%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU071+1 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n018.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 05:10:35 PM UTC 2026
% Result : Theorem 136.21s 105.68s
% Output : CNFRefutation 144.11s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named i_0_199)
% Comments :
%------------------------------------------------------------------------------
fof(t152_funct_1,conjecture,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( one_to_one(X2)
=> subset(relation_inverse_image(X2,relation_image(X2,X1)),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t152_funct_1) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(rc1_subset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(fc5_relat_1,axiom,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(rc2_relat_1,axiom,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
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/benchmark/theBenchmark.p',d13_funct_1) ).
fof(d12_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( X3 = relation_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,relation_dom(X1))
& in(X5,X2)
& X4 = apply(X1,X5) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_funct_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/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(cc1_relat_1,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(cc1_funct_1,axiom,
! [X1] :
( empty(X1)
=> function(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(rc3_relat_1,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(rc3_funct_1,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(rc2_funct_1,axiom,
? [X1] :
( relation(X1)
& empty(X1)
& function(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(rc1_relat_1,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(rc1_funct_1,axiom,
? [X1] :
( relation(X1)
& function(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(fc4_relat_1,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(i_0_35,negated_conjecture,
~ ! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( one_to_one(X2)
=> subset(relation_inverse_image(X2,relation_image(X2,X1)),X1) ) ),
inference(assume_negation,[status(cth)],[t152_funct_1]) ).
fof(i_0_36,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_37,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[rc1_subset_1]) ).
fof(i_0_38,plain,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
inference(fof_simplification,[status(thm)],[fc5_relat_1]) ).
fof(i_0_39,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(i_0_40,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_41,plain,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
inference(fof_simplification,[status(thm)],[rc2_relat_1]) ).
fof(i_0_42,plain,
! [X81,X82,X83,X84,X85,X86,X87] :
( ( in(X84,relation_dom(X81))
| ~ in(X84,X83)
| X83 != relation_inverse_image(X81,X82)
| ~ relation(X81)
| ~ function(X81) )
& ( in(apply(X81,X84),X82)
| ~ in(X84,X83)
| X83 != relation_inverse_image(X81,X82)
| ~ relation(X81)
| ~ function(X81) )
& ( ~ in(X85,relation_dom(X81))
| ~ in(apply(X81,X85),X82)
| in(X85,X83)
| X83 != relation_inverse_image(X81,X82)
| ~ relation(X81)
| ~ function(X81) )
& ( ~ in(esk4_3(X81,X86,X87),X87)
| ~ in(esk4_3(X81,X86,X87),relation_dom(X81))
| ~ in(apply(X81,esk4_3(X81,X86,X87)),X86)
| X87 = relation_inverse_image(X81,X86)
| ~ relation(X81)
| ~ function(X81) )
& ( in(esk4_3(X81,X86,X87),relation_dom(X81))
| in(esk4_3(X81,X86,X87),X87)
| X87 = relation_inverse_image(X81,X86)
| ~ relation(X81)
| ~ function(X81) )
& ( in(apply(X81,esk4_3(X81,X86,X87)),X86)
| in(esk4_3(X81,X86,X87),X87)
| X87 = relation_inverse_image(X81,X86)
| ~ relation(X81)
| ~ function(X81) ) ),
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)],[d13_funct_1])])])])])]) ).
fof(i_0_43,plain,
! [X69,X70,X71,X72,X74,X75,X76,X77,X79] :
( ( in(esk1_4(X69,X70,X71,X72),relation_dom(X69))
| ~ in(X72,X71)
| X71 != relation_image(X69,X70)
| ~ relation(X69)
| ~ function(X69) )
& ( in(esk1_4(X69,X70,X71,X72),X70)
| ~ in(X72,X71)
| X71 != relation_image(X69,X70)
| ~ relation(X69)
| ~ function(X69) )
& ( X72 = apply(X69,esk1_4(X69,X70,X71,X72))
| ~ in(X72,X71)
| X71 != relation_image(X69,X70)
| ~ relation(X69)
| ~ function(X69) )
& ( ~ in(X75,relation_dom(X69))
| ~ in(X75,X70)
| X74 != apply(X69,X75)
| in(X74,X71)
| X71 != relation_image(X69,X70)
| ~ relation(X69)
| ~ function(X69) )
& ( ~ in(esk2_3(X69,X76,X77),X77)
| ~ in(X79,relation_dom(X69))
| ~ in(X79,X76)
| esk2_3(X69,X76,X77) != apply(X69,X79)
| X77 = relation_image(X69,X76)
| ~ relation(X69)
| ~ function(X69) )
& ( in(esk3_3(X69,X76,X77),relation_dom(X69))
| in(esk2_3(X69,X76,X77),X77)
| X77 = relation_image(X69,X76)
| ~ relation(X69)
| ~ function(X69) )
& ( in(esk3_3(X69,X76,X77),X76)
| in(esk2_3(X69,X76,X77),X77)
| X77 = relation_image(X69,X76)
| ~ relation(X69)
| ~ function(X69) )
& ( esk2_3(X69,X76,X77) = apply(X69,esk3_3(X69,X76,X77))
| in(esk2_3(X69,X76,X77),X77)
| X77 = relation_image(X69,X76)
| ~ relation(X69)
| ~ function(X69) ) ),
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)],[d12_funct_1])])])])])]) ).
fof(i_0_44,plain,
! [X95,X96,X97] :
( ( ~ one_to_one(X95)
| ~ in(X96,relation_dom(X95))
| ~ in(X97,relation_dom(X95))
| apply(X95,X96) != apply(X95,X97)
| X96 = X97
| ~ relation(X95)
| ~ function(X95) )
& ( in(esk6_1(X95),relation_dom(X95))
| one_to_one(X95)
| ~ relation(X95)
| ~ function(X95) )
& ( in(esk7_1(X95),relation_dom(X95))
| one_to_one(X95)
| ~ relation(X95)
| ~ function(X95) )
& ( apply(X95,esk6_1(X95)) = apply(X95,esk7_1(X95))
| one_to_one(X95)
| ~ relation(X95)
| ~ function(X95) )
& ( esk6_1(X95) != esk7_1(X95)
| one_to_one(X95)
| ~ relation(X95)
| ~ function(X95) ) ),
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_45,negated_conjecture,
( relation(esk20_0)
& function(esk20_0)
& one_to_one(esk20_0)
& ~ subset(relation_inverse_image(esk20_0,relation_image(esk20_0,esk19_0)),esk19_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_35])])]) ).
fof(i_0_46,plain,
! [X89,X90,X91,X92,X93] :
( ( ~ subset(X89,X90)
| ~ in(X91,X89)
| in(X91,X90) )
& ( in(esk5_2(X92,X93),X92)
| subset(X92,X93) )
& ( ~ in(esk5_2(X92,X93),X93)
| subset(X92,X93) ) ),
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)],[d3_tarski])])])])])]) ).
fof(i_0_47,plain,
! [X126,X127,X128] :
( ~ in(X126,X127)
| ~ element(X127,powerset(X128))
| element(X126,X128) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(i_0_48,plain,
! [X129,X130,X131] :
( ~ in(X129,X130)
| ~ element(X130,powerset(X131))
| ~ empty(X131) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(i_0_49,plain,
! [X124,X125] :
( ( ~ element(X124,powerset(X125))
| subset(X124,X125) )
& ( ~ subset(X124,X125)
| element(X124,powerset(X125)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(i_0_50,plain,
! [X64,X65] :
( ~ in(X64,X65)
| ~ in(X65,X64) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_36])]) ).
fof(i_0_51,plain,
! [X122,X123] :
( ~ element(X122,X123)
| empty(X123)
| in(X122,X123) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(i_0_52,plain,
! [X120,X121] :
( ~ in(X120,X121)
| element(X120,X121) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(i_0_53,plain,
! [X107] :
( ( element(esk11_1(X107),powerset(X107))
| empty(X107) )
& ( ~ empty(esk11_1(X107))
| empty(X107) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_37])])])]) ).
fof(i_0_54,plain,
! [X133,X134] :
( ~ in(X133,X134)
| ~ empty(X134) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_55,plain,
! [X103] :
( empty(X103)
| ~ relation(X103)
| ~ empty(relation_dom(X103)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_38])]) ).
fof(i_0_56,plain,
! [X112] :
( element(esk15_1(X112),powerset(X112))
& empty(esk15_1(X112)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(i_0_57,plain,
! [X68] :
( ( relation(X68)
| ~ relation(X68)
| ~ empty(X68)
| ~ function(X68) )
& ( function(X68)
| ~ relation(X68)
| ~ empty(X68)
| ~ function(X68) )
& ( one_to_one(X68)
| ~ relation(X68)
| ~ empty(X68)
| ~ function(X68) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_funct_1])])]) ).
fof(i_0_58,plain,
! [X100] : element(esk8_1(X100),X100),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(i_0_59,plain,
! [X104] :
( ( empty(relation_dom(X104))
| ~ empty(X104) )
& ( relation(relation_dom(X104))
| ~ empty(X104) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc7_relat_1])])]) ).
fof(i_0_60,plain,
! [X102] : ~ empty(powerset(X102)),
inference(variable_rename,[status(thm)],[i_0_39]) ).
fof(i_0_61,plain,
! [X135,X136] :
( ~ empty(X135)
| X135 = X136
| ~ empty(X136) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_62,plain,
! [X117] : subset(X117,X117),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(i_0_63,plain,
! [X67] :
( ~ empty(X67)
| relation(X67) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relat_1])]) ).
fof(i_0_64,plain,
! [X66] :
( ~ empty(X66)
| function(X66) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_funct_1])]) ).
fof(i_0_65,plain,
! [X132] :
( ~ empty(X132)
| X132 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_66,plain,
~ empty(esk16_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_40])]) ).
fof(i_0_67,plain,
( ~ empty(esk14_0)
& relation(esk14_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_41])]) ).
fof(i_0_68,plain,
( relation(esk18_0)
& relation_empty_yielding(esk18_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_relat_1])]) ).
fof(i_0_69,plain,
( relation(esk17_0)
& function(esk17_0)
& one_to_one(esk17_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_funct_1])]) ).
fof(i_0_70,plain,
( relation(esk13_0)
& empty(esk13_0)
& function(esk13_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_funct_1])]) ).
fof(i_0_71,plain,
( empty(esk10_0)
& relation(esk10_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_relat_1])]) ).
fof(i_0_72,plain,
( relation(esk9_0)
& function(esk9_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_funct_1])]) ).
fof(i_0_73,plain,
empty(esk12_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_74,plain,
( X3 = relation_inverse_image(X1,X2)
| ~ in(esk4_3(X1,X2,X3),X3)
| ~ in(esk4_3(X1,X2,X3),relation_dom(X1))
| ~ in(apply(X1,esk4_3(X1,X2,X3)),X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_75,plain,
( in(esk1_4(X1,X2,X3,X4),relation_dom(X1))
| ~ in(X4,X3)
| X3 != relation_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_76,plain,
( X1 = apply(X2,esk1_4(X2,X3,X4,X1))
| ~ in(X1,X4)
| X4 != relation_image(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_77,plain,
( in(esk1_4(X1,X2,X3,X4),X2)
| ~ in(X4,X3)
| X3 != relation_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_78,plain,
( in(apply(X1,esk4_3(X1,X2,X3)),X2)
| in(esk4_3(X1,X2,X3),X3)
| X3 = relation_inverse_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_79,plain,
( X3 = relation_image(X1,X2)
| ~ in(esk2_3(X1,X2,X3),X3)
| ~ in(X4,relation_dom(X1))
| ~ in(X4,X2)
| esk2_3(X1,X2,X3) != apply(X1,X4)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_80,plain,
( esk2_3(X1,X2,X3) = apply(X1,esk3_3(X1,X2,X3))
| in(esk2_3(X1,X2,X3),X3)
| X3 = relation_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_81,plain,
( in(esk4_3(X1,X2,X3),relation_dom(X1))
| in(esk4_3(X1,X2,X3),X3)
| X3 = relation_inverse_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_82,plain,
( in(esk3_3(X1,X2,X3),relation_dom(X1))
| in(esk2_3(X1,X2,X3),X3)
| X3 = relation_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_83,plain,
( in(esk3_3(X1,X2,X3),X2)
| in(esk2_3(X1,X2,X3),X3)
| X3 = relation_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_84,plain,
( in(X1,X4)
| ~ in(X1,relation_dom(X2))
| ~ in(apply(X2,X1),X3)
| X4 != relation_inverse_image(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
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_44]),
[final] ).
cnf(i_0_86,plain,
( in(X4,X5)
| ~ in(X1,relation_dom(X2))
| ~ in(X1,X3)
| X4 != apply(X2,X1)
| X5 != relation_image(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_87,negated_conjecture,
~ subset(relation_inverse_image(esk20_0,relation_image(esk20_0,esk19_0)),esk19_0),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_88,plain,
( in(apply(X1,X2),X3)
| ~ in(X2,X4)
| X4 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_89,plain,
( in(X1,relation_dom(X2))
| ~ in(X1,X3)
| X3 != relation_inverse_image(X2,X4)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_90,plain,
( subset(X1,X2)
| ~ in(esk5_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_91,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_92,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_93,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_94,plain,
( apply(X1,esk6_1(X1)) = apply(X1,esk7_1(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_95,plain,
( in(esk5_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_96,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_97,plain,
( in(esk7_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_98,plain,
( in(esk6_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_99,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_100,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_101,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_102,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_103,plain,
( one_to_one(X1)
| esk6_1(X1) != esk7_1(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_104,plain,
( element(esk11_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_105,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_106,plain,
( empty(X1)
| ~ relation(X1)
| ~ empty(relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_107,plain,
element(esk15_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_108,plain,
( one_to_one(X1)
| ~ relation(X1)
| ~ empty(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_109,plain,
( empty(X1)
| ~ empty(esk11_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_110,plain,
element(esk8_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_111,plain,
( relation(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_112,plain,
( empty(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_113,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_114,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_115,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_116,plain,
( relation(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_117,plain,
( function(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_118,plain,
empty(esk15_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_119,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_120,plain,
~ empty(esk16_0),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_121,plain,
~ empty(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_122,plain,
relation_empty_yielding(esk18_0),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_123,plain,
relation_empty_yielding(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_124,negated_conjecture,
one_to_one(esk20_0),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_125,plain,
one_to_one(esk17_0),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_126,negated_conjecture,
relation(esk20_0),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_127,plain,
relation(esk18_0),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_128,plain,
relation(esk17_0),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_129,plain,
relation(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_130,plain,
relation(esk13_0),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_131,plain,
relation(esk10_0),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_132,plain,
relation(esk9_0),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_133,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_134,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_135,negated_conjecture,
function(esk20_0),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_136,plain,
function(esk17_0),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_137,plain,
function(esk13_0),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_138,plain,
function(esk9_0),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_139,plain,
empty(esk13_0),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_140,plain,
empty(esk12_0),
inference(split_conjunct,[status(thm)],[i_0_73]),
[final] ).
cnf(i_0_141,plain,
empty(esk10_0),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_142,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_143,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_144,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_145,axiom,
X1 = X1 ).
cnf(i_0_146,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_147,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_148,axiom,
( X1 != X2
| relation_inverse_image(X1,X3) = relation_inverse_image(X2,X3) ) ).
cnf(i_0_149,axiom,
( X1 != X2
| relation_inverse_image(X3,X1) = relation_inverse_image(X3,X2) ) ).
cnf(i_0_150,axiom,
( X1 != X2
| esk6_1(X1) = esk6_1(X2) ) ).
cnf(i_0_151,axiom,
( X1 != X2
| esk7_1(X1) = esk7_1(X2) ) ).
cnf(i_0_152,axiom,
( X1 != X2
| apply(X1,X3) = apply(X2,X3) ) ).
cnf(i_0_153,axiom,
( X1 != X2
| apply(X3,X1) = apply(X3,X2) ) ).
cnf(i_0_154,axiom,
( X1 != X2
| relation_image(X1,X3) = relation_image(X2,X3) ) ).
cnf(i_0_155,axiom,
( X1 != X2
| relation_image(X3,X1) = relation_image(X3,X2) ) ).
cnf(i_0_156,axiom,
( X1 != X2
| esk2_3(X1,X3,X4) = esk2_3(X2,X3,X4) ) ).
cnf(i_0_157,axiom,
( X1 != X2
| esk2_3(X3,X1,X4) = esk2_3(X3,X2,X4) ) ).
cnf(i_0_158,axiom,
( X1 != X2
| esk2_3(X3,X4,X1) = esk2_3(X3,X4,X2) ) ).
cnf(i_0_159,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_160,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_161,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_162,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_163,axiom,
( X1 != X2
| ~ one_to_one(X1)
| one_to_one(X2) ) ).
cnf(i_0_164,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_165,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_166,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_167,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_168,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_169,axiom,
( X1 != X2
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(X2) ) ).
cnf(i_0_324,plain,
~ in(X1,esk8_1(powerset(esk15_1(X2)))),
inference(scs_inference,[],[i_0_199,i_0_251,i_0_179,i_0_288,i_0_110,i_0_118,i_0_95,i_0_117,i_0_99,i_0_105,i_0_93,i_0_92]) ).
cnf(i_0_327,plain,
in(esk8_1(powerset(X1)),powerset(X1)),
inference(scs_inference,[],[i_0_199,i_0_251,i_0_179,i_0_288,i_0_110,i_0_325,i_0_118,i_0_113,i_0_95,i_0_117,i_0_99,i_0_105,i_0_93,i_0_92,i_0_101]) ).
cnf(i_0_332,plain,
esk15_1(X1) != powerset(X2),
inference(scs_inference,[],[i_0_87,i_0_199,i_0_251,i_0_221,i_0_179,i_0_288,i_0_110,i_0_325,i_0_118,i_0_113,i_0_95,i_0_117,i_0_99,i_0_105,i_0_93,i_0_92,i_0_101,i_0_164,i_0_168]) ).
cnf(i_0_333,plain,
powerset(X1) != esk8_1(powerset(esk10_0)),
inference(scs_inference,[],[i_0_87,i_0_199,i_0_251,i_0_221,i_0_179,i_0_236,i_0_288,i_0_110,i_0_325,i_0_118,i_0_113,i_0_95,i_0_117,i_0_99,i_0_105,i_0_93,i_0_92,i_0_101,i_0_164,i_0_168,i_0_160]) ).
cnf(i_0_335,plain,
~ in(X1,relation_inverse_image(esk12_0,relation_image(esk20_0,esk15_1(esk13_0)))),
inference(scs_inference,[],[i_0_87,i_0_199,i_0_322,i_0_251,i_0_221,i_0_179,i_0_236,i_0_288,i_0_110,i_0_325,i_0_118,i_0_181,i_0_183,i_0_113,i_0_95,i_0_117,i_0_99,i_0_105,i_0_93,i_0_92,i_0_101,i_0_164,i_0_168,i_0_160,i_0_175]) ).
cnf(i_0_338,plain,
one_to_one(esk12_0),
inference(scs_inference,[],[i_0_87,i_0_199,i_0_322,i_0_251,i_0_221,i_0_179,i_0_236,i_0_288,i_0_110,i_0_325,i_0_118,i_0_140,i_0_181,i_0_183,i_0_113,i_0_95,i_0_117,i_0_99,i_0_105,i_0_93,i_0_92,i_0_101,i_0_164,i_0_168,i_0_160,i_0_175,i_0_108]) ).
cnf(i_0_340,plain,
in(esk4_3(esk20_0,relation_image(esk20_0,esk19_0),esk15_1(esk19_0)),relation_dom(esk20_0)),
inference(scs_inference,[],[i_0_87,i_0_126,i_0_135,i_0_199,i_0_322,i_0_251,i_0_221,i_0_242,i_0_179,i_0_236,i_0_288,i_0_110,i_0_325,i_0_118,i_0_140,i_0_181,i_0_183,i_0_113,i_0_95,i_0_117,i_0_99,i_0_105,i_0_93,i_0_92,i_0_101,i_0_164,i_0_168,i_0_160,i_0_175,i_0_108,i_0_81]) ).
cnf(i_0_342,plain,
esk13_0 = relation_image(esk20_0,relation_image(esk20_0,esk15_1(esk13_0))),
inference(scs_inference,[],[i_0_87,i_0_126,i_0_135,i_0_199,i_0_322,i_0_336,i_0_251,i_0_221,i_0_242,i_0_179,i_0_313,i_0_236,i_0_288,i_0_110,i_0_325,i_0_118,i_0_140,i_0_181,i_0_183,i_0_113,i_0_95,i_0_117,i_0_99,i_0_105,i_0_93,i_0_92,i_0_101,i_0_164,i_0_168,i_0_160,i_0_175,i_0_108,i_0_81,i_0_83]) ).
cnf(i_0_346,plain,
relation_image(esk20_0,esk15_1(esk13_0)) = relation_inverse_image(esk20_0,esk13_0),
inference(scs_inference,[],[i_0_87,i_0_126,i_0_135,i_0_199,i_0_322,i_0_336,i_0_344,i_0_251,i_0_221,i_0_242,i_0_179,i_0_313,i_0_343,i_0_236,i_0_288,i_0_110,i_0_325,i_0_118,i_0_140,i_0_181,i_0_183,i_0_113,i_0_95,i_0_117,i_0_99,i_0_105,i_0_93,i_0_92,i_0_101,i_0_164,i_0_168,i_0_160,i_0_175,i_0_108,i_0_81,i_0_83,i_0_78]) ).
cnf(i_0_350,plain,
one_to_one(relation_image(esk20_0,relation_image(esk20_0,esk15_1(esk13_0)))),
inference(scs_inference,[],[i_0_87,i_0_126,i_0_135,i_0_199,i_0_322,i_0_336,i_0_344,i_0_251,i_0_221,i_0_242,i_0_179,i_0_313,i_0_343,i_0_236,i_0_288,i_0_110,i_0_325,i_0_118,i_0_140,i_0_181,i_0_183,i_0_113,i_0_95,i_0_117,i_0_99,i_0_105,i_0_93,i_0_92,i_0_101,i_0_164,i_0_168,i_0_160,i_0_175,i_0_108,i_0_81,i_0_83,i_0_78,i_0_263]) ).
cnf(i_0_351,plain,
relation_image(esk20_0,relation_image(esk20_0,esk15_1(esk13_0))) = esk13_0,
inference(scs_inference,[],[i_0_87,i_0_126,i_0_135,i_0_199,i_0_322,i_0_336,i_0_344,i_0_251,i_0_221,i_0_242,i_0_179,i_0_313,i_0_343,i_0_236,i_0_288,i_0_110,i_0_325,i_0_118,i_0_140,i_0_181,i_0_183,i_0_113,i_0_95,i_0_117,i_0_99,i_0_105,i_0_93,i_0_92,i_0_101,i_0_164,i_0_168,i_0_160,i_0_175,i_0_108,i_0_81,i_0_83,i_0_78,i_0_263,i_0_146]) ).
cnf(i_0_352,plain,
element(esk4_3(esk20_0,relation_image(esk20_0,esk19_0),esk15_1(esk19_0)),relation_dom(esk20_0)),
inference(scs_inference,[],[i_0_87,i_0_126,i_0_135,i_0_199,i_0_322,i_0_336,i_0_344,i_0_251,i_0_221,i_0_242,i_0_179,i_0_313,i_0_343,i_0_236,i_0_288,i_0_110,i_0_325,i_0_118,i_0_140,i_0_181,i_0_183,i_0_113,i_0_95,i_0_117,i_0_99,i_0_105,i_0_93,i_0_92,i_0_101,i_0_164,i_0_168,i_0_160,i_0_175,i_0_108,i_0_81,i_0_83,i_0_78,i_0_263,i_0_146,i_0_102]) ).
cnf(i_0_434,plain,
subset(esk4_3(esk20_0,relation_image(esk20_0,esk15_1(esk13_0)),powerset(X1)),X1),
inference(rename_variables,[],[i_0_274]) ).
cnf(i_0_589,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_280]) ).
cnf(i_0_669,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_280]) ).
cnf(i_0_678,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_280]) ).
cnf(i_0_796,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_280]) ).
cnf(i_0_808,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_280]) ).
cnf(i_0_1758,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_280]) ).
cnf(i_0_2661,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_280]) ).
cnf(i_0_308,plain,
relation(esk15_1(X1)),
inference(equality_inference,[],[302]) ).
cnf(i_0_309,plain,
function(esk9_0),
inference(equality_inference,[],[303]) ).
cnf(i_0_310,plain,
one_to_one(esk10_0),
inference(equality_inference,[],[304]) ).
cnf(i_0_311,plain,
~ in(powerset(X1),esk4_3(esk20_0,relation_image(esk20_0,esk15_1(esk13_0)),powerset(X1))),
inference(equality_inference,[],[305]) ).
cnf(i_0_363,plain,
relation_image(esk20_0,esk15_1(esk13_0)) = relation_inverse_image(esk20_0,esk13_0),
inference(equality_inference,[],[354]) ).
cnf(i_0_364,plain,
relation_inverse_image(esk20_0,esk13_0) = relation_image(esk20_0,esk15_1(esk13_0)),
inference(scs_inference,[],[i_0_346,i_0_146]) ).
cnf(i_0_365,plain,
subset(esk10_0,X1),
inference(scs_inference,[],[i_0_346,i_0_227,i_0_146,i_0_95]) ).
cnf(i_0_368,plain,
~ in(X1,esk12_0),
inference(scs_inference,[],[i_0_346,i_0_227,i_0_140,i_0_146,i_0_95,i_0_105]) ).
cnf(i_0_370,plain,
~ in(relation_dom(esk20_0),esk4_3(esk20_0,relation_image(esk20_0,esk19_0),esk15_1(esk19_0))),
inference(scs_inference,[],[i_0_346,i_0_340,i_0_227,i_0_140,i_0_146,i_0_95,i_0_105,i_0_99]) ).
cnf(i_0_372,plain,
powerset(X1) != relation_image(esk20_0,relation_image(esk20_0,esk15_1(esk13_0))),
inference(scs_inference,[],[i_0_346,i_0_340,i_0_227,i_0_195,i_0_351,i_0_140,i_0_146,i_0_95,i_0_105,i_0_99,i_0_147]) ).
cnf(i_0_373,plain,
~ subset(relation_dom(esk20_0),relation_image(esk20_0,esk15_1(esk13_0))),
inference(scs_inference,[],[i_0_199,i_0_346,i_0_340,i_0_227,i_0_195,i_0_351,i_0_140,i_0_146,i_0_95,i_0_105,i_0_99,i_0_147,i_0_93]) ).
cnf(i_0_376,plain,
~ in(X1,esk4_3(esk20_0,relation_image(esk20_0,esk15_1(esk13_0)),powerset(esk12_0))),
inference(scs_inference,[],[i_0_199,i_0_346,i_0_340,i_0_227,i_0_254,i_0_195,i_0_351,i_0_140,i_0_146,i_0_95,i_0_105,i_0_99,i_0_147,i_0_93,i_0_92]) ).
cnf(i_0_379,plain,
relation(relation_image(esk20_0,relation_image(esk20_0,esk15_1(esk13_0)))),
inference(scs_inference,[],[i_0_199,i_0_346,i_0_340,i_0_342,i_0_227,i_0_254,i_0_195,i_0_351,i_0_140,i_0_130,i_0_146,i_0_95,i_0_105,i_0_99,i_0_147,i_0_93,i_0_92,i_0_161]) ).
cnf(i_0_380,plain,
function(relation_image(esk20_0,relation_image(esk20_0,esk15_1(esk13_0)))),
inference(scs_inference,[],[i_0_199,i_0_346,i_0_340,i_0_342,i_0_227,i_0_254,i_0_195,i_0_351,i_0_140,i_0_130,i_0_137,i_0_146,i_0_95,i_0_105,i_0_99,i_0_147,i_0_93,i_0_92,i_0_161,i_0_162]) ).
cnf(i_0_381,plain,
relation_inverse_image(esk20_0,relation_image(esk20_0,esk15_1(esk13_0))) != powerset(X1),
inference(scs_inference,[],[i_0_199,i_0_203,i_0_346,i_0_340,i_0_342,i_0_227,i_0_254,i_0_195,i_0_351,i_0_207,i_0_140,i_0_130,i_0_137,i_0_146,i_0_95,i_0_105,i_0_99,i_0_147,i_0_93,i_0_92,i_0_161,i_0_162,i_0_164]) ).
cnf(i_0_383,plain,
esk12_0 != esk14_0,
inference(scs_inference,[],[i_0_199,i_0_203,i_0_346,i_0_340,i_0_342,i_0_227,i_0_254,i_0_195,i_0_351,i_0_207,i_0_140,i_0_130,i_0_121,i_0_137,i_0_146,i_0_95,i_0_105,i_0_99,i_0_147,i_0_93,i_0_92,i_0_161,i_0_162,i_0_164,i_0_168]) ).
cnf(i_0_384,plain,
~ in(X1,relation_inverse_image(esk20_0,esk13_0)),
inference(scs_inference,[],[i_0_199,i_0_374,i_0_203,i_0_346,i_0_340,i_0_342,i_0_227,i_0_254,i_0_195,i_0_351,i_0_207,i_0_140,i_0_130,i_0_121,i_0_137,i_0_146,i_0_95,i_0_105,i_0_99,i_0_147,i_0_93,i_0_92,i_0_161,i_0_162,i_0_164,i_0_168,i_0_160]) ).
cnf(i_0_385,plain,
~ subset(powerset(X1),relation_inverse_image(esk20_0,esk13_0)),
inference(scs_inference,[],[i_0_199,i_0_374,i_0_203,i_0_346,i_0_340,i_0_342,i_0_227,i_0_254,i_0_321,i_0_195,i_0_351,i_0_207,i_0_140,i_0_130,i_0_121,i_0_137,i_0_146,i_0_95,i_0_105,i_0_99,i_0_147,i_0_93,i_0_92,i_0_161,i_0_162,i_0_164,i_0_168,i_0_160,i_0_165]) ).
cnf(i_0_386,plain,
~ in(X1,relation_inverse_image(esk15_1(X2),relation_image(esk20_0,esk15_1(esk13_0)))),
inference(scs_inference,[],[i_0_199,i_0_374,i_0_203,i_0_346,i_0_340,i_0_342,i_0_227,i_0_254,i_0_321,i_0_195,i_0_351,i_0_207,i_0_140,i_0_315,i_0_229,i_0_130,i_0_121,i_0_137,i_0_146,i_0_95,i_0_105,i_0_99,i_0_147,i_0_93,i_0_92,i_0_161,i_0_162,i_0_164,i_0_168,i_0_160,i_0_165,i_0_175]) ).
cnf(i_0_390,plain,
one_to_one(esk15_1(X1)),
inference(scs_inference,[],[i_0_199,i_0_374,i_0_203,i_0_346,i_0_340,i_0_342,i_0_227,i_0_254,i_0_321,i_0_195,i_0_351,i_0_207,i_0_140,i_0_118,i_0_315,i_0_387,i_0_229,i_0_130,i_0_121,i_0_137,i_0_146,i_0_95,i_0_105,i_0_99,i_0_147,i_0_93,i_0_92,i_0_161,i_0_162,i_0_164,i_0_168,i_0_160,i_0_165,i_0_175,i_0_108]) ).
cnf(i_0_397,plain,
esk10_0 = relation_image(esk20_0,relation_image(esk20_0,esk15_1(esk13_0))),
inference(scs_inference,[],[i_0_126,i_0_135,i_0_199,i_0_374,i_0_388,i_0_395,i_0_203,i_0_346,i_0_330,i_0_340,i_0_342,i_0_227,i_0_366,i_0_254,i_0_321,i_0_195,i_0_351,i_0_207,i_0_140,i_0_118,i_0_315,i_0_387,i_0_229,i_0_130,i_0_121,i_0_137,i_0_146,i_0_95,i_0_105,i_0_99,i_0_147,i_0_93,i_0_92,i_0_161,i_0_162,i_0_164,i_0_168,i_0_160,i_0_165,i_0_175,i_0_108,i_0_81,i_0_83]) ).
cnf(i_0_401,plain,
relation_image(esk20_0,esk15_1(esk13_0)) = relation_inverse_image(esk20_0,esk10_0),
inference(scs_inference,[],[i_0_126,i_0_135,i_0_199,i_0_374,i_0_388,i_0_395,i_0_399,i_0_203,i_0_346,i_0_330,i_0_340,i_0_342,i_0_227,i_0_366,i_0_398,i_0_254,i_0_321,i_0_195,i_0_351,i_0_207,i_0_140,i_0_118,i_0_315,i_0_387,i_0_229,i_0_130,i_0_121,i_0_137,i_0_146,i_0_95,i_0_105,i_0_99,i_0_147,i_0_93,i_0_92,i_0_161,i_0_162,i_0_164,i_0_168,i_0_160,i_0_165,i_0_175,i_0_108,i_0_81,i_0_83,i_0_78]) ).
cnf(i_0_420,plain,
subset(esk15_1(X1),X2),
inference(scs_inference,[],[i_0_319,i_0_95]) ).
cnf(i_0_421,plain,
~ in(X1,esk15_1(X2)),
inference(rename_variables,[],[i_0_319]) ).
cnf(i_0_437,plain,
~ in(X1,esk15_1(X2)),
inference(rename_variables,[],[i_0_319]) ).
cnf(i_0_443,plain,
~ in(X1,esk15_1(X2)),
inference(rename_variables,[],[i_0_319]) ).
cnf(i_0_446,plain,
~ in(X1,esk15_1(X2)),
inference(rename_variables,[],[i_0_319]) ).
cnf(i_0_450,plain,
~ in(X1,esk15_1(X2)),
inference(rename_variables,[],[i_0_319]) ).
cnf(i_0_485,plain,
~ in(X1,esk15_1(X2)),
inference(rename_variables,[],[i_0_319]) ).
cnf(i_0_580,plain,
~ in(X1,esk15_1(X2)),
inference(rename_variables,[],[i_0_319]) ).
cnf(i_0_630,plain,
~ in(X1,esk15_1(X2)),
inference(rename_variables,[],[i_0_319]) ).
cnf(i_0_672,plain,
~ in(X1,esk15_1(X2)),
inference(rename_variables,[],[i_0_319]) ).
cnf(i_0_686,plain,
~ in(X1,esk15_1(X2)),
inference(rename_variables,[],[i_0_319]) ).
cnf(i_0_712,plain,
~ in(X1,esk15_1(X2)),
inference(rename_variables,[],[i_0_319]) ).
cnf(i_0_805,plain,
~ in(X1,esk15_1(X2)),
inference(rename_variables,[],[i_0_319]) ).
cnf(i_0_817,plain,
~ in(X1,esk15_1(X2)),
inference(rename_variables,[],[i_0_319]) ).
cnf(i_0_845,plain,
~ in(X1,esk15_1(X2)),
inference(rename_variables,[],[i_0_319]) ).
cnf(i_0_961,plain,
~ in(X1,esk15_1(X2)),
inference(rename_variables,[],[i_0_319]) ).
cnf(i_0_3225,plain,
~ in(X1,esk8_1(powerset(esk15_1(X2)))),
inference(rename_variables,[],[i_0_324]) ).
cnf(i_0_418,plain,
one_to_one(empty_set),
inference(equality_inference,[],[407]) ).
cnf(i_0_419,plain,
~ in(esk16_0,esk8_1(esk16_0)),
inference(equality_inference,[],[408]) ).
cnf(i_0_425,plain,
relation_inverse_image(esk20_0,esk10_0) = relation_image(esk20_0,esk15_1(esk13_0)),
inference(scs_inference,[],[i_0_394,i_0_401,i_0_319,i_0_95,i_0_99,i_0_146]) ).
cnf(i_0_426,plain,
~ subset(esk14_0,relation_image(esk20_0,esk15_1(esk13_0))),
inference(scs_inference,[],[i_0_199,i_0_394,i_0_401,i_0_319,i_0_239,i_0_95,i_0_99,i_0_146,i_0_93]) ).
cnf(i_0_429,plain,
~ in(X1,esk8_1(powerset(esk13_0))),
inference(scs_inference,[],[i_0_199,i_0_394,i_0_401,i_0_110,i_0_319,i_0_239,i_0_139,i_0_95,i_0_99,i_0_146,i_0_93,i_0_92]) ).
cnf(i_0_432,plain,
relation_inverse_image(esk20_0,esk13_0) = relation_inverse_image(esk20_0,esk10_0),
inference(scs_inference,[],[i_0_199,i_0_394,i_0_401,i_0_110,i_0_319,i_0_364,i_0_239,i_0_139,i_0_95,i_0_99,i_0_146,i_0_93,i_0_92,i_0_147]) ).
cnf(i_0_435,plain,
esk10_0 != esk16_0,
inference(scs_inference,[],[i_0_87,i_0_199,i_0_274,i_0_394,i_0_401,i_0_110,i_0_319,i_0_364,i_0_239,i_0_139,i_0_141,i_0_120,i_0_95,i_0_99,i_0_146,i_0_93,i_0_92,i_0_147,i_0_164,i_0_168]) ).
cnf(i_0_436,plain,
powerset(X1) != esk15_1(X2),
inference(scs_inference,[],[i_0_87,i_0_199,i_0_251,i_0_274,i_0_394,i_0_401,i_0_110,i_0_319,i_0_421,i_0_364,i_0_239,i_0_139,i_0_141,i_0_120,i_0_95,i_0_99,i_0_146,i_0_93,i_0_92,i_0_147,i_0_164,i_0_168,i_0_160]) ).
cnf(i_0_438,plain,
~ subset(relation_dom(esk20_0),relation_inverse_image(esk20_0,esk13_0)),
inference(scs_inference,[],[i_0_87,i_0_199,i_0_251,i_0_274,i_0_394,i_0_401,i_0_110,i_0_319,i_0_421,i_0_364,i_0_373,i_0_239,i_0_139,i_0_141,i_0_120,i_0_95,i_0_99,i_0_146,i_0_93,i_0_92,i_0_147,i_0_164,i_0_168,i_0_160,i_0_165]) ).
cnf(i_0_439,plain,
~ in(X1,relation_inverse_image(esk10_0,relation_image(esk20_0,esk15_1(esk13_0)))),
inference(scs_inference,[],[i_0_87,i_0_199,i_0_427,i_0_251,i_0_274,i_0_394,i_0_401,i_0_110,i_0_319,i_0_421,i_0_364,i_0_373,i_0_239,i_0_139,i_0_141,i_0_231,i_0_131,i_0_120,i_0_95,i_0_99,i_0_146,i_0_93,i_0_92,i_0_147,i_0_164,i_0_168,i_0_160,i_0_165,i_0_175]) ).
cnf(i_0_442,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(scs_inference,[],[i_0_87,i_0_126,i_0_135,i_0_199,i_0_427,i_0_251,i_0_274,i_0_394,i_0_401,i_0_110,i_0_319,i_0_421,i_0_437,i_0_364,i_0_373,i_0_239,i_0_139,i_0_141,i_0_231,i_0_131,i_0_120,i_0_95,i_0_99,i_0_146,i_0_93,i_0_92,i_0_147,i_0_164,i_0_168,i_0_160,i_0_165,i_0_175,i_0_77]) ).
cnf(i_0_445,plain,
esk15_1(X1) = relation_image(esk20_0,relation_image(esk20_0,esk15_1(esk13_0))),
inference(scs_inference,[],[i_0_87,i_0_126,i_0_135,i_0_199,i_0_427,i_0_440,i_0_251,i_0_274,i_0_394,i_0_401,i_0_110,i_0_319,i_0_421,i_0_437,i_0_443,i_0_364,i_0_373,i_0_239,i_0_139,i_0_141,i_0_231,i_0_131,i_0_120,i_0_95,i_0_99,i_0_146,i_0_93,i_0_92,i_0_147,i_0_164,i_0_168,i_0_160,i_0_165,i_0_175,i_0_77,i_0_83]) ).
cnf(i_0_449,plain,
relation_image(esk20_0,esk15_1(esk13_0)) = relation_inverse_image(esk20_0,esk15_1(X1)),
inference(scs_inference,[],[i_0_87,i_0_126,i_0_135,i_0_199,i_0_427,i_0_440,i_0_447,i_0_251,i_0_274,i_0_394,i_0_401,i_0_110,i_0_319,i_0_421,i_0_437,i_0_443,i_0_446,i_0_364,i_0_373,i_0_239,i_0_139,i_0_141,i_0_231,i_0_131,i_0_120,i_0_95,i_0_99,i_0_146,i_0_93,i_0_92,i_0_147,i_0_164,i_0_168,i_0_160,i_0_165,i_0_175,i_0_77,i_0_83,i_0_78]) ).
cnf(i_0_477,plain,
subset(esk15_1(X1),X2),
inference(rename_variables,[],[i_0_420]) ).
cnf(i_0_532,plain,
~ in(X1,relation_inverse_image(esk20_0,esk13_0)),
inference(rename_variables,[],[i_0_384]) ).
cnf(i_0_536,plain,
~ in(X1,relation_inverse_image(esk20_0,esk13_0)),
inference(rename_variables,[],[i_0_384]) ).
cnf(i_0_636,plain,
~ in(X1,esk12_0),
inference(rename_variables,[],[i_0_368]) ).
cnf(i_0_640,plain,
~ in(X1,esk12_0),
inference(rename_variables,[],[i_0_368]) ).
cnf(i_0_709,plain,
~ in(X1,esk12_0),
inference(rename_variables,[],[i_0_368]) ).
cnf(i_0_758,plain,
~ in(X1,relation_inverse_image(esk20_0,esk13_0)),
inference(rename_variables,[],[i_0_384]) ).
cnf(i_0_766,plain,
~ in(X1,esk12_0),
inference(rename_variables,[],[i_0_368]) ).
cnf(i_0_778,plain,
~ in(X1,relation_inverse_image(esk20_0,esk13_0)),
inference(rename_variables,[],[i_0_384]) ).
cnf(i_0_837,plain,
subset(esk10_0,X1),
inference(rename_variables,[],[i_0_365]) ).
cnf(i_0_901,plain,
~ in(X1,esk12_0),
inference(rename_variables,[],[i_0_368]) ).
cnf(i_0_924,plain,
~ in(X1,esk12_0),
inference(rename_variables,[],[i_0_368]) ).
cnf(i_0_1018,plain,
~ in(X1,relation_inverse_image(esk20_0,esk13_0)),
inference(rename_variables,[],[i_0_384]) ).
cnf(i_0_1072,plain,
~ in(X1,relation_inverse_image(esk20_0,esk13_0)),
inference(rename_variables,[],[i_0_384]) ).
cnf(i_0_1210,plain,
~ in(X1,esk12_0),
inference(rename_variables,[],[i_0_368]) ).
cnf(i_0_1288,plain,
~ in(X1,esk12_0),
inference(rename_variables,[],[i_0_368]) ).
cnf(i_0_2742,plain,
~ in(X1,relation_inverse_image(esk20_0,esk13_0)),
inference(rename_variables,[],[i_0_384]) ).
cnf(i_0_2748,plain,
~ in(X1,relation_inverse_image(esk20_0,esk13_0)),
inference(rename_variables,[],[i_0_384]) ).
cnf(i_0_2988,plain,
~ in(X1,relation_inverse_image(esk20_0,esk13_0)),
inference(rename_variables,[],[i_0_384]) ).
cnf(i_0_3046,plain,
~ in(X1,relation_inverse_image(esk20_0,esk13_0)),
inference(rename_variables,[],[i_0_384]) ).
cnf(i_0_459,plain,
relation(esk14_0),
inference(equality_inference,[],[453]) ).
cnf(i_0_460,plain,
function(empty_set),
inference(equality_inference,[],[454]) ).
cnf(i_0_461,plain,
~ in(relation_dom(esk20_0),esk4_3(esk20_0,relation_image(esk20_0,esk19_0),esk15_1(esk19_0))),
inference(equality_inference,[],[455]) ).
cnf(i_0_462,plain,
one_to_one(esk12_0),
inference(equality_inference,[],[456]) ).
cnf(i_0_463,plain,
subset(relation_inverse_image(esk20_0,esk10_0),X1),
inference(scs_inference,[],[i_0_442,i_0_95]) ).
cnf(i_0_464,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_466,plain,
~ in(powerset(X1),esk8_1(powerset(X1))),
inference(scs_inference,[],[i_0_442,i_0_327,i_0_95,i_0_99]) ).
cnf(i_0_468,plain,
relation_image(esk20_0,relation_image(esk20_0,esk15_1(esk13_0))) = esk10_0,
inference(scs_inference,[],[i_0_397,i_0_442,i_0_327,i_0_95,i_0_99,i_0_146]) ).
cnf(i_0_469,plain,
~ subset(esk16_0,relation_image(esk20_0,esk15_1(esk13_0))),
inference(scs_inference,[],[i_0_199,i_0_397,i_0_442,i_0_327,i_0_288,i_0_95,i_0_99,i_0_146,i_0_93]) ).
cnf(i_0_472,plain,
~ in(X1,esk4_3(esk20_0,relation_image(esk20_0,esk15_1(esk13_0)),powerset(esk13_0))),
inference(scs_inference,[],[i_0_199,i_0_397,i_0_442,i_0_254,i_0_327,i_0_288,i_0_139,i_0_95,i_0_99,i_0_146,i_0_93,i_0_92]) ).
cnf(i_0_475,plain,
relation_inverse_image(esk20_0,esk10_0) = relation_inverse_image(esk20_0,esk13_0),
inference(scs_inference,[],[i_0_346,i_0_199,i_0_397,i_0_442,i_0_254,i_0_327,i_0_425,i_0_288,i_0_139,i_0_95,i_0_99,i_0_146,i_0_93,i_0_92,i_0_147]) ).
cnf(i_0_476,plain,
esk15_1(X1) != relation_inverse_image(esk20_0,relation_image(esk20_0,esk19_0)),
inference(scs_inference,[],[i_0_87,i_0_346,i_0_199,i_0_397,i_0_420,i_0_442,i_0_254,i_0_327,i_0_425,i_0_288,i_0_139,i_0_95,i_0_99,i_0_146,i_0_93,i_0_92,i_0_147,i_0_164]) ).
cnf(i_0_478,plain,
esk13_0 != esk14_0,
inference(scs_inference,[],[i_0_87,i_0_346,i_0_199,i_0_397,i_0_420,i_0_442,i_0_254,i_0_327,i_0_425,i_0_288,i_0_139,i_0_121,i_0_95,i_0_99,i_0_146,i_0_93,i_0_92,i_0_147,i_0_164,i_0_168]) ).
cnf(i_0_479,plain,
~ in(X1,relation_image(esk20_0,relation_image(esk20_0,esk15_1(esk13_0)))),
inference(scs_inference,[],[i_0_87,i_0_346,i_0_199,i_0_397,i_0_420,i_0_442,i_0_254,i_0_179,i_0_327,i_0_425,i_0_288,i_0_351,i_0_139,i_0_121,i_0_95,i_0_99,i_0_146,i_0_93,i_0_92,i_0_147,i_0_164,i_0_168,i_0_160]) ).
cnf(i_0_480,plain,
~ subset(esk14_0,relation_inverse_image(esk20_0,esk10_0)),
inference(scs_inference,[],[i_0_87,i_0_346,i_0_199,i_0_397,i_0_420,i_0_442,i_0_254,i_0_179,i_0_327,i_0_425,i_0_426,i_0_288,i_0_351,i_0_139,i_0_121,i_0_95,i_0_99,i_0_146,i_0_93,i_0_92,i_0_147,i_0_164,i_0_168,i_0_160,i_0_165]) ).
cnf(i_0_481,plain,
~ in(X1,relation_inverse_image(esk13_0,relation_image(esk20_0,esk15_1(esk13_0)))),
inference(scs_inference,[],[i_0_87,i_0_346,i_0_199,i_0_470,i_0_397,i_0_420,i_0_442,i_0_254,i_0_179,i_0_327,i_0_425,i_0_426,i_0_288,i_0_351,i_0_139,i_0_130,i_0_137,i_0_121,i_0_95,i_0_99,i_0_146,i_0_93,i_0_92,i_0_147,i_0_164,i_0_168,i_0_160,i_0_165,i_0_175]) ).
cnf(i_0_484,plain,
in(esk4_3(esk20_0,relation_image(esk20_0,esk19_0),esk15_1(X1)),relation_dom(esk20_0)),
inference(scs_inference,[],[i_0_87,i_0_126,i_0_135,i_0_346,i_0_199,i_0_470,i_0_397,i_0_420,i_0_442,i_0_254,i_0_319,i_0_179,i_0_327,i_0_425,i_0_426,i_0_288,i_0_351,i_0_139,i_0_130,i_0_137,i_0_121,i_0_95,i_0_99,i_0_146,i_0_93,i_0_92,i_0_147,i_0_164,i_0_168,i_0_160,i_0_165,i_0_175,i_0_81]) ).
cnf(i_0_488,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_492,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_523,plain,
~ in(X1,esk8_1(powerset(esk13_0))),
inference(rename_variables,[],[i_0_429]) ).
cnf(i_0_529,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_604,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_719,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_727,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_752,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_833,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_839,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_842,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_855,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_888,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_895,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_927,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1054,plain,
~ in(X1,esk8_1(powerset(esk13_0))),
inference(rename_variables,[],[i_0_429]) ).
cnf(i_0_1063,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1066,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1076,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1103,plain,
~ in(X1,esk8_1(powerset(esk13_0))),
inference(rename_variables,[],[i_0_429]) ).
cnf(i_0_1126,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1129,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1132,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1139,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1242,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1245,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1248,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1255,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1328,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1332,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1336,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1343,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1371,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1374,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1377,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1381,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1417,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1491,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1494,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1500,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1504,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1569,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1572,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1578,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1582,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1687,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1697,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1723,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1727,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1731,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1798,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1802,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1834,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1989,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_1993,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_2100,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_2194,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_2198,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_2258,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_2262,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_2327,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_2331,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_2432,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_2501,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_2564,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_2568,plain,
~ in(X1,relation_inverse_image(esk20_0,esk10_0)),
inference(rename_variables,[],[i_0_442]) ).
cnf(i_0_2720,plain,
esk15_1(X1) = relation_image(esk20_0,relation_image(esk20_0,esk15_1(esk13_0))),
inference(rename_variables,[],[i_0_445]) ).
cnf(i_0_2737,plain,
esk15_1(X1) = relation_image(esk20_0,relation_image(esk20_0,esk15_1(esk13_0))),
inference(rename_variables,[],[i_0_445]) ).
cnf(i_0_495,plain,
element(esk4_3(esk20_0,relation_image(esk20_0,esk19_0),esk15_1(X1)),relation_dom(esk20_0)),
inference(scs_inference,[],[i_0_87,i_0_126,i_0_135,i_0_346,i_0_199,i_0_470,i_0_482,i_0_489,i_0_397,i_0_420,i_0_442,i_0_464,i_0_488,i_0_254,i_0_319,i_0_179,i_0_327,i_0_425,i_0_426,i_0_288,i_0_351,i_0_139,i_0_130,i_0_137,i_0_121,i_0_95,i_0_99,i_0_146,i_0_93,i_0_92,i_0_147,i_0_164,i_0_168,i_0_160,i_0_165,i_0_175,i_0_81,i_0_83,i_0_78,i_0_102]) ).
cnf(i_0_512,plain,
~ in(relation_dom(esk20_0),esk4_3(esk20_0,relation_image(esk20_0,esk19_0),esk15_1(X1))),
inference(scs_inference,[],[i_0_484,i_0_236,i_0_95,i_0_99]) ).
cnf(i_0_514,plain,
relation_image(esk20_0,relation_image(esk20_0,esk15_1(esk13_0))) = esk15_1(X1),
inference(scs_inference,[],[i_0_445,i_0_484,i_0_236,i_0_95,i_0_99,i_0_146]) ).
cnf(i_0_515,plain,
~ in(X1,esk8_1(powerset(empty_set))),
inference(scs_inference,[],[i_0_445,i_0_484,i_0_110,i_0_236,i_0_144,i_0_95,i_0_99,i_0_146,i_0_92]) ).
cnf(i_0_518,plain,
powerset(X1) != esk10_0,
inference(scs_inference,[],[i_0_397,i_0_445,i_0_484,i_0_110,i_0_236,i_0_372,i_0_144,i_0_95,i_0_99,i_0_146,i_0_92,i_0_147]) ).
cnf(i_0_520,plain,
subset(relation_inverse_image(esk20_0,esk10_0),X1),
inference(rename_variables,[],[i_0_463]) ).
cnf(i_0_521,plain,
empty_set != powerset(X1),
inference(scs_inference,[],[i_0_87,i_0_397,i_0_445,i_0_463,i_0_484,i_0_110,i_0_236,i_0_372,i_0_144,i_0_113,i_0_95,i_0_99,i_0_146,i_0_92,i_0_147,i_0_164,i_0_168]) ).
cnf(i_0_522,plain,
powerset(X1) != esk8_1(powerset(esk13_0)),
inference(scs_inference,[],[i_0_87,i_0_397,i_0_251,i_0_445,i_0_463,i_0_484,i_0_110,i_0_236,i_0_372,i_0_429,i_0_144,i_0_113,i_0_95,i_0_99,i_0_146,i_0_92,i_0_147,i_0_164,i_0_168,i_0_160]) ).
cnf(i_0_524,plain,
~ subset(esk16_0,relation_inverse_image(esk20_0,esk13_0)),
inference(scs_inference,[],[i_0_87,i_0_397,i_0_251,i_0_445,i_0_463,i_0_484,i_0_110,i_0_236,i_0_364,i_0_372,i_0_429,i_0_469,i_0_144,i_0_113,i_0_95,i_0_99,i_0_146,i_0_92,i_0_147,i_0_164,i_0_168,i_0_160,i_0_165]) ).
cnf(i_0_525,plain,
~ in(X1,relation_inverse_image(esk9_0,relation_image(esk20_0,esk15_1(esk13_0)))),
inference(scs_inference,[],[i_0_87,i_0_397,i_0_251,i_0_199,i_0_445,i_0_463,i_0_484,i_0_110,i_0_236,i_0_364,i_0_372,i_0_429,i_0_469,i_0_144,i_0_138,i_0_132,i_0_113,i_0_95,i_0_99,i_0_146,i_0_92,i_0_147,i_0_164,i_0_168,i_0_160,i_0_165,i_0_175]) ).
cnf(i_0_539,plain,
esk10_0 != relation_image(esk20_0,esk19_0),
inference(scs_inference,[],[i_0_87,i_0_126,i_0_135,i_0_397,i_0_251,i_0_199,i_0_526,i_0_533,i_0_445,i_0_463,i_0_484,i_0_442,i_0_110,i_0_236,i_0_364,i_0_372,i_0_384,i_0_532,i_0_429,i_0_469,i_0_144,i_0_138,i_0_132,i_0_113,i_0_95,i_0_99,i_0_146,i_0_92,i_0_147,i_0_164,i_0_168,i_0_160,i_0_165,i_0_175,i_0_81,i_0_83,i_0_78,i_0_149]) ).
cnf(i_0_543,plain,
in(esk3_3(esk20_0,esk19_0,esk10_0),relation_dom(esk20_0)),
inference(scs_inference,[],[i_0_87,i_0_126,i_0_135,i_0_397,i_0_251,i_0_199,i_0_526,i_0_533,i_0_445,i_0_463,i_0_484,i_0_442,i_0_110,i_0_236,i_0_227,i_0_364,i_0_466,i_0_372,i_0_384,i_0_532,i_0_429,i_0_469,i_0_144,i_0_138,i_0_132,i_0_113,i_0_95,i_0_99,i_0_146,i_0_92,i_0_147,i_0_164,i_0_168,i_0_160,i_0_165,i_0_175,i_0_81,i_0_83,i_0_78,i_0_149,i_0_102,i_0_159,i_0_82]) ).
cnf(i_0_505,plain,
function(esk12_0),
inference(equality_inference,[],[497]) ).
cnf(i_0_507,plain,
relation(empty_set),
inference(equality_inference,[],[499]) ).
cnf(i_0_508,plain,
one_to_one(esk17_0),
inference(equality_inference,[],[500]) ).
cnf(i_0_556,plain,
~ in(powerset(X1),esk8_1(powerset(X1))),
inference(equality_inference,[],[542]) ).
cnf(i_0_557,plain,
relation(esk12_0),
inference(equality_inference,[],[546]) ).
cnf(i_0_558,plain,
element(esk3_3(esk20_0,esk19_0,esk10_0),relation_dom(esk20_0)),
inference(scs_inference,[],[i_0_543,i_0_102]) ).
cnf(i_0_560,plain,
subset(esk8_1(powerset(empty_set)),X1),
inference(scs_inference,[],[i_0_543,i_0_515,i_0_102,i_0_95]) ).
cnf(i_0_561,plain,
~ in(X1,esk8_1(powerset(empty_set))),
inference(rename_variables,[],[i_0_515]) ).
cnf(i_0_565,plain,
relation_inverse_image(esk20_0,esk15_1(X1)) = relation_image(esk20_0,esk15_1(esk13_0)),
inference(scs_inference,[],[i_0_449,i_0_528,i_0_543,i_0_515,i_0_102,i_0_95,i_0_99,i_0_146]) ).
cnf(i_0_566,plain,
~ in(X1,esk8_1(powerset(esk12_0))),
inference(scs_inference,[],[i_0_449,i_0_528,i_0_543,i_0_110,i_0_515,i_0_140,i_0_102,i_0_95,i_0_99,i_0_146,i_0_92]) ).
cnf(i_0_569,plain,
relation_inverse_image(esk20_0,esk10_0) = relation_inverse_image(esk20_0,esk15_1(X1)),
inference(scs_inference,[],[i_0_449,i_0_528,i_0_543,i_0_110,i_0_425,i_0_515,i_0_140,i_0_102,i_0_95,i_0_99,i_0_146,i_0_92,i_0_147]) ).
cnf(i_0_570,plain,
esk8_1(powerset(esk10_0)) != relation_inverse_image(esk20_0,relation_image(esk20_0,esk19_0)),
inference(scs_inference,[],[i_0_87,i_0_449,i_0_528,i_0_509,i_0_543,i_0_110,i_0_425,i_0_515,i_0_140,i_0_102,i_0_95,i_0_99,i_0_146,i_0_92,i_0_147,i_0_164]) ).
cnf(i_0_572,plain,
esk12_0 != esk16_0,
inference(scs_inference,[],[i_0_87,i_0_449,i_0_528,i_0_509,i_0_543,i_0_110,i_0_425,i_0_515,i_0_140,i_0_120,i_0_102,i_0_95,i_0_99,i_0_146,i_0_92,i_0_147,i_0_164,i_0_168]) ).
cnf(i_0_574,plain,
~ in(X1,esk8_1(powerset(empty_set))),
inference(rename_variables,[],[i_0_515]) ).
cnf(i_0_633,plain,
~ in(X1,esk8_1(powerset(empty_set))),
inference(rename_variables,[],[i_0_515]) ).
cnf(i_0_573,plain,
powerset(X1) != esk8_1(powerset(empty_set)),
inference(scs_inference,[],[i_0_87,i_0_251,i_0_449,i_0_528,i_0_509,i_0_543,i_0_110,i_0_425,i_0_515,i_0_561,i_0_140,i_0_120,i_0_102,i_0_95,i_0_99,i_0_146,i_0_92,i_0_147,i_0_164,i_0_168,i_0_160]) ).
cnf(i_0_575,plain,
~ subset(relation_dom(esk20_0),relation_inverse_image(esk20_0,esk10_0)),
inference(scs_inference,[],[i_0_87,i_0_251,i_0_449,i_0_528,i_0_509,i_0_543,i_0_110,i_0_425,i_0_515,i_0_561,i_0_373,i_0_140,i_0_120,i_0_102,i_0_95,i_0_99,i_0_146,i_0_92,i_0_147,i_0_164,i_0_168,i_0_160,i_0_165]) ).
cnf(c_0_148,plain,
( in(X1,relation_dom(X2))
| ~ in(X1,X3)
| X3 != relation_inverse_image(X2,X4)
| ~ relation(X2)
| ~ function(X2) ),
i_0_89 ).
cnf(c_0_149,negated_conjecture,
~ subset(relation_inverse_image(esk20_0,relation_image(esk20_0,esk19_0)),esk19_0),
i_0_87 ).
cnf(c_0_150,plain,
( in(esk5_2(X1,X2),X1)
| subset(X1,X2) ),
i_0_95 ).
cnf(c_0_151,plain,
( in(apply(X1,X2),X3)
| ~ in(X2,X4)
| X4 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| ~ function(X1) ),
i_0_88 ).
cnf(c_0_152,plain,
( in(X1,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2)
| ~ in(X1,relation_inverse_image(X2,X3)) ),
inference(er,[status(thm)],[c_0_148]) ).
cnf(c_0_153,negated_conjecture,
in(esk5_2(relation_inverse_image(esk20_0,relation_image(esk20_0,esk19_0)),esk19_0),relation_inverse_image(esk20_0,relation_image(esk20_0,esk19_0))),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_154,negated_conjecture,
function(esk20_0),
i_0_135 ).
cnf(c_0_155,negated_conjecture,
relation(esk20_0),
i_0_126 ).
cnf(c_0_156,plain,
( in(esk1_4(X1,X2,X3,X4),relation_dom(X1))
| ~ in(X4,X3)
| X3 != relation_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
i_0_75 ).
cnf(c_0_157,plain,
( in(apply(X1,X2),X3)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
inference(er,[status(thm)],[c_0_151]) ).
cnf(c_0_158,plain,
( X1 = apply(X2,esk1_4(X2,X3,X4,X1))
| ~ in(X1,X4)
| X4 != relation_image(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
i_0_76 ).
cnf(c_0_159,plain,
( in(esk1_4(X1,X2,X3,X4),X2)
| ~ in(X4,X3)
| X3 != relation_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
i_0_77 ).
cnf(c_0_160,plain,
( X1 = X2
| ~ one_to_one(X3)
| ~ in(X1,relation_dom(X3))
| ~ in(X2,relation_dom(X3))
| apply(X3,X1) != apply(X3,X2)
| ~ relation(X3)
| ~ function(X3) ),
i_0_85 ).
cnf(c_0_161,plain,
in(esk5_2(relation_inverse_image(esk20_0,relation_image(esk20_0,esk19_0)),esk19_0),relation_dom(esk20_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_154]),c_0_155])]) ).
cnf(c_0_162,negated_conjecture,
one_to_one(esk20_0),
i_0_124 ).
cnf(c_0_163,plain,
( in(esk1_4(X1,X2,relation_image(X1,X2),X3),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X3,relation_image(X1,X2)) ),
inference(er,[status(thm)],[c_0_156]) ).
cnf(c_0_164,negated_conjecture,
in(apply(esk20_0,esk5_2(relation_inverse_image(esk20_0,relation_image(esk20_0,esk19_0)),esk19_0)),relation_image(esk20_0,esk19_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_153]),c_0_154]),c_0_155])]) ).
cnf(c_0_165,plain,
( apply(X1,esk1_4(X1,X2,relation_image(X1,X2),X3)) = X3
| ~ function(X1)
| ~ relation(X1)
| ~ in(X3,relation_image(X1,X2)) ),
inference(er,[status(thm)],[c_0_158]) ).
cnf(c_0_166,plain,
( in(esk1_4(X1,X2,relation_image(X1,X2),X3),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X3,relation_image(X1,X2)) ),
inference(er,[status(thm)],[c_0_159]) ).
cnf(c_0_167,plain,
( X1 = esk5_2(relation_inverse_image(esk20_0,relation_image(esk20_0,esk19_0)),esk19_0)
| apply(esk20_0,X1) != apply(esk20_0,esk5_2(relation_inverse_image(esk20_0,relation_image(esk20_0,esk19_0)),esk19_0))
| ~ in(X1,relation_dom(esk20_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_162]),c_0_154]),c_0_155])]) ).
cnf(c_0_168,plain,
in(esk1_4(esk20_0,esk19_0,relation_image(esk20_0,esk19_0),apply(esk20_0,esk5_2(relation_inverse_image(esk20_0,relation_image(esk20_0,esk19_0)),esk19_0))),relation_dom(esk20_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_164]),c_0_154]),c_0_155])]) ).
cnf(c_0_169,plain,
apply(esk20_0,esk1_4(esk20_0,esk19_0,relation_image(esk20_0,esk19_0),apply(esk20_0,esk5_2(relation_inverse_image(esk20_0,relation_image(esk20_0,esk19_0)),esk19_0)))) = apply(esk20_0,esk5_2(relation_inverse_image(esk20_0,relation_image(esk20_0,esk19_0)),esk19_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_164]),c_0_154]),c_0_155])]) ).
cnf(c_0_170,plain,
( subset(X1,X2)
| ~ in(esk5_2(X1,X2),X2) ),
i_0_90 ).
cnf(c_0_171,plain,
in(esk1_4(esk20_0,esk19_0,relation_image(esk20_0,esk19_0),apply(esk20_0,esk5_2(relation_inverse_image(esk20_0,relation_image(esk20_0,esk19_0)),esk19_0))),esk19_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_164]),c_0_154]),c_0_155])]) ).
cnf(c_0_172,plain,
esk1_4(esk20_0,esk19_0,relation_image(esk20_0,esk19_0),apply(esk20_0,esk5_2(relation_inverse_image(esk20_0,relation_image(esk20_0,esk19_0)),esk19_0))) = esk5_2(relation_inverse_image(esk20_0,relation_image(esk20_0,esk19_0)),esk19_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_168]),c_0_169])]) ).
cnf(c_0_173,negated_conjecture,
~ in(esk5_2(relation_inverse_image(esk20_0,relation_image(esk20_0,esk19_0)),esk19_0),esk19_0),
inference(spm,[status(thm)],[c_0_149,c_0_170]) ).
cnf(c_0_174,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_171,c_0_172]),c_0_173]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU071+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.12/0.31 % Computer : n018.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue May 5 02:43:17 EDT 2026
% 0.12/0.31 % CPUTime :
% 0.12/0.32 % start to proof: theBenchmark
% 136.21/105.68 % Version : CSE_E---1.7
% 136.21/105.68 % Problem : theBenchmark.p
% 136.21/105.68 % SZS status Theorem for theBenchmark.p
% 136.21/105.68 % SZS output start CNFRefutation
% See solution above
% 144.11/113.54 % Total time : 105.262s
%------------------------------------------------------------------------------