%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU291+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:24:35 PM UTC 2026
% Result : Theorem 8.78s 1.78s
% Output : CNFRefutation 8.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of formulae : 96 ( 35 unt; 0 def)
% Number of atoms : 254 ( 79 equ)
% Maximal formula atoms : 26 ( 2 avg)
% Number of connectives : 252 ( 94 ~; 92 |; 40 &)
% ( 8 <=>; 18 =>; 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 : 149 ( 14 sgn 89 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t9_funct_2,conjecture,
! [X1,X2,X3,X4] :
( ( relation_of2_as_subset(X4,X1,X2)
& quasi_total(X4,X1,X2)
& function(X4) )
=> ( subset(X2,X3)
=> ( ( relation_of2_as_subset(X4,X1,X3)
& quasi_total(X4,X1,X3)
& function(X4) )
| ( X1 != empty_set
& X2 = empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_funct_2) ).
fof(t1_xboole_1,lemma,
! [X1,X2,X3] :
( ( subset(X2,X3)
& subset(X1,X2) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(t12_relset_1,lemma,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( subset(relation_rng(X3),X2)
& subset(relation_dom(X3),X1) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/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
=> ( ( quasi_total(X3,X1,X2)
<=> X3 = empty_set )
| X1 = empty_set ) )
& ( ( X2 = empty_set
=> X1 = empty_set )
=> ( quasi_total(X3,X1,X2)
<=> X1 = relation_dom_as_subset(X1,X2,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_2) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(l32_xboole_1,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( empty(X3)
& element(X2,powerset(X3))
& in(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',d1_relset_1) ).
fof(t3_boole,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
fof(t2_xboole_1,lemma,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(t64_relat_1,lemma,
! [X1] :
( relation(X1)
=> ( ( relation_rng(X1) = empty_set
| relation_dom(X1) = empty_set )
=> X1 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_relat_1) ).
fof(fc12_relat_1,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(t60_relat_1,lemma,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
fof(c_0_18,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( relation_of2_as_subset(X4,X1,X2)
& quasi_total(X4,X1,X2)
& function(X4) )
=> ( subset(X2,X3)
=> ( ( relation_of2_as_subset(X4,X1,X3)
& quasi_total(X4,X1,X3)
& function(X4) )
| ( X1 != empty_set
& X2 = empty_set ) ) ) ),
inference(assume_negation,[status(cth)],[t9_funct_2]) ).
fof(c_0_19,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( relation_of2_as_subset(X4,X1,X2)
& quasi_total(X4,X1,X2)
& function(X4) )
=> ( subset(X2,X3)
=> ( ( relation_of2_as_subset(X4,X1,X3)
& quasi_total(X4,X1,X3)
& function(X4) )
| ( X1 != empty_set
& X2 = empty_set ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_20,lemma,
! [X964,X965,X966] :
( subset(X964,X966)
| ~ subset(X965,X966)
| ~ subset(X964,X965) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])])]) ).
fof(c_0_21,negated_conjecture,
( ( ~ relation_of2_as_subset(esk256_0,esk253_0,esk255_0)
| ~ quasi_total(esk256_0,esk253_0,esk255_0)
| ~ function(esk256_0) )
& ( esk253_0 = empty_set
| esk254_0 != empty_set )
& subset(esk254_0,esk255_0)
& relation_of2_as_subset(esk256_0,esk253_0,esk254_0)
& quasi_total(esk256_0,esk253_0,esk254_0)
& function(esk256_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])]) ).
fof(c_0_22,lemma,
! [X894,X895,X896] :
( ( ~ relation_of2_as_subset(X896,X894,X895)
| subset(relation_rng(X896),X895) )
& ( ~ relation_of2_as_subset(X896,X894,X895)
| subset(relation_dom(X896),X894) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_relset_1])])])]) ).
fof(c_0_23,lemma,
! [X924,X925,X926,X927] :
( relation_of2_as_subset(X927,X926,X925)
| ~ subset(relation_rng(X927),X925)
| ~ relation_of2_as_subset(X927,X926,X924) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t14_relset_1])])]) ).
cnf(c_0_24,lemma,
( ~ subset(X2,X3)
| ~ subset(X1,X2)
| subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
subset(esk254_0,esk255_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,lemma,
( ~ relation_of2_as_subset(X1,X3,X2)
| subset(relation_rng(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,negated_conjecture,
relation_of2_as_subset(esk256_0,esk253_0,esk254_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,lemma,
( ~ subset(relation_rng(X1),X4)
| ~ relation_of2_as_subset(X1,X2,X3)
| relation_of2_as_subset(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,negated_conjecture,
( ~ subset(X1,esk254_0)
| subset(X1,esk255_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,negated_conjecture,
subset(relation_rng(esk256_0),esk254_0),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_31,plain,
! [X627,X628,X629] :
( ( relation_of2_as_subset(X629,X627,X628)
| ~ relation_of2(X629,X627,X628) )
& ( relation_of2(X629,X627,X628)
| ~ relation_of2_as_subset(X629,X627,X628) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])])]) ).
cnf(c_0_32,negated_conjecture,
( ~ subset(relation_rng(esk256_0),X1)
| relation_of2_as_subset(esk256_0,esk253_0,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_27]) ).
cnf(c_0_33,negated_conjecture,
subset(relation_rng(esk256_0),esk255_0),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
fof(c_0_34,plain,
! [X614,X615,X616] :
( relation_dom_as_subset(X614,X615,X616) = relation_dom(X616)
| ~ relation_of2(X616,X614,X615) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_relset_1])])]) ).
cnf(c_0_35,plain,
( ~ relation_of2_as_subset(X1,X2,X3)
| relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,negated_conjecture,
relation_of2_as_subset(esk256_0,esk253_0,esk255_0),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
( ~ relation_of2_as_subset(esk256_0,esk253_0,esk255_0)
| ~ quasi_total(esk256_0,esk253_0,esk255_0)
| ~ function(esk256_0) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_38,negated_conjecture,
function(esk256_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_39,plain,
! [X134,X135,X136] :
( ( ~ relation_of2_as_subset(X136,X134,X135)
| X135 != empty_set
| X134 = empty_set
| quasi_total(X136,X134,X135)
| X136 != empty_set )
& ( ~ relation_of2_as_subset(X136,X134,X135)
| X135 != empty_set
| X134 = empty_set
| X136 = empty_set
| ~ quasi_total(X136,X134,X135) )
& ( ~ relation_of2_as_subset(X136,X134,X135)
| X134 != empty_set
| quasi_total(X136,X134,X135)
| X134 != relation_dom_as_subset(X134,X135,X136) )
& ( ~ relation_of2_as_subset(X136,X134,X135)
| X134 != empty_set
| X134 = relation_dom_as_subset(X134,X135,X136)
| ~ quasi_total(X136,X134,X135) )
& ( ~ relation_of2_as_subset(X136,X134,X135)
| X135 = empty_set
| quasi_total(X136,X134,X135)
| X134 != relation_dom_as_subset(X134,X135,X136) )
& ( ~ relation_of2_as_subset(X136,X134,X135)
| X135 = empty_set
| X134 = relation_dom_as_subset(X134,X135,X136)
| ~ quasi_total(X136,X134,X135) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_funct_2])])])]) ).
cnf(c_0_40,plain,
( ~ relation_of2(X1,X2,X3)
| relation_dom_as_subset(X2,X3,X1) = relation_dom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,negated_conjecture,
relation_of2(esk256_0,esk253_0,esk255_0),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,negated_conjecture,
( ~ relation_of2_as_subset(esk256_0,esk253_0,esk255_0)
| ~ quasi_total(esk256_0,esk253_0,esk255_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).
cnf(c_0_43,negated_conjecture,
relation_of2(esk256_0,esk253_0,esk254_0),
inference(spm,[status(thm)],[c_0_35,c_0_27]) ).
fof(c_0_44,plain,
! [X1084,X1085] :
( ( element(X1084,powerset(X1085))
| ~ subset(X1084,X1085) )
& ( subset(X1084,X1085)
| ~ element(X1084,powerset(X1085)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])]) ).
fof(c_0_45,lemma,
! [X559,X560] :
( ( set_difference(X559,X560) = empty_set
| ~ subset(X559,X560) )
& ( subset(X559,X560)
| set_difference(X559,X560) != empty_set ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])])]) ).
cnf(c_0_46,plain,
( ~ relation_of2_as_subset(X3,X1,X2)
| X1 != relation_dom_as_subset(X1,X2,X3)
| X2 = empty_set
| quasi_total(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_47,negated_conjecture,
relation_dom_as_subset(esk253_0,esk255_0,esk256_0) = relation_dom(esk256_0),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,negated_conjecture,
~ quasi_total(esk256_0,esk253_0,esk255_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_36])]) ).
cnf(c_0_49,plain,
( ~ relation_of2_as_subset(X1,X2,X3)
| ~ quasi_total(X1,X2,X3)
| X3 = empty_set
| X2 = relation_dom_as_subset(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_50,negated_conjecture,
quasi_total(esk256_0,esk253_0,esk254_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_51,negated_conjecture,
relation_dom_as_subset(esk253_0,esk254_0,esk256_0) = relation_dom(esk256_0),
inference(spm,[status(thm)],[c_0_40,c_0_43]) ).
fof(c_0_52,plain,
! [X1167,X1168,X1169] :
( ~ empty(X1169)
| ~ element(X1168,powerset(X1169))
| ~ in(X1167,X1168) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])])]) ).
cnf(c_0_53,plain,
( ~ subset(X1,X2)
| element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_54,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_55,plain,
! [X160,X161,X162] :
( ( relation_of2(X162,X160,X161)
| ~ subset(X162,cartesian_product2(X160,X161)) )
& ( subset(X162,cartesian_product2(X160,X161))
| ~ relation_of2(X162,X160,X161) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_relset_1])])]) ).
cnf(c_0_56,lemma,
( ~ subset(X1,X2)
| set_difference(X1,X2) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_57,negated_conjecture,
( relation_dom(esk256_0) != esk253_0
| esk255_0 = empty_set ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_36])]),c_0_48]) ).
cnf(c_0_58,negated_conjecture,
( esk254_0 = empty_set
| relation_dom(esk256_0) = esk253_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_27])]) ).
fof(c_0_59,plain,
! [X1080] : set_difference(X1080,empty_set) = X1080,
inference(variable_rename,[status(thm)],[t3_boole]) ).
cnf(c_0_60,plain,
( ~ empty(X3)
| ~ element(X2,powerset(X3))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_61,negated_conjecture,
element(relation_rng(esk256_0),powerset(esk254_0)),
inference(spm,[status(thm)],[c_0_53,c_0_30]) ).
fof(c_0_62,plain,
! [X197,X198,X199] :
( ( X199 = empty_set
| in(esk34_1(X199),X199) )
& ( ~ in(X198,X197)
| X197 != empty_set ) ),
inference(fof_nnf,[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)],[c_0_54])])])])])]) ).
cnf(c_0_63,plain,
( ~ relation_of2(X1,X2,X3)
| subset(X1,cartesian_product2(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
fof(c_0_64,lemma,
! [X1035] : subset(empty_set,X1035),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
cnf(c_0_65,negated_conjecture,
set_difference(esk254_0,esk255_0) = empty_set,
inference(spm,[status(thm)],[c_0_56,c_0_25]) ).
cnf(c_0_66,negated_conjecture,
( esk255_0 = empty_set
| esk254_0 = empty_set ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_67,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_68,negated_conjecture,
( ~ in(X1,relation_rng(esk256_0))
| ~ empty(esk254_0) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_69,plain,
( X1 = empty_set
| in(esk34_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
fof(c_0_70,plain,
! [X26,X27,X28] :
( relation(X28)
| ~ element(X28,powerset(cartesian_product2(X26,X27))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])])]) ).
cnf(c_0_71,negated_conjecture,
subset(esk256_0,cartesian_product2(esk253_0,esk254_0)),
inference(spm,[status(thm)],[c_0_63,c_0_43]) ).
cnf(c_0_72,plain,
( ~ subset(X1,cartesian_product2(X2,X3))
| relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_73,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_74,negated_conjecture,
( esk254_0 != empty_set
| esk253_0 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_75,negated_conjecture,
esk254_0 = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67])]) ).
fof(c_0_76,lemma,
! [X1178] :
( ( ~ relation(X1178)
| X1178 = empty_set
| relation_rng(X1178) != empty_set )
& ( ~ relation(X1178)
| X1178 = empty_set
| relation_dom(X1178) != empty_set ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t64_relat_1])])])]) ).
cnf(c_0_77,negated_conjecture,
( ~ empty(esk254_0)
| relation_rng(esk256_0) = empty_set ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_78,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]) ).
cnf(c_0_79,plain,
( ~ element(X1,powerset(cartesian_product2(X2,X3)))
| relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_80,negated_conjecture,
element(esk256_0,powerset(cartesian_product2(esk253_0,esk254_0))),
inference(spm,[status(thm)],[c_0_53,c_0_71]) ).
cnf(c_0_81,plain,
( ~ relation_of2_as_subset(X3,X1,X2)
| X1 != empty_set
| X1 != relation_dom_as_subset(X1,X2,X3)
| quasi_total(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_82,lemma,
relation_of2(empty_set,X1,X2),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_83,lemma,
relation_dom(empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[t60_relat_1]) ).
cnf(c_0_84,plain,
( ~ relation_of2(X1,X2,X3)
| relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_85,negated_conjecture,
esk253_0 = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75])]) ).
cnf(c_0_86,lemma,
( ~ relation(X1)
| relation_rng(X1) != empty_set
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_87,negated_conjecture,
relation_rng(esk256_0) = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_75]),c_0_78])]) ).
cnf(c_0_88,negated_conjecture,
relation(esk256_0),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_89,plain,
( ~ relation_of2_as_subset(X1,empty_set,X2)
| relation_dom_as_subset(empty_set,X2,X1) != empty_set
| quasi_total(X1,empty_set,X2) ),
inference(er,[status(thm)],[c_0_81]) ).
cnf(c_0_90,lemma,
relation_dom_as_subset(X1,X2,empty_set) = empty_set,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_82]),c_0_83]) ).
cnf(c_0_91,lemma,
relation_of2_as_subset(empty_set,X1,X2),
inference(spm,[status(thm)],[c_0_84,c_0_82]) ).
cnf(c_0_92,negated_conjecture,
~ quasi_total(esk256_0,empty_set,esk255_0),
inference(rw,[status(thm)],[c_0_48,c_0_85]) ).
cnf(c_0_93,lemma,
esk256_0 = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88])]) ).
cnf(c_0_94,lemma,
quasi_total(empty_set,empty_set,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91])]) ).
cnf(c_0_95,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_93]),c_0_94])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU291+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.46 % Computer : n010.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Mon Sep 21 06:08:27 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.53 Running first-order theorem proving
% 0.24/0.53 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.78/1.78 % Version: 3.5.1
% 8.78/1.78 % Preprocessing class: FSLSSMSSSSSNFFN.
% 8.78/1.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.78/1.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 8.78/1.78 % Starting new_bool_3 with 300s (1) cores
% 8.78/1.78 % Starting new_bool_1 with 300s (1) cores
% 8.78/1.78 % Starting sh5l with 300s (1) cores
% 8.78/1.78 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 179828 completed with status 0
% 8.78/1.78 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 8.78/1.78 % Preprocessing class: FSLSSMSSSSSNFFN.
% 8.78/1.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.78/1.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 8.78/1.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 8.78/1.78 % No SInE strategy applied
% 8.78/1.78 % Search class: FGHSM-SMLM32-MFFFFFNN
% 8.78/1.78 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 8.78/1.78 % Starting SubtermCWHack with 136s (1) cores
% 8.78/1.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 8.78/1.78 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 113s (1) cores
% 8.78/1.78 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 113s (1) cores
% 8.78/1.78 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 113s (1) cores
% 8.78/1.78 % G-E--_208_C18_F1_SE_CS_SP_PS_S2g with pid 179838 completed with status 0
% 8.78/1.78 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S2g
% 8.78/1.78 % Preprocessing class: FSLSSMSSSSSNFFN.
% 8.78/1.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.78/1.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 8.78/1.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 8.78/1.78 % No SInE strategy applied
% 8.78/1.78 % Search class: FGHSM-SMLM32-MFFFFFNN
% 8.78/1.78 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 8.78/1.78 % Starting SubtermCWHack with 136s (1) cores
% 8.78/1.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 8.78/1.78 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 113s (1) cores
% 8.78/1.78 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 113s (1) cores
% 8.78/1.78 % Preprocessing time : 0.043 s
% 8.78/1.78 % Presaturation interreduction done
% 8.78/1.78
% 8.78/1.78 % Proof found!
% 8.78/1.78 % SZS status Theorem
% 8.78/1.78 % SZS output start CNFRefutation
% See solution above
% 8.78/1.78 % Parsed axioms : 384
% 8.78/1.78 % Removed by relevancy pruning/SinE : 0
% 8.78/1.78 % Initial clauses : 1450
% 8.78/1.78 % Removed in clause preprocessing : 33
% 8.78/1.78 % Initial clauses in saturation : 1417
% 8.78/1.78 % Processed clauses : 4830
% 8.78/1.78 % ...of these trivial : 133
% 8.78/1.78 % ...subsumed : 1027
% 8.78/1.78 % ...remaining for further processing : 3670
% 8.78/1.78 % Other redundant clauses eliminated : 463
% 8.78/1.78 % Clauses deleted for lack of memory : 0
% 8.78/1.78 % Backward-subsumed : 29
% 8.78/1.78 % Backward-rewritten : 658
% 8.78/1.78 % Generated clauses : 16833
% 8.78/1.78 % ...of the previous two non-redundant : 15738
% 8.78/1.78 % ...aggressively subsumed : 0
% 8.78/1.78 % Contextual simplify-reflections : 188
% 8.78/1.78 % Paramodulations : 16477
% 8.78/1.78 % Factorizations : 0
% 8.78/1.78 % NegExts : 0
% 8.78/1.78 % Equation resolutions : 466
% 8.78/1.78 % Disequality decompositions : 0
% 8.78/1.78 % Total rewrite steps : 5095
% 8.78/1.78 % ...of those cached : 4281
% 8.78/1.78 % Propositional unsat checks : 0
% 8.78/1.78 % Propositional check models : 0
% 8.78/1.78 % Propositional check unsatisfiable : 0
% 8.78/1.78 % Propositional clauses : 0
% 8.78/1.78 % Propositional clauses after purity: 0
% 8.78/1.78 % Propositional unsat core size : 0
% 8.78/1.78 % Propositional preprocessing time : 0.000
% 8.78/1.78 % Propositional encoding time : 0.000
% 8.78/1.78 % Propositional solver time : 0.000
% 8.78/1.78 % Success case prop preproc time : 0.000
% 8.78/1.78 % Success case prop encoding time : 0.000
% 8.78/1.78 % Success case prop solver time : 0.000
% 8.78/1.78 % Current number of processed clauses : 1340
% 8.78/1.78 % Positive orientable unit clauses : 442
% 8.78/1.78 % Positive unorientable unit clauses: 3
% 8.78/1.78 % Negative unit clauses : 162
% 8.78/1.78 % Non-unit-clauses : 733
% 8.78/1.78 % Current number of unprocessed clauses: 13525
% 8.78/1.78 % ...number of literals in the above : 28662
% 8.78/1.78 % Current number of archived formulas : 0
% 8.78/1.78 % Current number of archived clauses : 2003
% 8.78/1.78 % Clause-clause subsumption calls (NU) : 1458628
% 8.78/1.78 % Rec. Clause-clause subsumption calls : 290982
% 8.78/1.78 % Non-unit clause-clause subsumptions : 664
% 8.78/1.78 % Unit Clause-clause subsumption calls : 67975
% 8.78/1.78 % Rewrite failures with RHS unbound : 0
% 8.78/1.78 % BW rewrite match attempts : 480
% 8.78/1.78 % BW rewrite match successes : 114
% 8.78/1.78 % Condensation attempts : 0
% 8.78/1.78 % Condensation successes : 0
% 8.78/1.78 % Termbank termtop insertions : 313230
% 8.78/1.78 % Search garbage collected termcells : 19752
% 8.78/1.78
% 8.78/1.78 % -------------------------------------------------
% 8.78/1.78 % User time : 1.145 s
% 8.78/1.78 % System time : 0.044 s
% 8.78/1.78 % Total time : 1.189 s
% 8.78/1.78 % Maximum resident set size: 7692 pages
% 8.78/1.78
% 8.78/1.78 % -------------------------------------------------
% 8.78/1.78 % User time : 5.238 s
% 8.78/1.78 % System time : 0.186 s
% 8.78/1.78 % Total time : 5.424 s
% 8.78/1.78 % Maximum resident set size: 5120 pages
% 8.78/1.78 % E exiting
%------------------------------------------------------------------------------