod
| ~ element(ElDom,Dom) )
& element(ElCod,Cod) )
| ~ morphism(Morphism,Dom,Cod) ),
inference(fof_nnf,[status(thm)],[properties_for_surjection]) ).
fof(f_5_2,plain,
! [U_23,U_22,U_21] :
( surjection(U_23)
| ? [U_20] :
( ! [U_19] :
( apply(U_23,U_19) != U_20
| ~ element(U_19,U_22) )
& element(U_20,U_21) )
| ~ morphism(U_23,U_22,U_21) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_23] :
( ! [U_22,U_21] :
( ? [U_20] :
( ! [U_19] :
( apply(U_23,U_19) != U_20
| ~ element(U_19,U_22) )
& element(U_20,U_21) )
| ~ morphism(U_23,U_22,U_21) )
| surjection(U_23) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
! [U_23] :
( ! [U_22,U_21] :
( ( ! [U_19] :
( apply(U_23,U_19) != sK4(U_23,U_22,U_21)
| ~ element(U_19,U_22) )
& element(sK4(U_23,U_22,U_21),U_21) )
| ~ morphism(U_23,U_22,U_21) )
| surjection(U_23) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_20,sK4(U_23,U_22,U_21))],[f_5_3]) ).
cnf(f_5_5,plain,
( element(sK4(U_23,U_22,U_21),U_21)
| ~ morphism(U_23,U_22,U_21)
| surjection(U_23) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_6,plain,
( apply(U_23,U_19) != sK4(U_23,U_22,U_21)
| ~ element(U_19,U_22)
| ~ morphism(U_23,U_22,U_21)
| surjection(U_23) ),
inference(clausify,[status(thm)],[f_5_4]) ).
fof(f_10_1,plain,
! [Dom,El1,El2] :
( element(subtract(Dom,El1,El2),Dom)
| ~ element(El2,Dom)
| ~ element(El1,Dom) ),
inference(fof_nnf,[status(thm)],[subtract_in_domain]) ).
fof(f_10_2,plain,
! [U_64,U_63,U_62] :
( element(subtract(U_64,U_63,U_62),U_64)
| ~ element(U_62,U_64)
| ~ element(U_63,U_64) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( element(subtract(U_64,U_63,U_62),U_64)
| ~ element(U_62,U_64)
| ~ element(U_63,U_64) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_19_1,plain,
morphism(g,b,e),
inference(fof_nnf,[status(thm)],[g_morphism]) ).
cnf(f_19_2,plain,
morphism(g,b,e),
inference(clausify,[status(thm)],[f_19_1]) ).
fof(f_33_1,plain,
! [E] :
( ? [B1,B2] :
( apply(g,subtract(b,B1,B2)) = E
& element(B2,b)
& element(B1,b) )
| ~ element(E,e) ),
inference(fof_nnf,[status(thm)],[lemma12]) ).
fof(f_33_2,plain,
! [U_84] :
( ? [U_83,U_82] :
( apply(g,subtract(b,U_83,U_82)) = U_84
& element(U_82,b)
& element(U_83,b) )
| ~ element(U_84,e) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_84] :
( ? [U_83] :
( ? [U_82] :
( apply(g,subtract(b,U_83,U_82)) = U_84
& element(U_82,b) )
& element(U_83,b) )
| ~ element(U_84,e) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
fof(f_33_4,plain,
! [U_84] :
( ( ? [U_82] :
( apply(g,subtract(b,sK15(U_84),U_82)) = U_84
& element(U_82,b) )
& element(sK15(U_84),b) )
| ~ element(U_84,e) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_83,sK15(U_84))],[f_33_3]) ).
fof(f_33_5,plain,
! [U_84] :
( ( apply(g,subtract(b,sK15(U_84),sK16(U_84))) = U_84
& element(sK16(U_84),b)
& element(sK15(U_84),b) )
| ~ element(U_84,e) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_82,sK16(U_84))],[f_33_4]) ).
cnf(f_33_6,plain,
( element(sK15(U_84),b)
| ~ element(U_84,e) ),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_7,plain,
( element(sK16(U_84),b)
| ~ element(U_84,e) ),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_8,plain,
( apply(g,subtract(b,sK15(U_84),sK16(U_84))) = U_84
| ~ element(U_84,e) ),
inference(clausify,[status(thm)],[f_33_5]) ).
fof(f_34_1,negated_conjecture,
~ surjection(g),
inference(negate,[status(cth)],[g_surjection]) ).
fof(f_34_2,negated_conjecture,
~ surjection(g),
inference(definitional_conversion,[status(esa)],[f_34_1]) ).
cnf(f_34_3,negated_conjecture,
~ surjection(g),
inference(clausify,[status(thm)],[f_34_2]) ).
cnf(t1,plain,
~ surjection(g),
inference(start,[status(thm),parent(0:0)],[f_34_3]) ).
cnf(t2,plain,
( ~ morphism(g,b,e)
| ~ element(subtract(b,sK15(sK4(g,b,e)),sK16(sK4(g,b,e))),b)
| apply(g,subtract(b,sK15(sK4(g,b,e)),sK16(sK4(g,b,e)))) != sK4(g,b,e)
| surjection(g) ),
inference(extension,[status(thm),parent(t1:1)],[f_5_6]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ element(sK4(g,b,e),e)
| apply(g,subtract(b,sK15(sK4(g,b,e)),sK16(sK4(g,b,e)))) = sK4(g,b,e) ),
inference(extension,[status(thm),parent(t2:2)],[f_33_8]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ morphism(g,b,e)
| surjection(g)
| element(sK4(g,b,e),e) ),
inference(extension,[status(thm),parent(t4:2)],[f_5_5]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
$false,
inference(reduction,[status(thm),parent(t6:2)],[t6:2,t1:1]) ).
cnf(t9,plain,
morphism(g,b,e),
inference(extension,[status(thm),parent(t6:3)],[f_19_2]) ).
cnf(t10,plain,
$false,
inference(connection,[status(thm),parent(t9:1)],[t9:1,t6:3]) ).
cnf(t11,plain,
( ~ element(sK16(sK4(g,b,e)),b)
| ~ element(sK15(sK4(g,b,e)),b)
| element(subtract(b,sK15(sK4(g,b,e)),sK16(sK4(g,b,e))),b) ),
inference(extension,[status(thm),parent(t2:3)],[f_10_3]) ).
cnf(t12,plain,
$false,
inference(connection,[status(thm),parent(t11:1)],[t11:1,t2:3]) ).
cnf(t13,plain,
( ~ element(sK4(g,b,e),e)
| element(sK15(sK4(g,b,e)),b) ),
inference(extension,[status(thm),parent(t11:2)],[f_33_6]) ).
cnf(t14,plain,
$false,
inference(connection,[status(thm),parent(t13:1)],[t13:1,t11:2]) ).
cnf(t15,plain,
( ~ morphism(g,b,e)
| surjection(g)
| element(sK4(g,b,e),e) ),
inference(extension,[status(thm),parent(t13:2)],[f_5_5]) ).
cnf(t16,plain,
$false,
inference(connection,[status(thm),parent(t15:1)],[t15:1,t13:2]) ).
cnf(t17,plain,
$false,
inference(reduction,[status(thm),parent(t15:2)],[t15:2,t1:1]) ).
cnf(t18,plain,
morphism(g,b,e),
inference(extension,[status(thm),parent(t15:3)],[f_19_2]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t15:3]) ).
cnf(t20,plain,
( ~ element(sK4(g,b,e),e)
| element(sK16(sK4(g,b,e)),b) ),
inference(extension,[status(thm),parent(t11:3)],[f_33_7]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t11:3]) ).
cnf(t22,plain,
( ~ morphism(g,b,e)
| surjection(g)
| element(sK4(g,b,e),e) ),
inference(extension,[status(thm),parent(t20:2)],[f_5_5]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
$false,
inference(reduction,[status(thm),parent(t22:2)],[t22:2,t1:1]) ).
cnf(t25,plain,
morphism(g,b,e),
inference(extension,[status(thm),parent(t22:3)],[f_19_2]) ).
cnf(t26,plain,
$false,
inference(connection,[status(thm),parent(t25:1)],[t25:1,t22:3]) ).
cnf(t27,plain,
morphism(g,b,e),
inference(extension,[status(thm),parent(t2:4)],[f_19_2]) ).
cnf(t28,plain,
$false,
inference(connection,[status(thm),parent(t27:1)],[t27:1,t2:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HAL003+3 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n010.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 19 10:36:38 UTC 2026
% 0.09/0.37 % CPUTime :
% 25.24/25.54 % SZS status Theorem for theBenchmark
% 25.24/25.54 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------