%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU291+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 : 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 3.88s 3.19s
% Output : CNFRefutation 3.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 18
% Syntax : Number of formulae : 95 ( 35 unt; 0 def)
% Number of atoms : 245 ( 77 equ)
% Maximal formula atoms : 26 ( 2 avg)
% Number of connectives : 242 ( 92 ~; 91 |; 35 &)
% ( 8 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 145 ( 14 sgn 85 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t9_funct_2,conjecture,
! [X1,X2,X3,X4] :
( ( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2) )
=> ( subset(X2,X3)
=> ( ( X2 = empty_set
& X1 != empty_set )
| ( function(X4)
& quasi_total(X4,X1,X3)
& relation_of2_as_subset(X4,X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_2) ).
fof(t1_xboole_1,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(t12_relset_1,lemma,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( subset(relation_dom(X3),X1)
& subset(relation_rng(X3),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_relset_1) ).
fof(t14_relset_1,lemma,
! [X1,X2,X3,X4] :
( relation_of2_as_subset(X4,X3,X1)
=> ( subset(relation_rng(X4),X2)
=> relation_of2_as_subset(X4,X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relset_1) ).
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_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(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(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(l32_xboole_1,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_xboole_1) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
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(t3_boole,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
fof(t2_xboole_1,lemma,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
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(t64_relat_1,lemma,
! [X1] :
( relation(X1)
=> ( ( relation_dom(X1) = empty_set
| relation_rng(X1) = empty_set )
=> X1 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_relat_1) ).
fof(fc12_relat_1,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(t60_relat_1,lemma,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).
fof(c_0_18,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2) )
=> ( subset(X2,X3)
=> ( ( X2 = empty_set
& X1 != empty_set )
| ( function(X4)
& quasi_total(X4,X1,X3)
& relation_of2_as_subset(X4,X1,X3) ) ) ) ),
inference(assume_negation,[status(cth)],[t9_funct_2]) ).
fof(c_0_19,lemma,
! [X1947,X1948,X1949] :
( ~ subset(X1947,X1948)
| ~ subset(X1948,X1949)
| subset(X1947,X1949) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).
fof(c_0_20,negated_conjecture,
( function(esk256_0)
& quasi_total(esk256_0,esk253_0,esk254_0)
& relation_of2_as_subset(esk256_0,esk253_0,esk254_0)
& subset(esk254_0,esk255_0)
& ( esk254_0 != empty_set
| esk253_0 = empty_set )
& ( ~ function(esk256_0)
| ~ quasi_total(esk256_0,esk253_0,esk255_0)
| ~ relation_of2_as_subset(esk256_0,esk253_0,esk255_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
fof(c_0_21,lemma,
! [X1877,X1878,X1879] :
( ( subset(relation_dom(X1879),X1877)
| ~ relation_of2_as_subset(X1879,X1877,X1878) )
& ( subset(relation_rng(X1879),X1878)
| ~ relation_of2_as_subset(X1879,X1877,X1878) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_relset_1])])]) ).
fof(c_0_22,lemma,
! [X1907,X1908,X1909,X1910] :
( ~ relation_of2_as_subset(X1910,X1909,X1907)
| ~ subset(relation_rng(X1910),X1908)
| relation_of2_as_subset(X1910,X1909,X1908) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t14_relset_1])]) ).
cnf(c_0_23,lemma,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
subset(esk254_0,esk255_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,lemma,
( subset(relation_rng(X1),X2)
| ~ relation_of2_as_subset(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,negated_conjecture,
relation_of2_as_subset(esk256_0,esk253_0,esk254_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,lemma,
( relation_of2_as_subset(X1,X2,X4)
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ subset(relation_rng(X1),X4) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,negated_conjecture,
( subset(X1,esk255_0)
| ~ subset(X1,esk254_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,negated_conjecture,
subset(relation_rng(esk256_0),esk254_0),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
fof(c_0_30,plain,
! [X1610,X1611,X1612] :
( ( ~ relation_of2_as_subset(X1612,X1610,X1611)
| relation_of2(X1612,X1610,X1611) )
& ( ~ relation_of2(X1612,X1610,X1611)
| relation_of2_as_subset(X1612,X1610,X1611) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
cnf(c_0_31,negated_conjecture,
( relation_of2_as_subset(esk256_0,esk253_0,X1)
| ~ subset(relation_rng(esk256_0),X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_26]) ).
cnf(c_0_32,negated_conjecture,
subset(relation_rng(esk256_0),esk255_0),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_33,plain,
! [X1597,X1598,X1599] :
( ~ relation_of2(X1599,X1597,X1598)
| relation_dom_as_subset(X1597,X1598,X1599) = relation_dom(X1599) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_relset_1])]) ).
cnf(c_0_34,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,negated_conjecture,
relation_of2_as_subset(esk256_0,esk253_0,esk255_0),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
( ~ function(esk256_0)
| ~ quasi_total(esk256_0,esk253_0,esk255_0)
| ~ relation_of2_as_subset(esk256_0,esk253_0,esk255_0) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_37,negated_conjecture,
function(esk256_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_38,plain,
! [X1117,X1118,X1119] :
( ( ~ quasi_total(X1119,X1117,X1118)
| X1117 = relation_dom_as_subset(X1117,X1118,X1119)
| X1118 = empty_set
| ~ relation_of2_as_subset(X1119,X1117,X1118) )
& ( X1117 != relation_dom_as_subset(X1117,X1118,X1119)
| quasi_total(X1119,X1117,X1118)
| X1118 = empty_set
| ~ relation_of2_as_subset(X1119,X1117,X1118) )
& ( ~ quasi_total(X1119,X1117,X1118)
| X1117 = relation_dom_as_subset(X1117,X1118,X1119)
| X1117 != empty_set
| ~ relation_of2_as_subset(X1119,X1117,X1118) )
& ( X1117 != relation_dom_as_subset(X1117,X1118,X1119)
| quasi_total(X1119,X1117,X1118)
| X1117 != empty_set
| ~ relation_of2_as_subset(X1119,X1117,X1118) )
& ( ~ quasi_total(X1119,X1117,X1118)
| X1119 = empty_set
| X1117 = empty_set
| X1118 != empty_set
| ~ relation_of2_as_subset(X1119,X1117,X1118) )
& ( X1119 != empty_set
| quasi_total(X1119,X1117,X1118)
| X1117 = empty_set
| X1118 != empty_set
| ~ relation_of2_as_subset(X1119,X1117,X1118) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_funct_2])])]) ).
cnf(c_0_39,plain,
( relation_dom_as_subset(X2,X3,X1) = relation_dom(X1)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,negated_conjecture,
relation_of2(esk256_0,esk253_0,esk255_0),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,negated_conjecture,
( ~ quasi_total(esk256_0,esk253_0,esk255_0)
| ~ relation_of2_as_subset(esk256_0,esk253_0,esk255_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]) ).
cnf(c_0_42,negated_conjecture,
relation_of2(esk256_0,esk253_0,esk254_0),
inference(spm,[status(thm)],[c_0_34,c_0_26]) ).
fof(c_0_43,plain,
! [X2067,X2068] :
( ( ~ element(X2067,powerset(X2068))
| subset(X2067,X2068) )
& ( ~ subset(X2067,X2068)
| element(X2067,powerset(X2068)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(c_0_44,lemma,
! [X1542,X1543] :
( ( set_difference(X1542,X1543) != empty_set
| subset(X1542,X1543) )
& ( ~ subset(X1542,X1543)
| set_difference(X1542,X1543) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])]) ).
cnf(c_0_45,plain,
( quasi_total(X3,X1,X2)
| X2 = empty_set
| X1 != relation_dom_as_subset(X1,X2,X3)
| ~ relation_of2_as_subset(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,negated_conjecture,
relation_dom_as_subset(esk253_0,esk255_0,esk256_0) = relation_dom(esk256_0),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_47,negated_conjecture,
~ quasi_total(esk256_0,esk253_0,esk255_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_35])]) ).
cnf(c_0_48,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_38]) ).
cnf(c_0_49,negated_conjecture,
quasi_total(esk256_0,esk253_0,esk254_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_50,negated_conjecture,
relation_dom_as_subset(esk253_0,esk254_0,esk256_0) = relation_dom(esk256_0),
inference(spm,[status(thm)],[c_0_39,c_0_42]) ).
fof(c_0_51,plain,
! [X2150,X2151,X2152] :
( ~ in(X2150,X2151)
| ~ element(X2151,powerset(X2152))
| ~ empty(X2152) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
cnf(c_0_52,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
fof(c_0_53,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_54,plain,
! [X1143,X1144,X1145] :
( ( ~ relation_of2(X1145,X1143,X1144)
| subset(X1145,cartesian_product2(X1143,X1144)) )
& ( ~ subset(X1145,cartesian_product2(X1143,X1144))
| relation_of2(X1145,X1143,X1144) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_relset_1])]) ).
cnf(c_0_55,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_56,negated_conjecture,
( esk255_0 = empty_set
| relation_dom(esk256_0) != esk253_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_35])]),c_0_47]) ).
cnf(c_0_57,negated_conjecture,
( relation_dom(esk256_0) = esk253_0
| esk254_0 = empty_set ),
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_26])]) ).
fof(c_0_58,plain,
! [X2063] : set_difference(X2063,empty_set) = X2063,
inference(variable_rename,[status(thm)],[t3_boole]) ).
cnf(c_0_59,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_60,negated_conjecture,
element(relation_rng(esk256_0),powerset(esk254_0)),
inference(spm,[status(thm)],[c_0_52,c_0_29]) ).
fof(c_0_61,plain,
! [X1180,X1181,X1182] :
( ( X1180 != empty_set
| ~ in(X1181,X1180) )
& ( in(esk34_1(X1182),X1182)
| X1182 = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])])])])]) ).
cnf(c_0_62,plain,
( subset(X1,cartesian_product2(X2,X3))
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
fof(c_0_63,lemma,
! [X2018] : subset(empty_set,X2018),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
cnf(c_0_64,negated_conjecture,
set_difference(esk254_0,esk255_0) = empty_set,
inference(spm,[status(thm)],[c_0_55,c_0_24]) ).
cnf(c_0_65,negated_conjecture,
( esk254_0 = empty_set
| esk255_0 = empty_set ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_66,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_67,negated_conjecture,
( ~ empty(esk254_0)
| ~ in(X1,relation_rng(esk256_0)) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_68,plain,
( in(esk34_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
fof(c_0_69,plain,
! [X1009,X1010,X1011] :
( ~ element(X1011,powerset(cartesian_product2(X1009,X1010)))
| relation(X1011) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])]) ).
cnf(c_0_70,negated_conjecture,
subset(esk256_0,cartesian_product2(esk253_0,esk254_0)),
inference(spm,[status(thm)],[c_0_62,c_0_42]) ).
cnf(c_0_71,plain,
( relation_of2(X1,X2,X3)
| ~ subset(X1,cartesian_product2(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_72,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_73,negated_conjecture,
( esk253_0 = empty_set
| esk254_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_74,negated_conjecture,
esk254_0 = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66])]) ).
fof(c_0_75,lemma,
! [X2161] :
( ( relation_dom(X2161) != empty_set
| X2161 = empty_set
| ~ relation(X2161) )
& ( relation_rng(X2161) != empty_set
| X2161 = empty_set
| ~ relation(X2161) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t64_relat_1])])]) ).
cnf(c_0_76,negated_conjecture,
( relation_rng(esk256_0) = empty_set
| ~ empty(esk254_0) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_77,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]) ).
cnf(c_0_78,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_79,negated_conjecture,
element(esk256_0,powerset(cartesian_product2(esk253_0,esk254_0))),
inference(spm,[status(thm)],[c_0_52,c_0_70]) ).
cnf(c_0_80,plain,
( quasi_total(X3,X1,X2)
| X1 != relation_dom_as_subset(X1,X2,X3)
| X1 != empty_set
| ~ relation_of2_as_subset(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_81,lemma,
relation_of2(empty_set,X1,X2),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_82,lemma,
relation_dom(empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[t60_relat_1]) ).
cnf(c_0_83,plain,
( relation_of2_as_subset(X1,X2,X3)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_84,negated_conjecture,
esk253_0 = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_74])]) ).
cnf(c_0_85,lemma,
( X1 = empty_set
| relation_rng(X1) != empty_set
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_86,negated_conjecture,
relation_rng(esk256_0) = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_74]),c_0_77])]) ).
cnf(c_0_87,negated_conjecture,
relation(esk256_0),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_88,plain,
( quasi_total(X1,empty_set,X2)
| relation_dom_as_subset(empty_set,X2,X1) != empty_set
| ~ relation_of2_as_subset(X1,empty_set,X2) ),
inference(er,[status(thm)],[c_0_80]) ).
cnf(c_0_89,lemma,
relation_dom_as_subset(X1,X2,empty_set) = empty_set,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_81]),c_0_82]) ).
cnf(c_0_90,lemma,
relation_of2_as_subset(empty_set,X1,X2),
inference(spm,[status(thm)],[c_0_83,c_0_81]) ).
cnf(c_0_91,negated_conjecture,
~ quasi_total(esk256_0,empty_set,esk255_0),
inference(rw,[status(thm)],[c_0_47,c_0_84]) ).
cnf(c_0_92,lemma,
esk256_0 = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87])]) ).
cnf(c_0_93,lemma,
quasi_total(empty_set,empty_set,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90])]) ).
cnf(c_0_94,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_92]),c_0_93])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU291+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
% 0.15/0.33 % Computer : n005.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:55:00 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 3.88/3.19 % Version : CSE_E---1.7
% 3.88/3.19 % Problem : theBenchmark.p
% 3.88/3.19 % SZS status Theorem for theBenchmark.p
% 3.88/3.19 % SZS output start CNFRefutation
% See solution above
% 3.88/3.19 % Total time : 2.533s
%------------------------------------------------------------------------------