%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU339+1 : 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 : n016.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 02:24:46 PM UTC 2026
% Result : Theorem 0.47s 0.72s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 22
% Syntax : Number of formulae : 120 ( 34 unt; 0 def)
% Number of atoms : 338 ( 31 equ)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 380 ( 162 ~; 155 |; 36 &)
% ( 4 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 4 con; 0-2 aty)
% Number of variables : 215 ( 21 sgn 95 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fc1_subset_1,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_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(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( in(X1,X2)
| empty(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
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(d4_relat_2,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_antisymmetric_in(X1,X2)
<=> ! [X3,X4] :
( ( in(ordered_pair(X4,X3),X1)
& in(ordered_pair(X3,X4),X1)
& in(X4,X2)
& in(X3,X2) )
=> X3 = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_2) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(d9_orders_2,axiom,
! [X1] :
( rel_str(X1)
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( related(X1,X2,X3)
<=> in(ordered_pair(X2,X3),the_InternalRel(X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_orders_2) ).
fof(dt_u1_orders_2,axiom,
! [X1] :
( rel_str(X1)
=> relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_orders_2) ).
fof(t25_orders_2,conjecture,
! [X1] :
( ( rel_str(X1)
& antisymmetric_relstr(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( related(X1,X3,X2)
& related(X1,X2,X3) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_orders_2) ).
fof(d6_orders_2,axiom,
! [X1] :
( rel_str(X1)
=> ( antisymmetric_relstr(X1)
<=> is_antisymmetric_in(the_InternalRel(X1),the_carrier(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_orders_2) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X3))
& in(X1,X2) )
=> element(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(t106_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X2,X4)
& in(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( empty(X2)
& element(X2,powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X2)
& X1 != X2
& empty(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
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(rc1_subset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( ~ empty(X2)
& element(X2,powerset(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( empty(X2)
& in(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(c_0_22,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(c_0_23,plain,
! [X7,X8,X9] :
( relation(X9)
| ~ element(X9,powerset(cartesian_product2(X7,X8))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])])]) ).
fof(c_0_24,plain,
! [X60,X61] :
( element(X60,X61)
| ~ in(X60,X61) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])])]) ).
fof(c_0_25,plain,
! [X65,X66] :
( in(X65,X66)
| empty(X66)
| ~ element(X65,X66) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])])]) ).
fof(c_0_26,plain,
! [X26,X27,X28] :
( element(X28,powerset(cartesian_product2(X26,X27)))
| ~ relation_of2_as_subset(X28,X26,X27) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_relset_1])])]) ).
fof(c_0_27,plain,
! [X40] : ~ empty(powerset(X40)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_22])]) ).
cnf(c_0_28,plain,
( ~ element(X1,powerset(cartesian_product2(X2,X3)))
| relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
( ~ in(X1,X2)
| element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
( ~ element(X1,X2)
| in(X1,X2)
| empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
( ~ relation_of2_as_subset(X1,X2,X3)
| element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_33,plain,
! [X12,X13,X14,X15,X16] :
( ( ~ relation(X12)
| is_antisymmetric_in(X12,X16)
| esk1_2(X12,X16) != esk2_2(X12,X16) )
& ( ~ relation(X12)
| is_antisymmetric_in(X12,X16)
| in(ordered_pair(esk2_2(X12,X16),esk1_2(X12,X16)),X12) )
& ( ~ relation(X12)
| is_antisymmetric_in(X12,X16)
| in(ordered_pair(esk1_2(X12,X16),esk2_2(X12,X16)),X12) )
& ( ~ relation(X12)
| is_antisymmetric_in(X12,X16)
| in(esk2_2(X12,X16),X16) )
& ( ~ relation(X12)
| is_antisymmetric_in(X12,X16)
| in(esk1_2(X12,X16),X16) )
& ( ~ relation(X12)
| X14 = X15
| ~ in(ordered_pair(X15,X14),X12)
| ~ in(ordered_pair(X14,X15),X12)
| ~ in(X15,X13)
| ~ in(X14,X13)
| ~ is_antisymmetric_in(X12,X13) ) ),
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)],[d4_relat_2])])])])])])]) ).
fof(c_0_34,plain,
! [X19,X20] : ordered_pair(X19,X20) = unordered_pair(unordered_pair(X19,X20),singleton(X19)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_35,plain,
! [X22,X23,X24] :
( ( ~ rel_str(X22)
| ~ element(X23,the_carrier(X22))
| ~ element(X24,the_carrier(X22))
| related(X22,X23,X24)
| ~ in(ordered_pair(X23,X24),the_InternalRel(X22)) )
& ( ~ rel_str(X22)
| ~ element(X23,the_carrier(X22))
| ~ element(X24,the_carrier(X22))
| in(ordered_pair(X23,X24),the_InternalRel(X22))
| ~ related(X22,X23,X24) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_orders_2])])])])]) ).
cnf(c_0_36,plain,
( ~ in(X1,powerset(cartesian_product2(X2,X3)))
| relation(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_37,plain,
( ~ relation_of2_as_subset(X1,X2,X3)
| in(X1,powerset(cartesian_product2(X2,X3))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
fof(c_0_38,plain,
! [X29] :
( relation_of2_as_subset(the_InternalRel(X29),the_carrier(X29),the_carrier(X29))
| ~ rel_str(X29) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_orders_2])])]) ).
cnf(c_0_39,plain,
( ~ relation(X1)
| ~ in(ordered_pair(X4,X3),X1)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X2)
| ~ in(X3,X2)
| ~ is_antisymmetric_in(X1,X2)
| X3 = X4 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,plain,
( ~ rel_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ related(X1,X2,X3)
| in(ordered_pair(X2,X3),the_InternalRel(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_42,plain,
( ~ relation_of2_as_subset(X1,X2,X3)
| relation(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_43,plain,
( ~ rel_str(X1)
| relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_44,plain,
( ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),X1)
| ~ in(unordered_pair(unordered_pair(X4,X3),singleton(X4)),X1)
| ~ is_antisymmetric_in(X1,X2)
| ~ in(X3,X2)
| ~ in(X4,X2)
| ~ relation(X1)
| X3 = X4 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40]),c_0_40]) ).
cnf(c_0_45,plain,
( ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ related(X1,X2,X3)
| ~ rel_str(X1)
| in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),the_InternalRel(X1)) ),
inference(rw,[status(thm)],[c_0_41,c_0_40]) ).
cnf(c_0_46,plain,
( ~ rel_str(X1)
| relation(the_InternalRel(X1)) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
fof(c_0_47,negated_conjecture,
~ ! [X1] :
( ( rel_str(X1)
& antisymmetric_relstr(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( related(X1,X3,X2)
& related(X1,X2,X3) )
=> X2 = X3 ) ) ) ),
inference(assume_negation,[status(cth)],[t25_orders_2]) ).
cnf(c_0_48,plain,
( ~ in(X1,X4)
| ~ in(X2,X4)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),the_InternalRel(X3))
| ~ element(X2,the_carrier(X3))
| ~ element(X1,the_carrier(X3))
| ~ is_antisymmetric_in(the_InternalRel(X3),X4)
| ~ rel_str(X3)
| ~ related(X3,X2,X1)
| X1 = X2 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
fof(c_0_49,plain,
! [X21] :
( ( ~ rel_str(X21)
| antisymmetric_relstr(X21)
| ~ is_antisymmetric_in(the_InternalRel(X21),the_carrier(X21)) )
& ( ~ rel_str(X21)
| is_antisymmetric_in(the_InternalRel(X21),the_carrier(X21))
| ~ antisymmetric_relstr(X21) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_orders_2])])])]) ).
fof(c_0_50,negated_conjecture,
( esk13_0 != esk14_0
& related(esk12_0,esk14_0,esk13_0)
& related(esk12_0,esk13_0,esk14_0)
& element(esk14_0,the_carrier(esk12_0))
& element(esk13_0,the_carrier(esk12_0))
& rel_str(esk12_0)
& antisymmetric_relstr(esk12_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])])]) ).
cnf(c_0_51,plain,
( ~ in(X1,X4)
| ~ in(X2,X4)
| ~ element(X2,the_carrier(X3))
| ~ element(X1,the_carrier(X3))
| ~ is_antisymmetric_in(the_InternalRel(X3),X4)
| ~ rel_str(X3)
| ~ related(X3,X1,X2)
| ~ related(X3,X2,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_48,c_0_45]) ).
cnf(c_0_52,plain,
( ~ rel_str(X1)
| ~ antisymmetric_relstr(X1)
| is_antisymmetric_in(the_InternalRel(X1),the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
fof(c_0_53,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_54,negated_conjecture,
element(esk14_0,the_carrier(esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_55,negated_conjecture,
element(esk13_0,the_carrier(esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
fof(c_0_56,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_57,plain,
( ~ in(X1,the_carrier(X3))
| ~ in(X2,the_carrier(X3))
| ~ rel_str(X3)
| ~ antisymmetric_relstr(X3)
| ~ related(X3,X1,X2)
| ~ related(X3,X2,X1)
| X1 = X2 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_29]),c_0_29]) ).
cnf(c_0_58,negated_conjecture,
related(esk12_0,esk14_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_59,negated_conjecture,
related(esk12_0,esk13_0,esk14_0),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_60,negated_conjecture,
antisymmetric_relstr(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_61,negated_conjecture,
rel_str(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_62,negated_conjecture,
esk13_0 != esk14_0,
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_63,plain,
( ~ empty(X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_64,negated_conjecture,
( in(esk14_0,the_carrier(esk12_0))
| empty(the_carrier(esk12_0)) ),
inference(spm,[status(thm)],[c_0_30,c_0_54]) ).
cnf(c_0_65,negated_conjecture,
( in(esk13_0,the_carrier(esk12_0))
| empty(the_carrier(esk12_0)) ),
inference(spm,[status(thm)],[c_0_30,c_0_55]) ).
cnf(c_0_66,plain,
( ~ element(X2,powerset(X3))
| ~ in(X1,X2)
| element(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_67,negated_conjecture,
( ~ in(esk13_0,the_carrier(esk12_0))
| ~ in(esk14_0,the_carrier(esk12_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]),c_0_60]),c_0_61])]),c_0_62]) ).
cnf(c_0_68,negated_conjecture,
( in(esk14_0,the_carrier(esk12_0))
| the_carrier(esk12_0) = empty_set ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_69,negated_conjecture,
( in(esk13_0,the_carrier(esk12_0))
| the_carrier(esk12_0) = empty_set ),
inference(spm,[status(thm)],[c_0_63,c_0_65]) ).
cnf(c_0_70,plain,
( ~ in(X1,X3)
| ~ in(X3,powerset(X2))
| element(X1,X2) ),
inference(spm,[status(thm)],[c_0_66,c_0_29]) ).
cnf(c_0_71,negated_conjecture,
the_carrier(esk12_0) = empty_set,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]) ).
fof(c_0_72,plain,
! [X56,X57,X58,X59] :
( ( in(ordered_pair(X56,X57),cartesian_product2(X58,X59))
| ~ in(X57,X59)
| ~ in(X56,X58) )
& ( ~ in(ordered_pair(X56,X57),cartesian_product2(X58,X59))
| in(X57,X59) )
& ( ~ in(ordered_pair(X56,X57),cartesian_product2(X58,X59))
| in(X56,X58) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t106_zfmisc_1])])])]) ).
cnf(c_0_73,plain,
( ~ in(X1,X4)
| ~ relation_of2_as_subset(X4,X2,X3)
| element(X1,cartesian_product2(X2,X3)) ),
inference(spm,[status(thm)],[c_0_70,c_0_37]) ).
cnf(c_0_74,negated_conjecture,
relation_of2_as_subset(the_InternalRel(esk12_0),empty_set,empty_set),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_71]),c_0_61])]) ).
fof(c_0_75,plain,
! [X10,X11] : unordered_pair(X10,X11) = unordered_pair(X11,X10),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_76,plain,
( ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2))
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_77,negated_conjecture,
( ~ in(X1,the_InternalRel(esk12_0))
| element(X1,cartesian_product2(empty_set,empty_set)) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_78,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
fof(c_0_79,plain,
! [X49] :
( empty(esk10_1(X49))
& element(esk10_1(X49),powerset(X49)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
cnf(c_0_80,plain,
( ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),cartesian_product2(X4,X2))
| in(X1,X2) ),
inference(rw,[status(thm)],[c_0_76,c_0_40]) ).
cnf(c_0_81,negated_conjecture,
( ~ in(X1,the_InternalRel(esk12_0))
| in(X1,cartesian_product2(empty_set,empty_set))
| empty(cartesian_product2(empty_set,empty_set)) ),
inference(spm,[status(thm)],[c_0_30,c_0_77]) ).
cnf(c_0_82,plain,
( ~ element(X1,the_carrier(X3))
| ~ element(X2,the_carrier(X3))
| ~ rel_str(X3)
| ~ related(X3,X1,X2)
| in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),the_InternalRel(X3)) ),
inference(spm,[status(thm)],[c_0_45,c_0_78]) ).
cnf(c_0_83,plain,
empty(esk10_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
fof(c_0_84,plain,
! [X1,X2] :
~ ( empty(X2)
& X1 != X2
& empty(X1) ),
inference(fof_simplification,[status(thm)],[t8_boole]) ).
cnf(c_0_85,plain,
( ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),cartesian_product2(X4,X2))
| in(X1,X2) ),
inference(spm,[status(thm)],[c_0_80,c_0_78]) ).
cnf(c_0_86,negated_conjecture,
( ~ element(X1,empty_set)
| ~ element(X2,empty_set)
| ~ related(esk12_0,X1,X2)
| in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(empty_set,empty_set))
| empty(cartesian_product2(empty_set,empty_set)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_61]),c_0_71]),c_0_71])]) ).
fof(c_0_87,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])])]) ).
cnf(c_0_88,plain,
element(esk10_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_89,plain,
esk10_1(X1) = empty_set,
inference(spm,[status(thm)],[c_0_63,c_0_83]) ).
fof(c_0_90,plain,
! [X78,X79] :
( ~ empty(X79)
| X78 = X79
| ~ empty(X78) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_84])])]) ).
cnf(c_0_91,negated_conjecture,
( ~ element(X2,empty_set)
| ~ element(X1,empty_set)
| ~ related(esk12_0,X2,X1)
| in(X1,empty_set)
| empty(cartesian_product2(empty_set,empty_set)) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_92,negated_conjecture,
element(esk13_0,empty_set),
inference(rw,[status(thm)],[c_0_55,c_0_71]) ).
cnf(c_0_93,negated_conjecture,
element(esk14_0,empty_set),
inference(rw,[status(thm)],[c_0_54,c_0_71]) ).
cnf(c_0_94,plain,
( ~ empty(X3)
| ~ element(X2,powerset(X3))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_95,plain,
element(empty_set,powerset(X1)),
inference(rw,[status(thm)],[c_0_88,c_0_89]) ).
fof(c_0_96,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( ~ empty(X2)
& element(X2,powerset(X1)) ) ),
inference(fof_simplification,[status(thm)],[rc1_subset_1]) ).
cnf(c_0_97,plain,
( ~ empty(X2)
| ~ empty(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_98,negated_conjecture,
( in(esk13_0,empty_set)
| empty(cartesian_product2(empty_set,empty_set)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_58]),c_0_92]),c_0_93])]) ).
cnf(c_0_99,plain,
( ~ in(X2,empty_set)
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
fof(c_0_100,plain,
! [X46] :
( ( empty(X46)
| ~ empty(esk8_1(X46)) )
& ( empty(X46)
| element(esk8_1(X46),powerset(X46)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_96])])])])]) ).
fof(c_0_101,plain,
! [X35] : element(esk6_1(X35),X35),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
cnf(c_0_102,negated_conjecture,
( ~ empty(X1)
| X1 = cartesian_product2(empty_set,empty_set) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_99]) ).
cnf(c_0_103,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).
cnf(c_0_104,plain,
( empty(X1)
| element(esk8_1(X1),powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_105,plain,
element(esk6_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
fof(c_0_106,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])])]) ).
cnf(c_0_107,plain,
( ~ in(X4,X3)
| ~ relation_of2_as_subset(X3,X1,X2)
| ~ empty(cartesian_product2(X1,X2)) ),
inference(spm,[status(thm)],[c_0_94,c_0_31]) ).
cnf(c_0_108,negated_conjecture,
cartesian_product2(empty_set,empty_set) = empty_set,
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_109,plain,
( ~ in(X2,esk8_1(X1))
| element(X2,X1)
| empty(X1) ),
inference(spm,[status(thm)],[c_0_66,c_0_104]) ).
cnf(c_0_110,plain,
( in(esk6_1(X1),X1)
| empty(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_105]) ).
cnf(c_0_111,plain,
( ~ empty(esk8_1(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_112,plain,
( ~ empty(X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_113,negated_conjecture,
( ~ in(X2,X1)
| ~ relation_of2_as_subset(X1,empty_set,empty_set) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_103])]) ).
cnf(c_0_114,plain,
( element(esk6_1(esk8_1(X1)),X1)
| empty(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_111]) ).
cnf(c_0_115,plain,
( ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ rel_str(X1)
| ~ related(X1,X2,X3)
| ~ empty(the_InternalRel(X1)) ),
inference(spm,[status(thm)],[c_0_112,c_0_45]) ).
cnf(c_0_116,negated_conjecture,
~ in(X1,the_InternalRel(esk12_0)),
inference(spm,[status(thm)],[c_0_113,c_0_74]) ).
cnf(c_0_117,plain,
( in(esk6_1(esk8_1(X1)),X1)
| empty(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_114]) ).
cnf(c_0_118,negated_conjecture,
~ empty(the_InternalRel(esk12_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_58]),c_0_61]),c_0_55]),c_0_54])]) ).
cnf(c_0_119,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_118]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU339+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.45 % Computer : n016.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Mon Sep 21 06:17:53 UTC 2026
% 0.17/0.46 % CPUTime :
% 0.17/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.54 Running first-order theorem proving
% 0.26/0.55 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
% 0.47/0.72 % Version: 3.5.1
% 0.47/0.72 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.47/0.72 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.47/0.72 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.47/0.72 % Starting new_bool_3 with 300s (1) cores
% 0.47/0.72 % Starting new_bool_1 with 300s (1) cores
% 0.47/0.72 % Starting sh5l with 300s (1) cores
% 0.47/0.72 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1735451 completed with status 0
% 0.47/0.72 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.47/0.72 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.47/0.72 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.47/0.72 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.47/0.72 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.47/0.72 % No SInE strategy applied
% 0.47/0.72 % Search class: FGHSM-FFMM21-MFFFFFNN
% 0.47/0.72 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.47/0.72 % Starting SubtermCWHack with 136s (1) cores
% 0.47/0.72 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.47/0.72 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.47/0.72 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.47/0.72 % Starting new_bool_3 with 136s (1) cores
% 0.47/0.72 % G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with pid 1735461 completed with status 0
% 0.47/0.72 % Result found by G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y
% 0.47/0.72 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.47/0.72 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.47/0.72 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.47/0.72 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.47/0.72 % No SInE strategy applied
% 0.47/0.72 % Search class: FGHSM-FFMM21-MFFFFFNN
% 0.47/0.72 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.47/0.72 % Starting SubtermCWHack with 136s (1) cores
% 0.47/0.72 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.47/0.72 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.47/0.72 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.47/0.72 % Preprocessing time : 0.004 s
% 0.47/0.72
% 0.47/0.72 % Proof found!
% 0.47/0.72 % SZS status Theorem
% 0.47/0.72 % SZS output start CNFRefutation
% See solution above
% 0.47/0.72 % Parsed axioms : 46
% 0.47/0.72 % Removed by relevancy pruning/SinE : 0
% 0.47/0.72 % Initial clauses : 65
% 0.47/0.72 % Removed in clause preprocessing : 11
% 0.47/0.72 % Initial clauses in saturation : 54
% 0.47/0.72 % Processed clauses : 637
% 0.47/0.72 % ...of these trivial : 5
% 0.47/0.72 % ...subsumed : 306
% 0.47/0.72 % ...remaining for further processing : 326
% 0.47/0.72 % Other redundant clauses eliminated : 0
% 0.47/0.72 % Clauses deleted for lack of memory : 0
% 0.47/0.72 % Backward-subsumed : 26
% 0.47/0.72 % Backward-rewritten : 48
% 0.47/0.72 % Generated clauses : 1260
% 0.47/0.72 % ...of the previous two non-redundant : 1116
% 0.47/0.72 % ...aggressively subsumed : 0
% 0.47/0.72 % Contextual simplify-reflections : 17
% 0.47/0.72 % Paramodulations : 1260
% 0.47/0.72 % Factorizations : 0
% 0.47/0.72 % NegExts : 0
% 0.47/0.72 % Equation resolutions : 0
% 0.47/0.72 % Disequality decompositions : 0
% 0.47/0.72 % Total rewrite steps : 393
% 0.47/0.72 % ...of those cached : 354
% 0.47/0.72 % Propositional unsat checks : 0
% 0.47/0.72 % Propositional check models : 0
% 0.47/0.72 % Propositional check unsatisfiable : 0
% 0.47/0.72 % Propositional clauses : 0
% 0.47/0.72 % Propositional clauses after purity: 0
% 0.47/0.72 % Propositional unsat core size : 0
% 0.47/0.72 % Propositional preprocessing time : 0.000
% 0.47/0.72 % Propositional encoding time : 0.000
% 0.47/0.72 % Propositional solver time : 0.000
% 0.47/0.72 % Success case prop preproc time : 0.000
% 0.47/0.72 % Success case prop encoding time : 0.000
% 0.47/0.72 % Success case prop solver time : 0.000
% 0.47/0.72 % Current number of processed clauses : 252
% 0.47/0.72 % Positive orientable unit clauses : 42
% 0.47/0.72 % Positive unorientable unit clauses: 1
% 0.47/0.72 % Negative unit clauses : 11
% 0.47/0.72 % Non-unit-clauses : 198
% 0.47/0.72 % Current number of unprocessed clauses: 487
% 0.47/0.72 % ...number of literals in the above : 2145
% 0.47/0.72 % Current number of archived formulas : 0
% 0.47/0.72 % Current number of archived clauses : 75
% 0.47/0.72 % Clause-clause subsumption calls (NU) : 18057
% 0.47/0.72 % Rec. Clause-clause subsumption calls : 8571
% 0.47/0.72 % Non-unit clause-clause subsumptions : 327
% 0.47/0.72 % Unit Clause-clause subsumption calls : 1128
% 0.47/0.72 % Rewrite failures with RHS unbound : 0
% 0.47/0.72 % BW rewrite match attempts : 22
% 0.47/0.72 % BW rewrite match successes : 8
% 0.47/0.72 % Condensation attempts : 0
% 0.47/0.72 % Condensation successes : 0
% 0.47/0.72 % Termbank termtop insertions : 24979
% 0.47/0.72 % Search garbage collected termcells : 656
% 0.47/0.72
% 0.47/0.72 % -------------------------------------------------
% 0.47/0.72 % User time : 0.104 s
% 0.47/0.72 % System time : 0.013 s
% 0.47/0.72 % Total time : 0.117 s
% 0.47/0.72 % Maximum resident set size: 3668 pages
% 0.47/0.72
% 0.47/0.72 % -------------------------------------------------
% 0.47/0.72 % User time : 0.420 s
% 0.47/0.72 % System time : 0.044 s
% 0.47/0.72 % Total time : 0.464 s
% 0.47/0.72 % Maximum resident set size: 4864 pages
% 0.47/0.72 % E exiting
%------------------------------------------------------------------------------