%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU363+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 : n011.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 05:12:04 PM UTC 2026
% Result : Theorem 6.24s 4.51s
% Output : CNFRefutation 6.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 20
% Syntax : Number of formulae : 132 ( 32 unt; 0 def)
% Number of atoms : 368 ( 20 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 379 ( 143 ~; 158 |; 41 &)
% ( 5 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 208 ( 22 sgn 96 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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_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(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(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(t61_yellow_0,conjecture,
! [X1] :
( rel_str(X1)
=> ! [X2] :
( ( full_subrelstr(X2,X1)
& subrelstr(X2,X1) )
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ! [X4] :
( element(X4,the_carrier(X1))
=> ! [X5] :
( element(X5,the_carrier(X2))
=> ! [X6] :
( element(X6,the_carrier(X2))
=> ( ( X5 = X3
& X6 = X4
& related(X1,X3,X4)
& in(X5,the_carrier(X2))
& in(X6,the_carrier(X2)) )
=> related(X2,X5,X6) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_yellow_0) ).
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(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(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(t16_wellord1,axiom,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_restriction(X3,X2))
<=> ( in(X1,X3)
& in(X1,cartesian_product2(X2,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_wellord1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
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(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(rc4_finset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2)
& finite(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
fof(redefinition_k1_toler_1,axiom,
! [X1,X2] :
( relation(X1)
=> relation_restriction_as_relation_of(X1,X2) = relation_restriction(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_toler_1) ).
fof(d14_yellow_0,axiom,
! [X1] :
( rel_str(X1)
=> ! [X2] :
( subrelstr(X2,X1)
=> ( full_subrelstr(X2,X1)
<=> the_InternalRel(X2) = relation_restriction_as_relation_of(the_InternalRel(X1),the_carrier(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_yellow_0) ).
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(dt_m1_yellow_0,axiom,
! [X1] :
( rel_str(X1)
=> ! [X2] :
( subrelstr(X2,X1)
=> rel_str(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_yellow_0) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(c_0_20,plain,
! [X153,X154,X155] :
( ~ in(X153,X154)
| ~ element(X154,powerset(X155))
| element(X153,X155) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(c_0_21,plain,
! [X109,X110,X111] :
( ~ relation_of2_as_subset(X111,X109,X110)
| element(X111,powerset(cartesian_product2(X109,X110))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_relset_1])]) ).
cnf(c_0_22,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_23,plain,
( element(X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_24,plain,
! [X112] :
( ~ rel_str(X112)
| relation_of2_as_subset(the_InternalRel(X112),the_carrier(X112),the_carrier(X112)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_orders_2])]) ).
fof(c_0_25,plain,
! [X149,X150] :
( ~ element(X149,X150)
| empty(X150)
| in(X149,X150) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
cnf(c_0_26,plain,
( element(X1,cartesian_product2(X2,X3))
| ~ relation_of2_as_subset(X4,X2,X3)
| ~ in(X1,X4) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
( relation_of2_as_subset(the_InternalRel(X1),the_carrier(X1),the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_28,negated_conjecture,
~ ! [X1] :
( rel_str(X1)
=> ! [X2] :
( ( full_subrelstr(X2,X1)
& subrelstr(X2,X1) )
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ! [X4] :
( element(X4,the_carrier(X1))
=> ! [X5] :
( element(X5,the_carrier(X2))
=> ! [X6] :
( element(X6,the_carrier(X2))
=> ( ( X5 = X3
& X6 = X4
& related(X1,X3,X4)
& in(X5,the_carrier(X2))
& in(X6,the_carrier(X2)) )
=> related(X2,X5,X6) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t61_yellow_0]) ).
cnf(c_0_29,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,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_26,c_0_27]) ).
fof(c_0_31,plain,
! [X99,X100,X101] :
( ( ~ related(X99,X100,X101)
| in(ordered_pair(X100,X101),the_InternalRel(X99))
| ~ element(X101,the_carrier(X99))
| ~ element(X100,the_carrier(X99))
| ~ rel_str(X99) )
& ( ~ in(ordered_pair(X100,X101),the_InternalRel(X99))
| related(X99,X100,X101)
| ~ element(X101,the_carrier(X99))
| ~ element(X100,the_carrier(X99))
| ~ rel_str(X99) ) ),
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_32,negated_conjecture,
( rel_str(esk12_0)
& full_subrelstr(esk13_0,esk12_0)
& subrelstr(esk13_0,esk12_0)
& element(esk14_0,the_carrier(esk12_0))
& element(esk15_0,the_carrier(esk12_0))
& element(esk16_0,the_carrier(esk13_0))
& element(esk17_0,the_carrier(esk13_0))
& esk16_0 = esk14_0
& esk17_0 = esk15_0
& related(esk12_0,esk14_0,esk15_0)
& in(esk16_0,the_carrier(esk13_0))
& in(esk17_0,the_carrier(esk13_0))
& ~ related(esk13_0,esk16_0,esk17_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])]) ).
cnf(c_0_33,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_29,c_0_30]) ).
cnf(c_0_34,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_31]) ).
cnf(c_0_35,negated_conjecture,
element(esk15_0,the_carrier(esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,negated_conjecture,
esk17_0 = esk15_0,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,plain,
( empty(powerset(cartesian_product2(X1,X2)))
| in(X3,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_23]) ).
cnf(c_0_38,plain,
( empty(cartesian_product2(the_carrier(X1),the_carrier(X1)))
| in(ordered_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_33,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
element(esk17_0,the_carrier(esk12_0)),
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
rel_str(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_41,negated_conjecture,
related(esk12_0,esk14_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_42,plain,
! [X92,X93,X94] :
( ~ element(X94,powerset(cartesian_product2(X92,X93)))
| relation(X94) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])]) ).
fof(c_0_43,plain,
! [X151,X152] :
( ( ~ element(X151,powerset(X152))
| subset(X151,X152) )
& ( ~ subset(X151,X152)
| element(X151,powerset(X152)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(c_0_44,plain,
! [X147,X148] :
( ~ in(X147,X148)
| element(X147,X148) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
cnf(c_0_45,plain,
( empty(powerset(cartesian_product2(the_carrier(X1),the_carrier(X1))))
| in(the_InternalRel(X1),powerset(cartesian_product2(the_carrier(X1),the_carrier(X1))))
| ~ rel_str(X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_27]) ).
fof(c_0_46,plain,
! [X144,X145,X146] :
( ( in(X144,X146)
| ~ in(X144,relation_restriction(X146,X145))
| ~ relation(X146) )
& ( in(X144,cartesian_product2(X145,X145))
| ~ in(X144,relation_restriction(X146,X145))
| ~ relation(X146) )
& ( ~ in(X144,X146)
| ~ in(X144,cartesian_product2(X145,X145))
| in(X144,relation_restriction(X146,X145))
| ~ relation(X146) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t16_wellord1])])]) ).
cnf(c_0_47,negated_conjecture,
( empty(cartesian_product2(the_carrier(esk12_0),the_carrier(esk12_0)))
| in(ordered_pair(X1,esk17_0),cartesian_product2(the_carrier(esk12_0),the_carrier(esk12_0)))
| ~ related(esk12_0,X1,esk17_0)
| ~ element(X1,the_carrier(esk12_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).
cnf(c_0_48,negated_conjecture,
related(esk12_0,esk14_0,esk17_0),
inference(rw,[status(thm)],[c_0_41,c_0_36]) ).
cnf(c_0_49,negated_conjecture,
element(esk14_0,the_carrier(esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_50,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_51,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
fof(c_0_52,plain,
! [X139] : subset(X139,X139),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_53,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_54,negated_conjecture,
( empty(powerset(cartesian_product2(the_carrier(esk12_0),the_carrier(esk12_0))))
| in(the_InternalRel(esk12_0),powerset(cartesian_product2(the_carrier(esk12_0),the_carrier(esk12_0)))) ),
inference(spm,[status(thm)],[c_0_45,c_0_40]) ).
cnf(c_0_55,plain,
( in(X1,relation_restriction(X2,X3))
| ~ in(X1,X2)
| ~ in(X1,cartesian_product2(X3,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_56,negated_conjecture,
( empty(cartesian_product2(the_carrier(esk12_0),the_carrier(esk12_0)))
| in(ordered_pair(esk14_0,esk17_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_47,c_0_48]),c_0_49])]) ).
fof(c_0_57,plain,
! [X140,X141,X142,X143] :
( ( in(X140,X142)
| ~ in(ordered_pair(X140,X141),cartesian_product2(X142,X143)) )
& ( in(X141,X143)
| ~ in(ordered_pair(X140,X141),cartesian_product2(X142,X143)) )
& ( ~ in(X140,X142)
| ~ in(X141,X143)
| in(ordered_pair(X140,X141),cartesian_product2(X142,X143)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t106_zfmisc_1])])]) ).
cnf(c_0_58,plain,
( relation(X1)
| ~ subset(X1,cartesian_product2(X2,X3)) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_59,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
fof(c_0_60,plain,
! [X165] :
( ~ empty(X165)
| X165 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
cnf(c_0_61,negated_conjecture,
( element(the_InternalRel(esk12_0),powerset(cartesian_product2(the_carrier(esk12_0),the_carrier(esk12_0))))
| empty(powerset(cartesian_product2(the_carrier(esk12_0),the_carrier(esk12_0)))) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_62,negated_conjecture,
( empty(cartesian_product2(the_carrier(esk12_0),the_carrier(esk12_0)))
| in(ordered_pair(esk14_0,esk17_0),relation_restriction(X1,the_carrier(esk12_0)))
| ~ relation(X1)
| ~ in(ordered_pair(esk14_0,esk17_0),X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_63,plain,
( in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| ~ in(X1,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_64,plain,
relation(cartesian_product2(X1,X2)),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_65,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_66,negated_conjecture,
( relation(the_InternalRel(esk12_0))
| empty(powerset(cartesian_product2(the_carrier(esk12_0),the_carrier(esk12_0)))) ),
inference(spm,[status(thm)],[c_0_50,c_0_61]) ).
cnf(c_0_67,negated_conjecture,
( empty(cartesian_product2(the_carrier(esk12_0),the_carrier(esk12_0)))
| in(ordered_pair(esk14_0,esk17_0),relation_restriction(cartesian_product2(X1,X2),the_carrier(esk12_0)))
| ~ in(esk17_0,X2)
| ~ in(esk14_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64])]) ).
cnf(c_0_68,negated_conjecture,
in(esk17_0,the_carrier(esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_69,negated_conjecture,
in(esk16_0,the_carrier(esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_70,negated_conjecture,
esk16_0 = esk14_0,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_71,plain,
( relation(X1)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_50,c_0_23]) ).
cnf(c_0_72,negated_conjecture,
( powerset(cartesian_product2(the_carrier(esk12_0),the_carrier(esk12_0))) = empty_set
| relation(the_InternalRel(esk12_0)) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_73,negated_conjecture,
( empty(cartesian_product2(the_carrier(esk12_0),the_carrier(esk12_0)))
| in(ordered_pair(esk14_0,esk17_0),relation_restriction(cartesian_product2(X1,the_carrier(esk13_0)),the_carrier(esk12_0)))
| ~ in(esk14_0,X1) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_74,negated_conjecture,
in(esk14_0,the_carrier(esk13_0)),
inference(rw,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_75,plain,
( relation(the_InternalRel(X1))
| ~ rel_str(X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_27]) ).
cnf(c_0_76,negated_conjecture,
( relation(the_InternalRel(esk12_0))
| element(X1,empty_set)
| ~ relation_of2_as_subset(X1,the_carrier(esk12_0),the_carrier(esk12_0)) ),
inference(spm,[status(thm)],[c_0_23,c_0_72]) ).
cnf(c_0_77,plain,
( in(X1,X2)
| ~ in(X1,relation_restriction(X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_78,negated_conjecture,
( empty(cartesian_product2(the_carrier(esk12_0),the_carrier(esk12_0)))
| in(ordered_pair(esk14_0,esk17_0),relation_restriction(cartesian_product2(the_carrier(esk13_0),the_carrier(esk13_0)),the_carrier(esk12_0))) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_79,negated_conjecture,
( empty(cartesian_product2(the_carrier(esk12_0),the_carrier(esk12_0)))
| in(ordered_pair(esk14_0,esk17_0),relation_restriction(the_InternalRel(X1),the_carrier(esk12_0)))
| ~ related(X1,esk14_0,esk17_0)
| ~ rel_str(X1)
| ~ element(esk17_0,the_carrier(X1))
| ~ element(esk14_0,the_carrier(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_34]),c_0_75]) ).
cnf(c_0_80,negated_conjecture,
( relation(the_InternalRel(esk12_0))
| relation(X1)
| ~ element(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_50,c_0_72]) ).
cnf(c_0_81,negated_conjecture,
( relation(the_InternalRel(esk12_0))
| element(the_InternalRel(esk12_0),empty_set) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_27]),c_0_40])]) ).
fof(c_0_82,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2)
& finite(X2) ) ),
inference(fof_simplification,[status(thm)],[rc4_finset_1]) ).
cnf(c_0_83,negated_conjecture,
( empty(cartesian_product2(the_carrier(esk12_0),the_carrier(esk12_0)))
| in(ordered_pair(esk14_0,esk17_0),cartesian_product2(the_carrier(esk13_0),the_carrier(esk13_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_64])]) ).
cnf(c_0_84,negated_conjecture,
( empty(cartesian_product2(the_carrier(esk12_0),the_carrier(esk12_0)))
| in(ordered_pair(esk14_0,esk17_0),relation_restriction(the_InternalRel(esk12_0),the_carrier(esk12_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_48]),c_0_40]),c_0_39]),c_0_49])]) ).
cnf(c_0_85,negated_conjecture,
relation(the_InternalRel(esk12_0)),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
fof(c_0_86,plain,
! [X134,X135] :
( ~ relation(X134)
| relation_restriction_as_relation_of(X134,X135) = relation_restriction(X134,X135) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k1_toler_1])]) ).
fof(c_0_87,plain,
! [X97,X98] :
( ( ~ full_subrelstr(X98,X97)
| the_InternalRel(X98) = relation_restriction_as_relation_of(the_InternalRel(X97),the_carrier(X98))
| ~ subrelstr(X98,X97)
| ~ rel_str(X97) )
& ( the_InternalRel(X98) != relation_restriction_as_relation_of(the_InternalRel(X97),the_carrier(X98))
| full_subrelstr(X98,X97)
| ~ subrelstr(X98,X97)
| ~ rel_str(X97) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d14_yellow_0])])])]) ).
fof(c_0_88,plain,
! [X156,X157,X158] :
( ~ in(X156,X157)
| ~ element(X157,powerset(X158))
| ~ empty(X158) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(c_0_89,plain,
! [X132] :
( ( element(esk11_1(X132),powerset(X132))
| empty(X132) )
& ( ~ empty(esk11_1(X132))
| empty(X132) )
& ( finite(esk11_1(X132))
| empty(X132) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_82])])])]) ).
fof(c_0_90,plain,
! [X118] : element(esk4_1(X118),X118),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
cnf(c_0_91,negated_conjecture,
( empty(cartesian_product2(the_carrier(esk12_0),the_carrier(esk12_0)))
| in(ordered_pair(esk14_0,esk17_0),relation_restriction(X1,the_carrier(esk13_0)))
| ~ relation(X1)
| ~ in(ordered_pair(esk14_0,esk17_0),X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_83]) ).
cnf(c_0_92,negated_conjecture,
( empty(cartesian_product2(the_carrier(esk12_0),the_carrier(esk12_0)))
| in(ordered_pair(esk14_0,esk17_0),the_InternalRel(esk12_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_84]),c_0_85])]) ).
cnf(c_0_93,plain,
( relation_restriction_as_relation_of(X1,X2) = relation_restriction(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_94,plain,
( the_InternalRel(X1) = relation_restriction_as_relation_of(the_InternalRel(X2),the_carrier(X1))
| ~ full_subrelstr(X1,X2)
| ~ subrelstr(X1,X2)
| ~ rel_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
fof(c_0_95,plain,
! [X107,X108] :
( ~ rel_str(X107)
| ~ subrelstr(X108,X107)
| rel_str(X108) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m1_yellow_0])])]) ).
cnf(c_0_96,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_97,plain,
( in(X1,X2)
| ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_98,plain,
( element(esk11_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_99,plain,
element(esk4_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
fof(c_0_100,plain,
! [X166,X167] :
( ~ in(X166,X167)
| ~ empty(X167) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
cnf(c_0_101,negated_conjecture,
( empty(cartesian_product2(the_carrier(esk12_0),the_carrier(esk12_0)))
| in(ordered_pair(esk14_0,esk17_0),relation_restriction(the_InternalRel(esk12_0),the_carrier(esk13_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_85])]) ).
cnf(c_0_102,plain,
( relation_restriction(the_InternalRel(X1),the_carrier(X2)) = the_InternalRel(X2)
| ~ full_subrelstr(X2,X1)
| ~ subrelstr(X2,X1)
| ~ rel_str(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_75]) ).
cnf(c_0_103,negated_conjecture,
full_subrelstr(esk13_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_104,negated_conjecture,
subrelstr(esk13_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_105,plain,
( rel_str(X2)
| ~ rel_str(X1)
| ~ subrelstr(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_106,negated_conjecture,
element(esk16_0,the_carrier(esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_107,negated_conjecture,
~ related(esk13_0,esk16_0,esk17_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_108,plain,
( ~ relation_of2_as_subset(X1,X2,X3)
| ~ empty(cartesian_product2(X2,X3))
| ~ in(X4,X1) ),
inference(spm,[status(thm)],[c_0_96,c_0_23]) ).
cnf(c_0_109,negated_conjecture,
( empty(cartesian_product2(the_carrier(esk12_0),the_carrier(esk12_0)))
| in(esk17_0,the_carrier(esk12_0)) ),
inference(spm,[status(thm)],[c_0_97,c_0_56]) ).
cnf(c_0_110,plain,
( element(X1,X2)
| empty(X2)
| ~ in(X1,esk11_1(X2)) ),
inference(spm,[status(thm)],[c_0_22,c_0_98]) ).
cnf(c_0_111,plain,
( empty(X1)
| in(esk4_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_99]) ).
cnf(c_0_112,plain,
( empty(X1)
| ~ empty(esk11_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_113,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_114,plain,
( related(X3,X1,X2)
| ~ in(ordered_pair(X1,X2),the_InternalRel(X3))
| ~ element(X2,the_carrier(X3))
| ~ element(X1,the_carrier(X3))
| ~ rel_str(X3) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_115,negated_conjecture,
( empty(cartesian_product2(the_carrier(esk12_0),the_carrier(esk12_0)))
| in(ordered_pair(esk14_0,esk17_0),the_InternalRel(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_103]),c_0_104]),c_0_40])]) ).
cnf(c_0_116,negated_conjecture,
rel_str(esk13_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_104]),c_0_40])]) ).
cnf(c_0_117,negated_conjecture,
element(esk17_0,the_carrier(esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_118,negated_conjecture,
element(esk14_0,the_carrier(esk13_0)),
inference(rw,[status(thm)],[c_0_106,c_0_70]) ).
cnf(c_0_119,negated_conjecture,
~ related(esk13_0,esk14_0,esk17_0),
inference(rw,[status(thm)],[c_0_107,c_0_70]) ).
cnf(c_0_120,negated_conjecture,
( in(esk17_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_108,c_0_109]) ).
cnf(c_0_121,plain,
( element(esk4_1(esk11_1(X1)),X1)
| empty(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_112]) ).
cnf(c_0_122,plain,
( ~ related(X1,X2,X3)
| ~ rel_str(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ empty(the_InternalRel(X1)) ),
inference(spm,[status(thm)],[c_0_113,c_0_34]) ).
cnf(c_0_123,plain,
( ~ empty(cartesian_product2(X1,X2))
| ~ in(X3,X2)
| ~ in(X4,X1) ),
inference(spm,[status(thm)],[c_0_113,c_0_63]) ).
cnf(c_0_124,negated_conjecture,
empty(cartesian_product2(the_carrier(esk12_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_114,c_0_115]),c_0_116]),c_0_117]),c_0_118])]),c_0_119]) ).
cnf(c_0_125,negated_conjecture,
( in(esk17_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_120,c_0_27]),c_0_40])]) ).
cnf(c_0_126,plain,
( empty(X1)
| in(esk4_1(esk11_1(X1)),X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_121]) ).
cnf(c_0_127,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_122,c_0_48]),c_0_40]),c_0_39]),c_0_49])]) ).
cnf(c_0_128,negated_conjecture,
( ~ in(X1,the_carrier(esk12_0))
| ~ in(X2,the_carrier(esk12_0)) ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_129,negated_conjecture,
in(esk17_0,the_carrier(esk12_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_127]) ).
cnf(c_0_130,negated_conjecture,
~ in(X1,the_carrier(esk12_0)),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_131,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_129,c_0_130]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU363+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 : n011.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 02:59:47 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 6.24/4.51 % Version : CSE_E---1.7
% 6.24/4.51 % Problem : theBenchmark.p
% 6.24/4.51 % SZS status Theorem for theBenchmark.p
% 6.24/4.51 % SZS output start CNFRefutation
% See solution above
% 6.24/4.53 % Total time : 3.373s
%------------------------------------------------------------------------------