%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU303+2 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n005.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 : Tue May 5 05:11:24 PM UTC 2026
% Result : Theorem 2.39s 2.05s
% Output : CNFRefutation 2.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 6 unt; 0 def)
% Number of atoms : 39 ( 4 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 36 ( 13 ~; 10 |; 7 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t26_finset_1,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( finite(relation_dom(X1))
=> finite(relation_rng(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finset_1) ).
fof(fc13_finset_1,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1)
& finite(X2) )
=> finite(relation_image(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_finset_1) ).
fof(t146_relat_1,lemma,
! [X1] :
( relation(X1)
=> relation_image(X1,relation_dom(X1)) = relation_rng(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_relat_1) ).
fof(c_0_3,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( finite(relation_dom(X1))
=> finite(relation_rng(X1)) ) ),
inference(assume_negation,[status(cth)],[t26_finset_1]) ).
fof(c_0_4,plain,
! [X1637,X1638] :
( ~ relation(X1637)
| ~ function(X1637)
| ~ finite(X1638)
| finite(relation_image(X1637,X1638)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc13_finset_1])]) ).
fof(c_0_5,negated_conjecture,
( relation(esk282_0)
& function(esk282_0)
& finite(relation_dom(esk282_0))
& ~ finite(relation_rng(esk282_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_6,lemma,
! [X2174] :
( ~ relation(X2174)
| relation_image(X2174,relation_dom(X2174)) = relation_rng(X2174) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t146_relat_1])]) ).
cnf(c_0_7,plain,
( finite(relation_image(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ finite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,negated_conjecture,
finite(relation_dom(esk282_0)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,lemma,
( relation_image(X1,relation_dom(X1)) = relation_rng(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
relation(esk282_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,negated_conjecture,
( finite(relation_image(X1,relation_dom(esk282_0)))
| ~ relation(X1)
| ~ function(X1) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,negated_conjecture,
function(esk282_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,negated_conjecture,
relation_image(esk282_0,relation_dom(esk282_0)) = relation_rng(esk282_0),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
~ finite(relation_rng(esk282_0)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_15,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_10])]),c_0_14]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU303+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n005.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:56:15 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 2.39/2.05 % Version : CSE_E---1.7
% 2.39/2.05 % Problem : theBenchmark.p
% 2.39/2.05 % SZS status Theorem for theBenchmark.p
% 2.39/2.05 % SZS output start CNFRefutation
% See solution above
% 2.39/2.05 % Total time : 1.533s
%------------------------------------------------------------------------------