%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU290+1 : TPTP v9.2.1. Released v3.3.0.
% 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 : 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 05:11:22 PM UTC 2026
% Result : Theorem 1.75s 1.87s
% Output : CNFRefutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 10 unt; 0 def)
% Number of atoms : 153 ( 48 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 186 ( 69 ~; 77 |; 23 &)
% ( 5 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 82 ( 4 sgn 48 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_relset_1,axiom,
! [X1,X2,X3] :
( element(X3,powerset(cartesian_product2(X1,X2)))
=> relation(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(dt_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> element(X3,powerset(cartesian_product2(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
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/sandbox/benchmark/theBenchmark.p',t6_funct_2) ).
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/sandbox/benchmark/theBenchmark.p',redefinition_k4_relset_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/sandbox/benchmark/theBenchmark.p',d1_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/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
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/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
fof(c_0_7,plain,
! [X94,X95,X96] :
( ~ element(X96,powerset(cartesian_product2(X94,X95)))
| relation(X96) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])]) ).
fof(c_0_8,plain,
! [X114,X115,X116] :
( ~ relation_of2_as_subset(X116,X114,X115)
| element(X116,powerset(cartesian_product2(X114,X115))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_relset_1])]) ).
fof(c_0_9,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_10,plain,
! [X152,X153,X154] :
( ~ relation_of2(X154,X152,X153)
| relation_dom_as_subset(X152,X153,X154) = relation_dom(X154) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_relset_1])]) ).
fof(c_0_11,plain,
! [X98,X99,X100] :
( ( ~ quasi_total(X100,X98,X99)
| X98 = relation_dom_as_subset(X98,X99,X100)
| X99 = empty_set
| ~ relation_of2_as_subset(X100,X98,X99) )
& ( X98 != relation_dom_as_subset(X98,X99,X100)
| quasi_total(X100,X98,X99)
| X99 = empty_set
| ~ relation_of2_as_subset(X100,X98,X99) )
& ( ~ quasi_total(X100,X98,X99)
| X98 = relation_dom_as_subset(X98,X99,X100)
| X98 != empty_set
| ~ relation_of2_as_subset(X100,X98,X99) )
& ( X98 != relation_dom_as_subset(X98,X99,X100)
| quasi_total(X100,X98,X99)
| X98 != empty_set
| ~ relation_of2_as_subset(X100,X98,X99) )
& ( ~ quasi_total(X100,X98,X99)
| X100 = empty_set
| X98 = empty_set
| X99 != empty_set
| ~ relation_of2_as_subset(X100,X98,X99) )
& ( X100 != empty_set
| quasi_total(X100,X98,X99)
| X98 = empty_set
| X99 != empty_set
| ~ relation_of2_as_subset(X100,X98,X99) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_funct_2])])]) ).
fof(c_0_12,plain,
! [X155,X156,X157] :
( ( ~ relation_of2_as_subset(X157,X155,X156)
| relation_of2(X157,X155,X156) )
& ( ~ relation_of2(X157,X155,X156)
| relation_of2_as_subset(X157,X155,X156) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
fof(c_0_13,plain,
! [X101,X102,X103,X105,X106,X107,X109] :
( ( in(esk1_3(X101,X102,X103),relation_dom(X101))
| ~ in(X103,X102)
| X102 != relation_rng(X101)
| ~ relation(X101)
| ~ function(X101) )
& ( X103 = apply(X101,esk1_3(X101,X102,X103))
| ~ in(X103,X102)
| X102 != relation_rng(X101)
| ~ relation(X101)
| ~ function(X101) )
& ( ~ in(X106,relation_dom(X101))
| X105 != apply(X101,X106)
| in(X105,X102)
| X102 != relation_rng(X101)
| ~ relation(X101)
| ~ function(X101) )
& ( ~ in(esk2_2(X101,X107),X107)
| ~ in(X109,relation_dom(X101))
| esk2_2(X101,X107) != apply(X101,X109)
| X107 = relation_rng(X101)
| ~ relation(X101)
| ~ function(X101) )
& ( in(esk3_2(X101,X107),relation_dom(X101))
| in(esk2_2(X101,X107),X107)
| X107 = relation_rng(X101)
| ~ relation(X101)
| ~ function(X101) )
& ( esk2_2(X101,X107) = apply(X101,esk3_2(X101,X107))
| in(esk2_2(X101,X107),X107)
| X107 = relation_rng(X101)
| ~ relation(X101)
| ~ function(X101) ) ),
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])])])])])]) ).
cnf(c_0_14,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,plain,
( element(X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_16,negated_conjecture,
( function(esk24_0)
& quasi_total(esk24_0,esk21_0,esk22_0)
& relation_of2_as_subset(esk24_0,esk21_0,esk22_0)
& in(esk23_0,esk21_0)
& esk22_0 != empty_set
& ~ in(apply(esk24_0,esk23_0),relation_rng(esk24_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_17,plain,
( relation_dom_as_subset(X2,X3,X1) = relation_dom(X1)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,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_11]) ).
cnf(c_0_19,plain,
( relation_of2_as_subset(X1,X2,X3)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,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_13]) ).
cnf(c_0_21,plain,
( relation(X1)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,negated_conjecture,
relation_of2_as_subset(esk24_0,esk21_0,esk22_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
( X1 = relation_dom(X2)
| X3 = empty_set
| ~ relation_of2(X2,X1,X3)
| ~ quasi_total(X2,X1,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_24,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_25,negated_conjecture,
~ in(apply(esk24_0,esk23_0),relation_rng(esk24_0)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,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_20])]) ).
cnf(c_0_27,negated_conjecture,
function(esk24_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_28,negated_conjecture,
relation(esk24_0),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,plain,
( X1 = relation_dom(X2)
| X3 = empty_set
| ~ quasi_total(X2,X1,X3)
| ~ relation_of2_as_subset(X2,X1,X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,negated_conjecture,
quasi_total(esk24_0,esk21_0,esk22_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_31,negated_conjecture,
esk22_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_32,negated_conjecture,
~ in(esk23_0,relation_dom(esk24_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]),c_0_28])]) ).
cnf(c_0_33,negated_conjecture,
relation_dom(esk24_0) = esk21_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_22])]),c_0_31]) ).
cnf(c_0_34,negated_conjecture,
in(esk23_0,esk21_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU290+1 : TPTP v9.2.1. Released v3.3.0.
% 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 : n005.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 02:55:15 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.75/1.87 % Version : CSE_E---1.7
% 1.75/1.87 % Problem : theBenchmark.p
% 1.75/1.87 % SZS status Theorem for theBenchmark.p
% 1.75/1.87 % SZS output start CNFRefutation
% See solution above
% 1.75/1.87 % Total time : 1.373s
%------------------------------------------------------------------------------