%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM403+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 : n017.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 04:57:14 PM UTC 2026
% Result : Theorem 260.69s 149.70s
% Output : CNFRefutation 270.49s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_69)
% Comments :
%------------------------------------------------------------------------------
fof(fc3_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ( ~ empty(succ(X1))
& epsilon_transitive(succ(X1))
& epsilon_connected(succ(X1))
& ordinal(succ(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_ordinal1) ).
fof(fc1_ordinal1,axiom,
! [X1] : ~ empty(succ(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_ordinal1) ).
fof(t34_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( in(X1,succ(X2))
<=> ordinal_subset(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_ordinal1) ).
fof(d1_ordinal1,axiom,
! [X1] : succ(X1) = set_union2(X1,singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(fc2_xboole_0,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(fc3_xboole_0,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(t29_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ordinal(succ(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_ordinal1) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(t36_ordinal1,conjecture,
! [X1] :
~ ( ! [X2] :
( in(X2,X1)
=> ordinal(X2) )
& ! [X2] :
( ordinal(X2)
=> ~ subset(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_ordinal1) ).
fof(rc3_ordinal1,axiom,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_ordinal1) ).
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(d4_tarski,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/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/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(redefinition_r1_ordinal1,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
<=> subset(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(fc2_relat_1,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_union2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_relat_1) ).
fof(connectedness_r1_ordinal1,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
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(t35_ordinal1,axiom,
! [X1] :
( ! [X2] :
( in(X2,X1)
=> ordinal(X2) )
=> ordinal(union(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_ordinal1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(reflexivity_r1_ordinal1,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ordinal_subset(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
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(cc2_ordinal1,axiom,
! [X1] :
( ( epsilon_transitive(X1)
& epsilon_connected(X1) )
=> ordinal(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(fc4_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_transitive(union(X1))
& epsilon_connected(union(X1))
& ordinal(union(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_ordinal1) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(idempotence_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t1_boole,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
fof(cc1_relat_1,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(cc1_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(cc3_ordinal1,axiom,
! [X1] :
( empty(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_ordinal1) ).
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(rc5_funct_1,axiom,
? [X1] :
( relation(X1)
& relation_non_empty(X1)
& function(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_funct_1) ).
fof(rc4_funct_1,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1)
& function(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_funct_1) ).
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_ordinal1,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1)
& empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_ordinal1) ).
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_ordinal1,axiom,
? [X1] :
( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal1) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(fc2_ordinal1,axiom,
( relation(empty_set)
& relation_empty_yielding(empty_set)
& function(empty_set)
& one_to_one(empty_set)
& empty(empty_set)
& epsilon_transitive(empty_set)
& epsilon_connected(empty_set)
& ordinal(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_ordinal1) ).
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_53,plain,
! [X1] :
( ordinal(X1)
=> ( ~ empty(succ(X1))
& epsilon_transitive(succ(X1))
& epsilon_connected(succ(X1))
& ordinal(succ(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc3_ordinal1]) ).
fof(i_0_54,plain,
! [X1] : ~ empty(succ(X1)),
inference(fof_simplification,[status(thm)],[fc1_ordinal1]) ).
fof(i_0_55,plain,
! [X149,X150] :
( ( ~ in(X149,succ(X150))
| ordinal_subset(X149,X150)
| ~ ordinal(X150)
| ~ ordinal(X149) )
& ( ~ ordinal_subset(X149,X150)
| in(X149,succ(X150))
| ~ ordinal(X150)
| ~ ordinal(X149) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t34_ordinal1])])])]) ).
fof(i_0_56,plain,
! [X95] : succ(X95) = set_union2(X95,singleton(X95)),
inference(variable_rename,[status(thm)],[d1_ordinal1]) ).
fof(i_0_57,plain,
! [X120] :
( ( ~ empty(succ(X120))
| ~ ordinal(X120) )
& ( epsilon_transitive(succ(X120))
| ~ ordinal(X120) )
& ( epsilon_connected(succ(X120))
| ~ ordinal(X120) )
& ( ordinal(succ(X120))
| ~ ordinal(X120) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_53])])]) ).
fof(i_0_58,plain,
! [X115] : ~ empty(succ(X115)),
inference(variable_rename,[status(thm)],[i_0_54]) ).
fof(i_0_59,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc2_xboole_0]) ).
fof(i_0_60,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[fc3_xboole_0]) ).
fof(i_0_61,plain,
! [X146] :
( ~ ordinal(X146)
| ordinal(succ(X146)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t29_ordinal1])]) ).
fof(i_0_62,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_63,negated_conjecture,
~ ! [X1] :
~ ( ! [X2] :
( in(X2,X1)
=> ordinal(X2) )
& ! [X2] :
( ordinal(X2)
=> ~ subset(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t36_ordinal1])]) ).
fof(i_0_64,plain,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
inference(fof_simplification,[status(thm)],[rc3_ordinal1]) ).
fof(i_0_65,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_66,plain,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
inference(fof_simplification,[status(thm)],[rc2_relat_1]) ).
fof(i_0_67,plain,
! [X102,X103,X104,X106,X107,X108,X109,X111] :
( ( in(X104,esk2_3(X102,X103,X104))
| ~ in(X104,X103)
| X103 != union(X102) )
& ( in(esk2_3(X102,X103,X104),X102)
| ~ in(X104,X103)
| X103 != union(X102) )
& ( ~ in(X106,X107)
| ~ in(X107,X102)
| in(X106,X103)
| X103 != union(X102) )
& ( ~ in(esk3_2(X108,X109),X109)
| ~ in(esk3_2(X108,X109),X111)
| ~ in(X111,X108)
| X109 = union(X108) )
& ( in(esk3_2(X108,X109),esk4_2(X108,X109))
| in(esk3_2(X108,X109),X109)
| X109 = union(X108) )
& ( in(esk4_2(X108,X109),X108)
| in(esk3_2(X108,X109),X109)
| X109 = union(X108) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_tarski])])])])])]) ).
cnf(i_0_68,plain,
( ordinal_subset(X1,X2)
| ~ in(X1,succ(X2))
| ~ ordinal(X2)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_55]) ).
cnf(i_0_69,plain,
succ(X1) = set_union2(X1,singleton(X1)),
inference(split_conjunct,[status(thm)],[i_0_56]) ).
cnf(i_0_70,plain,
( in(X1,succ(X2))
| ~ ordinal_subset(X1,X2)
| ~ ordinal(X2)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_55]) ).
fof(i_0_71,plain,
! [X96,X97,X98,X99,X100] :
( ( ~ subset(X96,X97)
| ~ in(X98,X96)
| in(X98,X97) )
& ( in(esk1_2(X99,X100),X99)
| subset(X99,X100) )
& ( ~ in(esk1_2(X99,X100),X100)
| subset(X99,X100) ) ),
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])])])])])]) ).
cnf(i_0_72,plain,
( ~ empty(succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_57]) ).
fof(i_0_73,plain,
! [X158,X159,X160] :
( ~ in(X158,X159)
| ~ element(X159,powerset(X160))
| element(X158,X160) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
cnf(i_0_74,plain,
~ empty(succ(X1)),
inference(split_conjunct,[status(thm)],[i_0_58]) ).
fof(i_0_75,plain,
! [X161,X162,X163] :
( ~ in(X161,X162)
| ~ element(X162,powerset(X163))
| ~ empty(X163) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(i_0_76,plain,
! [X118,X119] :
( empty(X118)
| ~ empty(set_union2(X118,X119)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_59])]) ).
fof(i_0_77,plain,
! [X121,X122] :
( empty(X121)
| ~ empty(set_union2(X122,X121)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_60])]) ).
fof(i_0_78,plain,
! [X138,X139] :
( ( ~ ordinal_subset(X138,X139)
| subset(X138,X139)
| ~ ordinal(X138)
| ~ ordinal(X139) )
& ( ~ subset(X138,X139)
| ordinal_subset(X138,X139)
| ~ ordinal(X138)
| ~ ordinal(X139) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r1_ordinal1])])]) ).
cnf(i_0_79,plain,
( epsilon_connected(succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_57]) ).
cnf(i_0_80,plain,
( epsilon_transitive(succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_57]) ).
cnf(i_0_81,plain,
( ordinal(succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_61]) ).
cnf(i_0_82,plain,
( ordinal(succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_57]) ).
fof(i_0_83,plain,
! [X156,X157] :
( ( ~ element(X156,powerset(X157))
| subset(X156,X157) )
& ( ~ subset(X156,X157)
| element(X156,powerset(X157)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(i_0_84,plain,
! [X83,X84] :
( ~ in(X83,X84)
| ~ in(X84,X83) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_62])]) ).
fof(i_0_85,plain,
! [X116,X117] :
( ~ relation(X116)
| ~ relation(X117)
| relation(set_union2(X116,X117)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc2_relat_1])]) ).
fof(i_0_86,plain,
! [X93,X94] :
( ~ ordinal(X93)
| ~ ordinal(X94)
| ordinal_subset(X93,X94)
| ordinal_subset(X94,X93) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[connectedness_r1_ordinal1])]) ).
fof(i_0_87,plain,
! [X147,X148] :
( ~ element(X147,X148)
| empty(X148)
| in(X147,X148) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(i_0_88,plain,
! [X144,X145] :
( ~ in(X144,X145)
| element(X144,X145) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(i_0_89,plain,
! [X151] :
( ( in(esk19_1(X151),X151)
| ordinal(union(X151)) )
& ( ~ ordinal(esk19_1(X151))
| ordinal(union(X151)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t35_ordinal1])])])]) ).
fof(i_0_90,plain,
! [X165,X166] :
( ~ in(X165,X166)
| ~ empty(X166) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_91,plain,
! [X140,X141] :
( ~ ordinal(X140)
| ~ ordinal(X141)
| ordinal_subset(X140,X140) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[reflexivity_r1_ordinal1])]) ).
fof(i_0_92,plain,
! [X91,X92] : set_union2(X91,X92) = set_union2(X92,X91),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(i_0_93,negated_conjecture,
! [X154,X155] :
( ( ~ in(X154,esk20_0)
| ordinal(X154) )
& ( ~ ordinal(X155)
| ~ subset(esk20_0,X155) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_63])])])]) ).
fof(i_0_94,plain,
! [X88] :
( ( relation(X88)
| ~ relation(X88)
| ~ empty(X88)
| ~ function(X88) )
& ( function(X88)
| ~ relation(X88)
| ~ empty(X88)
| ~ function(X88) )
& ( one_to_one(X88)
| ~ relation(X88)
| ~ empty(X88)
| ~ function(X88) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_funct_1])])]) ).
fof(i_0_95,plain,
! [X113] : element(esk5_1(X113),X113),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(i_0_96,plain,
! [X89] :
( ~ epsilon_transitive(X89)
| ~ epsilon_connected(X89)
| ordinal(X89) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_ordinal1])]) ).
fof(i_0_97,plain,
! [X123] :
( ( epsilon_transitive(union(X123))
| ~ ordinal(X123) )
& ( epsilon_connected(union(X123))
| ~ ordinal(X123) )
& ( ordinal(union(X123))
| ~ ordinal(X123) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc4_ordinal1])])]) ).
fof(i_0_98,plain,
! [X167,X168] :
( ~ empty(X167)
| X167 = X168
| ~ empty(X168) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_99,plain,
! [X124] : set_union2(X124,X124) = X124,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
fof(i_0_100,plain,
! [X142] : subset(X142,X142),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(i_0_101,plain,
! [X143] : set_union2(X143,empty_set) = X143,
inference(variable_rename,[status(thm)],[t1_boole]) ).
fof(i_0_102,plain,
! [X87] :
( ~ empty(X87)
| relation(X87) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relat_1])]) ).
fof(i_0_103,plain,
! [X86] :
( ( epsilon_transitive(X86)
| ~ ordinal(X86) )
& ( epsilon_connected(X86)
| ~ ordinal(X86) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_ordinal1])])]) ).
fof(i_0_104,plain,
! [X90] :
( ( epsilon_transitive(X90)
| ~ empty(X90) )
& ( epsilon_connected(X90)
| ~ empty(X90) )
& ( ordinal(X90)
| ~ empty(X90) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc3_ordinal1])])]) ).
fof(i_0_105,plain,
! [X85] :
( ~ empty(X85)
| function(X85) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_funct_1])]) ).
fof(i_0_106,plain,
! [X164] :
( ~ empty(X164)
| X164 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_107,plain,
( ~ empty(esk15_0)
& epsilon_transitive(esk15_0)
& epsilon_connected(esk15_0)
& ordinal(esk15_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_64])]) ).
fof(i_0_108,plain,
~ empty(esk13_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_65])]) ).
fof(i_0_109,plain,
( ~ empty(esk12_0)
& relation(esk12_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_66])]) ).
fof(i_0_110,plain,
( relation(esk18_0)
& relation_non_empty(esk18_0)
& function(esk18_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc5_funct_1])]) ).
fof(i_0_111,plain,
( relation(esk17_0)
& relation_empty_yielding(esk17_0)
& function(esk17_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc4_funct_1])]) ).
fof(i_0_112,plain,
( relation(esk16_0)
& relation_empty_yielding(esk16_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_relat_1])]) ).
fof(i_0_113,plain,
( relation(esk14_0)
& function(esk14_0)
& one_to_one(esk14_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_funct_1])]) ).
fof(i_0_114,plain,
( relation(esk11_0)
& function(esk11_0)
& one_to_one(esk11_0)
& empty(esk11_0)
& epsilon_transitive(esk11_0)
& epsilon_connected(esk11_0)
& ordinal(esk11_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_ordinal1])]) ).
fof(i_0_115,plain,
( relation(esk10_0)
& empty(esk10_0)
& function(esk10_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_funct_1])]) ).
fof(i_0_116,plain,
( empty(esk8_0)
& relation(esk8_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_relat_1])]) ).
fof(i_0_117,plain,
( relation(esk6_0)
& function(esk6_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_funct_1])]) ).
fof(i_0_118,plain,
( epsilon_transitive(esk7_0)
& epsilon_connected(esk7_0)
& ordinal(esk7_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_ordinal1])]) ).
fof(i_0_119,plain,
empty(esk9_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_120,plain,
( X2 = union(X1)
| ~ in(esk3_2(X1,X2),X2)
| ~ in(esk3_2(X1,X2),X3)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_121,plain,
( in(esk2_3(X1,X2,X3),X1)
| ~ in(X3,X2)
| X2 != union(X1) ),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_122,plain,
( in(X1,esk2_3(X2,X3,X1))
| ~ in(X1,X3)
| X3 != union(X2) ),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_123,plain,
( in(esk3_2(X1,X2),esk4_2(X1,X2))
| in(esk3_2(X1,X2),X2)
| X2 = union(X1) ),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_124,plain,
( ordinal_subset(X1,X2)
| ~ ordinal(X2)
| ~ ordinal(X1)
| ~ in(X1,set_union2(X2,singleton(X2))) ),
inference(rw,[status(thm)],[i_0_68,c_0_69]),
[final] ).
cnf(i_0_125,plain,
( in(X1,set_union2(X2,singleton(X2)))
| ~ ordinal(X2)
| ~ ordinal(X1)
| ~ ordinal_subset(X1,X2) ),
inference(rw,[status(thm)],[i_0_70,c_0_69]),
[final] ).
cnf(i_0_126,plain,
( in(esk4_2(X1,X2),X1)
| in(esk3_2(X1,X2),X2)
| X2 = union(X1) ),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_127,plain,
( subset(X1,X2)
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_128,plain,
( ~ ordinal(X1)
| ~ empty(set_union2(X1,singleton(X1))) ),
inference(rw,[status(thm)],[i_0_72,c_0_69]),
[final] ).
cnf(i_0_129,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_73]),
[final] ).
cnf(i_0_130,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X2,X3)
| X4 != union(X3) ),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_131,plain,
~ empty(set_union2(X1,singleton(X1))),
inference(rw,[status(thm)],[i_0_74,c_0_69]),
[final] ).
cnf(i_0_132,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_133,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_134,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_135,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_76]),
[final] ).
cnf(i_0_136,plain,
( empty(X1)
| ~ empty(set_union2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_77]),
[final] ).
cnf(i_0_137,plain,
( subset(X1,X2)
| ~ ordinal_subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_138,plain,
( ordinal_subset(X1,X2)
| ~ subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_139,plain,
( epsilon_connected(set_union2(X1,singleton(X1)))
| ~ ordinal(X1) ),
inference(rw,[status(thm)],[i_0_79,c_0_69]),
[final] ).
cnf(i_0_140,plain,
( epsilon_transitive(set_union2(X1,singleton(X1)))
| ~ ordinal(X1) ),
inference(rw,[status(thm)],[i_0_80,c_0_69]),
[final] ).
cnf(i_0_141,plain,
( ordinal(set_union2(X1,singleton(X1)))
| ~ ordinal(X1) ),
inference(rw,[status(thm)],[i_0_81,c_0_69]),
[final] ).
cnf(i_0_142,plain,
( ordinal(set_union2(X1,singleton(X1)))
| ~ ordinal(X1) ),
inference(rw,[status(thm)],[i_0_82,c_0_69]),
[final] ).
cnf(i_0_143,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_144,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_84]),
[final] ).
cnf(i_0_145,plain,
( relation(set_union2(X1,X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_85]),
[final] ).
cnf(i_0_146,plain,
( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_86]),
[final] ).
cnf(i_0_147,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_148,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_149,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_88]),
[final] ).
cnf(i_0_150,plain,
( in(esk19_1(X1),X1)
| ordinal(union(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_89]),
[final] ).
cnf(i_0_151,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_90]),
[final] ).
cnf(i_0_152,plain,
( ordinal_subset(X1,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_91]),
[final] ).
cnf(i_0_153,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_92]),
[final] ).
cnf(i_0_154,negated_conjecture,
( ~ ordinal(X1)
| ~ subset(esk20_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_93]),
[final] ).
cnf(i_0_155,plain,
( ordinal(union(X1))
| ~ ordinal(esk19_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_89]),
[final] ).
cnf(i_0_156,plain,
( one_to_one(X1)
| ~ relation(X1)
| ~ empty(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_94]),
[final] ).
cnf(i_0_157,negated_conjecture,
( ordinal(X1)
| ~ in(X1,esk20_0) ),
inference(split_conjunct,[status(thm)],[i_0_93]),
[final] ).
cnf(i_0_158,plain,
element(esk5_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_95]),
[final] ).
cnf(i_0_159,plain,
( ordinal(X1)
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[i_0_96]),
[final] ).
cnf(i_0_160,plain,
( epsilon_connected(union(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_97]),
[final] ).
cnf(i_0_161,plain,
( epsilon_transitive(union(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_97]),
[final] ).
cnf(i_0_162,plain,
( ordinal(union(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_97]),
[final] ).
cnf(i_0_163,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_98]),
[final] ).
cnf(i_0_164,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_99]),
[final] ).
cnf(i_0_165,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_100]),
[final] ).
cnf(i_0_166,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[i_0_101]),
[final] ).
cnf(i_0_167,plain,
( relation(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_102]),
[final] ).
cnf(i_0_168,plain,
( epsilon_connected(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_169,plain,
( epsilon_connected(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_170,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_171,plain,
( epsilon_transitive(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_172,plain,
( ordinal(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_173,plain,
( function(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_105]),
[final] ).
cnf(i_0_174,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_106]),
[final] ).
cnf(i_0_175,plain,
~ empty(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_107]),
[final] ).
cnf(i_0_176,plain,
~ empty(esk13_0),
inference(split_conjunct,[status(thm)],[i_0_108]),
[final] ).
cnf(i_0_177,plain,
~ empty(esk12_0),
inference(split_conjunct,[status(thm)],[i_0_109]),
[final] ).
cnf(i_0_178,plain,
relation_non_empty(esk18_0),
inference(split_conjunct,[status(thm)],[i_0_110]),
[final] ).
cnf(i_0_179,plain,
relation_empty_yielding(esk17_0),
inference(split_conjunct,[status(thm)],[i_0_111]),
[final] ).
cnf(i_0_180,plain,
relation_empty_yielding(esk16_0),
inference(split_conjunct,[status(thm)],[i_0_112]),
[final] ).
cnf(i_0_181,plain,
relation_empty_yielding(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_182,plain,
relation_empty_yielding(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_183,plain,
one_to_one(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_113]),
[final] ).
cnf(i_0_184,plain,
one_to_one(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_114]),
[final] ).
cnf(i_0_185,plain,
one_to_one(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_186,plain,
relation(esk18_0),
inference(split_conjunct,[status(thm)],[i_0_110]),
[final] ).
cnf(i_0_187,plain,
relation(esk17_0),
inference(split_conjunct,[status(thm)],[i_0_111]),
[final] ).
cnf(i_0_188,plain,
relation(esk16_0),
inference(split_conjunct,[status(thm)],[i_0_112]),
[final] ).
cnf(i_0_189,plain,
relation(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_113]),
[final] ).
cnf(i_0_190,plain,
relation(esk12_0),
inference(split_conjunct,[status(thm)],[i_0_109]),
[final] ).
cnf(i_0_191,plain,
relation(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_114]),
[final] ).
cnf(i_0_192,plain,
relation(esk10_0),
inference(split_conjunct,[status(thm)],[i_0_115]),
[final] ).
cnf(i_0_193,plain,
relation(esk8_0),
inference(split_conjunct,[status(thm)],[i_0_116]),
[final] ).
cnf(i_0_194,plain,
relation(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_117]),
[final] ).
cnf(i_0_195,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_196,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_197,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_198,plain,
epsilon_connected(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_107]),
[final] ).
cnf(i_0_199,plain,
epsilon_connected(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_114]),
[final] ).
cnf(i_0_200,plain,
epsilon_connected(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_118]),
[final] ).
cnf(i_0_201,plain,
epsilon_connected(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_202,plain,
epsilon_transitive(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_107]),
[final] ).
cnf(i_0_203,plain,
epsilon_transitive(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_114]),
[final] ).
cnf(i_0_204,plain,
epsilon_transitive(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_118]),
[final] ).
cnf(i_0_205,plain,
epsilon_transitive(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_206,plain,
ordinal(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_107]),
[final] ).
cnf(i_0_207,plain,
ordinal(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_114]),
[final] ).
cnf(i_0_208,plain,
ordinal(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_118]),
[final] ).
cnf(i_0_209,plain,
ordinal(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_210,plain,
function(esk18_0),
inference(split_conjunct,[status(thm)],[i_0_110]),
[final] ).
cnf(i_0_211,plain,
function(esk17_0),
inference(split_conjunct,[status(thm)],[i_0_111]),
[final] ).
cnf(i_0_212,plain,
function(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_113]),
[final] ).
cnf(i_0_213,plain,
function(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_114]),
[final] ).
cnf(i_0_214,plain,
function(esk10_0),
inference(split_conjunct,[status(thm)],[i_0_115]),
[final] ).
cnf(i_0_215,plain,
function(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_117]),
[final] ).
cnf(i_0_216,plain,
function(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_217,plain,
empty(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_114]),
[final] ).
cnf(i_0_218,plain,
empty(esk10_0),
inference(split_conjunct,[status(thm)],[i_0_115]),
[final] ).
cnf(i_0_219,plain,
empty(esk9_0),
inference(split_conjunct,[status(thm)],[i_0_119]),
[final] ).
cnf(i_0_220,plain,
empty(esk8_0),
inference(split_conjunct,[status(thm)],[i_0_116]),
[final] ).
cnf(i_0_221,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_222,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_223,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_224,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_225,axiom,
X1 = X1 ).
cnf(i_0_226,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_227,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_228,axiom,
( X1 != X2
| union(X1) = union(X2) ) ).
cnf(i_0_229,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_230,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_231,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_232,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_233,axiom,
( X1 != X2
| ~ one_to_one(X1)
| one_to_one(X2) ) ).
cnf(i_0_234,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_235,axiom,
( X1 != X2
| ~ relation_non_empty(X1)
| relation_non_empty(X2) ) ).
cnf(i_0_236,axiom,
( X1 != X2
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(X2) ) ).
cnf(i_0_237,axiom,
( X1 != X2
| ~ ordinal_subset(X1,X3)
| ordinal_subset(X2,X3) ) ).
cnf(i_0_238,axiom,
( X1 != X2
| ~ ordinal_subset(X3,X1)
| ordinal_subset(X3,X2) ) ).
cnf(i_0_239,axiom,
( X1 != X2
| ~ ordinal(X1)
| ordinal(X2) ) ).
cnf(i_0_240,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_241,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_242,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_243,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_244,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_245,axiom,
( X1 != X2
| ~ epsilon_connected(X1)
| epsilon_connected(X2) ) ).
cnf(i_0_246,axiom,
( X1 != X2
| ~ epsilon_transitive(X1)
| epsilon_transitive(X2) ) ).
cnf(i_0_247,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_252,plain,
~ ordinal(esk20_0),
inference(scs_inference,[],[i_0_165,i_0_154]) ).
cnf(i_0_253,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_165]) ).
cnf(i_0_255,plain,
subset(esk5_1(powerset(X1)),X1),
inference(scs_inference,[],[i_0_165,i_0_158,i_0_154,i_0_143]) ).
cnf(i_0_256,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_258,plain,
ordinal(esk10_0),
inference(scs_inference,[],[i_0_165,i_0_158,i_0_218,i_0_154,i_0_143,i_0_172]) ).
cnf(i_0_260,plain,
~ in(X1,esk11_0),
inference(scs_inference,[],[i_0_165,i_0_158,i_0_217,i_0_218,i_0_154,i_0_143,i_0_172,i_0_151]) ).
cnf(i_0_262,plain,
epsilon_connected(esk10_0),
inference(scs_inference,[],[i_0_165,i_0_158,i_0_217,i_0_218,i_0_154,i_0_143,i_0_172,i_0_151,i_0_169]) ).
cnf(i_0_264,plain,
epsilon_transitive(esk10_0),
inference(scs_inference,[],[i_0_165,i_0_158,i_0_217,i_0_218,i_0_154,i_0_143,i_0_172,i_0_151,i_0_169,i_0_171]) ).
cnf(i_0_266,plain,
X1 = set_union2(X1,X1),
inference(scs_inference,[],[i_0_165,i_0_164,i_0_158,i_0_217,i_0_218,i_0_154,i_0_143,i_0_172,i_0_151,i_0_169,i_0_171,i_0_226]) ).
cnf(i_0_267,plain,
relation(esk9_0),
inference(scs_inference,[],[i_0_165,i_0_164,i_0_158,i_0_217,i_0_218,i_0_219,i_0_154,i_0_143,i_0_172,i_0_151,i_0_169,i_0_171,i_0_226,i_0_167]) ).
cnf(i_0_269,plain,
function(esk9_0),
inference(scs_inference,[],[i_0_165,i_0_164,i_0_158,i_0_217,i_0_218,i_0_219,i_0_154,i_0_143,i_0_172,i_0_151,i_0_169,i_0_171,i_0_226,i_0_167,i_0_173]) ).
cnf(i_0_271,plain,
esk15_0 != esk20_0,
inference(scs_inference,[],[i_0_165,i_0_206,i_0_164,i_0_158,i_0_217,i_0_218,i_0_219,i_0_154,i_0_143,i_0_172,i_0_151,i_0_169,i_0_171,i_0_226,i_0_167,i_0_173,i_0_239]) ).
cnf(i_0_272,plain,
~ in(X1,set_union2(union(esk11_0),union(esk11_0))),
inference(scs_inference,[],[i_0_165,i_0_206,i_0_164,i_0_158,i_0_217,i_0_218,i_0_219,i_0_154,i_0_143,i_0_172,i_0_151,i_0_169,i_0_171,i_0_226,i_0_167,i_0_173,i_0_239,i_0_121]) ).
cnf(i_0_273,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_276,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_279,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_282,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_165]) ).
cnf(i_0_289,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_329,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_337,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_341,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_354,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_165]) ).
cnf(i_0_358,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_389,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_396,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_413,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_165]) ).
cnf(i_0_420,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_439,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_443,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_455,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_165]) ).
cnf(i_0_460,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_480,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_492,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_498,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_518,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_533,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_554,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_568,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_588,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_601,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_622,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_635,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_654,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_667,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_705,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_720,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_736,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_764,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_776,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_789,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_796,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_826,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_836,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_848,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_857,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_886,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_901,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_931,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_962,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_990,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1017,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1046,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1076,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1104,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1134,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1165,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1188,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_1195,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1218,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_1224,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1251,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1278,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1302,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1319,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_1326,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1342,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_1346,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1366,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1393,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1417,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1430,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_1436,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1449,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_1455,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1473,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1492,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1508,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1526,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1536,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_1542,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1557,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1572,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1587,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1603,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1613,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_1617,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1631,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1645,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1655,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_1659,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1672,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1684,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1696,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1704,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_1708,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1716,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_1720,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1732,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1743,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1754,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1765,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1776,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1787,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1802,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_1819,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_1832,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1840,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_1845,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_1859,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1875,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_1894,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_1912,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_1930,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_1942,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_1946,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1959,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1972,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_1989,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_2003,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_2017,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_2032,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_2048,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_2060,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_2072,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_2084,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_2092,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_2096,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_2107,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_2118,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_2143,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_2167,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_2179,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_2193,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_2208,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_2223,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_2235,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_2250,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_2262,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_2269,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_2286,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_2298,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_2305,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_2321,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_2333,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_2346,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_2362,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_2377,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_2393,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_2409,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_2425,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_2438,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_2450,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_2465,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_2477,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_2489,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_2493,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_2497,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2503,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2505,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2507,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2509,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2511,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2513,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2515,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2517,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2530,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_2533,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_2537,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_2550,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_2553,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_2556,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2562,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_2564,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2566,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2568,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2570,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2572,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2574,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2576,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2582,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_2590,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_2597,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_2600,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2606,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_2608,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2610,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2612,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2614,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2616,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2618,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2620,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2626,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_2632,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_2633,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_2641,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_2648,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_2650,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2652,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2654,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2656,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2658,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2660,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2662,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2677,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_2684,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_2686,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2688,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2690,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2692,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2694,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2696,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2698,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2712,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2714,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_2721,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_2723,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2725,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2727,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2729,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2731,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2733,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2735,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2749,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_2756,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_2758,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2760,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2762,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2764,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2766,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2768,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2770,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2772,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2785,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_2792,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2794,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2796,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2798,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2800,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2811,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2812,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_2813,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2814,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2815,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_2822,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_2829,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2831,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2833,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2835,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2837,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2852,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_2859,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2861,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2863,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2865,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2867,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2881,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_2888,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2890,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2892,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2894,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2896,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2908,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_2915,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2917,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2919,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2921,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2923,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2937,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2939,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_2946,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2948,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2950,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2952,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2954,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2969,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_2976,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2978,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2981,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2983,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2986,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_2999,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_3006,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_3009,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_3011,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_3021,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_3022,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_3023,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_3024,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_3025,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_3026,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_3034,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_3041,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_3043,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_3045,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_3052,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_3061,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_3067,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_3069,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_3071,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_3083,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_3089,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_3091,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_3104,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_3110,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_3112,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_3162,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_3169,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_3178,plain,
~ empty(set_union2(X1,singleton(X1))),
inference(rename_variables,[],[i_0_131]) ).
cnf(i_0_3179,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_3184,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_3186,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_3193,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_165]) ).
cnf(i_0_3281,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_3369,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_3382,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_165]) ).
cnf(i_0_3384,plain,
~ empty(set_union2(X1,singleton(X1))),
inference(rename_variables,[],[i_0_131]) ).
cnf(i_0_3455,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_3475,plain,
~ empty(set_union2(X1,singleton(X1))),
inference(rename_variables,[],[i_0_131]) ).
cnf(i_0_3535,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_3539,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_3551,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_165]) ).
cnf(i_0_3553,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_3615,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_3639,plain,
~ empty(set_union2(X1,singleton(X1))),
inference(rename_variables,[],[i_0_131]) ).
cnf(i_0_3647,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_3706,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_3710,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_3719,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_3723,plain,
~ empty(set_union2(X1,singleton(X1))),
inference(rename_variables,[],[i_0_131]) ).
cnf(i_0_3790,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_3804,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_3812,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_3818,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_165]) ).
cnf(i_0_3863,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_3866,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_3886,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_3942,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_3962,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_4013,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_4033,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_4112,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_4160,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_4165,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_4176,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_165]) ).
cnf(i_0_4242,plain,
element(esk5_1(X1),X1),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_4265,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_275,plain,
~ in(X1,esk5_1(powerset(esk11_0))),
inference(scs_inference,[],[i_0_165,i_0_206,i_0_164,i_0_158,i_0_256,i_0_217,i_0_218,i_0_219,i_0_154,i_0_143,i_0_172,i_0_151,i_0_169,i_0_171,i_0_226,i_0_167,i_0_173,i_0_239,i_0_121,i_0_132]) ).
cnf(i_0_278,plain,
esk15_0 != set_union2(esk20_0,esk20_0),
inference(scs_inference,[],[i_0_165,i_0_206,i_0_164,i_0_273,i_0_158,i_0_256,i_0_217,i_0_218,i_0_219,i_0_154,i_0_143,i_0_172,i_0_151,i_0_169,i_0_171,i_0_226,i_0_167,i_0_173,i_0_239,i_0_121,i_0_132,i_0_227]) ).
cnf(i_0_280,plain,
esk11_0 != set_union2(X1,singleton(X1)),
inference(scs_inference,[],[i_0_131,i_0_165,i_0_206,i_0_164,i_0_273,i_0_158,i_0_256,i_0_217,i_0_218,i_0_219,i_0_154,i_0_143,i_0_172,i_0_151,i_0_169,i_0_171,i_0_226,i_0_167,i_0_173,i_0_239,i_0_121,i_0_132,i_0_227,i_0_242]) ).
cnf(i_0_281,plain,
ordinal_subset(esk15_0,esk15_0),
inference(scs_inference,[],[i_0_131,i_0_165,i_0_253,i_0_206,i_0_164,i_0_273,i_0_158,i_0_256,i_0_217,i_0_218,i_0_219,i_0_154,i_0_143,i_0_172,i_0_151,i_0_169,i_0_171,i_0_226,i_0_167,i_0_173,i_0_239,i_0_121,i_0_132,i_0_227,i_0_242,i_0_138]) ).
cnf(i_0_284,plain,
one_to_one(esk10_0),
inference(scs_inference,[],[i_0_131,i_0_165,i_0_253,i_0_206,i_0_164,i_0_273,i_0_158,i_0_256,i_0_217,i_0_218,i_0_219,i_0_192,i_0_214,i_0_154,i_0_143,i_0_172,i_0_151,i_0_169,i_0_171,i_0_226,i_0_167,i_0_173,i_0_239,i_0_121,i_0_132,i_0_227,i_0_242,i_0_138,i_0_156]) ).
cnf(i_0_286,plain,
subset(set_union2(union(esk11_0),union(esk11_0)),X1),
inference(scs_inference,[],[i_0_131,i_0_165,i_0_253,i_0_206,i_0_164,i_0_273,i_0_158,i_0_256,i_0_217,i_0_218,i_0_219,i_0_192,i_0_214,i_0_154,i_0_143,i_0_172,i_0_151,i_0_169,i_0_171,i_0_226,i_0_167,i_0_173,i_0_239,i_0_121,i_0_132,i_0_227,i_0_242,i_0_138,i_0_156,i_0_134]) ).
cnf(i_0_301,plain,
~ in(X1,union(esk11_0)),
inference(scs_inference,[],[i_0_260,i_0_248]) ).
cnf(i_0_302,plain,
~ in(X1,esk11_0),
inference(rename_variables,[],[i_0_260]) ).
cnf(i_0_305,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_307,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_309,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_311,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_313,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_331,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_333,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_343,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_345,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_347,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_349,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_352,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_385,plain,
~ in(X1,set_union2(union(esk11_0),union(esk11_0))),
inference(rename_variables,[],[i_0_272]) ).
cnf(i_0_435,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_437,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_445,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_447,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_449,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_451,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_453,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_500,plain,
subset(esk5_1(powerset(X1)),X1),
inference(rename_variables,[],[i_0_255]) ).
cnf(i_0_514,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_516,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_520,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_523,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_525,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_527,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_529,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_565,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_619,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_624,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_626,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_628,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_630,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_656,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_658,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_660,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_662,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_664,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_706,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_747,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_749,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_751,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_753,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_755,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_807,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_809,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_811,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_813,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(i_0_815,plain,
X1 = set_union2(X1,X1),
inference(rename_variables,[],[i_0_266]) ).
cnf(c_0_168,plain,
( in(X1,X2)
| ~ in(X1,X3)
| ~ in(X3,X4)
| X2 != union(X4) ),
i_0_130 ).
cnf(c_0_169,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
i_0_134 ).
cnf(c_0_170,plain,
( subset(X1,X2)
| ~ in(esk1_2(X1,X2),X2) ),
i_0_127 ).
cnf(c_0_171,plain,
( in(X1,set_union2(X2,singleton(X2)))
| ~ ordinal(X2)
| ~ ordinal(X1)
| ~ ordinal_subset(X1,X2) ),
i_0_125 ).
cnf(c_0_172,plain,
( subset(X1,X2)
| in(X3,X4)
| X4 != union(X1)
| ~ in(X3,esk1_2(X1,X2)) ),
inference(spm,[status(thm)],[c_0_168,c_0_169]) ).
cnf(c_0_173,plain,
( subset(X1,set_union2(X2,singleton(X2)))
| ~ ordinal(esk1_2(X1,set_union2(X2,singleton(X2))))
| ~ ordinal(X2)
| ~ ordinal_subset(esk1_2(X1,set_union2(X2,singleton(X2))),X2) ),
inference(spm,[status(thm)],[c_0_170,c_0_171]) ).
cnf(c_0_174,plain,
( ordinal_subset(X1,X2)
| ~ subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
i_0_138 ).
cnf(c_0_175,plain,
( subset(esk1_2(X1,X2),X3)
| subset(X1,X2)
| in(esk1_2(esk1_2(X1,X2),X3),X4)
| X4 != union(X1) ),
inference(spm,[status(thm)],[c_0_172,c_0_169]) ).
cnf(c_0_176,plain,
( subset(X1,set_union2(X2,singleton(X2)))
| ~ subset(esk1_2(X1,set_union2(X2,singleton(X2))),X2)
| ~ ordinal(esk1_2(X1,set_union2(X2,singleton(X2))))
| ~ ordinal(X2) ),
inference(spm,[status(thm)],[c_0_173,c_0_174]) ).
cnf(c_0_177,plain,
( subset(esk1_2(X1,X2),X3)
| subset(X1,X2)
| X3 != union(X1) ),
inference(spm,[status(thm)],[c_0_170,c_0_175]) ).
cnf(c_0_178,negated_conjecture,
( ordinal(X1)
| ~ in(X1,esk20_0) ),
i_0_157 ).
cnf(c_0_179,plain,
( subset(X1,set_union2(X2,singleton(X2)))
| X2 != union(X1)
| ~ ordinal(esk1_2(X1,set_union2(X2,singleton(X2))))
| ~ ordinal(X2) ),
inference(spm,[status(thm)],[c_0_176,c_0_177]) ).
cnf(c_0_180,negated_conjecture,
( subset(esk20_0,X1)
| ordinal(esk1_2(esk20_0,X1)) ),
inference(spm,[status(thm)],[c_0_178,c_0_169]) ).
cnf(c_0_181,negated_conjecture,
( ~ ordinal(X1)
| ~ subset(esk20_0,X1) ),
i_0_154 ).
cnf(c_0_182,negated_conjecture,
( subset(esk20_0,set_union2(X1,singleton(X1)))
| X1 != union(esk20_0)
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[c_0_179,c_0_180]) ).
cnf(c_0_183,plain,
( ordinal(set_union2(X1,singleton(X1)))
| ~ ordinal(X1) ),
i_0_141 ).
cnf(c_0_184,plain,
( in(esk19_1(X1),X1)
| ordinal(union(X1)) ),
i_0_150 ).
cnf(c_0_185,plain,
( ordinal(union(X1))
| ~ ordinal(esk19_1(X1)) ),
i_0_155 ).
cnf(c_0_186,negated_conjecture,
( X1 != union(esk20_0)
| ~ ordinal(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_182]),c_0_183]) ).
cnf(c_0_187,negated_conjecture,
ordinal(union(esk20_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_184]),c_0_185]) ).
cnf(c_0_188,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_186]),c_0_187])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM403+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n017.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 00:29:42 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 260.69/149.70 % Version : CSE_E---1.7
% 260.69/149.70 % Problem : theBenchmark.p
% 260.69/149.70 % SZS status Theorem for theBenchmark.p
% 260.69/149.70 % SZS output start CNFRefutation
% See solution above
% 270.49/159.53 % Total time : 148.128s
%------------------------------------------------------------------------------