%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SEU098+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n031.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 : Fri Jul 25 03:44:28 PM UTC 2025
% Result : Theorem 81.02s 10.49s
% Output : CNFRefutation 81.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 13
% Syntax : Number of formulae : 58 ( 24 unt; 0 def)
% Number of atoms : 125 ( 9 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 108 ( 41 ~; 41 |; 12 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 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 : 55 ( 7 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t29_finset_1,plain,
! [A] :
( ( relation(A)
& function(A) )
=> ( finite(relation_dom(A))
<=> finite(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_finset_1) ).
fof(t29_finset_1_negated,plain,
~ ! [A] :
( ( relation(A)
& function(A) )
=> ( finite(relation_dom(A))
<=> finite(A) ) ),
inference(negate_conjecture,[status(cth)],[t29_finset_1]) ).
cnf(164,plain,
( ~ finite(relation_dom(sK30))
| ~ finite(sK30) ),
inference(cnf,[status(esa)],[t29_finset_1_negated]) ).
cnf(l0,plain,
( ~ finite(relation_dom(sK30))
| ~ finite(sK30) ),
inference(instantiation,[status(thm)],[164]) ).
fof(t13_finset_1,plain,
! [A,B] :
( ( subset(A,B)
& finite(B) )
=> finite(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finset_1) ).
cnf(155,plain,
( ~ finite(X0)
| ~ subset(X1,X0)
| finite(X1) ),
inference(cnf,[status(esa)],[t13_finset_1]) ).
cnf(l1,plain,
( ~ finite(relation_image(first_projection_as_func_of(relation_dom(sK30),relation_rng(sK30)),sK30))
| ~ subset(relation_dom(sK30),relation_image(first_projection_as_func_of(relation_dom(sK30),relation_rng(sK30)),sK30))
| finite(relation_dom(sK30)) ),
inference(instantiation,[status(thm)],[155]) ).
cnf(163,plain,
( finite(relation_dom(sK30))
| finite(sK30) ),
inference(cnf,[status(esa)],[t29_finset_1_negated]) ).
cnf(l445,plain,
( finite(relation_dom(sK30))
| finite(sK30) ),
inference(instantiation,[status(thm)],[163]) ).
fof(t17_finset_1,plain,
! [A,B] :
( ( relation(B)
& function(B) )
=> ( finite(A)
=> finite(relation_image(B,A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_finset_1) ).
cnf(156,plain,
( ~ function(X0)
| ~ finite(X1)
| ~ relation(X0)
| finite(relation_image(X0,X1)) ),
inference(cnf,[status(esa)],[t17_finset_1]) ).
cnf(l26,plain,
( ~ function(first_projection(relation_dom(sK30),relation_rng(sK30)))
| ~ finite(sK30)
| ~ relation(first_projection(relation_dom(sK30),relation_rng(sK30)))
| finite(relation_image(first_projection(relation_dom(sK30),relation_rng(sK30)),sK30)) ),
inference(instantiation,[status(thm)],[156]) ).
fof(reflexivity_r1_tarski,plain,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
cnf(153,plain,
subset(X0,X0),
inference(cnf,[status(esa)],[reflexivity_r1_tarski]) ).
cnf(l222,plain,
subset(function_image(cartesian_product2(relation_dom(sK30),relation_rng(sK30)),relation_dom(sK30),first_projection_as_func_of(relation_dom(sK30),relation_rng(sK30)),sK30),function_image(cartesian_product2(relation_dom(sK30),relation_rng(sK30)),relation_dom(sK30),first_projection_as_func_of(relation_dom(sK30),relation_rng(sK30)),sK30)),
inference(instantiation,[status(thm)],[153]) ).
fof(t100_funct_3,plain,
! [A] :
( ( relation(A)
& function(A) )
=> function_image(cartesian_product2(relation_dom(A),relation_rng(A)),relation_dom(A),first_projection_as_func_of(relation_dom(A),relation_rng(A)),A) = relation_dom(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_funct_3) ).
cnf(154,plain,
( ~ function(X0)
| ~ relation(X0)
| function_image(cartesian_product2(relation_dom(X0),relation_rng(X0)),relation_dom(X0),first_projection_as_func_of(relation_dom(X0),relation_rng(X0)),X0) = relation_dom(X0) ),
inference(cnf,[status(esa)],[t100_funct_3]) ).
cnf(l167,plain,
( ~ function(sK30)
| ~ relation(sK30)
| function_image(cartesian_product2(relation_dom(sK30),relation_rng(sK30)),relation_dom(sK30),first_projection_as_func_of(relation_dom(sK30),relation_rng(sK30)),sK30) = relation_dom(sK30) ),
inference(instantiation,[status(thm)],[154]) ).
fof(redefinition_k9_funct_3,plain,
! [A,B] : first_projection_as_func_of(A,B) = first_projection(A,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_funct_3) ).
cnf(150,plain,
first_projection_as_func_of(X0,X1) = first_projection(X0,X1),
inference(cnf,[status(esa)],[redefinition_k9_funct_3]) ).
cnf(l23,plain,
first_projection_as_func_of(relation_dom(sK30),relation_rng(sK30)) = first_projection(relation_dom(sK30),relation_rng(sK30)),
inference(instantiation,[status(thm)],[150]) ).
fof(dt_k7_funct_3,plain,
! [A,B] :
( relation(first_projection(A,B))
& function(first_projection(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_funct_3) ).
cnf(24,plain,
function(first_projection(X0,X1)),
inference(cnf,[status(esa)],[dt_k7_funct_3]) ).
cnf(l106,plain,
function(first_projection(relation_dom(sK30),relation_rng(sK30))),
inference(instantiation,[status(thm)],[24]) ).
fof(redefinition_k2_funct_2,plain,
! [A,B,C,D] :
( ( function(C)
& quasi_total(C,A,B)
& relation_of2(C,A,B) )
=> function_image(A,B,C,D) = relation_image(C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).
cnf(149,plain,
( ~ function(X0)
| ~ quasi_total(X0,X1,X2)
| ~ relation_of2(X0,X1,X2)
| function_image(X1,X2,X0,X3) = relation_image(X0,X3) ),
inference(cnf,[status(esa)],[redefinition_k2_funct_2]) ).
cnf(l168,plain,
( ~ function(first_projection_as_func_of(relation_dom(sK30),relation_rng(sK30)))
| ~ quasi_total(first_projection_as_func_of(relation_dom(sK30),relation_rng(sK30)),cartesian_product2(relation_dom(sK30),relation_rng(sK30)),relation_dom(sK30))
| ~ relation_of2(first_projection_as_func_of(relation_dom(sK30),relation_rng(sK30)),cartesian_product2(relation_dom(sK30),relation_rng(sK30)),relation_dom(sK30))
| function_image(cartesian_product2(relation_dom(sK30),relation_rng(sK30)),relation_dom(sK30),first_projection_as_func_of(relation_dom(sK30),relation_rng(sK30)),sK30) = relation_image(first_projection_as_func_of(relation_dom(sK30),relation_rng(sK30)),sK30) ),
inference(instantiation,[status(thm)],[149]) ).
cnf(l29,plain,
( finite(relation_dom(sK30))
| finite(sK30) ),
inference(instantiation,[status(thm)],[163]) ).
cnf(161,plain,
relation(sK30),
inference(cnf,[status(esa)],[t29_finset_1_negated]) ).
cnf(l170,plain,
relation(sK30),
inference(instantiation,[status(thm)],[161]) ).
fof(redefinition_m2_relset_1,plain,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
cnf(151,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| relation_of2(X0,X1,X2) ),
inference(cnf,[status(esa)],[redefinition_m2_relset_1]) ).
cnf(l210,plain,
( ~ relation_of2_as_subset(first_projection_as_func_of(relation_dom(sK30),relation_rng(sK30)),cartesian_product2(relation_dom(sK30),relation_rng(sK30)),relation_dom(sK30))
| relation_of2(first_projection_as_func_of(relation_dom(sK30),relation_rng(sK30)),cartesian_product2(relation_dom(sK30),relation_rng(sK30)),relation_dom(sK30)) ),
inference(instantiation,[status(thm)],[151]) ).
fof(dt_k9_funct_3,plain,
! [A,B] :
( function(first_projection_as_func_of(A,B))
& quasi_total(first_projection_as_func_of(A,B),cartesian_product2(A,B),A)
& relation_of2_as_subset(first_projection_as_func_of(A,B),cartesian_product2(A,B),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_funct_3) ).
cnf(26,plain,
quasi_total(first_projection_as_func_of(X0,X1),cartesian_product2(X0,X1),X0),
inference(cnf,[status(esa)],[dt_k9_funct_3]) ).
cnf(l169,plain,
quasi_total(first_projection_as_func_of(relation_dom(sK30),relation_rng(sK30)),cartesian_product2(relation_dom(sK30),relation_rng(sK30)),relation_dom(sK30)),
inference(instantiation,[status(thm)],[26]) ).
cnf(25,plain,
function(first_projection_as_func_of(X0,X1)),
inference(cnf,[status(esa)],[dt_k9_funct_3]) ).
cnf(l175,plain,
function(first_projection_as_func_of(relation_dom(sK30),relation_rng(sK30))),
inference(instantiation,[status(thm)],[25]) ).
fof(t19_finset_1,plain,
! [A,B] :
( ( finite(A)
& finite(B) )
=> finite(cartesian_product2(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_finset_1) ).
cnf(157,plain,
( ~ finite(X0)
| ~ finite(X1)
| finite(cartesian_product2(X0,X1)) ),
inference(cnf,[status(esa)],[t19_finset_1]) ).
cnf(l446,plain,
( ~ finite(relation_dom(sK30))
| ~ finite(relation_rng(sK30))
| finite(cartesian_product2(relation_dom(sK30),relation_rng(sK30))) ),
inference(instantiation,[status(thm)],[157]) ).
cnf(162,plain,
function(sK30),
inference(cnf,[status(esa)],[t29_finset_1_negated]) ).
cnf(l171,plain,
function(sK30),
inference(instantiation,[status(thm)],[162]) ).
cnf(27,plain,
relation_of2_as_subset(first_projection_as_func_of(X0,X1),cartesian_product2(X0,X1),X0),
inference(cnf,[status(esa)],[dt_k9_funct_3]) ).
cnf(l211,plain,
relation_of2_as_subset(first_projection_as_func_of(relation_dom(sK30),relation_rng(sK30)),cartesian_product2(relation_dom(sK30),relation_rng(sK30)),relation_dom(sK30)),
inference(instantiation,[status(thm)],[27]) ).
cnf(23,plain,
relation(first_projection(X0,X1)),
inference(cnf,[status(esa)],[dt_k7_funct_3]) ).
cnf(l27,plain,
relation(first_projection(relation_dom(sK30),relation_rng(sK30))),
inference(instantiation,[status(thm)],[23]) ).
cnf(l648,plain,
( ~ finite(cartesian_product2(relation_dom(sK30),relation_rng(sK30)))
| ~ subset(sK30,cartesian_product2(relation_dom(sK30),relation_rng(sK30)))
| finite(sK30) ),
inference(instantiation,[status(thm)],[155]) ).
fof(t26_finset_1,plain,
! [A] :
( ( relation(A)
& function(A) )
=> ( finite(relation_dom(A))
=> finite(relation_rng(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finset_1) ).
cnf(160,plain,
( ~ function(X0)
| ~ finite(relation_dom(X0))
| ~ relation(X0)
| finite(relation_rng(X0)) ),
inference(cnf,[status(esa)],[t26_finset_1]) ).
cnf(l450,plain,
( ~ function(sK30)
| ~ finite(relation_dom(sK30))
| ~ relation(sK30)
| finite(relation_rng(sK30)) ),
inference(instantiation,[status(thm)],[160]) ).
cnf(l451,plain,
function(sK30),
inference(instantiation,[status(thm)],[162]) ).
fof(t21_relat_1,plain,
! [A] :
( relation(A)
=> subset(A,cartesian_product2(relation_dom(A),relation_rng(A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relat_1) ).
cnf(159,plain,
( ~ relation(X0)
| subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
inference(cnf,[status(esa)],[t21_relat_1]) ).
cnf(l654,plain,
( ~ relation(sK30)
| subset(sK30,cartesian_product2(relation_dom(sK30),relation_rng(sK30))) ),
inference(instantiation,[status(thm)],[159]) ).
cnf(l656,plain,
relation(sK30),
inference(instantiation,[status(thm)],[161]) ).
cnf(l554,plain,
relation(sK30),
inference(instantiation,[status(thm)],[161]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l445,l26,l222,l167,l23,l106,l168,l29,l170,l210,l169,l175,l446,l171,l211,l27,l648,l450,l451,l654,l656,l554]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU098+1 : TPTP v9.0.0. Released v3.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n031.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 21 23:27:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 2
% 0.12/0.34 % launching worker at depth: 5
% 0.12/0.34 % launching worker at depth: 3
% 0.12/0.34 % launching worker at depth: 6
% 0.12/0.34 % launching worker at depth: 4
% 0.12/0.34 % launching worker at depth: 8
% 0.12/0.34 % launching worker at depth: 7
% 0.19/0.34 % launching worker at depth: 9
% 0.19/0.35 % launching worker at depth: 10
% 0.19/0.40 % launching worker at depth: 11
% 4.92/0.98 % launching worker at depth: 12
% 81.02/10.49 % SZS status Theorem for theBenchmark
% 81.02/10.49 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------