%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET766+4 : TPTP v9.2.1. Released v2.2.0.
% 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 : n025.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 05:08:27 PM UTC 2026
% Result : Theorem 0.34s 1.61s
% Output : CNFRefutation 0.34s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_17)
% Comments :
%------------------------------------------------------------------------------
fof(thIII02,conjecture,
! [X4,X7,X1] :
( ( equivalence(X7,X4)
& member(X1,X4) )
=> member(X1,equivalence_class(X1,X4,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIII02) ).
fof(difference,axiom,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',difference) ).
fof(equivalence,axiom,
! [X1,X7] :
( equivalence(X7,X1)
<=> ( ! [X3] :
( member(X3,X1)
=> apply(X7,X3,X3) )
& ! [X3,X5] :
( ( member(X3,X1)
& member(X5,X1) )
=> ( apply(X7,X3,X5)
=> apply(X7,X5,X3) ) )
& ! [X3,X5,X6] :
( ( member(X3,X1)
& member(X5,X1)
& member(X6,X1) )
=> ( ( apply(X7,X3,X5)
& apply(X7,X5,X6) )
=> apply(X7,X3,X6) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+2.ax',equivalence) ).
fof(empty_set,axiom,
! [X3] : ~ member(X3,empty_set),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',empty_set) ).
fof(pre_order,axiom,
! [X7,X4] :
( pre_order(X7,X4)
<=> ( ! [X3] :
( member(X3,X4)
=> apply(X7,X3,X3) )
& ! [X3,X5,X6] :
( ( member(X3,X4)
& member(X5,X4)
& member(X6,X4) )
=> ( ( apply(X7,X3,X5)
& apply(X7,X5,X6) )
=> apply(X7,X3,X6) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+2.ax',pre_order) ).
fof(equivalence_class,axiom,
! [X7,X4,X1,X3] :
( member(X3,equivalence_class(X1,X4,X7))
<=> ( member(X3,X4)
& apply(X7,X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+2.ax',equivalence_class) ).
fof(partition,axiom,
! [X1,X4] :
( partition(X1,X4)
<=> ( ! [X3] :
( member(X3,X1)
=> subset(X3,X4) )
& ! [X3] :
( member(X3,X4)
=> ? [X5] :
( member(X5,X1)
& member(X3,X5) ) )
& ! [X3,X5] :
( ( member(X3,X1)
& member(X5,X1) )
=> ( ? [X6] :
( member(X6,X3)
& member(X6,X5) )
=> X3 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+2.ax',partition) ).
fof(union,axiom,
! [X3,X1,X2] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',union) ).
fof(intersection,axiom,
! [X3,X1,X2] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',intersection) ).
fof(product,axiom,
! [X3,X1] :
( member(X3,product(X1))
<=> ! [X5] :
( member(X5,X1)
=> member(X3,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',product) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
fof(sum,axiom,
! [X3,X1] :
( member(X3,sum(X1))
<=> ? [X5] :
( member(X5,X1)
& member(X3,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',sum) ).
fof(disjoint,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> ~ ? [X3] :
( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+2.ax',disjoint) ).
fof(unordered_pair,axiom,
! [X3,X1,X2] :
( member(X3,unordered_pair(X1,X2))
<=> ( X3 = X1
| X3 = X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',unordered_pair) ).
fof(equal_set,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(power_set,axiom,
! [X3,X1] :
( member(X3,power_set(X1))
<=> subset(X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',power_set) ).
fof(singleton,axiom,
! [X3,X1] :
( member(X3,singleton(X1))
<=> X3 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',singleton) ).
fof(i_0_17,plain,
! [X1,X7] :
( epred1_2(X7,X1)
<=> ( ! [X3] :
( member(X3,X1)
=> apply(X7,X3,X3) )
& ! [X3,X5] :
( ( member(X3,X1)
& member(X5,X1) )
=> ( apply(X7,X3,X5)
=> apply(X7,X5,X3) ) )
& ! [X3,X5,X6] :
( ( member(X3,X1)
& member(X5,X1)
& member(X6,X1) )
=> ( ( apply(X7,X3,X5)
& apply(X7,X5,X6) )
=> apply(X7,X3,X6) ) ) ) ),
introduced(definition) ).
fof(i_0_18,negated_conjecture,
~ ! [X4,X7,X1] :
( ( equivalence(X7,X4)
& member(X1,X4) )
=> member(X1,equivalence_class(X1,X4,X7)) ),
inference(assume_negation,[status(cth)],[thIII02]) ).
fof(i_0_19,plain,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[difference]) ).
fof(i_0_20,axiom,
! [X1,X7] :
( equivalence(X7,X1)
<=> epred1_2(X7,X1) ),
inference(apply_def,[status(thm)],[equivalence,c_0_17]) ).
fof(i_0_21,plain,
! [X3] : ~ member(X3,empty_set),
inference(fof_simplification,[status(thm)],[empty_set]) ).
fof(i_0_22,plain,
! [X148,X149,X150,X151,X152,X153,X154,X155,X156,X157] :
( ( ~ member(X150,X148)
| apply(X149,X150,X150)
| ~ epred1_2(X149,X148) )
& ( ~ member(X151,X148)
| ~ member(X152,X148)
| ~ apply(X149,X151,X152)
| apply(X149,X152,X151)
| ~ epred1_2(X149,X148) )
& ( ~ member(X153,X148)
| ~ member(X154,X148)
| ~ member(X155,X148)
| ~ apply(X149,X153,X154)
| ~ apply(X149,X154,X155)
| apply(X149,X153,X155)
| ~ epred1_2(X149,X148) )
& ( member(esk21_2(X156,X157),X156)
| member(esk19_2(X156,X157),X156)
| member(esk18_2(X156,X157),X156)
| epred1_2(X157,X156) )
& ( member(esk22_2(X156,X157),X156)
| member(esk19_2(X156,X157),X156)
| member(esk18_2(X156,X157),X156)
| epred1_2(X157,X156) )
& ( member(esk23_2(X156,X157),X156)
| member(esk19_2(X156,X157),X156)
| member(esk18_2(X156,X157),X156)
| epred1_2(X157,X156) )
& ( apply(X157,esk21_2(X156,X157),esk22_2(X156,X157))
| member(esk19_2(X156,X157),X156)
| member(esk18_2(X156,X157),X156)
| epred1_2(X157,X156) )
& ( apply(X157,esk22_2(X156,X157),esk23_2(X156,X157))
| member(esk19_2(X156,X157),X156)
| member(esk18_2(X156,X157),X156)
| epred1_2(X157,X156) )
& ( ~ apply(X157,esk21_2(X156,X157),esk23_2(X156,X157))
| member(esk19_2(X156,X157),X156)
| member(esk18_2(X156,X157),X156)
| epred1_2(X157,X156) )
& ( member(esk21_2(X156,X157),X156)
| member(esk20_2(X156,X157),X156)
| member(esk18_2(X156,X157),X156)
| epred1_2(X157,X156) )
& ( member(esk22_2(X156,X157),X156)
| member(esk20_2(X156,X157),X156)
| member(esk18_2(X156,X157),X156)
| epred1_2(X157,X156) )
& ( member(esk23_2(X156,X157),X156)
| member(esk20_2(X156,X157),X156)
| member(esk18_2(X156,X157),X156)
| epred1_2(X157,X156) )
& ( apply(X157,esk21_2(X156,X157),esk22_2(X156,X157))
| member(esk20_2(X156,X157),X156)
| member(esk18_2(X156,X157),X156)
| epred1_2(X157,X156) )
& ( apply(X157,esk22_2(X156,X157),esk23_2(X156,X157))
| member(esk20_2(X156,X157),X156)
| member(esk18_2(X156,X157),X156)
| epred1_2(X157,X156) )
& ( ~ apply(X157,esk21_2(X156,X157),esk23_2(X156,X157))
| member(esk20_2(X156,X157),X156)
| member(esk18_2(X156,X157),X156)
| epred1_2(X157,X156) )
& ( member(esk21_2(X156,X157),X156)
| apply(X157,esk19_2(X156,X157),esk20_2(X156,X157))
| member(esk18_2(X156,X157),X156)
| epred1_2(X157,X156) )
& ( member(esk22_2(X156,X157),X156)
| apply(X157,esk19_2(X156,X157),esk20_2(X156,X157))
| member(esk18_2(X156,X157),X156)
| epred1_2(X157,X156) )
& ( member(esk23_2(X156,X157),X156)
| apply(X157,esk19_2(X156,X157),esk20_2(X156,X157))
| member(esk18_2(X156,X157),X156)
| epred1_2(X157,X156) )
& ( apply(X157,esk21_2(X156,X157),esk22_2(X156,X157))
| apply(X157,esk19_2(X156,X157),esk20_2(X156,X157))
| member(esk18_2(X156,X157),X156)
| epred1_2(X157,X156) )
& ( apply(X157,esk22_2(X156,X157),esk23_2(X156,X157))
| apply(X157,esk19_2(X156,X157),esk20_2(X156,X157))
| member(esk18_2(X156,X157),X156)
| epred1_2(X157,X156) )
& ( ~ apply(X157,esk21_2(X156,X157),esk23_2(X156,X157))
| apply(X157,esk19_2(X156,X157),esk20_2(X156,X157))
| member(esk18_2(X156,X157),X156)
| epred1_2(X157,X156) )
& ( member(esk21_2(X156,X157),X156)
| ~ apply(X157,esk20_2(X156,X157),esk19_2(X156,X157))
| member(esk18_2(X156,X157),X156)
| epred1_2(X157,X156) )
& ( member(esk22_2(X156,X157),X156)
| ~ apply(X157,esk20_2(X156,X157),esk19_2(X156,X157))
| member(esk18_2(X156,X157),X156)
| epred1_2(X157,X156) )
& ( member(esk23_2(X156,X157),X156)
| ~ apply(X157,esk20_2(X156,X157),esk19_2(X156,X157))
| member(esk18_2(X156,X157),X156)
| epred1_2(X157,X156) )
& ( apply(X157,esk21_2(X156,X157),esk22_2(X156,X157))
| ~ apply(X157,esk20_2(X156,X157),esk19_2(X156,X157))
| member(esk18_2(X156,X157),X156)
| epred1_2(X157,X156) )
& ( apply(X157,esk22_2(X156,X157),esk23_2(X156,X157))
| ~ apply(X157,esk20_2(X156,X157),esk19_2(X156,X157))
| member(esk18_2(X156,X157),X156)
| epred1_2(X157,X156) )
& ( ~ apply(X157,esk21_2(X156,X157),esk23_2(X156,X157))
| ~ apply(X157,esk20_2(X156,X157),esk19_2(X156,X157))
| member(esk18_2(X156,X157),X156)
| epred1_2(X157,X156) )
& ( member(esk21_2(X156,X157),X156)
| member(esk19_2(X156,X157),X156)
| ~ apply(X157,esk18_2(X156,X157),esk18_2(X156,X157))
| epred1_2(X157,X156) )
& ( member(esk22_2(X156,X157),X156)
| member(esk19_2(X156,X157),X156)
| ~ apply(X157,esk18_2(X156,X157),esk18_2(X156,X157))
| epred1_2(X157,X156) )
& ( member(esk23_2(X156,X157),X156)
| member(esk19_2(X156,X157),X156)
| ~ apply(X157,esk18_2(X156,X157),esk18_2(X156,X157))
| epred1_2(X157,X156) )
& ( apply(X157,esk21_2(X156,X157),esk22_2(X156,X157))
| member(esk19_2(X156,X157),X156)
| ~ apply(X157,esk18_2(X156,X157),esk18_2(X156,X157))
| epred1_2(X157,X156) )
& ( apply(X157,esk22_2(X156,X157),esk23_2(X156,X157))
| member(esk19_2(X156,X157),X156)
| ~ apply(X157,esk18_2(X156,X157),esk18_2(X156,X157))
| epred1_2(X157,X156) )
& ( ~ apply(X157,esk21_2(X156,X157),esk23_2(X156,X157))
| member(esk19_2(X156,X157),X156)
| ~ apply(X157,esk18_2(X156,X157),esk18_2(X156,X157))
| epred1_2(X157,X156) )
& ( member(esk21_2(X156,X157),X156)
| member(esk20_2(X156,X157),X156)
| ~ apply(X157,esk18_2(X156,X157),esk18_2(X156,X157))
| epred1_2(X157,X156) )
& ( member(esk22_2(X156,X157),X156)
| member(esk20_2(X156,X157),X156)
| ~ apply(X157,esk18_2(X156,X157),esk18_2(X156,X157))
| epred1_2(X157,X156) )
& ( member(esk23_2(X156,X157),X156)
| member(esk20_2(X156,X157),X156)
| ~ apply(X157,esk18_2(X156,X157),esk18_2(X156,X157))
| epred1_2(X157,X156) )
& ( apply(X157,esk21_2(X156,X157),esk22_2(X156,X157))
| member(esk20_2(X156,X157),X156)
| ~ apply(X157,esk18_2(X156,X157),esk18_2(X156,X157))
| epred1_2(X157,X156) )
& ( apply(X157,esk22_2(X156,X157),esk23_2(X156,X157))
| member(esk20_2(X156,X157),X156)
| ~ apply(X157,esk18_2(X156,X157),esk18_2(X156,X157))
| epred1_2(X157,X156) )
& ( ~ apply(X157,esk21_2(X156,X157),esk23_2(X156,X157))
| member(esk20_2(X156,X157),X156)
| ~ apply(X157,esk18_2(X156,X157),esk18_2(X156,X157))
| epred1_2(X157,X156) )
& ( member(esk21_2(X156,X157),X156)
| apply(X157,esk19_2(X156,X157),esk20_2(X156,X157))
| ~ apply(X157,esk18_2(X156,X157),esk18_2(X156,X157))
| epred1_2(X157,X156) )
& ( member(esk22_2(X156,X157),X156)
| apply(X157,esk19_2(X156,X157),esk20_2(X156,X157))
| ~ apply(X157,esk18_2(X156,X157),esk18_2(X156,X157))
| epred1_2(X157,X156) )
& ( member(esk23_2(X156,X157),X156)
| apply(X157,esk19_2(X156,X157),esk20_2(X156,X157))
| ~ apply(X157,esk18_2(X156,X157),esk18_2(X156,X157))
| epred1_2(X157,X156) )
& ( apply(X157,esk21_2(X156,X157),esk22_2(X156,X157))
| apply(X157,esk19_2(X156,X157),esk20_2(X156,X157))
| ~ apply(X157,esk18_2(X156,X157),esk18_2(X156,X157))
| epred1_2(X157,X156) )
& ( apply(X157,esk22_2(X156,X157),esk23_2(X156,X157))
| apply(X157,esk19_2(X156,X157),esk20_2(X156,X157))
| ~ apply(X157,esk18_2(X156,X157),esk18_2(X156,X157))
| epred1_2(X157,X156) )
& ( ~ apply(X157,esk21_2(X156,X157),esk23_2(X156,X157))
| apply(X157,esk19_2(X156,X157),esk20_2(X156,X157))
| ~ apply(X157,esk18_2(X156,X157),esk18_2(X156,X157))
| epred1_2(X157,X156) )
& ( member(esk21_2(X156,X157),X156)
| ~ apply(X157,esk20_2(X156,X157),esk19_2(X156,X157))
| ~ apply(X157,esk18_2(X156,X157),esk18_2(X156,X157))
| epred1_2(X157,X156) )
& ( member(esk22_2(X156,X157),X156)
| ~ apply(X157,esk20_2(X156,X157),esk19_2(X156,X157))
| ~ apply(X157,esk18_2(X156,X157),esk18_2(X156,X157))
| epred1_2(X157,X156) )
& ( member(esk23_2(X156,X157),X156)
| ~ apply(X157,esk20_2(X156,X157),esk19_2(X156,X157))
| ~ apply(X157,esk18_2(X156,X157),esk18_2(X156,X157))
| epred1_2(X157,X156) )
& ( apply(X157,esk21_2(X156,X157),esk22_2(X156,X157))
| ~ apply(X157,esk20_2(X156,X157),esk19_2(X156,X157))
| ~ apply(X157,esk18_2(X156,X157),esk18_2(X156,X157))
| epred1_2(X157,X156) )
& ( apply(X157,esk22_2(X156,X157),esk23_2(X156,X157))
| ~ apply(X157,esk20_2(X156,X157),esk19_2(X156,X157))
| ~ apply(X157,esk18_2(X156,X157),esk18_2(X156,X157))
| epred1_2(X157,X156) )
& ( ~ apply(X157,esk21_2(X156,X157),esk23_2(X156,X157))
| ~ apply(X157,esk20_2(X156,X157),esk19_2(X156,X157))
| ~ apply(X157,esk18_2(X156,X157),esk18_2(X156,X157))
| epred1_2(X157,X156) ) ),
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)],[i_0_17])])])])])]) ).
fof(i_0_23,plain,
! [X133,X134,X135,X136,X137,X138,X139,X140] :
( ( ~ member(X135,X134)
| apply(X133,X135,X135)
| ~ pre_order(X133,X134) )
& ( ~ member(X136,X134)
| ~ member(X137,X134)
| ~ member(X138,X134)
| ~ apply(X133,X136,X137)
| ~ apply(X133,X137,X138)
| apply(X133,X136,X138)
| ~ pre_order(X133,X134) )
& ( member(esk12_2(X139,X140),X140)
| member(esk11_2(X139,X140),X140)
| pre_order(X139,X140) )
& ( member(esk13_2(X139,X140),X140)
| member(esk11_2(X139,X140),X140)
| pre_order(X139,X140) )
& ( member(esk14_2(X139,X140),X140)
| member(esk11_2(X139,X140),X140)
| pre_order(X139,X140) )
& ( apply(X139,esk12_2(X139,X140),esk13_2(X139,X140))
| member(esk11_2(X139,X140),X140)
| pre_order(X139,X140) )
& ( apply(X139,esk13_2(X139,X140),esk14_2(X139,X140))
| member(esk11_2(X139,X140),X140)
| pre_order(X139,X140) )
& ( ~ apply(X139,esk12_2(X139,X140),esk14_2(X139,X140))
| member(esk11_2(X139,X140),X140)
| pre_order(X139,X140) )
& ( member(esk12_2(X139,X140),X140)
| ~ apply(X139,esk11_2(X139,X140),esk11_2(X139,X140))
| pre_order(X139,X140) )
& ( member(esk13_2(X139,X140),X140)
| ~ apply(X139,esk11_2(X139,X140),esk11_2(X139,X140))
| pre_order(X139,X140) )
& ( member(esk14_2(X139,X140),X140)
| ~ apply(X139,esk11_2(X139,X140),esk11_2(X139,X140))
| pre_order(X139,X140) )
& ( apply(X139,esk12_2(X139,X140),esk13_2(X139,X140))
| ~ apply(X139,esk11_2(X139,X140),esk11_2(X139,X140))
| pre_order(X139,X140) )
& ( apply(X139,esk13_2(X139,X140),esk14_2(X139,X140))
| ~ apply(X139,esk11_2(X139,X140),esk11_2(X139,X140))
| pre_order(X139,X140) )
& ( ~ apply(X139,esk12_2(X139,X140),esk14_2(X139,X140))
| ~ apply(X139,esk11_2(X139,X140),esk11_2(X139,X140))
| pre_order(X139,X140) ) ),
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)],[pre_order])])])])])]) ).
fof(i_0_24,plain,
! [X129,X130,X131,X132] :
( ( member(X132,X130)
| ~ member(X132,equivalence_class(X131,X130,X129)) )
& ( apply(X129,X131,X132)
| ~ member(X132,equivalence_class(X131,X130,X129)) )
& ( ~ member(X132,X130)
| ~ apply(X129,X131,X132)
| member(X132,equivalence_class(X131,X130,X129)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equivalence_class])])]) ).
fof(i_0_25,plain,
! [X111,X112,X113,X114,X116,X117,X118,X119,X120,X123] :
( ( ~ member(X113,X111)
| subset(X113,X112)
| ~ partition(X111,X112) )
& ( member(esk5_3(X111,X112,X114),X111)
| ~ member(X114,X112)
| ~ partition(X111,X112) )
& ( member(X114,esk5_3(X111,X112,X114))
| ~ member(X114,X112)
| ~ partition(X111,X112) )
& ( ~ member(X116,X111)
| ~ member(X117,X111)
| ~ member(X118,X116)
| ~ member(X118,X117)
| X116 = X117
| ~ partition(X111,X112) )
& ( member(esk8_2(X119,X120),X119)
| member(esk7_2(X119,X120),X120)
| member(esk6_2(X119,X120),X119)
| partition(X119,X120) )
& ( member(esk9_2(X119,X120),X119)
| member(esk7_2(X119,X120),X120)
| member(esk6_2(X119,X120),X119)
| partition(X119,X120) )
& ( member(esk10_2(X119,X120),esk8_2(X119,X120))
| member(esk7_2(X119,X120),X120)
| member(esk6_2(X119,X120),X119)
| partition(X119,X120) )
& ( member(esk10_2(X119,X120),esk9_2(X119,X120))
| member(esk7_2(X119,X120),X120)
| member(esk6_2(X119,X120),X119)
| partition(X119,X120) )
& ( esk8_2(X119,X120) != esk9_2(X119,X120)
| member(esk7_2(X119,X120),X120)
| member(esk6_2(X119,X120),X119)
| partition(X119,X120) )
& ( member(esk8_2(X119,X120),X119)
| ~ member(X123,X119)
| ~ member(esk7_2(X119,X120),X123)
| member(esk6_2(X119,X120),X119)
| partition(X119,X120) )
& ( member(esk9_2(X119,X120),X119)
| ~ member(X123,X119)
| ~ member(esk7_2(X119,X120),X123)
| member(esk6_2(X119,X120),X119)
| partition(X119,X120) )
& ( member(esk10_2(X119,X120),esk8_2(X119,X120))
| ~ member(X123,X119)
| ~ member(esk7_2(X119,X120),X123)
| member(esk6_2(X119,X120),X119)
| partition(X119,X120) )
& ( member(esk10_2(X119,X120),esk9_2(X119,X120))
| ~ member(X123,X119)
| ~ member(esk7_2(X119,X120),X123)
| member(esk6_2(X119,X120),X119)
| partition(X119,X120) )
& ( esk8_2(X119,X120) != esk9_2(X119,X120)
| ~ member(X123,X119)
| ~ member(esk7_2(X119,X120),X123)
| member(esk6_2(X119,X120),X119)
| partition(X119,X120) )
& ( member(esk8_2(X119,X120),X119)
| member(esk7_2(X119,X120),X120)
| ~ subset(esk6_2(X119,X120),X120)
| partition(X119,X120) )
& ( member(esk9_2(X119,X120),X119)
| member(esk7_2(X119,X120),X120)
| ~ subset(esk6_2(X119,X120),X120)
| partition(X119,X120) )
& ( member(esk10_2(X119,X120),esk8_2(X119,X120))
| member(esk7_2(X119,X120),X120)
| ~ subset(esk6_2(X119,X120),X120)
| partition(X119,X120) )
& ( member(esk10_2(X119,X120),esk9_2(X119,X120))
| member(esk7_2(X119,X120),X120)
| ~ subset(esk6_2(X119,X120),X120)
| partition(X119,X120) )
& ( esk8_2(X119,X120) != esk9_2(X119,X120)
| member(esk7_2(X119,X120),X120)
| ~ subset(esk6_2(X119,X120),X120)
| partition(X119,X120) )
& ( member(esk8_2(X119,X120),X119)
| ~ member(X123,X119)
| ~ member(esk7_2(X119,X120),X123)
| ~ subset(esk6_2(X119,X120),X120)
| partition(X119,X120) )
& ( member(esk9_2(X119,X120),X119)
| ~ member(X123,X119)
| ~ member(esk7_2(X119,X120),X123)
| ~ subset(esk6_2(X119,X120),X120)
| partition(X119,X120) )
& ( member(esk10_2(X119,X120),esk8_2(X119,X120))
| ~ member(X123,X119)
| ~ member(esk7_2(X119,X120),X123)
| ~ subset(esk6_2(X119,X120),X120)
| partition(X119,X120) )
& ( member(esk10_2(X119,X120),esk9_2(X119,X120))
| ~ member(X123,X119)
| ~ member(esk7_2(X119,X120),X123)
| ~ subset(esk6_2(X119,X120),X120)
| partition(X119,X120) )
& ( esk8_2(X119,X120) != esk9_2(X119,X120)
| ~ member(X123,X119)
| ~ member(esk7_2(X119,X120),X123)
| ~ subset(esk6_2(X119,X120),X120)
| partition(X119,X120) ) ),
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)],[partition])])])])])]) ).
fof(i_0_26,negated_conjecture,
( equivalence(esk16_0,esk15_0)
& member(esk17_0,esk15_0)
& ~ member(esk17_0,equivalence_class(esk17_0,esk15_0,esk16_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_18])])]) ).
fof(i_0_27,plain,
! [X81,X82,X83] :
( ( ~ member(X81,union(X82,X83))
| member(X81,X82)
| member(X81,X83) )
& ( ~ member(X81,X82)
| member(X81,union(X82,X83)) )
& ( ~ member(X81,X83)
| member(X81,union(X82,X83)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union])])]) ).
fof(i_0_28,plain,
! [X85,X86,X87] :
( ( member(X85,X87)
| ~ member(X85,difference(X87,X86)) )
& ( ~ member(X85,X86)
| ~ member(X85,difference(X87,X86)) )
& ( ~ member(X85,X87)
| member(X85,X86)
| member(X85,difference(X87,X86)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_19])])]) ).
fof(i_0_29,plain,
! [X78,X79,X80] :
( ( member(X78,X79)
| ~ member(X78,intersection(X79,X80)) )
& ( member(X78,X80)
| ~ member(X78,intersection(X79,X80)) )
& ( ~ member(X78,X79)
| ~ member(X78,X80)
| member(X78,intersection(X79,X80)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection])])]) ).
fof(i_0_30,plain,
! [X99,X100,X101,X102,X103] :
( ( ~ member(X99,product(X100))
| ~ member(X101,X100)
| member(X99,X101) )
& ( member(esk3_2(X102,X103),X103)
| member(X102,product(X103)) )
& ( ~ member(X102,esk3_2(X102,X103))
| member(X102,product(X103)) ) ),
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)],[product])])])])])]) ).
fof(i_0_31,plain,
! [X68,X69,X70,X71,X72] :
( ( ~ subset(X68,X69)
| ~ member(X70,X68)
| member(X70,X69) )
& ( member(esk1_2(X71,X72),X71)
| subset(X71,X72) )
& ( ~ member(esk1_2(X71,X72),X72)
| subset(X71,X72) ) ),
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)],[subset])])])])])]) ).
fof(i_0_32,plain,
! [X93,X94,X96,X97,X98] :
( ( member(esk2_2(X93,X94),X94)
| ~ member(X93,sum(X94)) )
& ( member(X93,esk2_2(X93,X94))
| ~ member(X93,sum(X94)) )
& ( ~ member(X98,X97)
| ~ member(X96,X98)
| member(X96,sum(X97)) ) ),
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)],[sum])])])])])]) ).
fof(i_0_33,plain,
! [X105,X106,X107,X108,X109] :
( ( ~ disjoint(X105,X106)
| ~ member(X107,X105)
| ~ member(X107,X106) )
& ( member(esk4_2(X108,X109),X108)
| disjoint(X108,X109) )
& ( member(esk4_2(X108,X109),X109)
| disjoint(X108,X109) ) ),
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)],[disjoint])])])])])]) ).
fof(i_0_34,plain,
! [X90,X91,X92] :
( ( ~ member(X90,unordered_pair(X91,X92))
| X90 = X91
| X90 = X92 )
& ( X90 != X91
| member(X90,unordered_pair(X91,X92)) )
& ( X90 != X92
| member(X90,unordered_pair(X91,X92)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unordered_pair])])]) ).
fof(i_0_35,plain,
! [X74,X75] :
( ( subset(X74,X75)
| ~ equal_set(X74,X75) )
& ( subset(X75,X74)
| ~ equal_set(X74,X75) )
& ( ~ subset(X74,X75)
| ~ subset(X75,X74)
| equal_set(X74,X75) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])]) ).
fof(i_0_36,plain,
! [X76,X77] :
( ( ~ member(X76,power_set(X77))
| subset(X76,X77) )
& ( ~ subset(X76,X77)
| member(X76,power_set(X77)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[power_set])]) ).
fof(i_0_37,plain,
! [X127,X128] :
( ( ~ equivalence(X128,X127)
| epred1_2(X128,X127) )
& ( ~ epred1_2(X128,X127)
| equivalence(X128,X127) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_20])]) ).
fof(i_0_38,plain,
! [X88,X89] :
( ( ~ member(X88,singleton(X89))
| X88 = X89 )
& ( X88 != X89
| member(X88,singleton(X89)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[singleton])]) ).
fof(i_0_39,plain,
! [X84] : ~ member(X84,empty_set),
inference(variable_rename,[status(thm)],[i_0_21]) ).
cnf(i_0_40,plain,
( epred1_2(X1,X2)
| ~ apply(X1,esk21_2(X2,X1),esk23_2(X2,X1))
| ~ apply(X1,esk20_2(X2,X1),esk19_2(X2,X1))
| ~ apply(X1,esk18_2(X2,X1),esk18_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_41,plain,
( apply(X1,esk22_2(X2,X1),esk23_2(X2,X1))
| epred1_2(X1,X2)
| ~ apply(X1,esk20_2(X2,X1),esk19_2(X2,X1))
| ~ apply(X1,esk18_2(X2,X1),esk18_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_42,plain,
( apply(X1,esk21_2(X2,X1),esk22_2(X2,X1))
| epred1_2(X1,X2)
| ~ apply(X1,esk20_2(X2,X1),esk19_2(X2,X1))
| ~ apply(X1,esk18_2(X2,X1),esk18_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_43,plain,
( apply(X1,esk19_2(X2,X1),esk20_2(X2,X1))
| epred1_2(X1,X2)
| ~ apply(X1,esk21_2(X2,X1),esk23_2(X2,X1))
| ~ apply(X1,esk18_2(X2,X1),esk18_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_44,plain,
( apply(X1,esk22_2(X2,X1),esk23_2(X2,X1))
| apply(X1,esk19_2(X2,X1),esk20_2(X2,X1))
| epred1_2(X1,X2)
| ~ apply(X1,esk18_2(X2,X1),esk18_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_45,plain,
( apply(X1,esk21_2(X2,X1),esk22_2(X2,X1))
| apply(X1,esk19_2(X2,X1),esk20_2(X2,X1))
| epred1_2(X1,X2)
| ~ apply(X1,esk18_2(X2,X1),esk18_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_46,plain,
( member(esk20_2(X2,X1),X2)
| epred1_2(X1,X2)
| ~ apply(X1,esk21_2(X2,X1),esk23_2(X2,X1))
| ~ apply(X1,esk18_2(X2,X1),esk18_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_47,plain,
( member(esk19_2(X2,X1),X2)
| epred1_2(X1,X2)
| ~ apply(X1,esk21_2(X2,X1),esk23_2(X2,X1))
| ~ apply(X1,esk18_2(X2,X1),esk18_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_48,plain,
( member(esk18_2(X2,X1),X2)
| epred1_2(X1,X2)
| ~ apply(X1,esk21_2(X2,X1),esk23_2(X2,X1))
| ~ apply(X1,esk20_2(X2,X1),esk19_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_49,plain,
( member(esk23_2(X1,X2),X1)
| epred1_2(X2,X1)
| ~ apply(X2,esk20_2(X1,X2),esk19_2(X1,X2))
| ~ apply(X2,esk18_2(X1,X2),esk18_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_50,plain,
( member(esk22_2(X1,X2),X1)
| epred1_2(X2,X1)
| ~ apply(X2,esk20_2(X1,X2),esk19_2(X1,X2))
| ~ apply(X2,esk18_2(X1,X2),esk18_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_51,plain,
( member(esk21_2(X1,X2),X1)
| epred1_2(X2,X1)
| ~ apply(X2,esk20_2(X1,X2),esk19_2(X1,X2))
| ~ apply(X2,esk18_2(X1,X2),esk18_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_52,plain,
( pre_order(X1,X2)
| ~ apply(X1,esk12_2(X1,X2),esk14_2(X1,X2))
| ~ apply(X1,esk11_2(X1,X2),esk11_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_53,plain,
( apply(X1,esk22_2(X2,X1),esk23_2(X2,X1))
| member(esk20_2(X2,X1),X2)
| epred1_2(X1,X2)
| ~ apply(X1,esk18_2(X2,X1),esk18_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_54,plain,
( apply(X1,esk21_2(X2,X1),esk22_2(X2,X1))
| member(esk20_2(X2,X1),X2)
| epred1_2(X1,X2)
| ~ apply(X1,esk18_2(X2,X1),esk18_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_55,plain,
( apply(X1,esk22_2(X2,X1),esk23_2(X2,X1))
| member(esk19_2(X2,X1),X2)
| epred1_2(X1,X2)
| ~ apply(X1,esk18_2(X2,X1),esk18_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_56,plain,
( apply(X1,esk21_2(X2,X1),esk22_2(X2,X1))
| member(esk19_2(X2,X1),X2)
| epred1_2(X1,X2)
| ~ apply(X1,esk18_2(X2,X1),esk18_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_57,plain,
( apply(X1,esk22_2(X2,X1),esk23_2(X2,X1))
| member(esk18_2(X2,X1),X2)
| epred1_2(X1,X2)
| ~ apply(X1,esk20_2(X2,X1),esk19_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_58,plain,
( apply(X1,esk21_2(X2,X1),esk22_2(X2,X1))
| member(esk18_2(X2,X1),X2)
| epred1_2(X1,X2)
| ~ apply(X1,esk20_2(X2,X1),esk19_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_59,plain,
( apply(X1,esk19_2(X2,X1),esk20_2(X2,X1))
| member(esk18_2(X2,X1),X2)
| epred1_2(X1,X2)
| ~ apply(X1,esk21_2(X2,X1),esk23_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_60,plain,
( member(esk23_2(X1,X2),X1)
| apply(X2,esk19_2(X1,X2),esk20_2(X1,X2))
| epred1_2(X2,X1)
| ~ apply(X2,esk18_2(X1,X2),esk18_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_61,plain,
( member(esk22_2(X1,X2),X1)
| apply(X2,esk19_2(X1,X2),esk20_2(X1,X2))
| epred1_2(X2,X1)
| ~ apply(X2,esk18_2(X1,X2),esk18_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_62,plain,
( member(esk21_2(X1,X2),X1)
| apply(X2,esk19_2(X1,X2),esk20_2(X1,X2))
| epred1_2(X2,X1)
| ~ apply(X2,esk18_2(X1,X2),esk18_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_63,plain,
( apply(X5,X1,X4)
| ~ member(X1,X2)
| ~ member(X3,X2)
| ~ member(X4,X2)
| ~ apply(X5,X1,X3)
| ~ apply(X5,X3,X4)
| ~ epred1_2(X5,X2) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_64,plain,
( apply(X5,X1,X4)
| ~ member(X1,X2)
| ~ member(X3,X2)
| ~ member(X4,X2)
| ~ apply(X5,X1,X3)
| ~ apply(X5,X3,X4)
| ~ pre_order(X5,X2) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_65,plain,
( apply(X1,esk13_2(X1,X2),esk14_2(X1,X2))
| pre_order(X1,X2)
| ~ apply(X1,esk11_2(X1,X2),esk11_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_66,plain,
( apply(X1,esk12_2(X1,X2),esk13_2(X1,X2))
| pre_order(X1,X2)
| ~ apply(X1,esk11_2(X1,X2),esk11_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_67,plain,
( apply(X1,esk22_2(X2,X1),esk23_2(X2,X1))
| apply(X1,esk19_2(X2,X1),esk20_2(X2,X1))
| member(esk18_2(X2,X1),X2)
| epred1_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_68,plain,
( apply(X1,esk21_2(X2,X1),esk22_2(X2,X1))
| apply(X1,esk19_2(X2,X1),esk20_2(X2,X1))
| member(esk18_2(X2,X1),X2)
| epred1_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_69,plain,
( member(esk20_2(X2,X1),X2)
| member(esk18_2(X2,X1),X2)
| epred1_2(X1,X2)
| ~ apply(X1,esk21_2(X2,X1),esk23_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_70,plain,
( member(esk19_2(X2,X1),X2)
| member(esk18_2(X2,X1),X2)
| epred1_2(X1,X2)
| ~ apply(X1,esk21_2(X2,X1),esk23_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_71,plain,
( member(esk23_2(X1,X2),X1)
| member(esk20_2(X1,X2),X1)
| epred1_2(X2,X1)
| ~ apply(X2,esk18_2(X1,X2),esk18_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_72,plain,
( member(esk22_2(X1,X2),X1)
| member(esk20_2(X1,X2),X1)
| epred1_2(X2,X1)
| ~ apply(X2,esk18_2(X1,X2),esk18_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_73,plain,
( member(esk21_2(X1,X2),X1)
| member(esk20_2(X1,X2),X1)
| epred1_2(X2,X1)
| ~ apply(X2,esk18_2(X1,X2),esk18_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_74,plain,
( member(esk23_2(X1,X2),X1)
| member(esk19_2(X1,X2),X1)
| epred1_2(X2,X1)
| ~ apply(X2,esk18_2(X1,X2),esk18_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_75,plain,
( member(esk22_2(X1,X2),X1)
| member(esk19_2(X1,X2),X1)
| epred1_2(X2,X1)
| ~ apply(X2,esk18_2(X1,X2),esk18_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_76,plain,
( member(esk21_2(X1,X2),X1)
| member(esk19_2(X1,X2),X1)
| epred1_2(X2,X1)
| ~ apply(X2,esk18_2(X1,X2),esk18_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_77,plain,
( member(esk23_2(X1,X2),X1)
| member(esk18_2(X1,X2),X1)
| epred1_2(X2,X1)
| ~ apply(X2,esk20_2(X1,X2),esk19_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_78,plain,
( member(esk22_2(X1,X2),X1)
| member(esk18_2(X1,X2),X1)
| epred1_2(X2,X1)
| ~ apply(X2,esk20_2(X1,X2),esk19_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_79,plain,
( member(esk21_2(X1,X2),X1)
| member(esk18_2(X1,X2),X1)
| epred1_2(X2,X1)
| ~ apply(X2,esk20_2(X1,X2),esk19_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_80,plain,
( apply(X1,X2,X3)
| ~ member(X3,equivalence_class(X2,X4,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_81,plain,
( member(esk10_2(X1,X2),esk9_2(X1,X2))
| partition(X1,X2)
| ~ member(X3,X1)
| ~ member(esk7_2(X1,X2),X3)
| ~ subset(esk6_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_82,plain,
( member(esk10_2(X1,X2),esk8_2(X1,X2))
| partition(X1,X2)
| ~ member(X3,X1)
| ~ member(esk7_2(X1,X2),X3)
| ~ subset(esk6_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_83,plain,
( member(X1,equivalence_class(X4,X2,X3))
| ~ member(X1,X2)
| ~ apply(X3,X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_84,plain,
( member(esk14_2(X1,X2),X2)
| pre_order(X1,X2)
| ~ apply(X1,esk11_2(X1,X2),esk11_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_85,plain,
( member(esk13_2(X1,X2),X2)
| pre_order(X1,X2)
| ~ apply(X1,esk11_2(X1,X2),esk11_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_86,plain,
( member(esk12_2(X1,X2),X2)
| pre_order(X1,X2)
| ~ apply(X1,esk11_2(X1,X2),esk11_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_87,plain,
( member(esk11_2(X1,X2),X2)
| pre_order(X1,X2)
| ~ apply(X1,esk12_2(X1,X2),esk14_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_88,plain,
( apply(X4,X3,X1)
| ~ member(X1,X2)
| ~ member(X3,X2)
| ~ apply(X4,X1,X3)
| ~ epred1_2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_89,plain,
( partition(X1,X2)
| esk8_2(X1,X2) != esk9_2(X1,X2)
| ~ member(X3,X1)
| ~ member(esk7_2(X1,X2),X3)
| ~ subset(esk6_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_90,plain,
( member(esk10_2(X1,X2),esk9_2(X1,X2))
| member(esk6_2(X1,X2),X1)
| partition(X1,X2)
| ~ member(X3,X1)
| ~ member(esk7_2(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_91,plain,
( member(esk10_2(X1,X2),esk8_2(X1,X2))
| member(esk6_2(X1,X2),X1)
| partition(X1,X2)
| ~ member(X3,X1)
| ~ member(esk7_2(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_92,plain,
( member(X1,X2)
| ~ member(X1,equivalence_class(X3,X2,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_93,plain,
( member(esk9_2(X1,X2),X1)
| partition(X1,X2)
| ~ member(X3,X1)
| ~ member(esk7_2(X1,X2),X3)
| ~ subset(esk6_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_94,plain,
( member(esk8_2(X1,X2),X1)
| partition(X1,X2)
| ~ member(X3,X1)
| ~ member(esk7_2(X1,X2),X3)
| ~ subset(esk6_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_95,plain,
( apply(X1,esk22_2(X2,X1),esk23_2(X2,X1))
| member(esk20_2(X2,X1),X2)
| member(esk18_2(X2,X1),X2)
| epred1_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_96,plain,
( apply(X1,esk21_2(X2,X1),esk22_2(X2,X1))
| member(esk20_2(X2,X1),X2)
| member(esk18_2(X2,X1),X2)
| epred1_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_97,plain,
( apply(X1,esk22_2(X2,X1),esk23_2(X2,X1))
| member(esk19_2(X2,X1),X2)
| member(esk18_2(X2,X1),X2)
| epred1_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_98,plain,
( apply(X1,esk21_2(X2,X1),esk22_2(X2,X1))
| member(esk19_2(X2,X1),X2)
| member(esk18_2(X2,X1),X2)
| epred1_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_99,plain,
( member(esk23_2(X1,X2),X1)
| apply(X2,esk19_2(X1,X2),esk20_2(X1,X2))
| member(esk18_2(X1,X2),X1)
| epred1_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_100,plain,
( member(esk22_2(X1,X2),X1)
| apply(X2,esk19_2(X1,X2),esk20_2(X1,X2))
| member(esk18_2(X1,X2),X1)
| epred1_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_101,plain,
( member(esk21_2(X1,X2),X1)
| apply(X2,esk19_2(X1,X2),esk20_2(X1,X2))
| member(esk18_2(X1,X2),X1)
| epred1_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_102,plain,
( member(esk6_2(X1,X2),X1)
| partition(X1,X2)
| esk8_2(X1,X2) != esk9_2(X1,X2)
| ~ member(X3,X1)
| ~ member(esk7_2(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_103,plain,
( member(esk10_2(X1,X2),esk9_2(X1,X2))
| member(esk7_2(X1,X2),X2)
| partition(X1,X2)
| ~ subset(esk6_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_104,plain,
( member(esk10_2(X1,X2),esk8_2(X1,X2))
| member(esk7_2(X1,X2),X2)
| partition(X1,X2)
| ~ subset(esk6_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_105,plain,
( member(esk9_2(X1,X2),X1)
| member(esk6_2(X1,X2),X1)
| partition(X1,X2)
| ~ member(X3,X1)
| ~ member(esk7_2(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_106,plain,
( member(esk8_2(X1,X2),X1)
| member(esk6_2(X1,X2),X1)
| partition(X1,X2)
| ~ member(X3,X1)
| ~ member(esk7_2(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_107,negated_conjecture,
~ member(esk17_0,equivalence_class(esk17_0,esk15_0,esk16_0)),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_108,plain,
( member(esk5_3(X1,X2,X3),X1)
| ~ member(X3,X2)
| ~ partition(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_109,plain,
( member(X1,esk5_3(X2,X3,X1))
| ~ member(X1,X3)
| ~ partition(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_110,plain,
( member(esk7_2(X1,X2),X2)
| partition(X1,X2)
| esk8_2(X1,X2) != esk9_2(X1,X2)
| ~ subset(esk6_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_111,plain,
( member(esk10_2(X1,X2),esk9_2(X1,X2))
| member(esk7_2(X1,X2),X2)
| member(esk6_2(X1,X2),X1)
| partition(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_112,plain,
( member(esk10_2(X1,X2),esk8_2(X1,X2))
| member(esk7_2(X1,X2),X2)
| member(esk6_2(X1,X2),X1)
| partition(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_113,plain,
( apply(X1,esk13_2(X1,X2),esk14_2(X1,X2))
| member(esk11_2(X1,X2),X2)
| pre_order(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_114,plain,
( apply(X1,esk12_2(X1,X2),esk13_2(X1,X2))
| member(esk11_2(X1,X2),X2)
| pre_order(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_115,plain,
( member(esk9_2(X1,X2),X1)
| member(esk7_2(X1,X2),X2)
| partition(X1,X2)
| ~ subset(esk6_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_116,plain,
( member(esk8_2(X1,X2),X1)
| member(esk7_2(X1,X2),X2)
| partition(X1,X2)
| ~ subset(esk6_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_117,plain,
( member(esk7_2(X1,X2),X2)
| member(esk6_2(X1,X2),X1)
| partition(X1,X2)
| esk8_2(X1,X2) != esk9_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_118,plain,
( member(esk23_2(X1,X2),X1)
| member(esk20_2(X1,X2),X1)
| member(esk18_2(X1,X2),X1)
| epred1_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_119,plain,
( member(esk22_2(X1,X2),X1)
| member(esk20_2(X1,X2),X1)
| member(esk18_2(X1,X2),X1)
| epred1_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_120,plain,
( member(esk21_2(X1,X2),X1)
| member(esk20_2(X1,X2),X1)
| member(esk18_2(X1,X2),X1)
| epred1_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_121,plain,
( member(esk23_2(X1,X2),X1)
| member(esk19_2(X1,X2),X1)
| member(esk18_2(X1,X2),X1)
| epred1_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_122,plain,
( member(esk22_2(X1,X2),X1)
| member(esk19_2(X1,X2),X1)
| member(esk18_2(X1,X2),X1)
| epred1_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_123,plain,
( member(esk21_2(X1,X2),X1)
| member(esk19_2(X1,X2),X1)
| member(esk18_2(X1,X2),X1)
| epred1_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_124,plain,
( member(esk9_2(X1,X2),X1)
| member(esk7_2(X1,X2),X2)
| member(esk6_2(X1,X2),X1)
| partition(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_125,plain,
( member(esk8_2(X1,X2),X1)
| member(esk7_2(X1,X2),X2)
| member(esk6_2(X1,X2),X1)
| partition(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_126,plain,
( X1 = X3
| ~ member(X1,X2)
| ~ member(X3,X2)
| ~ member(X4,X1)
| ~ member(X4,X3)
| ~ partition(X2,X5) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_127,plain,
( apply(X3,X1,X1)
| ~ member(X1,X2)
| ~ epred1_2(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_128,plain,
( apply(X3,X1,X1)
| ~ member(X1,X2)
| ~ pre_order(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_129,plain,
( member(esk14_2(X1,X2),X2)
| member(esk11_2(X1,X2),X2)
| pre_order(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_130,plain,
( member(esk13_2(X1,X2),X2)
| member(esk11_2(X1,X2),X2)
| pre_order(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_131,plain,
( member(esk12_2(X1,X2),X2)
| member(esk11_2(X1,X2),X2)
| pre_order(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_132,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_133,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_134,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_135,plain,
( member(X1,product(X2))
| ~ member(X1,esk3_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_136,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_137,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_138,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_139,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_140,plain,
( member(X1,X3)
| member(X1,difference(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_141,plain,
( member(esk2_2(X1,X2),X2)
| ~ member(X1,sum(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_142,plain,
( member(X1,esk2_2(X1,X2))
| ~ member(X1,sum(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_143,plain,
( member(X1,X3)
| ~ member(X1,product(X2))
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_144,plain,
( ~ disjoint(X1,X2)
| ~ member(X3,X1)
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_145,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_146,plain,
( member(X3,sum(X2))
| ~ member(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_147,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_148,plain,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_149,plain,
( member(esk3_2(X1,X2),X2)
| member(X1,product(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_150,plain,
( equal_set(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_151,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_152,plain,
( subset(X1,X3)
| ~ member(X1,X2)
| ~ partition(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_153,plain,
( member(esk4_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_154,plain,
( member(esk4_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_155,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_156,plain,
( subset(X1,X2)
| ~ member(X1,power_set(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_36]),
[final] ).
cnf(i_0_157,plain,
( member(X1,unordered_pair(X2,X3))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_158,plain,
( member(X1,unordered_pair(X3,X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_159,plain,
( member(X1,power_set(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_36]),
[final] ).
cnf(i_0_160,plain,
( epred1_2(X1,X2)
| ~ equivalence(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_161,plain,
( equivalence(X1,X2)
| ~ epred1_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_162,plain,
( subset(X1,X2)
| ~ equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_163,plain,
( subset(X1,X2)
| ~ equal_set(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_164,plain,
( X1 = X2
| ~ member(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_165,plain,
( member(X1,singleton(X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_166,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[i_0_39]),
[final] ).
cnf(i_0_167,negated_conjecture,
equivalence(esk16_0,esk15_0),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_168,negated_conjecture,
member(esk17_0,esk15_0),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_169,axiom,
X1 = X1 ).
cnf(i_0_170,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_171,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_172,axiom,
( X1 != X2
| esk9_2(X1,X3) = esk9_2(X2,X3) ) ).
cnf(i_0_173,axiom,
( X1 != X2
| esk9_2(X3,X1) = esk9_2(X3,X2) ) ).
cnf(i_0_174,axiom,
( X1 != X2
| esk8_2(X1,X3) = esk8_2(X2,X3) ) ).
cnf(i_0_175,axiom,
( X1 != X2
| esk8_2(X3,X1) = esk8_2(X3,X2) ) ).
cnf(i_0_176,axiom,
( X1 != X2
| ~ epred1_2(X1,X3)
| epred1_2(X2,X3) ) ).
cnf(i_0_177,axiom,
( X1 != X2
| ~ epred1_2(X3,X1)
| epred1_2(X3,X2) ) ).
cnf(i_0_178,axiom,
( X1 != X2
| ~ apply(X1,X3,X4)
| apply(X2,X3,X4) ) ).
cnf(i_0_179,axiom,
( X1 != X2
| ~ apply(X3,X1,X4)
| apply(X3,X2,X4) ) ).
cnf(i_0_180,axiom,
( X1 != X2
| ~ apply(X3,X4,X1)
| apply(X3,X4,X2) ) ).
cnf(i_0_181,axiom,
( X1 != X2
| ~ member(X1,X3)
| member(X2,X3) ) ).
cnf(i_0_182,axiom,
( X1 != X2
| ~ member(X3,X1)
| member(X3,X2) ) ).
cnf(i_0_183,axiom,
( X1 != X2
| ~ pre_order(X1,X3)
| pre_order(X2,X3) ) ).
cnf(i_0_184,axiom,
( X1 != X2
| ~ pre_order(X3,X1)
| pre_order(X3,X2) ) ).
cnf(i_0_185,axiom,
( X1 != X2
| ~ partition(X1,X3)
| partition(X2,X3) ) ).
cnf(i_0_186,axiom,
( X1 != X2
| ~ partition(X3,X1)
| partition(X3,X2) ) ).
cnf(i_0_187,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_188,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_189,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_190,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_191,axiom,
( X1 != X2
| ~ equal_set(X1,X3)
| equal_set(X2,X3) ) ).
cnf(i_0_192,axiom,
( X1 != X2
| ~ equal_set(X3,X1)
| equal_set(X3,X2) ) ).
cnf(i_0_193,axiom,
( X1 != X2
| ~ equivalence(X1,X3)
| equivalence(X2,X3) ) ).
cnf(i_0_194,axiom,
( X1 != X2
| ~ equivalence(X3,X1)
| equivalence(X3,X2) ) ).
cnf(i_0_169_001,axiom,
X1 = X1 ).
cnf(i_0_170_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_171_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_172_004,axiom,
( X1 != X2
| esk9_2(X1,X3) = esk9_2(X2,X3) ) ).
cnf(i_0_173_005,axiom,
( X1 != X2
| esk9_2(X3,X1) = esk9_2(X3,X2) ) ).
cnf(i_0_174_006,axiom,
( X1 != X2
| esk8_2(X1,X3) = esk8_2(X2,X3) ) ).
cnf(i_0_175_007,axiom,
( X1 != X2
| esk8_2(X3,X1) = esk8_2(X3,X2) ) ).
cnf(i_0_176_008,axiom,
( X1 != X2
| ~ epred1_2(X1,X3)
| epred1_2(X2,X3) ) ).
cnf(i_0_177_009,axiom,
( X1 != X2
| ~ epred1_2(X3,X1)
| epred1_2(X3,X2) ) ).
cnf(i_0_178_010,axiom,
( X1 != X2
| ~ apply(X1,X3,X4)
| apply(X2,X3,X4) ) ).
cnf(i_0_179_011,axiom,
( X1 != X2
| ~ apply(X3,X1,X4)
| apply(X3,X2,X4) ) ).
cnf(i_0_180_012,axiom,
( X1 != X2
| ~ apply(X3,X4,X1)
| apply(X3,X4,X2) ) ).
cnf(i_0_181_013,axiom,
( X1 != X2
| ~ member(X1,X3)
| member(X2,X3) ) ).
cnf(i_0_182_014,axiom,
( X1 != X2
| ~ member(X3,X1)
| member(X3,X2) ) ).
cnf(i_0_183_015,axiom,
( X1 != X2
| ~ pre_order(X1,X3)
| pre_order(X2,X3) ) ).
cnf(i_0_184_016,axiom,
( X1 != X2
| ~ pre_order(X3,X1)
| pre_order(X3,X2) ) ).
cnf(i_0_185_017,axiom,
( X1 != X2
| ~ partition(X1,X3)
| partition(X2,X3) ) ).
cnf(i_0_186_018,axiom,
( X1 != X2
| ~ partition(X3,X1)
| partition(X3,X2) ) ).
cnf(i_0_187_019,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_188_020,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_189_021,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_190_022,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_191_023,axiom,
( X1 != X2
| ~ equal_set(X1,X3)
| equal_set(X2,X3) ) ).
cnf(i_0_192_024,axiom,
( X1 != X2
| ~ equal_set(X3,X1)
| equal_set(X3,X2) ) ).
cnf(i_0_193_025,axiom,
( X1 != X2
| ~ equivalence(X1,X3)
| equivalence(X2,X3) ) ).
cnf(i_0_194_026,axiom,
( X1 != X2
| ~ equivalence(X3,X1)
| equivalence(X3,X2) ) ).
cnf(i_0_195,plain,
member(X1,unordered_pair(X1,X2)),
inference(equality_inference,[],[157]) ).
cnf(i_0_196,plain,
member(X1,unordered_pair(X2,X1)),
inference(equality_inference,[],[158]) ).
cnf(i_0_197,plain,
member(X1,singleton(X1)),
inference(equality_inference,[],[165]) ).
cnf(i_0_198,plain,
epred1_2(esk16_0,esk15_0),
inference(scs_inference,[],[i_0_167,i_0_160]) ).
cnf(i_0_199,plain,
( ~ equivalence(X1,X2)
| epred1_2(X1,X2) ),
inference(rename_variables,[],[i_0_160]) ).
cnf(i_0_200,plain,
disjoint(empty_set,X1),
inference(scs_inference,[],[i_0_167,i_0_166,i_0_160,i_0_153]) ).
cnf(i_0_201,plain,
~ member(X1,empty_set),
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_202,plain,
( member(esk4_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_153]) ).
cnf(i_0_203,plain,
disjoint(X1,empty_set),
inference(scs_inference,[],[i_0_167,i_0_166,i_0_201,i_0_160,i_0_153,i_0_154]) ).
cnf(i_0_204,plain,
~ member(X1,empty_set),
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_205,plain,
( member(esk4_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_154]) ).
cnf(i_0_206,plain,
subset(empty_set,X1),
inference(scs_inference,[],[i_0_167,i_0_166,i_0_201,i_0_204,i_0_160,i_0_153,i_0_154,i_0_155]) ).
cnf(i_0_207,plain,
~ member(X1,empty_set),
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_208,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_155]) ).
cnf(i_0_209,plain,
~ apply(esk16_0,esk17_0,esk17_0),
inference(scs_inference,[],[i_0_107,i_0_167,i_0_168,i_0_166,i_0_201,i_0_204,i_0_160,i_0_153,i_0_154,i_0_155,i_0_83]) ).
cnf(i_0_210,plain,
( member(X1,equivalence_class(X2,X3,X4))
| ~ member(X1,X3)
| ~ apply(X4,X2,X1) ),
inference(rename_variables,[],[i_0_83]) ).
cnf(i_0_211,plain,
~ partition(empty_set,esk15_0),
inference(scs_inference,[],[i_0_107,i_0_167,i_0_168,i_0_166,i_0_201,i_0_204,i_0_207,i_0_160,i_0_153,i_0_154,i_0_155,i_0_83,i_0_108]) ).
cnf(i_0_212,plain,
~ member(X1,empty_set),
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_213,plain,
( member(esk5_3(X1,X2,X3),X1)
| ~ member(X3,X2)
| ~ partition(X1,X2) ),
inference(rename_variables,[],[i_0_108]) ).
cnf(i_0_214,plain,
$false,
inference(scs_inference,[],[i_0_107,i_0_167,i_0_168,i_0_166,i_0_201,i_0_204,i_0_207,i_0_160,i_0_153,i_0_154,i_0_155,i_0_83,i_0_108,i_0_127]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET766+4 : TPTP v9.2.1. Released v2.2.0.
% 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
% 0.15/0.33 % Computer : n025.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:34:43 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.34/1.61 % Version : CSE_E---1.7
% 0.34/1.61 % Problem : theBenchmark.p
% 0.34/1.61 % SZS status Theorem for theBenchmark.p
% 0.34/1.61 % SZS output start CNFRefutation
% See solution above
% 0.34/1.67 % Total time : 1.272s
%------------------------------------------------------------------------------