%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU340+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 : n018.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 65.82s 10.02s
% Output : CNFRefutation 65.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 19
% Syntax : Number of formulae : 112 ( 24 unt; 0 def)
% Number of atoms : 363 ( 13 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 434 ( 183 ~; 186 |; 37 &)
% ( 4 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-2 aty)
% Number of variables : 214 ( 15 sgn 92 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(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(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(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(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( in(X1,X2)
| empty(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
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(t26_orders_2,conjecture,
! [X1] :
( ( rel_str(X1)
& transitive_relstr(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( ( related(X1,X3,X4)
& related(X1,X2,X3) )
=> related(X1,X2,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_orders_2) ).
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(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(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(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( empty(X2)
& in(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
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(d8_relat_2,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_transitive_in(X1,X2)
<=> ! [X3,X4,X5] :
( ( in(ordered_pair(X4,X5),X1)
& in(ordered_pair(X3,X4),X1)
& in(X5,X2)
& in(X4,X2)
& in(X3,X2) )
=> in(ordered_pair(X3,X5),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_2) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X2)
& X1 != X2
& empty(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(d5_orders_2,axiom,
! [X1] :
( rel_str(X1)
=> ( transitive_relstr(X1)
<=> is_transitive_in(the_InternalRel(X1),the_carrier(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_orders_2) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(c_0_19,plain,
! [X73,X74,X75] :
( element(X73,X75)
| ~ element(X74,powerset(X75))
| ~ in(X73,X74) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])])]) ).
fof(c_0_20,plain,
! [X29,X30,X31] :
( element(X31,powerset(cartesian_product2(X29,X30)))
| ~ relation_of2_as_subset(X31,X29,X30) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_relset_1])])]) ).
cnf(c_0_21,plain,
( ~ element(X2,powerset(X3))
| ~ in(X1,X2)
| element(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_22,plain,
( ~ relation_of2_as_subset(X1,X2,X3)
| element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_23,plain,
! [X32] :
( relation_of2_as_subset(the_InternalRel(X32),the_carrier(X32),the_carrier(X32))
| ~ rel_str(X32) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_orders_2])])]) ).
fof(c_0_24,plain,
! [X25,X26,X27] :
( ( ~ rel_str(X25)
| ~ element(X26,the_carrier(X25))
| ~ element(X27,the_carrier(X25))
| related(X25,X26,X27)
| ~ in(ordered_pair(X26,X27),the_InternalRel(X25)) )
& ( ~ rel_str(X25)
| ~ element(X26,the_carrier(X25))
| ~ element(X27,the_carrier(X25))
| in(ordered_pair(X26,X27),the_InternalRel(X25))
| ~ related(X25,X26,X27) ) ),
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])])])])]) ).
fof(c_0_25,plain,
! [X14,X15] : ordered_pair(X14,X15) = unordered_pair(unordered_pair(X14,X15),singleton(X14)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_26,plain,
! [X69,X70] :
( in(X69,X70)
| empty(X70)
| ~ element(X69,X70) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])])]) ).
cnf(c_0_27,plain,
( ~ in(X1,X4)
| ~ relation_of2_as_subset(X4,X2,X3)
| element(X1,cartesian_product2(X2,X3)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
( ~ rel_str(X1)
| relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,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_24]) ).
cnf(c_0_30,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_31,plain,
! [X11,X12] : unordered_pair(X11,X12) = unordered_pair(X12,X11),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_32,plain,
( ~ element(X1,X2)
| in(X1,X2)
| empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
( ~ in(X1,the_InternalRel(X2))
| ~ rel_str(X2)
| element(X1,cartesian_product2(the_carrier(X2),the_carrier(X2))) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,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_29,c_0_30]) ).
cnf(c_0_35,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_36,negated_conjecture,
~ ! [X1] :
( ( rel_str(X1)
& transitive_relstr(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ! [X4] :
( element(X4,the_carrier(X1))
=> ( ( related(X1,X3,X4)
& related(X1,X2,X3) )
=> related(X1,X2,X4) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t26_orders_2]) ).
cnf(c_0_37,plain,
( ~ in(X2,the_InternalRel(X1))
| ~ rel_str(X1)
| in(X2,cartesian_product2(the_carrier(X1),the_carrier(X1)))
| empty(cartesian_product2(the_carrier(X1),the_carrier(X1))) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,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_34,c_0_35]) ).
fof(c_0_39,negated_conjecture,
( ~ related(esk13_0,esk14_0,esk16_0)
& related(esk13_0,esk15_0,esk16_0)
& related(esk13_0,esk14_0,esk15_0)
& element(esk16_0,the_carrier(esk13_0))
& element(esk15_0,the_carrier(esk13_0))
& element(esk14_0,the_carrier(esk13_0))
& rel_str(esk13_0)
& transitive_relstr(esk13_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])])]) ).
fof(c_0_40,plain,
! [X59,X60,X61,X62] :
( ( in(ordered_pair(X59,X60),cartesian_product2(X61,X62))
| ~ in(X60,X62)
| ~ in(X59,X61) )
& ( ~ in(ordered_pair(X59,X60),cartesian_product2(X61,X62))
| in(X60,X62) )
& ( ~ in(ordered_pair(X59,X60),cartesian_product2(X61,X62))
| in(X59,X61) ) ),
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_41,plain,
( ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ rel_str(X1)
| ~ related(X1,X2,X3)
| in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),cartesian_product2(the_carrier(X1),the_carrier(X1)))
| empty(cartesian_product2(the_carrier(X1),the_carrier(X1))) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
element(esk16_0,the_carrier(esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_43,negated_conjecture,
rel_str(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_44,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( ~ empty(X2)
& element(X2,powerset(X1)) ) ),
inference(fof_simplification,[status(thm)],[rc1_subset_1]) ).
fof(c_0_45,plain,
! [X76,X77,X78] :
( ~ empty(X78)
| ~ element(X77,powerset(X78))
| ~ in(X76,X77) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])])]) ).
cnf(c_0_46,plain,
( ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_47,negated_conjecture,
( ~ element(X1,the_carrier(esk13_0))
| ~ related(esk13_0,X1,esk16_0)
| in(unordered_pair(unordered_pair(X1,esk16_0),singleton(X1)),cartesian_product2(the_carrier(esk13_0),the_carrier(esk13_0)))
| empty(cartesian_product2(the_carrier(esk13_0),the_carrier(esk13_0))) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]),c_0_35]) ).
cnf(c_0_48,negated_conjecture,
related(esk13_0,esk15_0,esk16_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_49,negated_conjecture,
element(esk15_0,the_carrier(esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_50,plain,
! [X49] :
( ( empty(X49)
| ~ empty(esk9_1(X49)) )
& ( empty(X49)
| element(esk9_1(X49),powerset(X49)) ) ),
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_44])])])])]) ).
fof(c_0_51,plain,
! [X38] : element(esk7_1(X38),X38),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
cnf(c_0_52,plain,
( ~ empty(X3)
| ~ element(X2,powerset(X3))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_53,plain,
( ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X4))
| in(X1,X2) ),
inference(rw,[status(thm)],[c_0_46,c_0_30]) ).
cnf(c_0_54,negated_conjecture,
( in(unordered_pair(unordered_pair(esk15_0,esk16_0),singleton(esk15_0)),cartesian_product2(the_carrier(esk13_0),the_carrier(esk13_0)))
| empty(cartesian_product2(the_carrier(esk13_0),the_carrier(esk13_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]) ).
cnf(c_0_55,plain,
( empty(X1)
| element(esk9_1(X1),powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_56,plain,
element(esk7_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
fof(c_0_57,plain,
! [X80,X81] :
( ~ empty(X81)
| ~ in(X80,X81) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])])]) ).
cnf(c_0_58,plain,
( ~ in(X4,X3)
| ~ relation_of2_as_subset(X3,X1,X2)
| ~ empty(cartesian_product2(X1,X2)) ),
inference(spm,[status(thm)],[c_0_52,c_0_22]) ).
cnf(c_0_59,negated_conjecture,
( in(esk15_0,the_carrier(esk13_0))
| empty(cartesian_product2(the_carrier(esk13_0),the_carrier(esk13_0))) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_60,plain,
( ~ in(X2,esk9_1(X1))
| element(X2,X1)
| empty(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_55]) ).
cnf(c_0_61,plain,
( in(esk7_1(X1),X1)
| empty(X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_56]) ).
cnf(c_0_62,plain,
( ~ empty(esk9_1(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
fof(c_0_63,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])])]) ).
cnf(c_0_64,plain,
( ~ empty(X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_65,negated_conjecture,
( ~ in(X2,X1)
| ~ relation_of2_as_subset(X1,the_carrier(esk13_0),the_carrier(esk13_0))
| in(esk15_0,the_carrier(esk13_0)) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_66,plain,
( element(esk7_1(esk9_1(X1)),X1)
| empty(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]) ).
fof(c_0_67,plain,
! [X16,X17,X18,X19,X20,X21] :
( ( ~ relation(X16)
| is_transitive_in(X16,X21)
| ~ in(ordered_pair(esk1_2(X16,X21),esk3_2(X16,X21)),X16) )
& ( ~ relation(X16)
| is_transitive_in(X16,X21)
| in(ordered_pair(esk2_2(X16,X21),esk3_2(X16,X21)),X16) )
& ( ~ relation(X16)
| is_transitive_in(X16,X21)
| in(ordered_pair(esk1_2(X16,X21),esk2_2(X16,X21)),X16) )
& ( ~ relation(X16)
| is_transitive_in(X16,X21)
| in(esk3_2(X16,X21),X21) )
& ( ~ relation(X16)
| is_transitive_in(X16,X21)
| in(esk2_2(X16,X21),X21) )
& ( ~ relation(X16)
| is_transitive_in(X16,X21)
| in(esk1_2(X16,X21),X21) )
& ( ~ relation(X16)
| in(ordered_pair(X18,X20),X16)
| ~ in(ordered_pair(X19,X20),X16)
| ~ in(ordered_pair(X18,X19),X16)
| ~ in(X20,X17)
| ~ in(X19,X17)
| ~ in(X18,X17)
| ~ is_transitive_in(X16,X17) ) ),
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)],[d8_relat_2])])])])])])]) ).
cnf(c_0_68,plain,
( ~ element(X1,powerset(cartesian_product2(X2,X3)))
| relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_69,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_64,c_0_34]) ).
cnf(c_0_70,negated_conjecture,
( ~ in(X1,the_InternalRel(esk13_0))
| in(esk15_0,the_carrier(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_28]),c_0_43])]) ).
cnf(c_0_71,plain,
( in(esk7_1(esk9_1(X1)),X1)
| empty(X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_66]) ).
cnf(c_0_72,plain,
( ~ relation(X1)
| ~ in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(X5,X2)
| ~ in(X4,X2)
| ~ in(X3,X2)
| ~ is_transitive_in(X1,X2)
| in(ordered_pair(X3,X5),X1) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_73,plain,
( ~ relation_of2_as_subset(X1,X2,X3)
| relation(X1) ),
inference(spm,[status(thm)],[c_0_68,c_0_22]) ).
cnf(c_0_74,negated_conjecture,
( ~ element(X1,the_carrier(esk13_0))
| ~ related(esk13_0,X1,esk15_0)
| ~ empty(the_InternalRel(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_49]),c_0_43])]) ).
cnf(c_0_75,negated_conjecture,
( in(esk15_0,the_carrier(esk13_0))
| empty(the_InternalRel(esk13_0)) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
fof(c_0_76,plain,
! [X1,X2] :
~ ( empty(X2)
& X1 != X2
& empty(X1) ),
inference(fof_simplification,[status(thm)],[t8_boole]) ).
cnf(c_0_77,plain,
( ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),X1)
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X1)
| ~ is_transitive_in(X1,X2)
| ~ in(X3,X2)
| ~ in(X4,X2)
| ~ in(X5,X2)
| ~ relation(X1)
| in(unordered_pair(unordered_pair(X3,X5),singleton(X3)),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_30]),c_0_30]),c_0_30]) ).
cnf(c_0_78,plain,
( ~ rel_str(X1)
| relation(the_InternalRel(X1)) ),
inference(spm,[status(thm)],[c_0_73,c_0_28]) ).
cnf(c_0_79,negated_conjecture,
( ~ element(X1,the_carrier(esk13_0))
| ~ related(esk13_0,X1,esk15_0)
| in(esk15_0,the_carrier(esk13_0)) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_80,negated_conjecture,
related(esk13_0,esk14_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_81,negated_conjecture,
element(esk14_0,the_carrier(esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_82,plain,
! [X82,X83] :
( ~ empty(X83)
| X82 = X83
| ~ empty(X82) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_76])])]) ).
cnf(c_0_83,plain,
( ~ in(X1,X5)
| ~ in(X4,X5)
| ~ in(X2,X5)
| ~ in(unordered_pair(unordered_pair(X1,X4),singleton(X1)),the_InternalRel(X3))
| ~ element(X4,the_carrier(X3))
| ~ element(X2,the_carrier(X3))
| ~ rel_str(X3)
| ~ is_transitive_in(the_InternalRel(X3),X5)
| ~ related(X3,X4,X2)
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),the_InternalRel(X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_34]),c_0_78]) ).
fof(c_0_84,plain,
! [X13] :
( ( ~ rel_str(X13)
| transitive_relstr(X13)
| ~ is_transitive_in(the_InternalRel(X13),the_carrier(X13)) )
& ( ~ rel_str(X13)
| is_transitive_in(the_InternalRel(X13),the_carrier(X13))
| ~ transitive_relstr(X13) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_orders_2])])])]) ).
fof(c_0_85,plain,
! [X63,X64] :
( element(X63,X64)
| ~ in(X63,X64) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])])]) ).
cnf(c_0_86,negated_conjecture,
in(esk15_0,the_carrier(esk13_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81])]) ).
cnf(c_0_87,plain,
( ~ empty(X2)
| ~ empty(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_88,negated_conjecture,
( in(esk14_0,the_carrier(esk13_0))
| empty(the_carrier(esk13_0)) ),
inference(spm,[status(thm)],[c_0_32,c_0_81]) ).
cnf(c_0_89,plain,
( ~ in(X2,esk7_1(powerset(X1)))
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_56]) ).
cnf(c_0_90,plain,
( ~ in(X1,X5)
| ~ in(X4,X5)
| ~ in(X2,X5)
| ~ element(X1,the_carrier(X3))
| ~ element(X4,the_carrier(X3))
| ~ element(X2,the_carrier(X3))
| ~ rel_str(X3)
| ~ is_transitive_in(the_InternalRel(X3),X5)
| ~ related(X3,X1,X4)
| ~ related(X3,X4,X2)
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),the_InternalRel(X3)) ),
inference(spm,[status(thm)],[c_0_83,c_0_34]) ).
cnf(c_0_91,plain,
( ~ rel_str(X1)
| ~ transitive_relstr(X1)
| is_transitive_in(the_InternalRel(X1),the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_92,plain,
( ~ in(X1,X2)
| element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_93,negated_conjecture,
( in(esk16_0,the_carrier(esk13_0))
| empty(the_carrier(esk13_0)) ),
inference(spm,[status(thm)],[c_0_32,c_0_42]) ).
cnf(c_0_94,negated_conjecture,
~ empty(the_carrier(esk13_0)),
inference(spm,[status(thm)],[c_0_64,c_0_86]) ).
cnf(c_0_95,negated_conjecture,
( ~ empty(X1)
| in(esk14_0,the_carrier(esk13_0))
| X1 = the_carrier(esk13_0) ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_96,plain,
( ~ empty(X1)
| empty(esk7_1(powerset(X1))) ),
inference(spm,[status(thm)],[c_0_89,c_0_61]) ).
cnf(c_0_97,plain,
( ~ in(X1,the_carrier(X3))
| ~ in(X4,the_carrier(X3))
| ~ in(X2,the_carrier(X3))
| ~ rel_str(X3)
| ~ transitive_relstr(X3)
| ~ related(X3,X1,X4)
| ~ related(X3,X4,X2)
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),the_InternalRel(X3)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]),c_0_92]),c_0_92]) ).
cnf(c_0_98,negated_conjecture,
in(esk16_0,the_carrier(esk13_0)),
inference(sr,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_99,negated_conjecture,
transitive_relstr(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_100,negated_conjecture,
( ~ empty(X1)
| in(esk14_0,the_carrier(esk13_0))
| esk7_1(powerset(X1)) = the_carrier(esk13_0) ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_101,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).
cnf(c_0_102,plain,
( ~ rel_str(X3)
| ~ element(X1,the_carrier(X3))
| ~ element(X2,the_carrier(X3))
| ~ in(ordered_pair(X1,X2),the_InternalRel(X3))
| related(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_103,negated_conjecture,
( ~ in(X1,the_carrier(esk13_0))
| ~ in(X2,the_carrier(esk13_0))
| ~ related(esk13_0,X1,X2)
| ~ related(esk13_0,X2,esk16_0)
| in(unordered_pair(unordered_pair(X1,esk16_0),singleton(X1)),the_InternalRel(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_99]),c_0_43])]) ).
cnf(c_0_104,negated_conjecture,
( in(esk14_0,the_carrier(esk13_0))
| esk7_1(powerset(empty_set)) = the_carrier(esk13_0) ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_105,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),the_InternalRel(X3))
| ~ element(X1,the_carrier(X3))
| ~ element(X2,the_carrier(X3))
| ~ rel_str(X3)
| related(X3,X1,X2) ),
inference(rw,[status(thm)],[c_0_102,c_0_30]) ).
cnf(c_0_106,negated_conjecture,
( ~ in(X1,the_carrier(esk13_0))
| ~ related(esk13_0,X1,esk15_0)
| in(unordered_pair(unordered_pair(X1,esk16_0),singleton(X1)),the_InternalRel(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_48]),c_0_86])]) ).
cnf(c_0_107,negated_conjecture,
( ~ in(X1,the_carrier(esk13_0))
| in(esk14_0,the_carrier(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_104]),c_0_101])]) ).
cnf(c_0_108,negated_conjecture,
~ related(esk13_0,esk14_0,esk16_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_109,negated_conjecture,
( ~ in(X1,the_carrier(esk13_0))
| ~ related(esk13_0,X1,esk15_0)
| related(esk13_0,X1,esk16_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_43]),c_0_42])]),c_0_92]) ).
cnf(c_0_110,negated_conjecture,
in(esk14_0,the_carrier(esk13_0)),
inference(spm,[status(thm)],[c_0_107,c_0_86]) ).
cnf(c_0_111,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_80]),c_0_110])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU340+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n018.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 06:15:45 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 65.82/10.01 % Version: 3.5.1
% 65.82/10.01 % Preprocessing class: FSMSSMSSSSSNFFN.
% 65.82/10.01 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 65.82/10.01 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 65.82/10.01 % Starting new_bool_3 with 300s (1) cores
% 65.82/10.01 % Starting new_bool_1 with 300s (1) cores
% 65.82/10.01 % Starting sh5l with 300s (1) cores
% 65.82/10.01 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1148858 completed with status 0
% 65.82/10.01 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 65.82/10.01 % Preprocessing class: FSMSSMSSSSSNFFN.
% 65.82/10.01 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 65.82/10.01 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 65.82/10.01 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 65.82/10.01 % No SInE strategy applied
% 65.82/10.01 % Search class: FGHSM-FFMM21-MFFFFFNN
% 65.82/10.01 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 65.82/10.01 % Starting SubtermCWHack with 136s (1) cores
% 65.82/10.01 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 65.82/10.01 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 65.82/10.02 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 65.82/10.02 % Starting new_bool_3 with 136s (1) cores
% 65.82/10.02 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1148865 completed with status 0
% 65.82/10.02 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 65.82/10.02 % Preprocessing class: FSMSSMSSSSSNFFN.
% 65.82/10.02 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 65.82/10.02 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 65.82/10.02 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 65.82/10.02 % No SInE strategy applied
% 65.82/10.02 % Search class: FGHSM-FFMM21-MFFFFFNN
% 65.82/10.02 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 65.82/10.02 % Starting SubtermCWHack with 136s (1) cores
% 65.82/10.02 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 65.82/10.02 % Preprocessing time : 0.001 s
% 65.82/10.02 % Presaturation interreduction done
% 65.82/10.02
% 65.82/10.02 % Proof found!
% 65.82/10.02 % SZS status Theorem
% 65.82/10.02 % SZS output start CNFRefutation
% See solution above
% 65.82/10.02 % Parsed axioms : 46
% 65.82/10.02 % Removed by relevancy pruning/SinE : 0
% 65.82/10.02 % Initial clauses : 67
% 65.82/10.02 % Removed in clause preprocessing : 11
% 65.82/10.02 % Initial clauses in saturation : 56
% 65.82/10.02 % Processed clauses : 62859
% 65.82/10.02 % ...of these trivial : 77
% 65.82/10.02 % ...subsumed : 56399
% 65.82/10.02 % ...remaining for further processing : 6383
% 65.82/10.02 % Other redundant clauses eliminated : 0
% 65.82/10.02 % Clauses deleted for lack of memory : 0
% 65.82/10.02 % Backward-subsumed : 902
% 65.82/10.02 % Backward-rewritten : 2406
% 65.82/10.02 % Generated clauses : 802985
% 65.82/10.02 % ...of the previous two non-redundant : 788377
% 65.82/10.02 % ...aggressively subsumed : 0
% 65.82/10.02 % Contextual simplify-reflections : 265
% 65.82/10.02 % Paramodulations : 802983
% 65.82/10.02 % Factorizations : 0
% 65.82/10.02 % NegExts : 0
% 65.82/10.02 % Equation resolutions : 0
% 65.82/10.02 % Disequality decompositions : 0
% 65.82/10.02 % Total rewrite steps : 84965
% 65.82/10.02 % ...of those cached : 84603
% 65.82/10.02 % Propositional unsat checks : 1
% 65.82/10.02 % Propositional check models : 0
% 65.82/10.02 % Propositional check unsatisfiable : 0
% 65.82/10.02 % Propositional clauses : 0
% 65.82/10.02 % Propositional clauses after purity: 0
% 65.82/10.02 % Propositional unsat core size : 0
% 65.82/10.02 % Propositional preprocessing time : 0.000
% 65.82/10.02 % Propositional encoding time : 0.435
% 65.82/10.02 % Propositional solver time : 0.249
% 65.82/10.02 % Success case prop preproc time : 0.000
% 65.82/10.02 % Success case prop encoding time : 0.000
% 65.82/10.02 % Success case prop solver time : 0.000
% 65.82/10.02 % Current number of processed clauses : 3017
% 65.82/10.02 % Positive orientable unit clauses : 49
% 65.82/10.02 % Positive unorientable unit clauses: 1
% 65.82/10.02 % Negative unit clauses : 15
% 65.82/10.02 % Non-unit-clauses : 2952
% 65.82/10.02 % Current number of unprocessed clauses: 713312
% 65.82/10.02 % ...number of literals in the above : 2758596
% 65.82/10.02 % Current number of archived formulas : 0
% 65.82/10.02 % Current number of archived clauses : 3367
% 65.82/10.02 % Clause-clause subsumption calls (NU) : 7756396
% 65.82/10.02 % Rec. Clause-clause subsumption calls : 4368265
% 65.82/10.02 % Non-unit clause-clause subsumptions : 51815
% 65.82/10.02 % Unit Clause-clause subsumption calls : 18161
% 65.82/10.02 % Rewrite failures with RHS unbound : 0
% 65.82/10.02 % BW rewrite match attempts : 239
% 65.82/10.02 % BW rewrite match successes : 57
% 65.82/10.02 % Condensation attempts : 0
% 65.82/10.02 % Condensation successes : 0
% 65.82/10.02 % Termbank termtop insertions : 23184586
% 65.82/10.02 % Search garbage collected termcells : 699
% 65.82/10.02
% 65.82/10.02 % -------------------------------------------------
% 65.82/10.02 % User time : 8.985 s
% 65.82/10.02 % System time : 0.391 s
% 65.82/10.02 % Total time : 9.376 s
% 65.82/10.02 % Maximum resident set size: 3672 pages
% 65.82/10.02
% 65.82/10.02 % -------------------------------------------------
% 65.82/10.02 % User time : 45.603 s
% 65.82/10.02 % System time : 1.390 s
% 65.82/10.02 % Total time : 46.992 s
% 65.82/10.02 % Maximum resident set size: 4864 pages
% 65.82/10.02 % E exiting
%------------------------------------------------------------------------------