%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU096+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 08:58:02 AM UTC 2026
% Result : Theorem 1.26s 6.51s
% Output : Proof 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 40 ( 21 unt; 0 def)
% Number of atoms : 102 ( 7 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 98 ( 36 ~; 28 |; 26 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 16 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t147_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( subset(A,relation_rng(B))
=> relation_image(B,relation_inverse_image(B,A)) = A ) ),
file('theBenchmark.p',t147_funct_1) ).
fof(t17_finset_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( finite(A)
=> finite(relation_image(B,A)) ) ),
file('theBenchmark.p',t17_finset_1) ).
fof(t27_finset_1,conjecture,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( ( finite(relation_inverse_image(B,A))
& subset(A,relation_rng(B)) )
=> finite(A) ) ),
file('theBenchmark.p',t27_finset_1) ).
fof(f_50_1,plain,
! [A,B] :
( relation_image(B,relation_inverse_image(B,A)) = A
| ~ subset(A,relation_rng(B))
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t147_funct_1]) ).
fof(f_50_2,plain,
! [U_55,U_54] :
( relation_image(U_54,relation_inverse_image(U_54,U_55)) = U_55
| ~ subset(U_55,relation_rng(U_54))
| ~ function(U_54)
| ~ relation(U_54) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
cnf(f_50_3,plain,
( relation_image(U_54,relation_inverse_image(U_54,U_55)) = U_55
| ~ subset(U_55,relation_rng(U_54))
| ~ function(U_54)
| ~ relation(U_54) ),
inference(clausify,[status(thm)],[f_50_2]) ).
fof(f_51_1,plain,
! [A,B] :
( finite(relation_image(B,A))
| ~ finite(A)
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t17_finset_1]) ).
fof(f_51_2,plain,
! [U_57,U_56] :
( finite(relation_image(U_56,U_57))
| ~ finite(U_57)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
cnf(f_51_3,plain,
( finite(relation_image(U_56,U_57))
| ~ finite(U_57)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_51_2]) ).
fof(f_53_1,negated_conjecture,
~ ! [A,B] :
( ( function(B)
& relation(B) )
=> ( ( finite(relation_inverse_image(B,A))
& subset(A,relation_rng(B)) )
=> finite(A) ) ),
inference(negate,[status(cth)],[t27_finset_1]) ).
fof(f_53_2,negated_conjecture,
? [A,B] :
( ~ finite(A)
& finite(relation_inverse_image(B,A))
& subset(A,relation_rng(B))
& function(B)
& relation(B) ),
inference(fof_nnf,[status(thm)],[f_53_1]) ).
fof(f_53_3,negated_conjecture,
? [U_61,U_60] :
( ~ finite(U_61)
& finite(relation_inverse_image(U_60,U_61))
& subset(U_61,relation_rng(U_60))
& function(U_60)
& relation(U_60) ),
inference(variable_rename,[status(thm)],[f_53_2]) ).
fof(f_53_4,negated_conjecture,
? [U_60] :
( ~ finite(sK27)
& finite(relation_inverse_image(U_60,sK27))
& subset(sK27,relation_rng(U_60))
& function(U_60)
& relation(U_60) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_61,sK27)],[f_53_3]) ).
fof(f_53_5,negated_conjecture,
( ~ finite(sK27)
& finite(relation_inverse_image(sK28,sK27))
& subset(sK27,relation_rng(sK28))
& function(sK28)
& relation(sK28) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_60,sK28)],[f_53_4]) ).
fof(f_53_6,negated_conjecture,
( ~ finite(sK27)
& finite(relation_inverse_image(sK28,sK27))
& subset(sK27,relation_rng(sK28))
& function(sK28)
& relation(sK28) ),
inference(definitional_conversion,[status(esa)],[f_53_5]) ).
cnf(f_53_7,negated_conjecture,
relation(sK28),
inference(clausify,[status(thm)],[f_53_6]) ).
cnf(f_53_8,negated_conjecture,
function(sK28),
inference(clausify,[status(thm)],[f_53_6]) ).
cnf(f_53_9,negated_conjecture,
subset(sK27,relation_rng(sK28)),
inference(clausify,[status(thm)],[f_53_6]) ).
cnf(f_53_10,negated_conjecture,
finite(relation_inverse_image(sK28,sK27)),
inference(clausify,[status(thm)],[f_53_6]) ).
cnf(f_53_11,negated_conjecture,
~ finite(sK27),
inference(clausify,[status(thm)],[f_53_6]) ).
cnf(equality_19,axiom,
( finite(Eq_y_0)
| ~ finite(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
~ finite(sK27),
inference(start,[status(thm),parent(0:0)],[f_53_11]) ).
cnf(t2,plain,
( ~ finite(relation_image(sK28,relation_inverse_image(sK28,sK27)))
| relation_image(sK28,relation_inverse_image(sK28,sK27)) != sK27
| finite(sK27) ),
inference(extension,[status(thm),parent(t1:1)],[equality_19]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ function(sK28)
| ~ subset(sK27,relation_rng(sK28))
| ~ relation(sK28)
| relation_image(sK28,relation_inverse_image(sK28,sK27)) = sK27 ),
inference(extension,[status(thm),parent(t2:2)],[f_50_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
relation(sK28),
inference(extension,[status(thm),parent(t4:2)],[f_53_7]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
subset(sK27,relation_rng(sK28)),
inference(extension,[status(thm),parent(t4:3)],[f_53_9]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
function(sK28),
inference(extension,[status(thm),parent(t4:4)],[f_53_8]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t4:4]) ).
cnf(t12,plain,
( ~ function(sK28)
| ~ finite(relation_inverse_image(sK28,sK27))
| ~ relation(sK28)
| finite(relation_image(sK28,relation_inverse_image(sK28,sK27))) ),
inference(extension,[status(thm),parent(t2:3)],[f_51_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t2:3]) ).
cnf(t14,plain,
relation(sK28),
inference(extension,[status(thm),parent(t12:2)],[f_53_7]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
finite(relation_inverse_image(sK28,sK27)),
inference(extension,[status(thm),parent(t12:3)],[f_53_10]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t12:3]) ).
cnf(t18,plain,
function(sK28),
inference(extension,[status(thm),parent(t12:4)],[f_53_8]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t12:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU096+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.37 % Computer : n018.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Sat Sep 19 23:20:47 UTC 2026
% 0.11/5.37 % CPUTime :
% 1.26/6.51 % SZS status Theorem for theBenchmark
% 1.26/6.51 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------