%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU266+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 02:24:30 PM UTC 2026
% Result : Theorem 0.25s 0.61s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 20
% Syntax : Number of formulae : 101 ( 22 unt; 0 def)
% Number of atoms : 252 ( 57 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 273 ( 122 ~; 111 |; 17 &)
% ( 9 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 3 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 5 con; 0-3 aty)
% Number of variables : 189 ( 13 sgn 102 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t23_relset_1,conjecture,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( ! [X4] :
~ ( ! [X5] : ~ in(ordered_pair(X5,X4),X3)
& in(X4,X2) )
<=> relation_rng_as_subset(X1,X2,X3) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_relset_1) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( empty(X3)
& element(X2,powerset(X3))
& in(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( empty(X2)
& in(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(t2_tarski,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(t20_relat_1,axiom,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X2,relation_rng(X3))
& in(X1,relation_dom(X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(d5_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X4,X3),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_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(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/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
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(dt_k5_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> element(relation_rng_as_subset(X1,X2,X3),powerset(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relset_1) ).
fof(redefinition_k5_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> relation_rng_as_subset(X1,X2,X3) = relation_rng(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_relset_1) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X3))
& in(X1,X2) )
=> element(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( in(X1,X2)
| empty(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(c_0_18,negated_conjecture,
~ ! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( ! [X4] :
~ ( ! [X5] : ~ in(ordered_pair(X5,X4),X3)
& in(X4,X2) )
<=> relation_rng_as_subset(X1,X2,X3) = X2 ) ),
inference(assume_negation,[status(cth)],[t23_relset_1]) ).
fof(c_0_19,negated_conjecture,
~ ! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( ! [X4] :
~ ( ! [X5] : ~ in(ordered_pair(X5,X4),X3)
& in(X4,X2) )
<=> relation_rng_as_subset(X1,X2,X3) = X2 ) ),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_20,plain,
! [X72,X73,X74] :
( ~ empty(X74)
| ~ element(X73,powerset(X74))
| ~ in(X72,X73) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])])]) ).
fof(c_0_21,plain,
! [X34] : element(esk5_1(X34),X34),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_22,plain,
! [X76,X77] :
( ~ empty(X77)
| ~ in(X76,X77) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])])]) ).
fof(c_0_23,plain,
! [X64,X65] :
( ( X64 = X65
| in(esk14_2(X64,X65),X65)
| in(esk14_2(X64,X65),X64) )
& ( X64 = X65
| ~ in(esk14_2(X64,X65),X65)
| ~ in(esk14_2(X64,X65),X64) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])])]) ).
fof(c_0_24,negated_conjecture,
! [X59,X60] :
( ( relation_rng_as_subset(esk9_0,esk10_0,esk11_0) = esk10_0
| in(ordered_pair(esk13_1(X60),X60),esk11_0)
| ~ in(X60,esk10_0) )
& ( relation_rng_as_subset(esk9_0,esk10_0,esk11_0) != esk10_0
| ~ in(ordered_pair(X59,esk12_0),esk11_0) )
& ( relation_rng_as_subset(esk9_0,esk10_0,esk11_0) != esk10_0
| in(esk12_0,esk10_0) )
& relation_of2_as_subset(esk11_0,esk9_0,esk10_0) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])])])]) ).
fof(c_0_25,plain,
! [X23,X24] : ordered_pair(X23,X24) = unordered_pair(unordered_pair(X23,X24),singleton(X23)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
cnf(c_0_26,plain,
( ~ empty(X3)
| ~ element(X2,powerset(X3))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
element(esk5_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
( ~ empty(X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
( X1 = X2
| in(esk14_2(X1,X2),X2)
| in(esk14_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_30,plain,
! [X52,X53,X54] :
( ( ~ relation(X54)
| ~ in(ordered_pair(X52,X53),X54)
| in(X53,relation_rng(X54)) )
& ( ~ relation(X54)
| ~ in(ordered_pair(X52,X53),X54)
| in(X52,relation_dom(X54)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t20_relat_1])])])]) ).
cnf(c_0_31,negated_conjecture,
( relation_rng_as_subset(esk9_0,esk10_0,esk11_0) != esk10_0
| ~ in(ordered_pair(X1,esk12_0),esk11_0) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_33,plain,
! [X11,X12] : unordered_pair(X11,X12) = unordered_pair(X12,X11),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(c_0_34,plain,
! [X13,X14,X15,X17,X18,X19,X21] :
( ( ~ relation(X13)
| X19 = relation_rng(X13)
| in(ordered_pair(esk3_2(X13,X19),esk2_2(X13,X19)),X13)
| in(esk2_2(X13,X19),X19) )
& ( ~ relation(X13)
| X19 = relation_rng(X13)
| ~ in(ordered_pair(X21,esk2_2(X13,X19)),X13)
| ~ in(esk2_2(X13,X19),X19) )
& ( ~ relation(X13)
| X14 != relation_rng(X13)
| in(X17,X14)
| ~ in(ordered_pair(X18,X17),X13) )
& ( ~ relation(X13)
| X14 != relation_rng(X13)
| in(ordered_pair(esk1_3(X13,X14,X15),X15),X13)
| ~ in(X15,X14) ) ),
inference(distribute,[status(thm)],[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)],[d5_relat_1])])])])])])]) ).
fof(c_0_35,plain,
! [X8,X9,X10] :
( relation(X10)
| ~ element(X10,powerset(cartesian_product2(X8,X9))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])])]) ).
fof(c_0_36,plain,
! [X28,X29,X30] :
( element(X30,powerset(cartesian_product2(X28,X29)))
| ~ relation_of2_as_subset(X30,X28,X29) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_relset_1])])]) ).
cnf(c_0_37,plain,
( ~ in(X2,esk5_1(powerset(X1)))
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_38,plain,
( ~ empty(X2)
| in(esk14_2(X1,X2),X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_39,plain,
( ~ relation(X2)
| ~ in(ordered_pair(X3,X1),X2)
| in(X1,relation_rng(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_40,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(X1,esk12_0),singleton(X1)),esk11_0)
| relation_rng_as_subset(esk9_0,esk10_0,esk11_0) != esk10_0 ),
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_41,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_42,plain,
( ~ relation(X3)
| X2 != relation_rng(X3)
| ~ in(X1,X2)
| in(ordered_pair(esk1_3(X3,X2,X1),X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_43,plain,
( ~ element(X1,powerset(cartesian_product2(X2,X3)))
| relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,plain,
( ~ relation_of2_as_subset(X1,X2,X3)
| element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_45,plain,
( ~ empty(X2)
| ~ empty(X1)
| esk5_1(powerset(X1)) = X2 ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_46,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).
fof(c_0_47,plain,
( ~ epred1_0
<=> ! [X1] : ~ empty(X1) ),
introduced(definition) ).
cnf(c_0_48,plain,
( ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X2)
| ~ relation(X2)
| in(X1,relation_rng(X2)) ),
inference(rw,[status(thm)],[c_0_39,c_0_32]) ).
cnf(c_0_49,negated_conjecture,
( ~ in(X1,esk10_0)
| relation_rng_as_subset(esk9_0,esk10_0,esk11_0) = esk10_0
| in(ordered_pair(esk13_1(X1),X1),esk11_0) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_50,negated_conjecture,
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,esk12_0)),esk11_0)
| relation_rng_as_subset(esk9_0,esk10_0,esk11_0) != esk10_0 ),
inference(rw,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_51,plain,
( ~ in(X1,X2)
| ~ relation(X3)
| X2 != relation_rng(X3)
| in(unordered_pair(unordered_pair(esk1_3(X3,X2,X1),X1),singleton(esk1_3(X3,X2,X1))),X3) ),
inference(rw,[status(thm)],[c_0_42,c_0_32]) ).
cnf(c_0_52,plain,
( ~ relation_of2_as_subset(X1,X2,X3)
| relation(X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_53,negated_conjecture,
relation_of2_as_subset(esk11_0,esk9_0,esk10_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_54,plain,
! [X46,X47,X48] :
( ( relation_of2_as_subset(X48,X46,X47)
| ~ relation_of2(X48,X46,X47) )
& ( relation_of2(X48,X46,X47)
| ~ relation_of2_as_subset(X48,X46,X47) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])])]) ).
fof(c_0_55,plain,
! [X25,X26,X27] :
( element(relation_rng_as_subset(X25,X26,X27),powerset(X26))
| ~ relation_of2(X27,X25,X26) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relset_1])])]) ).
fof(c_0_56,plain,
! [X43,X44,X45] :
( relation_rng_as_subset(X43,X44,X45) = relation_rng(X45)
| ~ relation_of2(X45,X43,X44) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_relset_1])])]) ).
fof(c_0_57,plain,
( ~ epred2_0
<=> ! [X2] : ~ in(X2,empty_set) ),
introduced(definition) ).
cnf(c_0_58,plain,
( ~ empty(X1)
| esk5_1(powerset(X1)) = empty_set ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_59,plain,
( ~ empty(X1)
| epred1_0 ),
inference(split_equiv,[status(thm)],[c_0_47]) ).
cnf(c_0_60,plain,
( ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),X2)
| ~ relation(X2)
| in(X1,relation_rng(X2)) ),
inference(rw,[status(thm)],[c_0_48,c_0_41]) ).
cnf(c_0_61,negated_conjecture,
( ~ in(X1,esk10_0)
| in(unordered_pair(unordered_pair(esk13_1(X1),X1),singleton(esk13_1(X1))),esk11_0)
| relation_rng_as_subset(esk9_0,esk10_0,esk11_0) = esk10_0 ),
inference(rw,[status(thm)],[c_0_49,c_0_32]) ).
cnf(c_0_62,negated_conjecture,
( ~ in(unordered_pair(singleton(X1),unordered_pair(esk12_0,X1)),esk11_0)
| relation_rng_as_subset(esk9_0,esk10_0,esk11_0) != esk10_0 ),
inference(spm,[status(thm)],[c_0_50,c_0_41]) ).
cnf(c_0_63,plain,
( ~ in(X3,X2)
| ~ relation(X1)
| X2 != relation_rng(X1)
| in(unordered_pair(singleton(esk1_3(X1,X2,X3)),unordered_pair(X3,esk1_3(X1,X2,X3))),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_41]),c_0_41]) ).
cnf(c_0_64,negated_conjecture,
relation(esk11_0),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_65,plain,
( ~ relation_of2_as_subset(X1,X2,X3)
| relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_66,plain,
( ~ relation_of2(X1,X2,X3)
| element(relation_rng_as_subset(X2,X3,X1),powerset(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_67,plain,
( ~ relation_of2(X1,X2,X3)
| relation_rng_as_subset(X2,X3,X1) = relation_rng(X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_68,plain,
( ~ epred1_0
| ~ epred2_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_58]),c_0_47]),c_0_57]) ).
cnf(c_0_69,plain,
epred1_0,
inference(spm,[status(thm)],[c_0_59,c_0_46]) ).
cnf(c_0_70,plain,
( ~ in(unordered_pair(singleton(X3),unordered_pair(X1,X3)),X2)
| ~ relation(X2)
| in(X1,relation_rng(X2)) ),
inference(spm,[status(thm)],[c_0_60,c_0_41]) ).
cnf(c_0_71,negated_conjecture,
( ~ in(X1,esk10_0)
| in(unordered_pair(singleton(esk13_1(X1)),unordered_pair(X1,esk13_1(X1))),esk11_0)
| relation_rng_as_subset(esk9_0,esk10_0,esk11_0) = esk10_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_41]),c_0_41]) ).
cnf(c_0_72,negated_conjecture,
( ~ in(esk12_0,X1)
| X1 != relation_rng(esk11_0)
| relation_rng_as_subset(esk9_0,esk10_0,esk11_0) != esk10_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64])]) ).
cnf(c_0_73,negated_conjecture,
relation_of2(esk11_0,esk9_0,esk10_0),
inference(spm,[status(thm)],[c_0_65,c_0_53]) ).
cnf(c_0_74,negated_conjecture,
( relation_rng_as_subset(esk9_0,esk10_0,esk11_0) != esk10_0
| in(esk12_0,esk10_0) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_75,plain,
( ~ relation_of2(X1,X3,X2)
| element(relation_rng(X1),powerset(X2)) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_76,plain,
~ epred2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_69])]) ).
cnf(c_0_77,negated_conjecture,
( ~ in(X1,esk10_0)
| in(X1,relation_rng(esk11_0))
| relation_rng_as_subset(esk9_0,esk10_0,esk11_0) = esk10_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_64])]) ).
cnf(c_0_78,negated_conjecture,
( ~ in(esk12_0,X1)
| X1 != relation_rng(esk11_0)
| relation_rng(esk11_0) != esk10_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_67]),c_0_73])]) ).
cnf(c_0_79,negated_conjecture,
( relation_rng(esk11_0) != esk10_0
| in(esk12_0,esk10_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_67]),c_0_73])]) ).
cnf(c_0_80,negated_conjecture,
element(relation_rng(esk11_0),powerset(esk10_0)),
inference(spm,[status(thm)],[c_0_75,c_0_73]) ).
cnf(c_0_81,plain,
~ in(X1,empty_set),
inference(sr,[status(thm)],[inference(split_equiv,[status(thm)],[c_0_57]),c_0_76]) ).
fof(c_0_82,plain,
! [X69,X70,X71] :
( element(X69,X71)
| ~ element(X70,powerset(X71))
| ~ in(X69,X70) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])])]) ).
cnf(c_0_83,negated_conjecture,
( in(esk14_2(esk10_0,X1),X1)
| in(esk14_2(esk10_0,X1),relation_rng(esk11_0))
| esk10_0 = X1
| relation_rng_as_subset(esk9_0,esk10_0,esk11_0) = esk10_0 ),
inference(spm,[status(thm)],[c_0_77,c_0_29]) ).
cnf(c_0_84,negated_conjecture,
relation_rng(esk11_0) != esk10_0,
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_85,negated_conjecture,
( ~ in(X1,relation_rng(esk11_0))
| ~ empty(esk10_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_80]) ).
cnf(c_0_86,plain,
( in(esk14_2(empty_set,X1),X1)
| empty_set = X1 ),
inference(spm,[status(thm)],[c_0_81,c_0_29]) ).
fof(c_0_87,plain,
! [X75] :
( X75 = empty_set
| ~ empty(X75) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])]) ).
cnf(c_0_88,plain,
( ~ element(X2,powerset(X3))
| ~ in(X1,X2)
| element(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_89,plain,
( ~ in(esk14_2(X1,X2),X2)
| ~ in(esk14_2(X1,X2),X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_90,negated_conjecture,
( in(esk14_2(esk10_0,relation_rng(esk11_0)),relation_rng(esk11_0))
| relation_rng_as_subset(esk9_0,esk10_0,esk11_0) = esk10_0 ),
inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_83]),c_0_84]) ).
fof(c_0_91,plain,
! [X62,X63] :
( in(X62,X63)
| empty(X63)
| ~ element(X62,X63) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])])]) ).
cnf(c_0_92,negated_conjecture,
( ~ empty(esk10_0)
| relation_rng(esk11_0) = empty_set ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_93,plain,
( ~ empty(X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_94,negated_conjecture,
( ~ in(X1,relation_rng(esk11_0))
| element(X1,esk10_0) ),
inference(spm,[status(thm)],[c_0_88,c_0_80]) ).
cnf(c_0_95,negated_conjecture,
( ~ in(esk14_2(esk10_0,relation_rng(esk11_0)),esk10_0)
| relation_rng_as_subset(esk9_0,esk10_0,esk11_0) = esk10_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_84]) ).
cnf(c_0_96,plain,
( ~ element(X1,X2)
| in(X1,X2)
| empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_97,negated_conjecture,
~ empty(esk10_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_92]),c_0_93]) ).
cnf(c_0_98,negated_conjecture,
( element(esk14_2(esk10_0,relation_rng(esk11_0)),esk10_0)
| relation_rng_as_subset(esk9_0,esk10_0,esk11_0) = esk10_0 ),
inference(spm,[status(thm)],[c_0_94,c_0_90]) ).
cnf(c_0_99,negated_conjecture,
relation_rng_as_subset(esk9_0,esk10_0,esk11_0) = esk10_0,
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97]),c_0_98]) ).
cnf(c_0_100,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_99]),c_0_73])]),c_0_84]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU266+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.42 % Computer : n020.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Mon Sep 21 06:06:02 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.50 Running first-order theorem proving
% 0.17/0.50 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.25/0.61 % Version: 3.5.1
% 0.25/0.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.61 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.61 % Starting sh5l with 300s (1) cores
% 0.25/0.61 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2167526 completed with status 0
% 0.25/0.61 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.25/0.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.61 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.61 % No SInE strategy applied
% 0.25/0.61 % Search class: FGHSM-FFMS31-MFFFFFNN
% 0.25/0.61 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.61 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.25/0.61 % Starting G-E--_107_C37_SOS_F1_PI_AE_Q4_CS_SP_PS_S0Y with 380s (1) cores
% 0.25/0.61 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 136s (1) cores
% 0.25/0.61 % Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AA with 136s (1) cores
% 0.25/0.61 % G-E--_107_C37_SOS_F1_PI_AE_Q4_CS_SP_PS_S0Y with pid 2167533 completed with status 0
% 0.25/0.61 % Result found by G-E--_107_C37_SOS_F1_PI_AE_Q4_CS_SP_PS_S0Y
% 0.25/0.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.61 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.61 % No SInE strategy applied
% 0.25/0.61 % Search class: FGHSM-FFMS31-MFFFFFNN
% 0.25/0.61 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.61 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.25/0.61 % Starting G-E--_107_C37_SOS_F1_PI_AE_Q4_CS_SP_PS_S0Y with 380s (1) cores
% 0.25/0.61 % Preprocessing time : 0.003 s
% 0.25/0.61 % Presaturation interreduction done
% 0.25/0.61
% 0.25/0.61 % Proof found!
% 0.25/0.61 % SZS status Theorem
% 0.25/0.61 % SZS output start CNFRefutation
% See solution above
% 0.25/0.61 % Parsed axioms : 38
% 0.25/0.61 % Removed by relevancy pruning/SinE : 0
% 0.25/0.61 % Initial clauses : 48
% 0.25/0.61 % Removed in clause preprocessing : 11
% 0.25/0.61 % Initial clauses in saturation : 37
% 0.25/0.61 % Processed clauses : 515
% 0.25/0.61 % ...of these trivial : 4
% 0.25/0.61 % ...subsumed : 184
% 0.25/0.61 % ...remaining for further processing : 327
% 0.25/0.61 % Other redundant clauses eliminated : 0
% 0.25/0.61 % Clauses deleted for lack of memory : 0
% 0.25/0.61 % Backward-subsumed : 55
% 0.25/0.61 % Backward-rewritten : 54
% 0.25/0.61 % Generated clauses : 1274
% 0.25/0.61 % ...of the previous two non-redundant : 1228
% 0.25/0.61 % ...aggressively subsumed : 0
% 0.25/0.61 % Contextual simplify-reflections : 2
% 0.25/0.61 % Paramodulations : 1259
% 0.25/0.61 % Factorizations : 6
% 0.25/0.61 % NegExts : 0
% 0.25/0.61 % Equation resolutions : 6
% 0.25/0.61 % Disequality decompositions : 0
% 0.25/0.61 % Total rewrite steps : 249
% 0.25/0.61 % ...of those cached : 209
% 0.25/0.61 % Propositional unsat checks : 0
% 0.25/0.61 % Propositional check models : 0
% 0.25/0.61 % Propositional check unsatisfiable : 0
% 0.25/0.61 % Propositional clauses : 0
% 0.25/0.61 % Propositional clauses after purity: 0
% 0.25/0.61 % Propositional unsat core size : 0
% 0.25/0.61 % Propositional preprocessing time : 0.000
% 0.25/0.61 % Propositional encoding time : 0.000
% 0.25/0.61 % Propositional solver time : 0.000
% 0.25/0.61 % Success case prop preproc time : 0.000
% 0.25/0.61 % Success case prop encoding time : 0.000
% 0.25/0.61 % Success case prop solver time : 0.000
% 0.25/0.61 % Current number of processed clauses : 180
% 0.25/0.61 % Positive orientable unit clauses : 26
% 0.25/0.61 % Positive unorientable unit clauses: 1
% 0.25/0.61 % Negative unit clauses : 10
% 0.25/0.61 % Non-unit-clauses : 143
% 0.25/0.61 % Current number of unprocessed clauses: 662
% 0.25/0.61 % ...number of literals in the above : 2747
% 0.25/0.61 % Current number of archived formulas : 0
% 0.25/0.61 % Current number of archived clauses : 147
% 0.25/0.61 % Clause-clause subsumption calls (NU) : 7381
% 0.25/0.61 % Rec. Clause-clause subsumption calls : 4825
% 0.25/0.61 % Non-unit clause-clause subsumptions : 161
% 0.25/0.61 % Unit Clause-clause subsumption calls : 409
% 0.25/0.61 % Rewrite failures with RHS unbound : 0
% 0.25/0.61 % BW rewrite match attempts : 3
% 0.25/0.61 % BW rewrite match successes : 3
% 0.25/0.61 % Condensation attempts : 0
% 0.25/0.61 % Condensation successes : 0
% 0.25/0.61 % Termbank termtop insertions : 18942
% 0.25/0.61 % Search garbage collected termcells : 578
% 0.25/0.61
% 0.25/0.61 % -------------------------------------------------
% 0.25/0.61 % User time : 0.074 s
% 0.25/0.61 % System time : 0.007 s
% 0.25/0.61 % Total time : 0.082 s
% 0.25/0.61 % Maximum resident set size: 3660 pages
% 0.25/0.61
% 0.25/0.61 % -------------------------------------------------
% 0.25/0.61 % User time : 0.311 s
% 0.25/0.61 % System time : 0.032 s
% 0.25/0.61 % Total time : 0.343 s
% 0.25/0.61 % Maximum resident set size: 4864 pages
% 0.25/0.61 % E exiting
%------------------------------------------------------------------------------