%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU096+1 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n011.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 05:10:37 PM UTC 2026
% Result : Theorem 1.32s 1.73s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 6 unt; 0 def)
% Number of atoms : 50 ( 3 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 53 ( 19 ~; 16 |; 11 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 18 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fc13_finset_1,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1)
& finite(X2) )
=> finite(relation_image(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc13_finset_1) ).
fof(t147_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( subset(X1,relation_rng(X2))
=> relation_image(X2,relation_inverse_image(X2,X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_funct_1) ).
fof(t27_finset_1,conjecture,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( subset(X1,relation_rng(X2))
& finite(relation_inverse_image(X2,X1)) )
=> finite(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_finset_1) ).
fof(c_0_3,plain,
! [X98,X99] :
( ~ relation(X98)
| ~ function(X98)
| ~ finite(X99)
| finite(relation_image(X98,X99)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc13_finset_1])]) ).
fof(c_0_4,plain,
! [X134,X135] :
( ~ relation(X135)
| ~ function(X135)
| ~ subset(X134,relation_rng(X135))
| relation_image(X135,relation_inverse_image(X135,X134)) = X134 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t147_funct_1])]) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( subset(X1,relation_rng(X2))
& finite(relation_inverse_image(X2,X1)) )
=> finite(X1) ) ),
inference(assume_negation,[status(cth)],[t27_finset_1]) ).
cnf(c_0_6,plain,
( finite(relation_image(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ finite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_7,plain,
( relation_image(X1,relation_inverse_image(X1,X2)) = X2
| ~ relation(X1)
| ~ function(X1)
| ~ subset(X2,relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_8,negated_conjecture,
( relation(esk28_0)
& function(esk28_0)
& subset(esk27_0,relation_rng(esk28_0))
& finite(relation_inverse_image(esk28_0,esk27_0))
& ~ finite(esk27_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_9,plain,
( finite(X1)
| ~ subset(X1,relation_rng(X2))
| ~ relation(X2)
| ~ function(X2)
| ~ finite(relation_inverse_image(X2,X1)) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,negated_conjecture,
subset(esk27_0,relation_rng(esk28_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,negated_conjecture,
relation(esk28_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
function(esk28_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
finite(relation_inverse_image(esk28_0,esk27_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
~ finite(esk27_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12]),c_0_13])]),c_0_14]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU096+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n011.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:42:32 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.32/1.73 % Version : CSE_E---1.7
% 1.32/1.73 % Problem : theBenchmark.p
% 1.32/1.73 % SZS status Theorem for theBenchmark.p
% 1.32/1.73 % SZS output start CNFRefutation
% See solution above
% 1.32/1.73 % Total time : 1.369s
%------------------------------------------------------------------------------