%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU098+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n014.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 1.33s 1.73s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 54 ( 15 unt; 0 def)
% Number of atoms : 139 ( 11 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 138 ( 53 ~; 52 |; 20 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-4 aty)
% Number of variables : 83 ( 4 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t13_finset_1,axiom,
! [X1,X2] :
( ( subset(X1,X2)
& finite(X2) )
=> finite(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_finset_1) ).
fof(t21_relat_1,axiom,
! [X1] :
( relation(X1)
=> subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).
fof(t29_finset_1,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( finite(relation_dom(X1))
<=> finite(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_finset_1) ).
fof(dt_k9_funct_3,axiom,
! [X1,X2] :
( function(first_projection_as_func_of(X1,X2))
& quasi_total(first_projection_as_func_of(X1,X2),cartesian_product2(X1,X2),X1)
& relation_of2_as_subset(first_projection_as_func_of(X1,X2),cartesian_product2(X1,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_funct_3) ).
fof(redefinition_k9_funct_3,axiom,
! [X1,X2] : first_projection_as_func_of(X1,X2) = first_projection(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k9_funct_3) ).
fof(fc14_finset_1,axiom,
! [X1,X2] :
( ( finite(X1)
& finite(X2) )
=> finite(cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_finset_1) ).
fof(t26_finset_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( finite(relation_dom(X1))
=> finite(relation_rng(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finset_1) ).
fof(t100_funct_3,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> function_image(cartesian_product2(relation_dom(X1),relation_rng(X1)),relation_dom(X1),first_projection_as_func_of(relation_dom(X1),relation_rng(X1)),X1) = relation_dom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_funct_3) ).
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(redefinition_k2_funct_2,axiom,
! [X1,X2,X3,X4] :
( ( function(X3)
& quasi_total(X3,X1,X2)
& relation_of2(X3,X1,X2) )
=> function_image(X1,X2,X3,X4) = relation_image(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).
fof(dt_k7_funct_3,axiom,
! [X1,X2] :
( relation(first_projection(X1,X2))
& function(first_projection(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_funct_3) ).
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(c_0_12,plain,
! [X216,X217] :
( ~ subset(X216,X217)
| ~ finite(X217)
| finite(X216) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t13_finset_1])]) ).
fof(c_0_13,plain,
! [X224] :
( ~ relation(X224)
| subset(X224,cartesian_product2(relation_dom(X224),relation_rng(X224))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_relat_1])]) ).
fof(c_0_14,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( finite(relation_dom(X1))
<=> finite(X1) ) ),
inference(assume_negation,[status(cth)],[t29_finset_1]) ).
fof(c_0_15,plain,
! [X148,X149] :
( function(first_projection_as_func_of(X148,X149))
& quasi_total(first_projection_as_func_of(X148,X149),cartesian_product2(X148,X149),X148)
& relation_of2_as_subset(first_projection_as_func_of(X148,X149),cartesian_product2(X148,X149),X148) ),
inference(variable_rename,[status(thm)],[dt_k9_funct_3]) ).
fof(c_0_16,plain,
! [X209,X210] : first_projection_as_func_of(X209,X210) = first_projection(X209,X210),
inference(variable_rename,[status(thm)],[redefinition_k9_funct_3]) ).
cnf(c_0_17,plain,
( finite(X1)
| ~ subset(X1,X2)
| ~ finite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1)))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_19,plain,
! [X163,X164] :
( ~ finite(X163)
| ~ finite(X164)
| finite(cartesian_product2(X163,X164)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc14_finset_1])]) ).
fof(c_0_20,plain,
! [X225] :
( ~ relation(X225)
| ~ function(X225)
| ~ finite(relation_dom(X225))
| finite(relation_rng(X225)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t26_finset_1])]) ).
fof(c_0_21,negated_conjecture,
( relation(esk30_0)
& function(esk30_0)
& ( ~ finite(relation_dom(esk30_0))
| ~ finite(esk30_0) )
& ( finite(relation_dom(esk30_0))
| finite(esk30_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
fof(c_0_22,plain,
! [X215] :
( ~ relation(X215)
| ~ function(X215)
| function_image(cartesian_product2(relation_dom(X215),relation_rng(X215)),relation_dom(X215),first_projection_as_func_of(relation_dom(X215),relation_rng(X215)),X215) = relation_dom(X215) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t100_funct_3])]) ).
fof(c_0_23,plain,
! [X211,X212,X213] :
( ( ~ relation_of2_as_subset(X213,X211,X212)
| relation_of2(X213,X211,X212) )
& ( ~ relation_of2(X213,X211,X212)
| relation_of2_as_subset(X213,X211,X212) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
cnf(c_0_24,plain,
relation_of2_as_subset(first_projection_as_func_of(X1,X2),cartesian_product2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_25,plain,
first_projection_as_func_of(X1,X2) = first_projection(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,plain,
( finite(X1)
| ~ relation(X1)
| ~ finite(cartesian_product2(relation_dom(X1),relation_rng(X1))) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_27,plain,
( finite(cartesian_product2(X1,X2))
| ~ finite(X1)
| ~ finite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,plain,
( finite(relation_rng(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ finite(relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,negated_conjecture,
( finite(relation_dom(esk30_0))
| finite(esk30_0) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,negated_conjecture,
relation(esk30_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_31,negated_conjecture,
function(esk30_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_32,plain,
! [X205,X206,X207,X208] :
( ~ function(X207)
| ~ quasi_total(X207,X205,X206)
| ~ relation_of2(X207,X205,X206)
| function_image(X205,X206,X207,X208) = relation_image(X207,X208) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k2_funct_2])]) ).
cnf(c_0_33,plain,
( function_image(cartesian_product2(relation_dom(X1),relation_rng(X1)),relation_dom(X1),first_projection_as_func_of(relation_dom(X1),relation_rng(X1)),X1) = relation_dom(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_34,plain,
quasi_total(first_projection_as_func_of(X1,X2),cartesian_product2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_35,plain,
! [X146,X147] :
( relation(first_projection(X146,X147))
& function(first_projection(X146,X147)) ),
inference(variable_rename,[status(thm)],[dt_k7_funct_3]) ).
cnf(c_0_36,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_37,plain,
relation_of2_as_subset(first_projection(X1,X2),cartesian_product2(X1,X2),X1),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_38,plain,
( finite(X1)
| ~ relation(X1)
| ~ finite(relation_rng(X1))
| ~ finite(relation_dom(X1)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_39,negated_conjecture,
( finite(relation_rng(esk30_0))
| finite(esk30_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31])]) ).
fof(c_0_40,plain,
! [X161,X162] :
( ~ relation(X161)
| ~ function(X161)
| ~ finite(X162)
| finite(relation_image(X161,X162)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc13_finset_1])]) ).
cnf(c_0_41,plain,
( function_image(X2,X3,X1,X4) = relation_image(X1,X4)
| ~ function(X1)
| ~ quasi_total(X1,X2,X3)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_42,plain,
( function_image(cartesian_product2(relation_dom(X1),relation_rng(X1)),relation_dom(X1),first_projection(relation_dom(X1),relation_rng(X1)),X1) = relation_dom(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[c_0_33,c_0_25]) ).
cnf(c_0_43,plain,
quasi_total(first_projection(X1,X2),cartesian_product2(X1,X2),X1),
inference(rw,[status(thm)],[c_0_34,c_0_25]) ).
cnf(c_0_44,plain,
function(first_projection(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_45,plain,
relation_of2(first_projection(X1,X2),cartesian_product2(X1,X2),X1),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_46,negated_conjecture,
( ~ finite(relation_dom(esk30_0))
| ~ finite(esk30_0) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_47,negated_conjecture,
finite(esk30_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_29]),c_0_30])]),c_0_39]) ).
cnf(c_0_48,plain,
( finite(relation_image(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ finite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_49,plain,
( relation_image(first_projection(relation_dom(X1),relation_rng(X1)),X1) = relation_dom(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]),c_0_44])]),c_0_45])]) ).
cnf(c_0_50,plain,
relation(first_projection(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_51,negated_conjecture,
~ finite(relation_dom(esk30_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).
cnf(c_0_52,plain,
( finite(relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ finite(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_44])]) ).
cnf(c_0_53,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_30]),c_0_31]),c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU098+1 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.14/0.33 % Computer : n014.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 02:42:51 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.33/1.73 % Version : CSE_E---1.7
% 1.33/1.73 % Problem : theBenchmark.p
% 1.33/1.73 % SZS status Theorem for theBenchmark.p
% 1.33/1.73 % SZS output start CNFRefutation
% See solution above
% 1.33/1.73 % Total time : 1.368s
%------------------------------------------------------------------------------