%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU055+1 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n026.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 05:10:33 PM UTC 2026
% Result : Theorem 151.04s 121.45s
% Output : CNFRefutation 159.44s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named i_0_316)
% Comments :
%------------------------------------------------------------------------------
fof(t124_funct_1,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ! [X2,X3] : relation_image(X1,set_difference(X2,X3)) = set_difference(relation_image(X1,X2),relation_image(X1,X3))
=> one_to_one(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t124_funct_1) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(rc1_subset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(fc5_relat_1,axiom,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(fc2_subset_1,axiom,
! [X1] : ~ empty(singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(rc2_relat_1,axiom,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(d8_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
<=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
& in(X3,relation_dom(X1))
& apply(X1,X2) = apply(X1,X3) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
fof(t117_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,relation_dom(X2))
=> relation_image(X2,singleton(X1)) = singleton(apply(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_funct_1) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(t20_zfmisc_1,axiom,
! [X1,X2] :
( set_difference(singleton(X1),singleton(X2)) = singleton(X1)
<=> X1 != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_zfmisc_1) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(fc3_relat_1,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_difference(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_relat_1) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(t37_xboole_1,axiom,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(cc2_funct_1,axiom,
! [X1] :
( ( relation(X1)
& empty(X1)
& function(X1) )
=> ( relation(X1)
& function(X1)
& one_to_one(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(fc7_relat_1,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_dom(X1))
& relation(relation_dom(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t3_boole,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
fof(t4_boole,axiom,
! [X1] : set_difference(empty_set,X1) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
fof(cc1_relat_1,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(cc1_funct_1,axiom,
! [X1] :
( empty(X1)
=> function(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(rc3_relat_1,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(rc3_funct_1,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(rc2_funct_1,axiom,
? [X1] :
( relation(X1)
& empty(X1)
& function(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(rc1_relat_1,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(rc1_funct_1,axiom,
? [X1] :
( relation(X1)
& function(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(fc12_relat_1,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(fc4_relat_1,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(i_0_40,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ! [X2,X3] : relation_image(X1,set_difference(X2,X3)) = set_difference(relation_image(X1,X2),relation_image(X1,X3))
=> one_to_one(X1) ) ),
inference(assume_negation,[status(cth)],[t124_funct_1]) ).
fof(i_0_41,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_42,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[rc1_subset_1]) ).
fof(i_0_43,plain,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
inference(fof_simplification,[status(thm)],[fc5_relat_1]) ).
fof(i_0_44,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(i_0_45,plain,
! [X1] : ~ empty(singleton(X1)),
inference(fof_simplification,[status(thm)],[fc2_subset_1]) ).
fof(i_0_46,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_47,plain,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
inference(fof_simplification,[status(thm)],[rc2_relat_1]) ).
fof(i_0_48,plain,
! [X77,X78,X79] :
( ( ~ one_to_one(X77)
| ~ in(X78,relation_dom(X77))
| ~ in(X79,relation_dom(X77))
| apply(X77,X78) != apply(X77,X79)
| X78 = X79
| ~ relation(X77)
| ~ function(X77) )
& ( in(esk2_1(X77),relation_dom(X77))
| one_to_one(X77)
| ~ relation(X77)
| ~ function(X77) )
& ( in(esk3_1(X77),relation_dom(X77))
| one_to_one(X77)
| ~ relation(X77)
| ~ function(X77) )
& ( apply(X77,esk2_1(X77)) = apply(X77,esk3_1(X77))
| one_to_one(X77)
| ~ relation(X77)
| ~ function(X77) )
& ( esk2_1(X77) != esk3_1(X77)
| one_to_one(X77)
| ~ relation(X77)
| ~ function(X77) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_funct_1])])])])]) ).
fof(i_0_49,negated_conjecture,
! [X106,X107] :
( relation(esk15_0)
& function(esk15_0)
& relation_image(esk15_0,set_difference(X106,X107)) = set_difference(relation_image(esk15_0,X106),relation_image(esk15_0,X107))
& ~ one_to_one(esk15_0) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_40])])])]) ).
fof(i_0_50,plain,
! [X103,X104] :
( ~ relation(X104)
| ~ function(X104)
| ~ in(X103,relation_dom(X104))
| relation_image(X104,singleton(X103)) = singleton(apply(X104,X103)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t117_funct_1])]) ).
fof(i_0_51,plain,
! [X70,X71,X72,X73,X74,X75] :
( ( ~ in(X72,X71)
| X72 = X70
| X71 != singleton(X70) )
& ( X73 != X70
| in(X73,X71)
| X71 != singleton(X70) )
& ( ~ in(esk1_2(X74,X75),X75)
| esk1_2(X74,X75) != X74
| X75 = singleton(X74) )
& ( in(esk1_2(X74,X75),X75)
| esk1_2(X74,X75) = X74
| X75 = singleton(X74) ) ),
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)],[d1_tarski])])])])])]) ).
fof(i_0_52,plain,
! [X120,X121,X122] :
( ~ in(X120,X121)
| ~ element(X121,powerset(X122))
| element(X120,X122) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(i_0_53,plain,
! [X123,X124,X125] :
( ~ in(X123,X124)
| ~ element(X124,powerset(X125))
| ~ empty(X125) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(i_0_54,plain,
! [X110,X111] :
( ( set_difference(singleton(X110),singleton(X111)) != singleton(X110)
| X110 != X111 )
& ( X110 = X111
| set_difference(singleton(X110),singleton(X111)) = singleton(X110) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t20_zfmisc_1])]) ).
fof(i_0_55,plain,
! [X117,X118] :
( ( ~ element(X117,powerset(X118))
| subset(X117,X118) )
& ( ~ subset(X117,X118)
| element(X117,powerset(X118)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(i_0_56,plain,
! [X65,X66] :
( ~ in(X65,X66)
| ~ in(X66,X65) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_41])]) ).
fof(i_0_57,plain,
! [X86,X87] :
( ~ relation(X86)
| ~ relation(X87)
| relation(set_difference(X86,X87)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc3_relat_1])]) ).
fof(i_0_58,plain,
! [X112,X113] :
( ~ element(X112,X113)
| empty(X113)
| in(X112,X113) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(i_0_59,plain,
! [X108,X109] :
( ~ in(X108,X109)
| element(X108,X109) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(i_0_60,plain,
! [X114,X115] :
( ( set_difference(X114,X115) != empty_set
| subset(X114,X115) )
& ( ~ subset(X114,X115)
| set_difference(X114,X115) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])]) ).
fof(i_0_61,plain,
! [X92] :
( ( element(esk7_1(X92),powerset(X92))
| empty(X92) )
& ( ~ empty(esk7_1(X92))
| empty(X92) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_42])])])]) ).
fof(i_0_62,plain,
! [X127,X128] :
( ~ in(X127,X128)
| ~ empty(X128) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_63,plain,
! [X88] :
( empty(X88)
| ~ relation(X88)
| ~ empty(relation_dom(X88)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_43])]) ).
fof(i_0_64,plain,
! [X97] :
( element(esk11_1(X97),powerset(X97))
& empty(esk11_1(X97)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(i_0_65,plain,
! [X69] :
( ( relation(X69)
| ~ relation(X69)
| ~ empty(X69)
| ~ function(X69) )
& ( function(X69)
| ~ relation(X69)
| ~ empty(X69)
| ~ function(X69) )
& ( one_to_one(X69)
| ~ relation(X69)
| ~ empty(X69)
| ~ function(X69) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_funct_1])])]) ).
fof(i_0_66,plain,
! [X82] : element(esk4_1(X82),X82),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(i_0_67,plain,
! [X89] :
( ( empty(relation_dom(X89))
| ~ empty(X89) )
& ( relation(relation_dom(X89))
| ~ empty(X89) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc7_relat_1])])]) ).
fof(i_0_68,plain,
! [X84] : ~ empty(powerset(X84)),
inference(variable_rename,[status(thm)],[i_0_44]) ).
fof(i_0_69,plain,
! [X85] : ~ empty(singleton(X85)),
inference(variable_rename,[status(thm)],[i_0_45]) ).
fof(i_0_70,plain,
! [X129,X130] :
( ~ empty(X129)
| X129 = X130
| ~ empty(X130) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_71,plain,
! [X102] : subset(X102,X102),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(i_0_72,plain,
! [X116] : set_difference(X116,empty_set) = X116,
inference(variable_rename,[status(thm)],[t3_boole]) ).
fof(i_0_73,plain,
! [X119] : set_difference(empty_set,X119) = empty_set,
inference(variable_rename,[status(thm)],[t4_boole]) ).
fof(i_0_74,plain,
! [X68] :
( ~ empty(X68)
| relation(X68) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relat_1])]) ).
fof(i_0_75,plain,
! [X67] :
( ~ empty(X67)
| function(X67) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_funct_1])]) ).
fof(i_0_76,plain,
! [X126] :
( ~ empty(X126)
| X126 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_77,plain,
~ empty(esk12_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_46])]) ).
fof(i_0_78,plain,
( ~ empty(esk10_0)
& relation(esk10_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_47])]) ).
fof(i_0_79,plain,
( relation(esk14_0)
& relation_empty_yielding(esk14_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_relat_1])]) ).
fof(i_0_80,plain,
( relation(esk13_0)
& function(esk13_0)
& one_to_one(esk13_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_funct_1])]) ).
fof(i_0_81,plain,
( relation(esk9_0)
& empty(esk9_0)
& function(esk9_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_funct_1])]) ).
fof(i_0_82,plain,
( empty(esk6_0)
& relation(esk6_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_relat_1])]) ).
fof(i_0_83,plain,
( relation(esk5_0)
& function(esk5_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_funct_1])]) ).
fof(i_0_84,plain,
empty(esk8_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_85,plain,
( X2 = X3
| ~ one_to_one(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(X3,relation_dom(X1))
| apply(X1,X2) != apply(X1,X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_86,negated_conjecture,
relation_image(esk15_0,set_difference(X1,X2)) = set_difference(relation_image(esk15_0,X1),relation_image(esk15_0,X2)),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_87,plain,
( relation_image(X1,singleton(X2)) = singleton(apply(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_88,plain,
( X2 = singleton(X1)
| ~ in(esk1_2(X1,X2),X2)
| esk1_2(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_89,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_90,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_91,plain,
( in(esk1_2(X1,X2),X2)
| esk1_2(X1,X2) = X1
| X2 = singleton(X1) ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_92,plain,
( apply(X1,esk2_1(X1)) = apply(X1,esk3_1(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_93,plain,
( set_difference(singleton(X1),singleton(X2)) != singleton(X1)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_94,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_95,plain,
( in(esk3_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_96,plain,
( in(esk2_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_97,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_98,plain,
( relation(set_difference(X1,X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_99,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_100,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_101,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_102,plain,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_103,plain,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_104,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_105,plain,
( X1 = X2
| set_difference(singleton(X1),singleton(X2)) = singleton(X1) ),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_106,plain,
( one_to_one(X1)
| esk2_1(X1) != esk3_1(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_107,plain,
( element(esk7_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_108,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_109,plain,
( empty(X1)
| ~ relation(X1)
| ~ empty(relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_110,plain,
element(esk11_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_111,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_112,plain,
( one_to_one(X1)
| ~ relation(X1)
| ~ empty(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_113,plain,
( empty(X1)
| ~ empty(esk7_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_114,plain,
element(esk4_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_115,plain,
( relation(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_116,plain,
( empty(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_117,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_118,plain,
~ empty(singleton(X1)),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_119,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_120,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_121,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_122,plain,
set_difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_73]),
[final] ).
cnf(i_0_123,plain,
( relation(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_74]),
[final] ).
cnf(i_0_124,plain,
( function(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_125,plain,
empty(esk11_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_126,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_76]),
[final] ).
cnf(i_0_127,negated_conjecture,
~ one_to_one(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_128,plain,
~ empty(esk12_0),
inference(split_conjunct,[status(thm)],[i_0_77]),
[final] ).
cnf(i_0_129,plain,
~ empty(esk10_0),
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_130,plain,
relation_empty_yielding(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_79]),
[final] ).
cnf(i_0_131,plain,
relation_empty_yielding(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_132,plain,
one_to_one(esk13_0),
inference(split_conjunct,[status(thm)],[i_0_80]),
[final] ).
cnf(i_0_133,negated_conjecture,
relation(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_134,plain,
relation(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_79]),
[final] ).
cnf(i_0_135,plain,
relation(esk13_0),
inference(split_conjunct,[status(thm)],[i_0_80]),
[final] ).
cnf(i_0_136,plain,
relation(esk10_0),
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_137,plain,
relation(esk9_0),
inference(split_conjunct,[status(thm)],[i_0_81]),
[final] ).
cnf(i_0_138,plain,
relation(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_82]),
[final] ).
cnf(i_0_139,plain,
relation(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_140,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_141,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_142,negated_conjecture,
function(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_143,plain,
function(esk13_0),
inference(split_conjunct,[status(thm)],[i_0_80]),
[final] ).
cnf(i_0_144,plain,
function(esk9_0),
inference(split_conjunct,[status(thm)],[i_0_81]),
[final] ).
cnf(i_0_145,plain,
function(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_146,plain,
empty(esk9_0),
inference(split_conjunct,[status(thm)],[i_0_81]),
[final] ).
cnf(i_0_147,plain,
empty(esk8_0),
inference(split_conjunct,[status(thm)],[i_0_84]),
[final] ).
cnf(i_0_148,plain,
empty(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_82]),
[final] ).
cnf(i_0_149,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_150,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_151,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_152,axiom,
X1 = X1 ).
cnf(i_0_153,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_154,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_155,axiom,
( X1 != X2
| apply(X1,X3) = apply(X2,X3) ) ).
cnf(i_0_156,axiom,
( X1 != X2
| apply(X3,X1) = apply(X3,X2) ) ).
cnf(i_0_157,axiom,
( X1 != X2
| relation_image(X1,X3) = relation_image(X2,X3) ) ).
cnf(i_0_158,axiom,
( X1 != X2
| relation_image(X3,X1) = relation_image(X3,X2) ) ).
cnf(i_0_159,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_160,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_161,axiom,
( X1 != X2
| singleton(X1) = singleton(X2) ) ).
cnf(i_0_162,axiom,
( X1 != X2
| esk1_2(X1,X3) = esk1_2(X2,X3) ) ).
cnf(i_0_163,axiom,
( X1 != X2
| esk1_2(X3,X1) = esk1_2(X3,X2) ) ).
cnf(i_0_164,axiom,
( X1 != X2
| esk2_1(X1) = esk2_1(X2) ) ).
cnf(i_0_165,axiom,
( X1 != X2
| esk3_1(X1) = esk3_1(X2) ) ).
cnf(i_0_166,axiom,
( X1 != X2
| ~ one_to_one(X1)
| one_to_one(X2) ) ).
cnf(i_0_167,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_168,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_169,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_170,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_171,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_172,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_173,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_174,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_175,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_176,axiom,
( X1 != X2
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(X2) ) ).
cnf(i_0_703,plain,
esk4_1(singleton(X1)) = X1,
inference(rename_variables,[],[i_0_316]) ).
cnf(i_0_705,plain,
esk4_1(singleton(X1)) = X1,
inference(rename_variables,[],[i_0_316]) ).
cnf(i_0_1156,plain,
esk4_1(singleton(X1)) = X1,
inference(rename_variables,[],[i_0_316]) ).
cnf(i_0_1249,plain,
esk4_1(singleton(X1)) = X1,
inference(rename_variables,[],[i_0_316]) ).
cnf(i_0_1595,plain,
esk4_1(singleton(X1)) = X1,
inference(rename_variables,[],[i_0_316]) ).
cnf(i_0_1599,plain,
esk4_1(singleton(X1)) = X1,
inference(rename_variables,[],[i_0_316]) ).
cnf(i_0_1612,plain,
esk4_1(singleton(X1)) = X1,
inference(rename_variables,[],[i_0_316]) ).
cnf(i_0_1769,plain,
esk4_1(singleton(X1)) = X1,
inference(rename_variables,[],[i_0_316]) ).
cnf(i_0_1934,plain,
esk4_1(singleton(X1)) = X1,
inference(rename_variables,[],[i_0_316]) ).
cnf(i_0_2294,plain,
esk4_1(singleton(X1)) = X1,
inference(rename_variables,[],[i_0_316]) ).
cnf(i_0_2393,plain,
~ in(singleton(X1),esk4_1(singleton(X1))),
inference(rename_variables,[],[i_0_318]) ).
cnf(i_0_2763,plain,
esk4_1(singleton(X1)) = X1,
inference(rename_variables,[],[i_0_316]) ).
cnf(i_0_2866,plain,
esk4_1(singleton(X1)) = X1,
inference(rename_variables,[],[i_0_316]) ).
cnf(i_0_3040,plain,
esk4_1(singleton(X1)) = X1,
inference(rename_variables,[],[i_0_316]) ).
cnf(i_0_333,plain,
~ in(esk11_1(X1),esk1_2(singleton(singleton(X2)),esk11_1(esk9_0))),
inference(scs_inference,[],[i_0_310,i_0_330,i_0_147,i_0_290,i_0_316,i_0_320,i_0_108,i_0_153,i_0_91,i_0_104]) ).
cnf(i_0_336,plain,
~ in(X1,esk4_1(powerset(esk8_0))),
inference(scs_inference,[],[i_0_310,i_0_330,i_0_147,i_0_290,i_0_316,i_0_320,i_0_114,i_0_108,i_0_153,i_0_91,i_0_104,i_0_90]) ).
cnf(i_0_339,plain,
in(esk4_1(esk12_0),esk12_0),
inference(scs_inference,[],[i_0_310,i_0_330,i_0_147,i_0_290,i_0_316,i_0_320,i_0_128,i_0_114,i_0_337,i_0_108,i_0_153,i_0_91,i_0_104,i_0_90,i_0_100]) ).
cnf(i_0_342,plain,
relation_empty_yielding(set_difference(empty_set,X1)),
inference(scs_inference,[],[i_0_310,i_0_330,i_0_294,i_0_131,i_0_147,i_0_290,i_0_316,i_0_320,i_0_128,i_0_114,i_0_337,i_0_108,i_0_153,i_0_91,i_0_104,i_0_90,i_0_100,i_0_176]) ).
cnf(i_0_343,plain,
~ in(set_difference(esk10_0,empty_set),esk4_1(singleton(esk4_1(esk10_0)))),
inference(scs_inference,[],[i_0_310,i_0_330,i_0_312,i_0_294,i_0_131,i_0_147,i_0_290,i_0_316,i_0_320,i_0_128,i_0_114,i_0_337,i_0_108,i_0_153,i_0_91,i_0_104,i_0_90,i_0_100,i_0_176,i_0_168]) ).
cnf(i_0_345,plain,
esk8_0 != esk12_0,
inference(scs_inference,[],[i_0_310,i_0_330,i_0_312,i_0_294,i_0_131,i_0_147,i_0_290,i_0_316,i_0_320,i_0_128,i_0_114,i_0_337,i_0_108,i_0_153,i_0_91,i_0_104,i_0_90,i_0_100,i_0_176,i_0_168,i_0_173]) ).
cnf(i_0_346,plain,
singleton(singleton(set_difference(empty_set,X1))) != empty_set,
inference(scs_inference,[],[i_0_310,i_0_330,i_0_323,i_0_312,i_0_294,i_0_131,i_0_147,i_0_290,i_0_316,i_0_320,i_0_128,i_0_114,i_0_337,i_0_108,i_0_153,i_0_91,i_0_104,i_0_90,i_0_100,i_0_176,i_0_168,i_0_173,i_0_154]) ).
cnf(i_0_348,plain,
function(set_difference(empty_set,X1)),
inference(scs_inference,[],[i_0_310,i_0_330,i_0_323,i_0_312,i_0_294,i_0_131,i_0_147,i_0_290,i_0_316,i_0_320,i_0_128,i_0_263,i_0_114,i_0_337,i_0_108,i_0_153,i_0_91,i_0_104,i_0_90,i_0_100,i_0_176,i_0_168,i_0_173,i_0_154,i_0_170]) ).
cnf(i_0_349,plain,
relation(set_difference(empty_set,X1)),
inference(scs_inference,[],[i_0_310,i_0_330,i_0_323,i_0_312,i_0_294,i_0_131,i_0_147,i_0_290,i_0_316,i_0_320,i_0_128,i_0_263,i_0_141,i_0_114,i_0_337,i_0_108,i_0_153,i_0_91,i_0_104,i_0_90,i_0_100,i_0_176,i_0_168,i_0_173,i_0_154,i_0_170,i_0_169]) ).
cnf(i_0_350,plain,
~ in(esk4_1(singleton(set_difference(esk10_0,empty_set))),esk4_1(esk10_0)),
inference(scs_inference,[],[i_0_310,i_0_330,i_0_323,i_0_312,i_0_294,i_0_131,i_0_147,i_0_290,i_0_316,i_0_344,i_0_320,i_0_128,i_0_263,i_0_141,i_0_114,i_0_337,i_0_108,i_0_153,i_0_91,i_0_104,i_0_90,i_0_100,i_0_176,i_0_168,i_0_173,i_0_154,i_0_170,i_0_169,i_0_167]) ).
cnf(i_0_352,plain,
one_to_one(esk11_1(X1)),
inference(scs_inference,[],[i_0_310,i_0_330,i_0_323,i_0_312,i_0_294,i_0_131,i_0_147,i_0_125,i_0_290,i_0_292,i_0_316,i_0_344,i_0_320,i_0_226,i_0_128,i_0_263,i_0_141,i_0_114,i_0_337,i_0_108,i_0_153,i_0_91,i_0_104,i_0_90,i_0_100,i_0_176,i_0_168,i_0_173,i_0_154,i_0_170,i_0_169,i_0_167,i_0_112]) ).
cnf(i_0_356,plain,
~ in(esk12_0,esk4_1(esk12_0)),
inference(scs_inference,[],[i_0_310,i_0_330,i_0_323,i_0_312,i_0_294,i_0_131,i_0_147,i_0_125,i_0_290,i_0_292,i_0_316,i_0_344,i_0_320,i_0_226,i_0_128,i_0_263,i_0_141,i_0_114,i_0_337,i_0_108,i_0_153,i_0_91,i_0_104,i_0_90,i_0_100,i_0_176,i_0_168,i_0_173,i_0_154,i_0_170,i_0_169,i_0_167,i_0_112,i_0_97]) ).
cnf(i_0_358,plain,
esk11_1(X1) != esk15_0,
inference(scs_inference,[],[i_0_127,i_0_310,i_0_330,i_0_323,i_0_312,i_0_294,i_0_131,i_0_147,i_0_125,i_0_290,i_0_292,i_0_316,i_0_344,i_0_320,i_0_226,i_0_128,i_0_263,i_0_141,i_0_114,i_0_337,i_0_108,i_0_153,i_0_91,i_0_104,i_0_90,i_0_100,i_0_176,i_0_168,i_0_173,i_0_154,i_0_170,i_0_169,i_0_167,i_0_112,i_0_97,i_0_166]) ).
cnf(i_0_359,plain,
relation(esk4_1(singleton(esk15_0))),
inference(scs_inference,[],[i_0_328,i_0_211]) ).
cnf(i_0_360,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_362,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_364,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_366,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_369,plain,
esk1_2(X1,esk11_1(X2)) = X1,
inference(rename_variables,[],[i_0_329]) ).
cnf(i_0_378,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_380,plain,
esk1_2(X1,esk11_1(X2)) = X1,
inference(rename_variables,[],[i_0_329]) ).
cnf(i_0_383,plain,
esk1_2(X1,esk11_1(X2)) = X1,
inference(rename_variables,[],[i_0_329]) ).
cnf(i_0_385,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_387,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_389,plain,
esk1_2(X1,esk11_1(X2)) = X1,
inference(rename_variables,[],[i_0_329]) ).
cnf(i_0_434,plain,
esk1_2(X1,esk11_1(X2)) = X1,
inference(rename_variables,[],[i_0_329]) ).
cnf(i_0_452,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_459,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_461,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_472,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_474,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_476,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_482,plain,
esk1_2(X1,esk11_1(X2)) = X1,
inference(rename_variables,[],[i_0_329]) ).
cnf(i_0_510,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_512,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_518,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_528,plain,
esk1_2(X1,esk11_1(X2)) = X1,
inference(rename_variables,[],[i_0_329]) ).
cnf(i_0_540,plain,
esk1_2(X1,esk11_1(X2)) = X1,
inference(rename_variables,[],[i_0_329]) ).
cnf(i_0_567,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_571,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_583,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_585,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_606,plain,
function(esk4_1(singleton(esk8_0))),
inference(scs_inference,[],[i_0_328,i_0_188,i_0_170]) ).
cnf(i_0_607,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_609,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_625,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_664,plain,
function(esk4_1(singleton(esk6_0))),
inference(scs_inference,[],[i_0_328,i_0_228,i_0_170]) ).
cnf(i_0_665,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_667,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_686,plain,
function(esk4_1(singleton(empty_set))),
inference(scs_inference,[],[i_0_328,i_0_263,i_0_170]) ).
cnf(i_0_687,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_689,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_708,plain,
relation(esk4_1(singleton(esk11_1(X1)))),
inference(scs_inference,[],[i_0_328,i_0_226,i_0_169]) ).
cnf(i_0_709,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_725,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_740,plain,
relation(esk4_1(singleton(empty_set))),
inference(scs_inference,[],[i_0_328,i_0_141,i_0_169]) ).
cnf(i_0_741,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_767,plain,
esk1_2(X1,esk11_1(X2)) = X1,
inference(rename_variables,[],[i_0_329]) ).
cnf(i_0_769,plain,
esk1_2(X1,esk11_1(X2)) = X1,
inference(rename_variables,[],[i_0_329]) ).
cnf(i_0_771,plain,
esk1_2(X1,esk11_1(X2)) = X1,
inference(rename_variables,[],[i_0_329]) ).
cnf(i_0_776,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_1153,plain,
esk1_2(X1,esk11_1(X2)) = X1,
inference(rename_variables,[],[i_0_329]) ).
cnf(i_0_1166,plain,
esk1_2(X1,esk11_1(X2)) = X1,
inference(rename_variables,[],[i_0_329]) ).
cnf(i_0_1237,plain,
esk1_2(X1,esk11_1(X2)) = X1,
inference(rename_variables,[],[i_0_329]) ).
cnf(i_0_1242,plain,
esk1_2(X1,esk11_1(X2)) = X1,
inference(rename_variables,[],[i_0_329]) ).
cnf(i_0_1246,plain,
esk1_2(X1,esk11_1(X2)) = X1,
inference(rename_variables,[],[i_0_329]) ).
cnf(i_0_1251,plain,
esk1_2(X1,esk11_1(X2)) = X1,
inference(rename_variables,[],[i_0_329]) ).
cnf(i_0_1330,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_1332,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_1417,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_1430,plain,
esk1_2(X1,esk11_1(X2)) = X1,
inference(rename_variables,[],[i_0_329]) ).
cnf(i_0_1436,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_1499,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_1501,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_1524,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_1577,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_1601,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_1691,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_1840,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_1842,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_1847,plain,
esk1_2(X1,esk11_1(X2)) = X1,
inference(rename_variables,[],[i_0_329]) ).
cnf(i_0_1859,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_1997,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_1999,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_2004,plain,
esk1_2(X1,esk11_1(X2)) = X1,
inference(rename_variables,[],[i_0_329]) ).
cnf(i_0_2013,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_2088,plain,
esk1_2(X1,esk11_1(X2)) = X1,
inference(rename_variables,[],[i_0_329]) ).
cnf(i_0_2152,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_2303,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_2456,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_2615,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_2818,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_2820,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_2883,plain,
esk1_2(X1,esk11_1(X2)) = X1,
inference(rename_variables,[],[i_0_329]) ).
cnf(i_0_2899,plain,
esk1_2(X1,esk11_1(X2)) = X1,
inference(rename_variables,[],[i_0_329]) ).
cnf(i_0_2969,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_2982,plain,
esk1_2(X1,esk11_1(X2)) = X1,
inference(rename_variables,[],[i_0_329]) ).
cnf(i_0_2984,plain,
X1 = esk4_1(singleton(X1)),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_3087,plain,
esk1_2(X1,esk11_1(X2)) = X1,
inference(rename_variables,[],[i_0_329]) ).
cnf(i_0_3089,plain,
esk1_2(X1,esk11_1(X2)) = X1,
inference(rename_variables,[],[i_0_329]) ).
cnf(i_0_3094,plain,
esk1_2(X1,esk11_1(X2)) = X1,
inference(rename_variables,[],[i_0_329]) ).
cnf(i_0_361,plain,
function(esk4_1(singleton(esk15_0))),
inference(scs_inference,[],[i_0_328,i_0_360,i_0_211,i_0_212]) ).
cnf(i_0_363,plain,
relation_empty_yielding(esk4_1(singleton(esk14_0))),
inference(scs_inference,[],[i_0_328,i_0_360,i_0_362,i_0_211,i_0_212,i_0_213]) ).
cnf(i_0_365,plain,
function(esk4_1(singleton(esk13_0))),
inference(scs_inference,[],[i_0_328,i_0_360,i_0_362,i_0_364,i_0_211,i_0_212,i_0_213,i_0_257]) ).
cnf(i_0_367,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(scs_inference,[],[i_0_328,i_0_360,i_0_362,i_0_364,i_0_329,i_0_211,i_0_212,i_0_213,i_0_257,i_0_153]) ).
cnf(i_0_371,plain,
~ in(X1,esk4_1(powerset(esk9_0))),
inference(scs_inference,[],[i_0_328,i_0_360,i_0_362,i_0_364,i_0_266,i_0_146,i_0_329,i_0_114,i_0_211,i_0_212,i_0_213,i_0_257,i_0_153,i_0_104,i_0_90]) ).
cnf(i_0_374,plain,
in(esk4_1(powerset(X1)),powerset(X1)),
inference(scs_inference,[],[i_0_328,i_0_360,i_0_362,i_0_364,i_0_266,i_0_146,i_0_329,i_0_117,i_0_114,i_0_372,i_0_211,i_0_212,i_0_213,i_0_257,i_0_153,i_0_104,i_0_90,i_0_100]) ).
cnf(i_0_377,plain,
relation_empty_yielding(esk4_1(singleton(set_difference(empty_set,X1)))),
inference(scs_inference,[],[i_0_328,i_0_360,i_0_362,i_0_364,i_0_366,i_0_266,i_0_342,i_0_146,i_0_329,i_0_117,i_0_114,i_0_372,i_0_211,i_0_212,i_0_213,i_0_257,i_0_153,i_0_104,i_0_90,i_0_100,i_0_176]) ).
cnf(i_0_381,plain,
esk9_0 != powerset(X1),
inference(scs_inference,[],[i_0_328,i_0_360,i_0_362,i_0_364,i_0_366,i_0_266,i_0_342,i_0_307,i_0_146,i_0_329,i_0_369,i_0_117,i_0_114,i_0_372,i_0_211,i_0_212,i_0_213,i_0_257,i_0_153,i_0_104,i_0_90,i_0_100,i_0_176,i_0_168,i_0_173]) ).
cnf(i_0_382,plain,
set_difference(set_difference(esk13_0,empty_set),empty_set) != esk1_2(esk15_0,esk11_1(X1)),
inference(scs_inference,[],[i_0_328,i_0_360,i_0_362,i_0_364,i_0_366,i_0_266,i_0_342,i_0_307,i_0_146,i_0_329,i_0_369,i_0_380,i_0_117,i_0_114,i_0_372,i_0_211,i_0_212,i_0_213,i_0_257,i_0_153,i_0_104,i_0_90,i_0_100,i_0_176,i_0_168,i_0_173,i_0_154]) ).
cnf(i_0_384,plain,
function(esk4_1(singleton(set_difference(empty_set,X1)))),
inference(scs_inference,[],[i_0_328,i_0_360,i_0_362,i_0_364,i_0_366,i_0_378,i_0_266,i_0_342,i_0_348,i_0_307,i_0_146,i_0_329,i_0_369,i_0_380,i_0_117,i_0_114,i_0_372,i_0_211,i_0_212,i_0_213,i_0_257,i_0_153,i_0_104,i_0_90,i_0_100,i_0_176,i_0_168,i_0_173,i_0_154,i_0_170]) ).
cnf(i_0_386,plain,
relation(esk4_1(singleton(set_difference(empty_set,X1)))),
inference(scs_inference,[],[i_0_328,i_0_360,i_0_362,i_0_364,i_0_366,i_0_378,i_0_385,i_0_266,i_0_342,i_0_348,i_0_349,i_0_307,i_0_146,i_0_329,i_0_369,i_0_380,i_0_117,i_0_114,i_0_372,i_0_211,i_0_212,i_0_213,i_0_257,i_0_153,i_0_104,i_0_90,i_0_100,i_0_176,i_0_168,i_0_173,i_0_154,i_0_170,i_0_169]) ).
cnf(i_0_390,plain,
one_to_one(empty_set),
inference(scs_inference,[],[i_0_328,i_0_360,i_0_362,i_0_364,i_0_366,i_0_378,i_0_385,i_0_266,i_0_342,i_0_348,i_0_349,i_0_307,i_0_146,i_0_151,i_0_329,i_0_369,i_0_380,i_0_383,i_0_117,i_0_263,i_0_141,i_0_114,i_0_372,i_0_211,i_0_212,i_0_213,i_0_257,i_0_153,i_0_104,i_0_90,i_0_100,i_0_176,i_0_168,i_0_173,i_0_154,i_0_170,i_0_169,i_0_167,i_0_112]) ).
cnf(i_0_392,plain,
~ in(powerset(X1),esk4_1(powerset(X1))),
inference(scs_inference,[],[i_0_328,i_0_360,i_0_362,i_0_364,i_0_366,i_0_378,i_0_385,i_0_266,i_0_342,i_0_348,i_0_349,i_0_307,i_0_146,i_0_151,i_0_329,i_0_369,i_0_380,i_0_383,i_0_117,i_0_263,i_0_141,i_0_114,i_0_372,i_0_211,i_0_212,i_0_213,i_0_257,i_0_153,i_0_104,i_0_90,i_0_100,i_0_176,i_0_168,i_0_173,i_0_154,i_0_170,i_0_169,i_0_167,i_0_112,i_0_97]) ).
cnf(i_0_561,plain,
relation(set_difference(empty_set,X1)),
inference(rename_variables,[],[i_0_349]) ).
cnf(i_0_608,plain,
relation(esk4_1(singleton(esk9_0))),
inference(scs_inference,[],[i_0_328,i_0_607,i_0_137,i_0_188,i_0_170,i_0_169]) ).
cnf(i_0_666,plain,
relation(esk4_1(singleton(esk6_0))),
inference(scs_inference,[],[i_0_328,i_0_665,i_0_138,i_0_228,i_0_170,i_0_169]) ).
cnf(i_0_688,plain,
relation(esk4_1(singleton(esk8_0))),
inference(scs_inference,[],[i_0_328,i_0_687,i_0_186,i_0_263,i_0_170,i_0_169]) ).
cnf(i_0_394,plain,
relation(esk1_2(esk15_0,esk11_1(X1))),
inference(scs_inference,[],[i_0_367,i_0_211]) ).
cnf(i_0_395,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_397,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_399,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_401,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_407,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_414,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_416,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_420,plain,
relation(esk4_1(singleton(set_difference(empty_set,X1)))),
inference(rename_variables,[],[i_0_386]) ).
cnf(i_0_455,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_485,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_491,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_493,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_526,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_530,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_532,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_548,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_550,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_554,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_576,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_595,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_597,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_599,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_629,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_631,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_633,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_641,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_643,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_645,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_653,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_655,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_657,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_674,plain,
relation_empty_yielding(esk1_2(esk4_1(singleton(esk14_0)),esk11_1(X1))),
inference(scs_inference,[],[i_0_367,i_0_363,i_0_176]) ).
cnf(i_0_675,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_677,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_679,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_696,plain,
relation_empty_yielding(esk1_2(empty_set,esk11_1(X1))),
inference(scs_inference,[],[i_0_367,i_0_131,i_0_176]) ).
cnf(i_0_697,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_699,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_701,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_717,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_719,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_721,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_729,plain,
function(esk1_2(set_difference(empty_set,X1),esk11_1(X2))),
inference(scs_inference,[],[i_0_367,i_0_348,i_0_170]) ).
cnf(i_0_730,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_732,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_749,plain,
function(esk1_2(set_difference(set_difference(empty_set,X1),empty_set),esk11_1(X2))),
inference(scs_inference,[],[i_0_367,i_0_279,i_0_170]) ).
cnf(i_0_750,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_752,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_760,plain,
~ in(set_difference(powerset(X1),empty_set),esk4_1(powerset(X1))),
inference(scs_inference,[],[i_0_121,i_0_392,i_0_167]) ).
cnf(i_0_762,plain,
~ in(X1,set_difference(esk6_0,empty_set)),
inference(scs_inference,[],[i_0_121,i_0_761,i_0_224,i_0_392,i_0_167,i_0_168]) ).
cnf(i_0_1136,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_1151,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_1175,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_1195,plain,
relation(esk1_2(esk11_1(X1),esk11_1(X2))),
inference(scs_inference,[],[i_0_230,i_0_205,i_0_125,i_0_367,i_0_155,i_0_156,i_0_157,i_0_158,i_0_160,i_0_162,i_0_163,i_0_164,i_0_165,i_0_113,i_0_115,i_0_116,i_0_287]) ).
cnf(i_0_1196,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_1197,plain,
element(X1,powerset(X1)),
inference(scs_inference,[],[i_0_120,i_0_230,i_0_205,i_0_125,i_0_367,i_0_155,i_0_156,i_0_157,i_0_158,i_0_160,i_0_162,i_0_163,i_0_164,i_0_165,i_0_113,i_0_115,i_0_116,i_0_287,i_0_99]) ).
cnf(i_0_1199,plain,
element(esk7_1(esk15_0),powerset(esk15_0)),
inference(scs_inference,[],[i_0_120,i_0_230,i_0_205,i_0_125,i_0_367,i_0_155,i_0_156,i_0_157,i_0_158,i_0_160,i_0_162,i_0_163,i_0_164,i_0_165,i_0_113,i_0_115,i_0_116,i_0_287,i_0_99,i_0_107]) ).
cnf(i_0_1201,plain,
set_difference(singleton(empty_set),singleton(set_difference(empty_set,X1))) != singleton(empty_set),
inference(scs_inference,[],[i_0_120,i_0_230,i_0_205,i_0_294,i_0_125,i_0_367,i_0_155,i_0_156,i_0_157,i_0_158,i_0_160,i_0_162,i_0_163,i_0_164,i_0_165,i_0_113,i_0_115,i_0_116,i_0_287,i_0_99,i_0_107,i_0_93]) ).
cnf(i_0_1203,plain,
set_difference(singleton(empty_set),singleton(esk15_0)) = singleton(empty_set),
inference(scs_inference,[],[i_0_120,i_0_280,i_0_230,i_0_205,i_0_294,i_0_125,i_0_367,i_0_155,i_0_156,i_0_157,i_0_158,i_0_160,i_0_162,i_0_163,i_0_164,i_0_165,i_0_113,i_0_115,i_0_116,i_0_287,i_0_99,i_0_107,i_0_93,i_0_105]) ).
cnf(i_0_1206,plain,
set_difference(X1,X1) = empty_set,
inference(scs_inference,[],[i_0_120,i_0_280,i_0_230,i_0_205,i_0_294,i_0_125,i_0_367,i_0_155,i_0_156,i_0_157,i_0_158,i_0_160,i_0_162,i_0_163,i_0_164,i_0_165,i_0_113,i_0_115,i_0_116,i_0_287,i_0_99,i_0_107,i_0_93,i_0_105,i_0_159,i_0_103]) ).
cnf(i_0_1208,plain,
~ in(empty_set,singleton(esk15_0)),
inference(scs_inference,[],[i_0_120,i_0_280,i_0_230,i_0_205,i_0_294,i_0_125,i_0_367,i_0_155,i_0_156,i_0_157,i_0_158,i_0_160,i_0_162,i_0_163,i_0_164,i_0_165,i_0_113,i_0_115,i_0_116,i_0_287,i_0_99,i_0_107,i_0_93,i_0_105,i_0_159,i_0_103,i_0_178]) ).
cnf(i_0_1273,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_1749,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_1771,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_1914,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_1936,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_2074,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_2094,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_2212,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_2230,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_2338,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_2357,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_2396,plain,
in(esk4_1(powerset(X1)),powerset(X1)),
inference(rename_variables,[],[i_0_374]) ).
cnf(i_0_2517,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_2519,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_2532,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_2669,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_2885,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_3078,plain,
X1 = esk1_2(X1,esk11_1(X2)),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_396,plain,
function(esk1_2(esk15_0,esk11_1(X1))),
inference(scs_inference,[],[i_0_367,i_0_395,i_0_211,i_0_212]) ).
cnf(i_0_398,plain,
relation_empty_yielding(esk1_2(esk14_0,esk11_1(X1))),
inference(scs_inference,[],[i_0_367,i_0_395,i_0_397,i_0_211,i_0_212,i_0_213]) ).
cnf(i_0_400,plain,
function(esk1_2(esk13_0,esk11_1(X1))),
inference(scs_inference,[],[i_0_367,i_0_395,i_0_397,i_0_399,i_0_211,i_0_212,i_0_213,i_0_257]) ).
cnf(i_0_402,plain,
X1 = set_difference(X1,empty_set),
inference(scs_inference,[],[i_0_367,i_0_395,i_0_397,i_0_399,i_0_121,i_0_211,i_0_212,i_0_213,i_0_257,i_0_153]) ).
cnf(i_0_403,plain,
~ in(esk6_0,esk4_1(singleton(singleton(esk15_0)))),
inference(scs_inference,[],[i_0_367,i_0_395,i_0_397,i_0_399,i_0_288,i_0_316,i_0_121,i_0_211,i_0_212,i_0_213,i_0_257,i_0_153,i_0_104]) ).
cnf(i_0_406,plain,
relation_empty_yielding(esk1_2(set_difference(set_difference(empty_set,X1),empty_set),esk11_1(X2))),
inference(scs_inference,[],[i_0_246,i_0_367,i_0_395,i_0_397,i_0_399,i_0_401,i_0_288,i_0_316,i_0_121,i_0_211,i_0_212,i_0_213,i_0_257,i_0_153,i_0_104,i_0_176]) ).
cnf(i_0_408,plain,
~ in(X1,esk4_1(singleton(set_difference(esk9_0,empty_set)))),
inference(scs_inference,[],[i_0_246,i_0_367,i_0_395,i_0_397,i_0_399,i_0_401,i_0_288,i_0_193,i_0_316,i_0_404,i_0_121,i_0_211,i_0_212,i_0_213,i_0_257,i_0_153,i_0_104,i_0_176,i_0_168]) ).
cnf(i_0_410,plain,
empty_set != esk10_0,
inference(scs_inference,[],[i_0_246,i_0_367,i_0_395,i_0_397,i_0_399,i_0_401,i_0_288,i_0_193,i_0_151,i_0_316,i_0_404,i_0_129,i_0_121,i_0_211,i_0_212,i_0_213,i_0_257,i_0_153,i_0_104,i_0_176,i_0_168,i_0_173]) ).
cnf(i_0_411,plain,
esk6_0 != esk4_1(singleton(esk15_0)),
inference(scs_inference,[],[i_0_246,i_0_367,i_0_395,i_0_397,i_0_399,i_0_401,i_0_288,i_0_193,i_0_151,i_0_316,i_0_404,i_0_409,i_0_129,i_0_121,i_0_211,i_0_212,i_0_213,i_0_257,i_0_153,i_0_104,i_0_176,i_0_168,i_0_173,i_0_154]) ).
cnf(i_0_413,plain,
function(esk1_2(esk4_1(singleton(esk15_0)),esk11_1(X1))),
inference(scs_inference,[],[i_0_246,i_0_367,i_0_395,i_0_397,i_0_399,i_0_401,i_0_407,i_0_288,i_0_361,i_0_193,i_0_151,i_0_316,i_0_404,i_0_409,i_0_129,i_0_121,i_0_211,i_0_212,i_0_213,i_0_257,i_0_153,i_0_104,i_0_176,i_0_168,i_0_173,i_0_154,i_0_170]) ).
cnf(i_0_415,plain,
relation(esk1_2(esk4_1(singleton(esk15_0)),esk11_1(X1))),
inference(scs_inference,[],[i_0_246,i_0_367,i_0_395,i_0_397,i_0_399,i_0_401,i_0_407,i_0_414,i_0_288,i_0_359,i_0_361,i_0_193,i_0_151,i_0_316,i_0_404,i_0_409,i_0_129,i_0_121,i_0_211,i_0_212,i_0_213,i_0_257,i_0_153,i_0_104,i_0_176,i_0_168,i_0_173,i_0_154,i_0_170,i_0_169]) ).
cnf(i_0_417,plain,
~ in(esk4_1(singleton(esk13_0)),set_difference(singleton(esk15_0),empty_set)),
inference(scs_inference,[],[i_0_246,i_0_367,i_0_395,i_0_397,i_0_399,i_0_401,i_0_407,i_0_414,i_0_288,i_0_359,i_0_361,i_0_193,i_0_151,i_0_202,i_0_316,i_0_404,i_0_409,i_0_412,i_0_129,i_0_121,i_0_211,i_0_212,i_0_213,i_0_257,i_0_153,i_0_104,i_0_176,i_0_168,i_0_173,i_0_154,i_0_170,i_0_169,i_0_167]) ).
cnf(i_0_591,plain,
relation(esk1_2(esk15_0,esk11_1(X1))),
inference(rename_variables,[],[i_0_394]) ).
cnf(i_0_676,plain,
function(esk1_2(esk4_1(singleton(esk6_0)),esk11_1(X1))),
inference(scs_inference,[],[i_0_367,i_0_675,i_0_664,i_0_363,i_0_176,i_0_170]) ).
cnf(i_0_698,plain,
function(esk1_2(esk4_1(singleton(empty_set)),esk11_1(X1))),
inference(scs_inference,[],[i_0_367,i_0_697,i_0_686,i_0_131,i_0_176,i_0_170]) ).
cnf(i_0_700,plain,
relation(esk1_2(esk4_1(singleton(esk9_0)),esk11_1(X1))),
inference(scs_inference,[],[i_0_367,i_0_697,i_0_699,i_0_608,i_0_686,i_0_131,i_0_176,i_0_170,i_0_169]) ).
cnf(i_0_716,plain,
relation_empty_yielding(esk1_2(esk1_2(empty_set,esk11_1(X1)),esk11_1(X2))),
inference(scs_inference,[],[i_0_367,i_0_696,i_0_176]) ).
cnf(i_0_731,plain,
relation(esk1_2(esk4_1(singleton(esk8_0)),esk11_1(X1))),
inference(scs_inference,[],[i_0_367,i_0_730,i_0_688,i_0_348,i_0_170,i_0_169]) ).
cnf(i_0_1289,plain,
set_difference(singleton(esk8_0),singleton(esk15_0)) = singleton(esk8_0),
inference(scs_inference,[],[i_0_325,i_0_182,i_0_1189,i_0_1206,i_0_1193,i_0_113,i_0_115,i_0_116,i_0_99,i_0_107,i_0_93,i_0_105]) ).
cnf(i_0_1337,plain,
~ in(X1,set_difference(esk6_0,empty_set)),
inference(rename_variables,[],[i_0_762]) ).
cnf(i_0_1355,plain,
set_difference(X1,X1) = empty_set,
inference(rename_variables,[],[i_0_1206]) ).
cnf(i_0_1411,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_1197]) ).
cnf(i_0_1574,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_1197]) ).
cnf(i_0_1685,plain,
function(esk1_2(set_difference(empty_set,X1),esk11_1(X2))),
inference(rename_variables,[],[i_0_729]) ).
cnf(i_0_1746,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_1197]) ).
cnf(i_0_1911,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_1197]) ).
cnf(i_0_2069,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_1197]) ).
cnf(i_0_2207,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_1197]) ).
cnf(i_0_2313,plain,
~ in(X1,set_difference(esk6_0,empty_set)),
inference(rename_variables,[],[i_0_762]) ).
cnf(i_0_2453,plain,
element(X1,powerset(X1)),
inference(rename_variables,[],[i_0_1197]) ).
cnf(c_0_1219,plain,
( in(esk2_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
i_0_96 ).
cnf(c_0_1220,negated_conjecture,
function(esk15_0),
i_0_142 ).
cnf(c_0_1221,negated_conjecture,
relation(esk15_0),
i_0_133 ).
cnf(c_0_1222,negated_conjecture,
~ one_to_one(esk15_0),
i_0_127 ).
cnf(c_0_1223,plain,
( relation_image(X1,singleton(X2)) = singleton(apply(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(X1)) ),
i_0_87 ).
cnf(c_0_1224,negated_conjecture,
in(esk2_1(esk15_0),relation_dom(esk15_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1219,c_0_1220]),c_0_1221])]),c_0_1222]) ).
cnf(c_0_1225,plain,
( in(esk3_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
i_0_95 ).
cnf(c_0_1226,plain,
( apply(X1,esk2_1(X1)) = apply(X1,esk3_1(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
i_0_92 ).
cnf(c_0_1227,negated_conjecture,
relation_image(esk15_0,set_difference(X1,X2)) = set_difference(relation_image(esk15_0,X1),relation_image(esk15_0,X2)),
i_0_86 ).
cnf(c_0_1228,negated_conjecture,
relation_image(esk15_0,singleton(esk2_1(esk15_0))) = singleton(apply(esk15_0,esk2_1(esk15_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1223,c_0_1224]),c_0_1220]),c_0_1221])]) ).
cnf(c_0_1229,negated_conjecture,
in(esk3_1(esk15_0),relation_dom(esk15_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1225,c_0_1220]),c_0_1221])]),c_0_1222]) ).
cnf(c_0_1230,negated_conjecture,
apply(esk15_0,esk3_1(esk15_0)) = apply(esk15_0,esk2_1(esk15_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1226,c_0_1220]),c_0_1221])]),c_0_1222]) ).
cnf(c_0_1231,negated_conjecture,
set_difference(singleton(apply(esk15_0,esk2_1(esk15_0))),relation_image(esk15_0,X1)) = relation_image(esk15_0,set_difference(singleton(esk2_1(esk15_0)),X1)),
inference(spm,[status(thm)],[c_0_1227,c_0_1228]) ).
cnf(c_0_1232,plain,
relation_image(esk15_0,singleton(esk3_1(esk15_0))) = singleton(apply(esk15_0,esk2_1(esk15_0))),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1223,c_0_1229]),c_0_1220]),c_0_1221])]),c_0_1230]) ).
cnf(c_0_1233,plain,
set_difference(X1,X1) = empty_set,
i_0_1206 ).
cnf(c_0_1234,plain,
( set_difference(singleton(X1),singleton(X2)) != singleton(X1)
| X1 != X2 ),
i_0_93 ).
cnf(c_0_1235,plain,
relation_image(esk15_0,set_difference(singleton(esk2_1(esk15_0)),singleton(esk3_1(esk15_0)))) = empty_set,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1231,c_0_1232]),c_0_1233]) ).
cnf(c_0_1236,plain,
( X1 = X2
| set_difference(singleton(X1),singleton(X2)) = singleton(X1) ),
i_0_105 ).
cnf(c_0_1237,plain,
singleton(X1) != empty_set,
inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_1234]),c_0_1233]) ).
cnf(c_0_1238,plain,
( one_to_one(X1)
| esk2_1(X1) != esk3_1(X1)
| ~ relation(X1)
| ~ function(X1) ),
i_0_106 ).
cnf(c_0_1239,plain,
esk3_1(esk15_0) = esk2_1(esk15_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1235,c_0_1236]),c_0_1228]),c_0_1237]) ).
cnf(c_0_1240,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1238,c_0_1239]),c_0_1220]),c_0_1221])]),c_0_1222]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.18 % Problem : SEU055+1 : TPTP v9.2.1. Released v3.2.0.
% 0.06/0.18 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.13/0.41 % Computer : n026.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8042.1875MB
% 0.13/0.41 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Tue May 5 02:42:54 EDT 2026
% 0.13/0.42 % CPUTime :
% 0.16/0.45 % start to proof: theBenchmark
% 151.04/121.45 % Version : CSE_E---1.7
% 151.04/121.45 % Problem : theBenchmark.p
% 151.04/121.45 % SZS status Theorem for theBenchmark.p
% 151.04/121.45 % SZS output start CNFRefutation
% See solution above
% 159.44/129.80 % Total time : 120.986s
%------------------------------------------------------------------------------