TSTP Solution File: SEU078+1 by ET---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SEU078+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n003.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 : 600s
% DateTime : Tue Jul 19 09:16:43 EDT 2022
% Result : Theorem 0.27s 9.46s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 25
% Syntax : Number of formulae : 119 ( 25 unt; 0 def)
% Number of atoms : 393 ( 86 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 469 ( 195 ~; 204 |; 43 &)
% ( 11 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 3 con; 0-3 aty)
% Number of variables : 217 ( 28 sgn 103 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t7_boole) ).
fof(d5_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',d5_funct_1) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t6_boole) ).
fof(fc7_relat_1,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_dom(X1))
& relation(relation_dom(X1)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fc7_relat_1) ).
fof(cc1_funct_1,axiom,
! [X1] :
( empty(X1)
=> function(X1) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',cc1_funct_1) ).
fof(cc1_relat_1,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',cc1_relat_1) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t2_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',existence_m1_subset_1) ).
fof(t159_funct_1,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
<=> ! [X2] :
? [X3] : subset(relation_inverse_image(X1,singleton(X2)),singleton(X3)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t159_funct_1) ).
fof(fc12_relat_1,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fc12_relat_1) ).
fof(fc8_relat_1,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_rng(X1))
& relation(relation_rng(X1)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fc8_relat_1) ).
fof(symmetry_r1_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t56_zfmisc_1,axiom,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t56_zfmisc_1) ).
fof(t144_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ! [X2] :
~ ( in(X2,relation_rng(X1))
& ! [X3] : relation_inverse_image(X1,singleton(X2)) != singleton(X3) )
<=> one_to_one(X1) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t144_funct_1) ).
fof(t173_relat_1,axiom,
! [X1,X2] :
( relation(X2)
=> ( relation_inverse_image(X2,X1) = empty_set
<=> disjoint(relation_rng(X2),X1) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t173_relat_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t5_subset) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',rc2_subset_1) ).
fof(t39_zfmisc_1,axiom,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t39_zfmisc_1) ).
fof(t2_xboole_1,axiom,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t2_xboole_1) ).
fof(fc2_subset_1,axiom,
! [X1] : ~ empty(singleton(X1)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fc2_subset_1) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',t4_subset) ).
fof(rc1_subset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',rc1_subset_1) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',d1_tarski) ).
fof(d13_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( X3 = relation_inverse_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,relation_dom(X1))
& in(apply(X1,X4),X2) ) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',d13_funct_1) ).
fof(c_0_25,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ empty(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(c_0_26,plain,
! [X5,X6,X7,X7,X9,X6,X11] :
( ( in(esk3_3(X5,X6,X7),relation_dom(X5))
| ~ in(X7,X6)
| X6 != relation_rng(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( X7 = apply(X5,esk3_3(X5,X6,X7))
| ~ in(X7,X6)
| X6 != relation_rng(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( ~ in(X9,relation_dom(X5))
| X7 != apply(X5,X9)
| in(X7,X6)
| X6 != relation_rng(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( ~ in(esk4_2(X5,X6),X6)
| ~ in(X11,relation_dom(X5))
| esk4_2(X5,X6) != apply(X5,X11)
| X6 = relation_rng(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( in(esk5_2(X5,X6),relation_dom(X5))
| in(esk4_2(X5,X6),X6)
| X6 = relation_rng(X5)
| ~ relation(X5)
| ~ function(X5) )
& ( esk4_2(X5,X6) = apply(X5,esk5_2(X5,X6))
| in(esk4_2(X5,X6),X6)
| X6 = relation_rng(X5)
| ~ relation(X5)
| ~ function(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_funct_1])])])])])])]) ).
fof(c_0_27,plain,
! [X2] :
( ~ empty(X2)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_28,plain,
! [X2] :
( ( empty(relation_dom(X2))
| ~ empty(X2) )
& ( relation(relation_dom(X2))
| ~ empty(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc7_relat_1])])]) ).
cnf(c_0_29,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,plain,
( in(esk3_3(X1,X2,X3),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,plain,
( empty(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_33,plain,
! [X2] :
( ~ empty(X2)
| function(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_funct_1])]) ).
fof(c_0_34,plain,
! [X2] :
( ~ empty(X2)
| relation(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relat_1])]) ).
fof(c_0_35,plain,
! [X3,X4] :
( ~ element(X3,X4)
| empty(X4)
| in(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_36,plain,
! [X3] : element(esk6_1(X3),X3),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_37,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
<=> ! [X2] :
? [X3] : subset(relation_inverse_image(X1,singleton(X2)),singleton(X3)) ) ),
inference(assume_negation,[status(cth)],[t159_funct_1]) ).
cnf(c_0_38,plain,
( X1 != relation_rng(X2)
| ~ relation(X2)
| ~ function(X2)
| ~ empty(relation_dom(X2))
| ~ in(X3,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_39,plain,
( relation_dom(X1) = empty_set
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_40,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]) ).
cnf(c_0_41,plain,
( function(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_42,plain,
( relation(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_43,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,plain,
element(esk6_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_45,plain,
! [X2] :
( ( empty(relation_rng(X2))
| ~ empty(X2) )
& ( relation(relation_rng(X2))
| ~ empty(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc8_relat_1])])]) ).
fof(c_0_46,plain,
! [X3,X4] :
( ~ disjoint(X3,X4)
| disjoint(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).
fof(c_0_47,plain,
! [X3,X4] :
( in(X3,X4)
| disjoint(singleton(X3),X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t56_zfmisc_1])])]) ).
fof(c_0_48,negated_conjecture,
! [X6,X7] :
( relation(esk19_0)
& function(esk19_0)
& ( ~ one_to_one(esk19_0)
| ~ subset(relation_inverse_image(esk19_0,singleton(esk20_0)),singleton(X6)) )
& ( one_to_one(esk19_0)
| subset(relation_inverse_image(esk19_0,singleton(X7)),singleton(esk21_1(X7))) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])])])])]) ).
fof(c_0_49,plain,
! [X4,X6,X7] :
( ( in(esk17_1(X4),relation_rng(X4))
| one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) )
& ( relation_inverse_image(X4,singleton(esk17_1(X4))) != singleton(X6)
| one_to_one(X4)
| ~ relation(X4)
| ~ function(X4) )
& ( ~ one_to_one(X4)
| ~ in(X7,relation_rng(X4))
| relation_inverse_image(X4,singleton(X7)) = singleton(esk18_2(X4,X7))
| ~ relation(X4)
| ~ function(X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t144_funct_1])])])])])])]) ).
cnf(c_0_50,plain,
( X1 != relation_rng(X2)
| ~ empty(X2)
| ~ in(X3,X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]),c_0_41]),c_0_42]) ).
cnf(c_0_51,plain,
( empty(X1)
| in(esk6_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_52,plain,
( empty(relation_rng(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
fof(c_0_53,plain,
! [X3,X4] :
( ( relation_inverse_image(X4,X3) != empty_set
| disjoint(relation_rng(X4),X3)
| ~ relation(X4) )
& ( ~ disjoint(relation_rng(X4),X3)
| relation_inverse_image(X4,X3) = empty_set
| ~ relation(X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t173_relat_1])])]) ).
cnf(c_0_54,plain,
( disjoint(X1,X2)
| ~ disjoint(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_55,plain,
( disjoint(singleton(X1),X2)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_56,negated_conjecture,
( ~ subset(relation_inverse_image(esk19_0,singleton(esk20_0)),singleton(X1))
| ~ one_to_one(esk19_0) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_57,plain,
( relation_inverse_image(X1,singleton(X2)) = singleton(esk18_2(X1,X2))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_rng(X1))
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
fof(c_0_58,plain,
! [X3] : subset(X3,X3),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(c_0_59,plain,
! [X4,X5,X6] :
( ~ in(X4,X5)
| ~ element(X5,powerset(X6))
| ~ empty(X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(c_0_60,plain,
! [X3] :
( element(esk13_1(X3),powerset(X3))
& empty(esk13_1(X3)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
cnf(c_0_61,plain,
( empty(X1)
| X1 != relation_rng(X2)
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_62,plain,
( relation_rng(X1) = empty_set
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_52]) ).
fof(c_0_63,plain,
! [X3,X4,X3,X4] :
( ( ~ subset(X3,singleton(X4))
| X3 = empty_set
| X3 = singleton(X4) )
& ( X3 != empty_set
| subset(X3,singleton(X4)) )
& ( X3 != singleton(X4)
| subset(X3,singleton(X4)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t39_zfmisc_1])])])])]) ).
cnf(c_0_64,plain,
( relation_inverse_image(X1,X2) = empty_set
| ~ relation(X1)
| ~ disjoint(relation_rng(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_65,plain,
( disjoint(X1,singleton(X2))
| in(X2,X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
fof(c_0_66,plain,
! [X2] : subset(empty_set,X2),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
cnf(c_0_67,negated_conjecture,
( ~ subset(relation_inverse_image(esk19_0,singleton(esk20_0)),relation_inverse_image(X1,singleton(X2)))
| ~ one_to_one(esk19_0)
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_68,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_69,negated_conjecture,
relation(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_70,negated_conjecture,
function(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_71,plain,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_72,plain,
element(esk13_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_73,plain,
empty(esk13_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
fof(c_0_74,plain,
! [X2] : ~ empty(singleton(X2)),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fc2_subset_1])]) ).
cnf(c_0_75,plain,
( empty(X1)
| X1 != empty_set
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
fof(c_0_76,plain,
! [X4,X5,X6] :
( ~ in(X4,X5)
| ~ element(X5,powerset(X6))
| element(X4,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(c_0_77,plain,
! [X3] :
( ( element(esk9_1(X3),powerset(X3))
| empty(X3) )
& ( ~ empty(esk9_1(X3))
| empty(X3) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[rc1_subset_1])])])])])])]) ).
cnf(c_0_78,plain,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_79,negated_conjecture,
( subset(relation_inverse_image(esk19_0,singleton(X1)),singleton(esk21_1(X1)))
| one_to_one(esk19_0) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_80,plain,
( relation_inverse_image(X1,singleton(X2)) = empty_set
| in(X2,relation_rng(X1))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_81,plain,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_82,negated_conjecture,
( ~ one_to_one(esk19_0)
| ~ in(esk20_0,relation_rng(esk19_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]),c_0_70])]) ).
cnf(c_0_83,plain,
( ~ empty(X1)
| ~ in(X2,esk13_1(X1)) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_84,plain,
esk13_1(X1) = empty_set,
inference(spm,[status(thm)],[c_0_31,c_0_73]) ).
fof(c_0_85,plain,
! [X4,X5,X6,X6,X4,X5] :
( ( ~ in(X6,X5)
| X6 = X4
| X5 != singleton(X4) )
& ( X6 != X4
| in(X6,X5)
| X5 != singleton(X4) )
& ( ~ in(esk2_2(X4,X5),X5)
| esk2_2(X4,X5) != X4
| X5 = singleton(X4) )
& ( in(esk2_2(X4,X5),X5)
| esk2_2(X4,X5) = X4
| X5 = singleton(X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_tarski])])])])])])]) ).
cnf(c_0_86,plain,
~ empty(singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_87,plain,
( empty(X1)
| X1 != empty_set ),
inference(spm,[status(thm)],[c_0_75,c_0_40]) ).
cnf(c_0_88,plain,
( element(X1,X2)
| ~ element(X3,powerset(X2))
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_89,plain,
( empty(X1)
| element(esk9_1(X1),powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
fof(c_0_90,plain,
! [X5,X6,X7,X8,X8,X6,X7] :
( ( in(X8,relation_dom(X5))
| ~ in(X8,X7)
| X7 != relation_inverse_image(X5,X6)
| ~ relation(X5)
| ~ function(X5) )
& ( in(apply(X5,X8),X6)
| ~ in(X8,X7)
| X7 != relation_inverse_image(X5,X6)
| ~ relation(X5)
| ~ function(X5) )
& ( ~ in(X8,relation_dom(X5))
| ~ in(apply(X5,X8),X6)
| in(X8,X7)
| X7 != relation_inverse_image(X5,X6)
| ~ relation(X5)
| ~ function(X5) )
& ( ~ in(esk1_3(X5,X6,X7),X7)
| ~ in(esk1_3(X5,X6,X7),relation_dom(X5))
| ~ in(apply(X5,esk1_3(X5,X6,X7)),X6)
| X7 = relation_inverse_image(X5,X6)
| ~ relation(X5)
| ~ function(X5) )
& ( in(esk1_3(X5,X6,X7),relation_dom(X5))
| in(esk1_3(X5,X6,X7),X7)
| X7 = relation_inverse_image(X5,X6)
| ~ relation(X5)
| ~ function(X5) )
& ( in(apply(X5,esk1_3(X5,X6,X7)),X6)
| in(esk1_3(X5,X6,X7),X7)
| X7 = relation_inverse_image(X5,X6)
| ~ relation(X5)
| ~ function(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d13_funct_1])])])])])])]) ).
cnf(c_0_91,negated_conjecture,
( singleton(esk21_1(X1)) = relation_inverse_image(esk19_0,singleton(X1))
| relation_inverse_image(esk19_0,singleton(X1)) = empty_set
| one_to_one(esk19_0) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_92,negated_conjecture,
~ one_to_one(esk19_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_80]),c_0_81]),c_0_69])]),c_0_82]) ).
cnf(c_0_93,plain,
( ~ empty(X1)
| ~ in(X2,empty_set) ),
inference(rw,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_94,plain,
( X1 = singleton(X2)
| esk2_2(X2,X1) = X2
| in(esk2_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_95,plain,
singleton(X1) != empty_set,
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_96,plain,
( element(X1,X2)
| empty(X2)
| ~ in(X1,esk9_1(X2)) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_97,plain,
( empty(X1)
| ~ empty(esk9_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_98,plain,
( in(X4,X2)
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_inverse_image(X1,X3)
| ~ in(apply(X1,X4),X3)
| ~ in(X4,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_99,plain,
( X3 = apply(X1,esk3_3(X1,X2,X3))
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_rng(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_100,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| relation_inverse_image(X1,singleton(esk17_1(X1))) != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_101,negated_conjecture,
( singleton(esk21_1(X1)) = relation_inverse_image(esk19_0,singleton(X1))
| relation_inverse_image(esk19_0,singleton(X1)) = empty_set ),
inference(sr,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_102,plain,
( esk2_2(X1,empty_set) = X1
| ~ empty(X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95]) ).
cnf(c_0_103,plain,
( element(esk6_1(esk9_1(X1)),X1)
| empty(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_51]),c_0_97]) ).
cnf(c_0_104,plain,
( in(esk3_3(X1,X2,X3),X4)
| X4 != relation_inverse_image(X1,X5)
| X2 != relation_rng(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X3,X5)
| ~ in(X3,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_30]) ).
cnf(c_0_105,negated_conjecture,
( relation_inverse_image(esk19_0,singleton(X1)) = empty_set
| one_to_one(X2)
| relation_inverse_image(X2,singleton(esk17_1(X2))) != relation_inverse_image(esk19_0,singleton(X1))
| ~ relation(X2)
| ~ function(X2) ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_106,plain,
( X1 = singleton(X2)
| esk2_2(X2,X1) != X2
| ~ in(esk2_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_107,plain,
esk2_2(X1,empty_set) = X1,
inference(spm,[status(thm)],[c_0_102,c_0_40]) ).
cnf(c_0_108,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_109,plain,
( empty(X1)
| in(esk6_1(esk9_1(X1)),X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_103]) ).
cnf(c_0_110,plain,
( in(esk3_3(X1,X2,X3),relation_inverse_image(X1,X4))
| X2 != relation_rng(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X3,X4)
| ~ in(X3,X2) ),
inference(er,[status(thm)],[c_0_104]) ).
cnf(c_0_111,negated_conjecture,
relation_inverse_image(esk19_0,singleton(esk17_1(esk19_0))) = empty_set,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_105]),c_0_69]),c_0_70])]),c_0_92]) ).
cnf(c_0_112,plain,
~ in(X1,empty_set),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_95]) ).
cnf(c_0_113,plain,
( X1 = esk6_1(esk9_1(X2))
| empty(X2)
| X2 != singleton(X1) ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_114,negated_conjecture,
( X1 != relation_rng(esk19_0)
| ~ in(X2,singleton(esk17_1(esk19_0)))
| ~ in(X2,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_69]),c_0_70])]),c_0_112]) ).
cnf(c_0_115,plain,
esk6_1(esk9_1(singleton(X1))) = X1,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_113]),c_0_86]) ).
cnf(c_0_116,negated_conjecture,
( X1 != relation_rng(esk19_0)
| ~ in(esk17_1(esk19_0),X1) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_109]),c_0_115]),c_0_86]) ).
cnf(c_0_117,plain,
( one_to_one(X1)
| in(esk17_1(X1),relation_rng(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_118,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_116,c_0_117]),c_0_69]),c_0_70])]),c_0_92]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU078+1 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 19 14:59:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.27/9.46 # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.27/9.46 # Preprocessing time : 0.018 s
% 0.27/9.46
% 0.27/9.46 # Proof found!
% 0.27/9.46 # SZS status Theorem
% 0.27/9.46 # SZS output start CNFRefutation
% See solution above
% 0.27/9.46 # Proof object total steps : 119
% 0.27/9.46 # Proof object clause steps : 69
% 0.27/9.46 # Proof object formula steps : 50
% 0.27/9.46 # Proof object conjectures : 17
% 0.27/9.46 # Proof object clause conjectures : 14
% 0.27/9.46 # Proof object formula conjectures : 3
% 0.27/9.46 # Proof object initial clauses used : 35
% 0.27/9.46 # Proof object initial formulas used : 25
% 0.27/9.46 # Proof object generating inferences : 32
% 0.27/9.46 # Proof object simplifying inferences : 32
% 0.27/9.46 # Training examples: 0 positive, 0 negative
% 0.27/9.46 # Parsed axioms : 43
% 0.27/9.46 # Removed by relevancy pruning/SinE : 0
% 0.27/9.46 # Initial clauses : 82
% 0.27/9.46 # Removed in clause preprocessing : 2
% 0.27/9.46 # Initial clauses in saturation : 80
% 0.27/9.46 # Processed clauses : 24424
% 0.27/9.46 # ...of these trivial : 82
% 0.27/9.46 # ...subsumed : 20302
% 0.27/9.46 # ...remaining for further processing : 4040
% 0.27/9.46 # Other redundant clauses eliminated : 6
% 0.27/9.46 # Clauses deleted for lack of memory : 205542
% 0.27/9.46 # Backward-subsumed : 309
% 0.27/9.46 # Backward-rewritten : 47
% 0.27/9.46 # Generated clauses : 361027
% 0.27/9.46 # ...of the previous two non-trivial : 346331
% 0.27/9.46 # Contextual simplify-reflections : 28803
% 0.27/9.46 # Paramodulations : 360362
% 0.27/9.46 # Factorizations : 36
% 0.27/9.46 # Equation resolutions : 627
% 0.27/9.46 # Current number of processed clauses : 3681
% 0.27/9.46 # Positive orientable unit clauses : 46
% 0.27/9.46 # Positive unorientable unit clauses: 0
% 0.27/9.46 # Negative unit clauses : 30
% 0.27/9.46 # Non-unit-clauses : 3605
% 0.27/9.46 # Current number of unprocessed clauses: 101543
% 0.27/9.46 # ...number of literals in the above : 658066
% 0.27/9.46 # Current number of archived formulas : 0
% 0.27/9.46 # Current number of archived clauses : 358
% 0.27/9.46 # Clause-clause subsumption calls (NU) : 10084592
% 0.27/9.46 # Rec. Clause-clause subsumption calls : 3093399
% 0.27/9.46 # Non-unit clause-clause subsumptions : 45052
% 0.27/9.46 # Unit Clause-clause subsumption calls : 2348
% 0.27/9.46 # Rewrite failures with RHS unbound : 0
% 0.27/9.46 # BW rewrite match attempts : 31
% 0.27/9.46 # BW rewrite match successes : 23
% 0.27/9.46 # Condensation attempts : 0
% 0.27/9.46 # Condensation successes : 0
% 0.27/9.46 # Termbank termtop insertions : 8329753
% 0.27/9.46
% 0.27/9.46 # -------------------------------------------------
% 0.27/9.46 # User time : 8.144 s
% 0.27/9.46 # System time : 0.086 s
% 0.27/9.46 # Total time : 8.230 s
% 0.27/9.46 # Maximum resident set size: 137324 pages
% 0.27/23.41 eprover: CPU time limit exceeded, terminating
% 0.27/23.41 eprover: CPU time limit exceeded, terminating
% 0.27/23.42 eprover: CPU time limit exceeded, terminating
% 0.27/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.43 eprover: No such file or directory
% 0.27/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.43 eprover: No such file or directory
% 0.27/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.43 eprover: No such file or directory
% 0.27/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.43 eprover: No such file or directory
% 0.27/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.43 eprover: No such file or directory
% 0.27/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.43 eprover: No such file or directory
% 0.27/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.44 eprover: No such file or directory
% 0.27/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.44 eprover: No such file or directory
% 0.27/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.44 eprover: No such file or directory
% 0.27/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.44 eprover: No such file or directory
% 0.27/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.44 eprover: No such file or directory
% 0.27/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.44 eprover: No such file or directory
% 0.27/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.44 eprover: No such file or directory
% 0.27/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.45 eprover: No such file or directory
% 0.27/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.45 eprover: No such file or directory
% 0.27/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.45 eprover: No such file or directory
% 0.27/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.45 eprover: No such file or directory
% 0.27/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.45 eprover: No such file or directory
% 0.27/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.45 eprover: No such file or directory
% 0.27/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.46 eprover: No such file or directory
% 0.27/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.46 eprover: No such file or directory
% 0.27/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.46 eprover: No such file or directory
% 0.27/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.46 eprover: No such file or directory
% 0.27/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.46 eprover: No such file or directory
% 0.27/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.46 eprover: No such file or directory
% 0.27/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.47 eprover: No such file or directory
% 0.27/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.47 eprover: No such file or directory
% 0.27/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.47 eprover: No such file or directory
% 0.27/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.47 eprover: No such file or directory
% 0.27/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.47 eprover: No such file or directory
% 0.27/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.47 eprover: No such file or directory
% 0.27/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.48 eprover: No such file or directory
% 0.27/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.48 eprover: No such file or directory
%------------------------------------------------------------------------------