%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU290+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 : n001.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 05:11:22 PM UTC 2026
% Result : Theorem 4.20s 3.18s
% Output : CNFRefutation 4.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 13 unt; 0 def)
% Number of atoms : 156 ( 45 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 184 ( 67 ~; 74 |; 25 &)
% ( 7 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 77 ( 2 sgn 52 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t6_funct_2,conjecture,
! [X1,X2,X3,X4] :
( ( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2) )
=> ( in(X3,X1)
=> ( X2 = empty_set
| in(apply(X4,X3),relation_rng(X4)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_funct_2) ).
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(d1_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
<=> subset(X3,cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relset_1) ).
fof(redefinition_k4_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> relation_dom_as_subset(X1,X2,X3) = relation_dom(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(d5_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(d1_funct_2,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( ( ( X2 = empty_set
=> X1 = empty_set )
=> ( quasi_total(X3,X1,X2)
<=> X1 = relation_dom_as_subset(X1,X2,X3) ) )
& ( X2 = empty_set
=> ( X1 = empty_set
| ( quasi_total(X3,X1,X2)
<=> X3 = empty_set ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_2) ).
fof(cc1_relset_1,axiom,
! [X1,X2,X3] :
( element(X3,powerset(cartesian_product2(X1,X2)))
=> relation(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2) )
=> ( in(X3,X1)
=> ( X2 = empty_set
| in(apply(X4,X3),relation_rng(X4)) ) ) ),
inference(assume_negation,[status(cth)],[t6_funct_2]) ).
fof(c_0_9,plain,
! [X1606,X1607,X1608] :
( ( ~ relation_of2_as_subset(X1608,X1606,X1607)
| relation_of2(X1608,X1606,X1607) )
& ( ~ relation_of2(X1608,X1606,X1607)
| relation_of2_as_subset(X1608,X1606,X1607) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
fof(c_0_10,negated_conjecture,
( function(esk255_0)
& quasi_total(esk255_0,esk252_0,esk253_0)
& relation_of2_as_subset(esk255_0,esk252_0,esk253_0)
& in(esk254_0,esk252_0)
& esk253_0 != empty_set
& ~ in(apply(esk255_0,esk254_0),relation_rng(esk255_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_11,plain,
! [X1139,X1140,X1141] :
( ( ~ relation_of2(X1141,X1139,X1140)
| subset(X1141,cartesian_product2(X1139,X1140)) )
& ( ~ subset(X1141,cartesian_product2(X1139,X1140))
| relation_of2(X1141,X1139,X1140) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_relset_1])]) ).
cnf(c_0_12,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
relation_of2_as_subset(esk255_0,esk252_0,esk253_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X1593,X1594,X1595] :
( ~ relation_of2(X1595,X1593,X1594)
| relation_dom_as_subset(X1593,X1594,X1595) = relation_dom(X1595) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_relset_1])]) ).
fof(c_0_15,plain,
! [X2063,X2064] :
( ( ~ element(X2063,powerset(X2064))
| subset(X2063,X2064) )
& ( ~ subset(X2063,X2064)
| element(X2063,powerset(X2064)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
cnf(c_0_16,plain,
( subset(X1,cartesian_product2(X2,X3))
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
relation_of2(esk255_0,esk252_0,esk253_0),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_18,plain,
! [X1333,X1334,X1335,X1337,X1338,X1339,X1341] :
( ( in(esk68_3(X1333,X1334,X1335),relation_dom(X1333))
| ~ in(X1335,X1334)
| X1334 != relation_rng(X1333)
| ~ relation(X1333)
| ~ function(X1333) )
& ( X1335 = apply(X1333,esk68_3(X1333,X1334,X1335))
| ~ in(X1335,X1334)
| X1334 != relation_rng(X1333)
| ~ relation(X1333)
| ~ function(X1333) )
& ( ~ in(X1338,relation_dom(X1333))
| X1337 != apply(X1333,X1338)
| in(X1337,X1334)
| X1334 != relation_rng(X1333)
| ~ relation(X1333)
| ~ function(X1333) )
& ( ~ in(esk69_2(X1333,X1339),X1339)
| ~ in(X1341,relation_dom(X1333))
| esk69_2(X1333,X1339) != apply(X1333,X1341)
| X1339 = relation_rng(X1333)
| ~ relation(X1333)
| ~ function(X1333) )
& ( in(esk70_2(X1333,X1339),relation_dom(X1333))
| in(esk69_2(X1333,X1339),X1339)
| X1339 = relation_rng(X1333)
| ~ relation(X1333)
| ~ function(X1333) )
& ( esk69_2(X1333,X1339) = apply(X1333,esk70_2(X1333,X1339))
| in(esk69_2(X1333,X1339),X1339)
| X1339 = relation_rng(X1333)
| ~ relation(X1333)
| ~ function(X1333) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_funct_1])])])])])]) ).
fof(c_0_19,plain,
! [X1113,X1114,X1115] :
( ( ~ quasi_total(X1115,X1113,X1114)
| X1113 = relation_dom_as_subset(X1113,X1114,X1115)
| X1114 = empty_set
| ~ relation_of2_as_subset(X1115,X1113,X1114) )
& ( X1113 != relation_dom_as_subset(X1113,X1114,X1115)
| quasi_total(X1115,X1113,X1114)
| X1114 = empty_set
| ~ relation_of2_as_subset(X1115,X1113,X1114) )
& ( ~ quasi_total(X1115,X1113,X1114)
| X1113 = relation_dom_as_subset(X1113,X1114,X1115)
| X1113 != empty_set
| ~ relation_of2_as_subset(X1115,X1113,X1114) )
& ( X1113 != relation_dom_as_subset(X1113,X1114,X1115)
| quasi_total(X1115,X1113,X1114)
| X1113 != empty_set
| ~ relation_of2_as_subset(X1115,X1113,X1114) )
& ( ~ quasi_total(X1115,X1113,X1114)
| X1115 = empty_set
| X1113 = empty_set
| X1114 != empty_set
| ~ relation_of2_as_subset(X1115,X1113,X1114) )
& ( X1115 != empty_set
| quasi_total(X1115,X1113,X1114)
| X1113 = empty_set
| X1114 != empty_set
| ~ relation_of2_as_subset(X1115,X1113,X1114) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_funct_2])])]) ).
cnf(c_0_20,plain,
( relation_dom_as_subset(X2,X3,X1) = relation_dom(X1)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_21,plain,
! [X1005,X1006,X1007] :
( ~ element(X1007,powerset(cartesian_product2(X1005,X1006)))
| relation(X1007) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])]) ).
cnf(c_0_22,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,negated_conjecture,
subset(esk255_0,cartesian_product2(esk252_0,esk253_0)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,plain,
( in(X3,X4)
| ~ in(X1,relation_dom(X2))
| X3 != apply(X2,X1)
| X4 != relation_rng(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( X2 = relation_dom_as_subset(X2,X3,X1)
| X3 = empty_set
| ~ quasi_total(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,negated_conjecture,
quasi_total(esk255_0,esk252_0,esk253_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_27,negated_conjecture,
relation_dom_as_subset(esk252_0,esk253_0,esk255_0) = relation_dom(esk255_0),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_28,negated_conjecture,
esk253_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_29,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,negated_conjecture,
element(esk255_0,powerset(cartesian_product2(esk252_0,esk253_0))),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_31,plain,
( in(apply(X1,X2),relation_rng(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_24])]) ).
cnf(c_0_32,negated_conjecture,
relation_dom(esk255_0) = esk252_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_13])]),c_0_28]) ).
cnf(c_0_33,negated_conjecture,
relation(esk255_0),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,negated_conjecture,
function(esk255_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_35,negated_conjecture,
( in(apply(esk255_0,X1),relation_rng(esk255_0))
| ~ in(X1,esk252_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_34])]) ).
cnf(c_0_36,negated_conjecture,
in(esk254_0,esk252_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_37,negated_conjecture,
~ in(apply(esk255_0,esk254_0),relation_rng(esk255_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU290+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
% 0.16/0.33 % Computer : n001.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 02:56:03 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 4.20/3.18 % Version : CSE_E---1.7
% 4.20/3.18 % Problem : theBenchmark.p
% 4.20/3.18 % SZS status Theorem for theBenchmark.p
% 4.20/3.18 % SZS output start CNFRefutation
% See solution above
% 4.20/3.19 % Total time : 2.486s
%------------------------------------------------------------------------------