%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU292+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 : n009.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 1.64s 2.25s
% Output : CNFRefutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 49 ( 14 unt; 0 def)
% Number of atoms : 156 ( 41 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 167 ( 60 ~; 63 |; 23 &)
% ( 3 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 94 ( 5 sgn 58 !; 0 ?)
% 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(t21_funct_2,conjecture,
! [X1,X2,X3,X4] :
( ( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2) )
=> ! [X5] :
( ( relation(X5)
& function(X5) )
=> ( in(X3,X1)
=> ( X2 = empty_set
| apply(relation_composition(X4,X5),X3) = apply(X5,apply(X4,X3)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_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(t23_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(X2))
=> apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(c_0_10,plain,
! [X101,X102,X103] :
( ~ element(X103,powerset(cartesian_product2(X101,X102)))
| relation(X103) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])]) ).
fof(c_0_11,plain,
! [X113,X114,X115] :
( ~ relation_of2_as_subset(X115,X113,X114)
| element(X115,powerset(cartesian_product2(X113,X114))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_relset_1])]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2) )
=> ! [X5] :
( ( relation(X5)
& function(X5) )
=> ( in(X3,X1)
=> ( X2 = empty_set
| apply(relation_composition(X4,X5),X3) = apply(X5,apply(X4,X3)) ) ) ) ),
inference(assume_negation,[status(cth)],[t21_funct_2]) ).
cnf(c_0_13,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( element(X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,negated_conjecture,
( function(esk21_0)
& quasi_total(esk21_0,esk18_0,esk19_0)
& relation_of2_as_subset(esk21_0,esk18_0,esk19_0)
& relation(esk22_0)
& function(esk22_0)
& in(esk20_0,esk18_0)
& esk19_0 != empty_set
& apply(relation_composition(esk21_0,esk22_0),esk20_0) != apply(esk22_0,apply(esk21_0,esk20_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_16,plain,
! [X155,X156,X157] :
( ~ relation_of2(X157,X155,X156)
| relation_dom_as_subset(X155,X156,X157) = relation_dom(X157) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_relset_1])]) ).
fof(c_0_17,plain,
! [X105,X106,X107] :
( ( ~ quasi_total(X107,X105,X106)
| X105 = relation_dom_as_subset(X105,X106,X107)
| X106 = empty_set
| ~ relation_of2_as_subset(X107,X105,X106) )
& ( X105 != relation_dom_as_subset(X105,X106,X107)
| quasi_total(X107,X105,X106)
| X106 = empty_set
| ~ relation_of2_as_subset(X107,X105,X106) )
& ( ~ quasi_total(X107,X105,X106)
| X105 = relation_dom_as_subset(X105,X106,X107)
| X105 != empty_set
| ~ relation_of2_as_subset(X107,X105,X106) )
& ( X105 != relation_dom_as_subset(X105,X106,X107)
| quasi_total(X107,X105,X106)
| X105 != empty_set
| ~ relation_of2_as_subset(X107,X105,X106) )
& ( ~ quasi_total(X107,X105,X106)
| X107 = empty_set
| X105 = empty_set
| X106 != empty_set
| ~ relation_of2_as_subset(X107,X105,X106) )
& ( X107 != empty_set
| quasi_total(X107,X105,X106)
| X105 = empty_set
| X106 != empty_set
| ~ relation_of2_as_subset(X107,X105,X106) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_funct_2])])]) ).
fof(c_0_18,plain,
! [X158,X159,X160] :
( ( ~ relation_of2_as_subset(X160,X158,X159)
| relation_of2(X160,X158,X159) )
& ( ~ relation_of2(X160,X158,X159)
| relation_of2_as_subset(X160,X158,X159) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
fof(c_0_19,plain,
! [X169,X170,X171] :
( ~ relation(X170)
| ~ function(X170)
| ~ relation(X171)
| ~ function(X171)
| ~ in(X169,relation_dom(X170))
| apply(relation_composition(X170,X171),X169) = apply(X171,apply(X170,X169)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_funct_1])])]) ).
cnf(c_0_20,plain,
( relation(X1)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_21,negated_conjecture,
relation_of2_as_subset(esk21_0,esk18_0,esk19_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
( relation_dom_as_subset(X2,X3,X1) = relation_dom(X1)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,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_17]) ).
cnf(c_0_24,plain,
( relation_of2_as_subset(X1,X2,X3)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,negated_conjecture,
apply(relation_composition(esk21_0,esk22_0),esk20_0) != apply(esk22_0,apply(esk21_0,esk20_0)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_26,plain,
( apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X3,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,negated_conjecture,
relation(esk22_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_28,negated_conjecture,
function(esk22_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_29,negated_conjecture,
function(esk21_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_30,negated_conjecture,
relation(esk21_0),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_31,plain,
! [X172,X173] :
( ~ element(X172,X173)
| empty(X173)
| in(X172,X173) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
cnf(c_0_32,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_22,c_0_23]),c_0_24]) ).
cnf(c_0_33,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_34,plain,
! [X162,X163] :
( ~ in(X162,X163)
| element(X162,X163) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(c_0_35,plain,
! [X183,X184] :
( ~ in(X183,X184)
| ~ empty(X184) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
cnf(c_0_36,negated_conjecture,
~ in(esk20_0,relation_dom(esk21_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[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_28]),c_0_29])]),c_0_30])]) ).
cnf(c_0_37,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,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_32,c_0_33]) ).
cnf(c_0_39,negated_conjecture,
quasi_total(esk21_0,esk18_0,esk19_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_40,negated_conjecture,
esk19_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_41,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,negated_conjecture,
in(esk20_0,esk18_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_43,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,negated_conjecture,
( empty(relation_dom(esk21_0))
| ~ element(esk20_0,relation_dom(esk21_0)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_45,negated_conjecture,
relation_dom(esk21_0) = esk18_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_21])]),c_0_40]) ).
cnf(c_0_46,negated_conjecture,
element(esk20_0,esk18_0),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,negated_conjecture,
~ empty(esk18_0),
inference(spm,[status(thm)],[c_0_43,c_0_42]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45]),c_0_45]),c_0_46])]),c_0_47]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.38 % Problem : SEU292+1 : TPTP v9.2.1. Released v3.3.0.
% 0.07/0.38 % 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
% 0.13/0.62 % Computer : n009.cluster.edu
% 0.13/0.62 % Model : x86_64 x86_64
% 0.13/0.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.62 % Memory : 8042.1875MB
% 0.13/0.62 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.62 % CPULimit : 300
% 0.13/0.62 % WCLimit : 300
% 0.13/0.62 % DateTime : Tue May 5 02:54:56 EDT 2026
% 0.15/0.63 % CPUTime :
% 0.15/0.64 % start to proof: theBenchmark
% 1.64/2.25 % Version : CSE_E---1.7
% 1.64/2.25 % Problem : theBenchmark.p
% 1.64/2.25 % SZS status Theorem for theBenchmark.p
% 1.64/2.25 % SZS output start CNFRefutation
% See solution above
% 1.64/2.26 % Total time : 1.426s
%------------------------------------------------------------------------------