%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU339+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:11:32 PM UTC 2026
% Result : Theorem 4.79s 3.45s
% Output : CNFRefutation 4.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 19
% Syntax : Number of formulae : 113 ( 24 unt; 0 def)
% Number of atoms : 347 ( 20 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 412 ( 178 ~; 176 |; 31 &)
% ( 5 <=>; 22 =>; 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 : 14 ( 14 usr; 3 con; 0-2 aty)
% Number of variables : 242 ( 25 sgn 89 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fc1_subset_1,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
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(t25_orders_2,conjecture,
! [X1] :
( ( antisymmetric_relstr(X1)
& rel_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( related(X1,X2,X3)
& related(X1,X3,X2) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_orders_2) ).
fof(t106_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(rc1_subset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(d4_relat_2,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_antisymmetric_in(X1,X2)
<=> ! [X3,X4] :
( ( in(X3,X2)
& in(X4,X2)
& in(ordered_pair(X3,X4),X1)
& in(ordered_pair(X4,X3),X1) )
=> X3 = X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_2) ).
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(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(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] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(d6_orders_2,axiom,
! [X1] :
( rel_str(X1)
=> ( antisymmetric_relstr(X1)
<=> is_antisymmetric_in(the_InternalRel(X1),the_carrier(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_orders_2) ).
fof(c_0_19,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(c_0_20,plain,
! [X140,X141] :
( ( ~ element(X140,powerset(X141))
| subset(X140,X141) )
& ( ~ subset(X140,X141)
| element(X140,powerset(X141)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(c_0_21,plain,
! [X133,X134] :
( ~ in(X133,X134)
| element(X133,X134) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(c_0_22,plain,
! [X138,X139] :
( ~ element(X138,X139)
| empty(X139)
| in(X138,X139) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_23,plain,
! [X99,X100,X101] :
( ~ relation_of2_as_subset(X101,X99,X100)
| element(X101,powerset(cartesian_product2(X99,X100))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_relset_1])]) ).
fof(c_0_24,plain,
! [X113] : ~ empty(powerset(X113)),
inference(variable_rename,[status(thm)],[c_0_19]) ).
fof(c_0_25,plain,
! [X142,X143,X144] :
( ~ in(X142,X143)
| ~ element(X143,powerset(X144))
| element(X142,X144) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
cnf(c_0_26,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
( element(X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_33,plain,
( subset(X1,X2)
| ~ in(X1,powerset(X2)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,plain,
( in(X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_35,plain,
( element(X1,X2)
| ~ subset(X3,X2)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
( subset(X1,cartesian_product2(X2,X3))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
fof(c_0_37,plain,
! [X102] :
( ~ rel_str(X102)
| relation_of2_as_subset(the_InternalRel(X102),the_carrier(X102),the_carrier(X102)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_orders_2])]) ).
fof(c_0_38,plain,
! [X95,X96,X97] :
( ( ~ related(X95,X96,X97)
| in(ordered_pair(X96,X97),the_InternalRel(X95))
| ~ element(X97,the_carrier(X95))
| ~ element(X96,the_carrier(X95))
| ~ rel_str(X95) )
& ( ~ in(ordered_pair(X96,X97),the_InternalRel(X95))
| related(X95,X96,X97)
| ~ element(X97,the_carrier(X95))
| ~ element(X96,the_carrier(X95))
| ~ rel_str(X95) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_orders_2])])])]) ).
fof(c_0_39,plain,
! [X92,X93] : ordered_pair(X92,X93) = unordered_pair(unordered_pair(X92,X93),singleton(X92)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
cnf(c_0_40,plain,
( element(X1,cartesian_product2(X2,X3))
| ~ relation_of2_as_subset(X4,X2,X3)
| ~ in(X1,X4) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,plain,
( relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_42,plain,
( in(ordered_pair(X2,X3),the_InternalRel(X1))
| ~ related(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_43,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_44,plain,
! [X83,X84] : unordered_pair(X83,X84) = unordered_pair(X84,X83),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_45,plain,
( element(X1,cartesian_product2(the_carrier(X2),the_carrier(X2)))
| ~ rel_str(X2)
| ~ in(X1,the_InternalRel(X2)) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,plain,
( in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),the_InternalRel(X1))
| ~ rel_str(X1)
| ~ related(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1)) ),
inference(rw,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_48,negated_conjecture,
~ ! [X1] :
( ( antisymmetric_relstr(X1)
& rel_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( related(X1,X2,X3)
& related(X1,X3,X2) )
=> X2 = X3 ) ) ) ),
inference(assume_negation,[status(cth)],[t25_orders_2]) ).
fof(c_0_49,plain,
! [X129,X130,X131,X132] :
( ( in(X129,X131)
| ~ in(ordered_pair(X129,X130),cartesian_product2(X131,X132)) )
& ( in(X130,X132)
| ~ in(ordered_pair(X129,X130),cartesian_product2(X131,X132)) )
& ( ~ in(X129,X131)
| ~ in(X130,X132)
| in(ordered_pair(X129,X130),cartesian_product2(X131,X132)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t106_zfmisc_1])])]) ).
cnf(c_0_50,plain,
( empty(cartesian_product2(the_carrier(X1),the_carrier(X1)))
| in(X2,cartesian_product2(the_carrier(X1),the_carrier(X1)))
| ~ rel_str(X1)
| ~ in(X2,the_InternalRel(X1)) ),
inference(spm,[status(thm)],[c_0_28,c_0_45]) ).
cnf(c_0_51,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),the_InternalRel(X3))
| ~ related(X3,X1,X2)
| ~ rel_str(X3)
| ~ element(X2,the_carrier(X3))
| ~ element(X1,the_carrier(X3)) ),
inference(rw,[status(thm)],[c_0_46,c_0_47]) ).
fof(c_0_52,negated_conjecture,
( antisymmetric_relstr(esk12_0)
& rel_str(esk12_0)
& element(esk13_0,the_carrier(esk12_0))
& element(esk14_0,the_carrier(esk12_0))
& related(esk12_0,esk13_0,esk14_0)
& related(esk12_0,esk14_0,esk13_0)
& esk13_0 != esk14_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])])]) ).
cnf(c_0_53,plain,
( in(X1,X2)
| ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_54,plain,
( empty(cartesian_product2(the_carrier(X1),the_carrier(X1)))
| in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),cartesian_product2(the_carrier(X1),the_carrier(X1)))
| ~ related(X1,X2,X3)
| ~ rel_str(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1)) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_55,negated_conjecture,
element(esk14_0,the_carrier(esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_56,negated_conjecture,
rel_str(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
fof(c_0_57,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[rc1_subset_1]) ).
fof(c_0_58,plain,
! [X85,X86,X87,X88,X89] :
( ( ~ is_antisymmetric_in(X85,X86)
| ~ in(X87,X86)
| ~ in(X88,X86)
| ~ in(ordered_pair(X87,X88),X85)
| ~ in(ordered_pair(X88,X87),X85)
| X87 = X88
| ~ relation(X85) )
& ( in(esk1_2(X85,X89),X89)
| is_antisymmetric_in(X85,X89)
| ~ relation(X85) )
& ( in(esk2_2(X85,X89),X89)
| is_antisymmetric_in(X85,X89)
| ~ relation(X85) )
& ( in(ordered_pair(esk1_2(X85,X89),esk2_2(X85,X89)),X85)
| is_antisymmetric_in(X85,X89)
| ~ relation(X85) )
& ( in(ordered_pair(esk2_2(X85,X89),esk1_2(X85,X89)),X85)
| is_antisymmetric_in(X85,X89)
| ~ relation(X85) )
& ( esk1_2(X85,X89) != esk2_2(X85,X89)
| is_antisymmetric_in(X85,X89)
| ~ relation(X85) ) ),
inference(distribute,[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_59,plain,
! [X80,X81,X82] :
( ~ element(X82,powerset(cartesian_product2(X80,X81)))
| relation(X82) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])]) ).
fof(c_0_60,plain,
! [X145,X146,X147] :
( ~ in(X145,X146)
| ~ element(X146,powerset(X147))
| ~ empty(X147) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
cnf(c_0_61,plain,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),cartesian_product2(X4,X2)) ),
inference(rw,[status(thm)],[c_0_53,c_0_43]) ).
cnf(c_0_62,negated_conjecture,
( empty(cartesian_product2(the_carrier(esk12_0),the_carrier(esk12_0)))
| in(unordered_pair(singleton(X1),unordered_pair(X1,esk14_0)),cartesian_product2(the_carrier(esk12_0),the_carrier(esk12_0)))
| ~ related(esk12_0,X1,esk14_0)
| ~ element(X1,the_carrier(esk12_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56])]) ).
cnf(c_0_63,negated_conjecture,
related(esk12_0,esk13_0,esk14_0),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_64,negated_conjecture,
element(esk13_0,the_carrier(esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
fof(c_0_65,plain,
! [X119] :
( ( element(esk8_1(X119),powerset(X119))
| empty(X119) )
& ( ~ empty(esk8_1(X119))
| empty(X119) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])])]) ).
fof(c_0_66,plain,
! [X108] : element(esk6_1(X108),X108),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
cnf(c_0_67,plain,
( X3 = X4
| ~ is_antisymmetric_in(X1,X2)
| ~ in(X3,X2)
| ~ in(X4,X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(ordered_pair(X4,X3),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_68,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_69,plain,
( in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| ~ in(X1,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_70,plain,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_71,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_72,plain,
( in(X1,X2)
| ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),cartesian_product2(X4,X2)) ),
inference(rw,[status(thm)],[c_0_61,c_0_47]) ).
cnf(c_0_73,negated_conjecture,
( empty(cartesian_product2(the_carrier(esk12_0),the_carrier(esk12_0)))
| in(unordered_pair(singleton(esk13_0),unordered_pair(esk13_0,esk14_0)),cartesian_product2(the_carrier(esk12_0),the_carrier(esk12_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_74,plain,
( element(esk8_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_75,plain,
element(esk6_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
fof(c_0_76,plain,
! [X149,X150] :
( ~ in(X149,X150)
| ~ empty(X150) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
cnf(c_0_77,plain,
( X3 = X4
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X3,X2)
| ~ is_antisymmetric_in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X4,X3),singleton(X4)),X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_43]),c_0_43]) ).
cnf(c_0_78,plain,
( relation(X1)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_68,c_0_29]) ).
cnf(c_0_79,plain,
( in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X4))
| ~ in(X3,X4)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_69,c_0_43]) ).
cnf(c_0_80,plain,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X4)) ),
inference(rw,[status(thm)],[c_0_70,c_0_43]) ).
cnf(c_0_81,plain,
( ~ empty(cartesian_product2(X1,X2))
| ~ relation_of2_as_subset(X3,X1,X2)
| ~ in(X4,X3) ),
inference(spm,[status(thm)],[c_0_71,c_0_29]) ).
cnf(c_0_82,negated_conjecture,
( empty(cartesian_product2(the_carrier(esk12_0),the_carrier(esk12_0)))
| in(esk14_0,the_carrier(esk12_0)) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_83,plain,
( empty(X1)
| element(X2,X1)
| ~ in(X2,esk8_1(X1)) ),
inference(spm,[status(thm)],[c_0_31,c_0_74]) ).
cnf(c_0_84,plain,
( empty(X1)
| in(esk6_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_75]) ).
cnf(c_0_85,plain,
( empty(X1)
| ~ empty(esk8_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_86,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_87,plain,
( X1 = X2
| ~ is_antisymmetric_in(X3,X4)
| ~ relation(X3)
| ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X1)),X3)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X3)
| ~ in(X2,X4)
| ~ in(X1,X4) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_47]),c_0_47]) ).
cnf(c_0_88,plain,
( relation(the_InternalRel(X1))
| ~ rel_str(X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_41]) ).
cnf(c_0_89,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[c_0_79,c_0_47]) ).
cnf(c_0_90,plain,
( in(X1,X2)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),cartesian_product2(X2,X4)) ),
inference(rw,[status(thm)],[c_0_80,c_0_47]) ).
cnf(c_0_91,negated_conjecture,
( in(esk14_0,the_carrier(esk12_0))
| ~ relation_of2_as_subset(X1,the_carrier(esk12_0),the_carrier(esk12_0))
| ~ in(X2,X1) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_92,plain,
( empty(X1)
| element(esk6_1(esk8_1(X1)),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85]) ).
cnf(c_0_93,plain,
( ~ empty(the_InternalRel(X1))
| ~ related(X1,X2,X3)
| ~ rel_str(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1)) ),
inference(spm,[status(thm)],[c_0_86,c_0_51]) ).
cnf(c_0_94,negated_conjecture,
related(esk12_0,esk14_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_95,plain,
( X1 = X2
| ~ related(X3,X2,X1)
| ~ rel_str(X3)
| ~ is_antisymmetric_in(the_InternalRel(X3),X4)
| ~ element(X1,the_carrier(X3))
| ~ element(X2,the_carrier(X3))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),the_InternalRel(X3))
| ~ in(X2,X4)
| ~ in(X1,X4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_51]),c_0_88]) ).
fof(c_0_96,plain,
! [X94] :
( ( ~ antisymmetric_relstr(X94)
| is_antisymmetric_in(the_InternalRel(X94),the_carrier(X94))
| ~ rel_str(X94) )
& ( ~ is_antisymmetric_in(the_InternalRel(X94),the_carrier(X94))
| antisymmetric_relstr(X94)
| ~ rel_str(X94) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_orders_2])])]) ).
cnf(c_0_97,plain,
( ~ empty(cartesian_product2(X1,X2))
| ~ in(X3,X2)
| ~ in(X4,X1) ),
inference(spm,[status(thm)],[c_0_86,c_0_89]) ).
cnf(c_0_98,negated_conjecture,
( empty(cartesian_product2(the_carrier(esk12_0),the_carrier(esk12_0)))
| in(esk13_0,the_carrier(esk12_0)) ),
inference(spm,[status(thm)],[c_0_90,c_0_73]) ).
cnf(c_0_99,negated_conjecture,
( in(esk14_0,the_carrier(esk12_0))
| ~ in(X1,the_InternalRel(esk12_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_41]),c_0_56])]) ).
cnf(c_0_100,plain,
( empty(X1)
| in(esk6_1(esk8_1(X1)),X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_92]) ).
cnf(c_0_101,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_93,c_0_94]),c_0_56]),c_0_64]),c_0_55])]) ).
cnf(c_0_102,plain,
( X1 = X2
| ~ related(X3,X2,X1)
| ~ related(X3,X1,X2)
| ~ rel_str(X3)
| ~ is_antisymmetric_in(the_InternalRel(X3),X4)
| ~ element(X1,the_carrier(X3))
| ~ element(X2,the_carrier(X3))
| ~ in(X2,X4)
| ~ in(X1,X4) ),
inference(spm,[status(thm)],[c_0_95,c_0_51]) ).
cnf(c_0_103,plain,
( is_antisymmetric_in(the_InternalRel(X1),the_carrier(X1))
| ~ antisymmetric_relstr(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_104,negated_conjecture,
( in(esk13_0,the_carrier(esk12_0))
| ~ in(X1,the_carrier(esk12_0))
| ~ in(X2,the_carrier(esk12_0)) ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_105,negated_conjecture,
in(esk14_0,the_carrier(esk12_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_101]) ).
cnf(c_0_106,plain,
( X1 = X2
| ~ related(X3,X2,X1)
| ~ related(X3,X1,X2)
| ~ antisymmetric_relstr(X3)
| ~ rel_str(X3)
| ~ in(X2,the_carrier(X3))
| ~ in(X1,the_carrier(X3)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_27]),c_0_27]) ).
cnf(c_0_107,negated_conjecture,
antisymmetric_relstr(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_108,negated_conjecture,
( in(esk13_0,the_carrier(esk12_0))
| ~ in(X1,the_carrier(esk12_0)) ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_109,negated_conjecture,
( X1 = esk14_0
| ~ related(esk12_0,esk14_0,X1)
| ~ related(esk12_0,X1,esk14_0)
| ~ in(X1,the_carrier(esk12_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_105]),c_0_107]),c_0_56])]) ).
cnf(c_0_110,negated_conjecture,
in(esk13_0,the_carrier(esk12_0)),
inference(spm,[status(thm)],[c_0_108,c_0_105]) ).
cnf(c_0_111,negated_conjecture,
esk13_0 != esk14_0,
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_112,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_94]),c_0_63]),c_0_110])]),c_0_111]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU339+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n009.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:58:26 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 4.79/3.45 % Version : CSE_E---1.7
% 4.79/3.45 % Problem : theBenchmark.p
% 4.79/3.45 % SZS status Theorem for theBenchmark.p
% 4.79/3.45 % SZS output start CNFRefutation
% See solution above
% 4.79/3.47 % Total time : 2.366s
%------------------------------------------------------------------------------