%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEV521+1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:35:10 PM UTC 2026
% Result : Theorem 46.04s 8.49s
% Output : CNFRefutation 46.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 72
% Number of leaves : 5
% Syntax : Number of formulae : 175 ( 18 unt; 0 def)
% Number of atoms : 652 ( 95 equ)
% Maximal formula atoms : 105 ( 3 avg)
% Number of connectives : 685 ( 208 ~; 434 |; 32 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 39 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 299 ( 34 sgn 34 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(singleton,axiom,
! [X3,X1] :
( member(X3,singleton(X1))
<=> X3 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',singleton) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(empty_set,axiom,
! [X3] : ~ member(X3,empty_set),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',empty_set) ).
fof(partition,axiom,
! [X1,X4] :
( partition(X1,X4)
<=> ( ! [X3,X5] :
( ( member(X5,X1)
& member(X3,X1) )
=> ( ? [X6] :
( member(X6,X5)
& member(X6,X3) )
=> X3 = X5 ) )
& ! [X3] :
( member(X3,X4)
=> ? [X5] :
( member(X3,X5)
& member(X5,X1) ) )
& ! [X3] :
( member(X3,X1)
=> subset(X3,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax',partition) ).
fof(set_partitions_itself,conjecture,
! [X4] :
( X4 != empty_set
=> partition(singleton(X4),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_partitions_itself) ).
fof(c_0_5,plain,
! [X28,X29] :
( ( member(X28,singleton(X29))
| X28 != X29 )
& ( X28 = X29
| ~ member(X28,singleton(X29)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[singleton])])]) ).
fof(c_0_6,plain,
! [X31,X32,X33,X34,X35] :
( ( subset(X34,X35)
| ~ member(esk8_2(X34,X35),X35) )
& ( subset(X34,X35)
| member(esk8_2(X34,X35),X34) )
& ( member(X33,X32)
| ~ member(X33,X31)
| ~ subset(X31,X32) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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])])])])])])]) ).
cnf(c_0_7,plain,
( ~ member(X1,singleton(X2))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( subset(X1,X2)
| member(esk8_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X3] : ~ member(X3,empty_set),
inference(fof_simplification,[status(thm)],[empty_set]) ).
cnf(c_0_10,plain,
( ~ member(esk8_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( subset(singleton(X1),X2)
| esk8_2(singleton(X1),X2) = X1 ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
fof(c_0_12,plain,
! [X30] : ~ member(X30,empty_set),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_9])]) ).
fof(c_0_13,plain,
! [X12,X13,X14,X15,X17,X18,X19,X20,X21,X24] :
( ( partition(X20,X21)
| ~ subset(esk3_2(X20,X21),X21)
| ~ member(esk4_2(X20,X21),X24)
| ~ member(X24,X20)
| esk5_2(X20,X21) != esk6_2(X20,X21) )
& ( partition(X20,X21)
| ~ subset(esk3_2(X20,X21),X21)
| ~ member(esk4_2(X20,X21),X24)
| ~ member(X24,X20)
| member(esk7_2(X20,X21),esk6_2(X20,X21)) )
& ( partition(X20,X21)
| ~ subset(esk3_2(X20,X21),X21)
| ~ member(esk4_2(X20,X21),X24)
| ~ member(X24,X20)
| member(esk7_2(X20,X21),esk5_2(X20,X21)) )
& ( partition(X20,X21)
| ~ subset(esk3_2(X20,X21),X21)
| ~ member(esk4_2(X20,X21),X24)
| ~ member(X24,X20)
| member(esk6_2(X20,X21),X20) )
& ( partition(X20,X21)
| ~ subset(esk3_2(X20,X21),X21)
| ~ member(esk4_2(X20,X21),X24)
| ~ member(X24,X20)
| member(esk5_2(X20,X21),X20) )
& ( partition(X20,X21)
| ~ subset(esk3_2(X20,X21),X21)
| member(esk4_2(X20,X21),X21)
| esk5_2(X20,X21) != esk6_2(X20,X21) )
& ( partition(X20,X21)
| ~ subset(esk3_2(X20,X21),X21)
| member(esk4_2(X20,X21),X21)
| member(esk7_2(X20,X21),esk6_2(X20,X21)) )
& ( partition(X20,X21)
| ~ subset(esk3_2(X20,X21),X21)
| member(esk4_2(X20,X21),X21)
| member(esk7_2(X20,X21),esk5_2(X20,X21)) )
& ( partition(X20,X21)
| ~ subset(esk3_2(X20,X21),X21)
| member(esk4_2(X20,X21),X21)
| member(esk6_2(X20,X21),X20) )
& ( partition(X20,X21)
| ~ subset(esk3_2(X20,X21),X21)
| member(esk4_2(X20,X21),X21)
| member(esk5_2(X20,X21),X20) )
& ( partition(X20,X21)
| member(esk3_2(X20,X21),X20)
| ~ member(esk4_2(X20,X21),X24)
| ~ member(X24,X20)
| esk5_2(X20,X21) != esk6_2(X20,X21) )
& ( partition(X20,X21)
| member(esk3_2(X20,X21),X20)
| ~ member(esk4_2(X20,X21),X24)
| ~ member(X24,X20)
| member(esk7_2(X20,X21),esk6_2(X20,X21)) )
& ( partition(X20,X21)
| member(esk3_2(X20,X21),X20)
| ~ member(esk4_2(X20,X21),X24)
| ~ member(X24,X20)
| member(esk7_2(X20,X21),esk5_2(X20,X21)) )
& ( partition(X20,X21)
| member(esk3_2(X20,X21),X20)
| ~ member(esk4_2(X20,X21),X24)
| ~ member(X24,X20)
| member(esk6_2(X20,X21),X20) )
& ( partition(X20,X21)
| member(esk3_2(X20,X21),X20)
| ~ member(esk4_2(X20,X21),X24)
| ~ member(X24,X20)
| member(esk5_2(X20,X21),X20) )
& ( partition(X20,X21)
| member(esk3_2(X20,X21),X20)
| member(esk4_2(X20,X21),X21)
| esk5_2(X20,X21) != esk6_2(X20,X21) )
& ( partition(X20,X21)
| member(esk3_2(X20,X21),X20)
| member(esk4_2(X20,X21),X21)
| member(esk7_2(X20,X21),esk6_2(X20,X21)) )
& ( partition(X20,X21)
| member(esk3_2(X20,X21),X20)
| member(esk4_2(X20,X21),X21)
| member(esk7_2(X20,X21),esk5_2(X20,X21)) )
& ( partition(X20,X21)
| member(esk3_2(X20,X21),X20)
| member(esk4_2(X20,X21),X21)
| member(esk6_2(X20,X21),X20) )
& ( partition(X20,X21)
| member(esk3_2(X20,X21),X20)
| member(esk4_2(X20,X21),X21)
| member(esk5_2(X20,X21),X20) )
& ( ~ partition(X12,X13)
| X17 = X18
| ~ member(X19,X18)
| ~ member(X19,X17)
| ~ member(X18,X12)
| ~ member(X17,X12) )
& ( ~ partition(X12,X13)
| ~ member(X15,X13)
| member(X15,esk2_3(X12,X13,X15)) )
& ( ~ partition(X12,X13)
| ~ member(X15,X13)
| member(esk2_3(X12,X13,X15),X12) )
& ( ~ partition(X12,X13)
| subset(X14,X13)
| ~ member(X14,X12) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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])])])])])])]) ).
cnf(c_0_14,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,plain,
( ~ member(X1,X2)
| subset(singleton(X1),X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( partition(X1,X2)
| member(esk3_2(X1,X2),X1)
| member(esk4_2(X1,X2),X2)
| member(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( ~ member(X3,X2)
| ~ member(X1,singleton(X3))
| member(X1,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
( member(esk4_2(empty_set,X1),X1)
| partition(empty_set,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_16]) ).
cnf(c_0_20,plain,
( ~ member(X1,X2)
| member(esk4_2(empty_set,singleton(X1)),X2)
| partition(empty_set,singleton(X1)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,plain,
( ~ member(X1,singleton(X2))
| partition(empty_set,singleton(X1))
| esk4_2(empty_set,singleton(X1)) = X2 ),
inference(spm,[status(thm)],[c_0_7,c_0_20]) ).
cnf(c_0_22,plain,
( ~ partition(X1,X2)
| ~ member(X3,X2)
| member(esk2_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_23,plain,
( subset(singleton(X1),X2)
| partition(empty_set,singleton(esk8_2(singleton(X1),X2)))
| esk4_2(empty_set,singleton(esk8_2(singleton(X1),X2))) = X1 ),
inference(spm,[status(thm)],[c_0_21,c_0_8]) ).
cnf(c_0_24,plain,
( ~ member(X2,X1)
| ~ partition(empty_set,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_22]) ).
cnf(c_0_25,plain,
( subset(singleton(X1),X2)
| member(X1,singleton(esk8_2(singleton(X1),X2)))
| partition(empty_set,singleton(esk8_2(singleton(X1),X2))) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_23]),c_0_16]),c_0_16]) ).
cnf(c_0_26,plain,
( X1 != X2
| member(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_27,plain,
( ~ member(X1,X3)
| subset(singleton(X1),X2)
| member(esk8_2(singleton(X1),X2),X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_8]) ).
cnf(c_0_28,plain,
( ~ member(X3,singleton(esk8_2(singleton(X1),X2)))
| subset(singleton(X1),X2)
| member(X1,singleton(esk8_2(singleton(X1),X2))) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
member(X1,singleton(X1)),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_30,plain,
( ~ member(X1,singleton(X3))
| subset(singleton(X1),X2)
| esk8_2(singleton(X1),X2) = X3 ),
inference(spm,[status(thm)],[c_0_7,c_0_27]) ).
cnf(c_0_31,plain,
( subset(singleton(X1),X2)
| member(X1,singleton(esk8_2(singleton(X1),X2))) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,plain,
( subset(singleton(X1),X2)
| subset(singleton(X1),X3)
| esk8_2(singleton(X1),X2) = esk8_2(singleton(X1),X3) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,plain,
( ~ member(esk4_2(X1,X2),X3)
| ~ member(X3,X1)
| partition(X1,X2)
| member(esk3_2(X1,X2),X1)
| member(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_34,plain,
( ~ member(esk8_2(singleton(X1),X2),X3)
| subset(singleton(X1),X3)
| subset(singleton(X1),X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_32]) ).
cnf(c_0_35,plain,
( ~ member(X2,X1)
| member(esk5_2(X1,X2),X1)
| member(esk3_2(X1,X2),X1)
| partition(X1,X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_17]) ).
cnf(c_0_36,plain,
( subset(singleton(X1),X2)
| subset(singleton(X1),singleton(esk8_2(singleton(X1),X2))) ),
inference(spm,[status(thm)],[c_0_34,c_0_29]) ).
cnf(c_0_37,plain,
( ~ member(X1,X3)
| ~ member(X2,singleton(X1))
| member(esk5_2(singleton(X1),X2),X3)
| member(esk3_2(singleton(X1),X2),singleton(X1))
| partition(singleton(X1),X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_35]) ).
cnf(c_0_38,plain,
( ~ member(X1,singleton(X2))
| subset(singleton(X2),X3)
| member(X1,singleton(esk8_2(singleton(X2),X3))) ),
inference(spm,[status(thm)],[c_0_14,c_0_36]) ).
cnf(c_0_39,plain,
( ~ member(X1,X2)
| member(esk5_2(singleton(X1),X1),X2)
| member(esk3_2(singleton(X1),X1),singleton(X1))
| partition(singleton(X1),X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_29]) ).
cnf(c_0_40,plain,
( ~ member(X1,singleton(X2))
| subset(singleton(X2),X3)
| X1 = esk8_2(singleton(X2),X3) ),
inference(spm,[status(thm)],[c_0_7,c_0_38]) ).
cnf(c_0_41,plain,
( member(esk3_2(singleton(X1),X1),singleton(X1))
| member(esk5_2(singleton(X1),X1),singleton(X1))
| partition(singleton(X1),X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_29]) ).
cnf(c_0_42,plain,
( ~ member(esk4_2(X1,X2),X3)
| ~ member(X3,X1)
| partition(X1,X2)
| member(esk3_2(X1,X2),X1)
| member(esk6_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_43,plain,
( partition(X1,X2)
| member(esk3_2(X1,X2),X1)
| member(esk4_2(X1,X2),X2)
| member(esk6_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_44,plain,
( subset(singleton(X1),X2)
| member(esk3_2(singleton(X1),X1),singleton(X1))
| partition(singleton(X1),X1)
| esk5_2(singleton(X1),X1) = esk8_2(singleton(X1),X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,plain,
( ~ member(X2,X1)
| member(esk6_2(X1,X2),X1)
| member(esk3_2(X1,X2),X1)
| partition(X1,X2) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_46,plain,
( ~ member(esk5_2(singleton(X1),X1),X2)
| subset(singleton(X1),X2)
| member(esk3_2(singleton(X1),X1),singleton(X1))
| partition(singleton(X1),X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_44]) ).
cnf(c_0_47,plain,
( ~ member(X1,X3)
| ~ member(X2,singleton(X1))
| member(esk6_2(singleton(X1),X2),X3)
| member(esk3_2(singleton(X1),X2),singleton(X1))
| partition(singleton(X1),X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_45]) ).
cnf(c_0_48,plain,
( subset(singleton(X1),singleton(esk5_2(singleton(X1),X1)))
| member(esk3_2(singleton(X1),X1),singleton(X1))
| partition(singleton(X1),X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_29]) ).
cnf(c_0_49,plain,
( ~ member(X1,X2)
| member(esk6_2(singleton(X1),X1),X2)
| member(esk3_2(singleton(X1),X1),singleton(X1))
| partition(singleton(X1),X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_29]) ).
cnf(c_0_50,plain,
( ~ member(X2,singleton(X1))
| member(X2,singleton(esk5_2(singleton(X1),X1)))
| member(esk3_2(singleton(X1),X1),singleton(X1))
| partition(singleton(X1),X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_48]) ).
cnf(c_0_51,plain,
( member(esk3_2(singleton(X1),X1),singleton(X1))
| member(esk6_2(singleton(X1),X1),singleton(X1))
| partition(singleton(X1),X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_29]) ).
cnf(c_0_52,plain,
( member(esk3_2(singleton(X1),X1),singleton(X1))
| member(esk6_2(singleton(X1),X1),singleton(esk5_2(singleton(X1),X1)))
| partition(singleton(X1),X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_53,plain,
( member(esk3_2(singleton(X1),X1),singleton(X1))
| partition(singleton(X1),X1)
| esk6_2(singleton(X1),X1) = esk5_2(singleton(X1),X1) ),
inference(spm,[status(thm)],[c_0_7,c_0_52]) ).
cnf(c_0_54,plain,
( esk5_2(X1,X2) != esk6_2(X1,X2)
| partition(X1,X2)
| member(esk3_2(X1,X2),X1)
| member(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_55,plain,
( partition(singleton(X1),X1)
| esk3_2(singleton(X1),X1) = X1
| esk6_2(singleton(X1),X1) = esk5_2(singleton(X1),X1) ),
inference(spm,[status(thm)],[c_0_7,c_0_53]) ).
cnf(c_0_56,plain,
( member(esk4_2(singleton(X1),X1),X1)
| partition(singleton(X1),X1)
| esk3_2(singleton(X1),X1) = X1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_7]) ).
cnf(c_0_57,plain,
( ~ subset(esk3_2(X1,X2),X2)
| partition(X1,X2)
| member(esk4_2(X1,X2),X2)
| member(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_58,plain,
( partition(singleton(empty_set),empty_set)
| esk3_2(singleton(empty_set),empty_set) = empty_set ),
inference(spm,[status(thm)],[c_0_16,c_0_56]) ).
cnf(c_0_59,plain,
subset(X1,X1),
inference(spm,[status(thm)],[c_0_10,c_0_8]) ).
cnf(c_0_60,plain,
( member(esk5_2(singleton(empty_set),empty_set),singleton(empty_set))
| partition(singleton(empty_set),empty_set) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59])]),c_0_16]) ).
cnf(c_0_61,plain,
( ~ subset(esk3_2(X1,X2),X2)
| partition(X1,X2)
| member(esk4_2(X1,X2),X2)
| member(esk7_2(X1,X2),esk5_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_62,plain,
( partition(singleton(empty_set),empty_set)
| esk5_2(singleton(empty_set),empty_set) = empty_set ),
inference(spm,[status(thm)],[c_0_7,c_0_60]) ).
cnf(c_0_63,plain,
( ~ subset(esk3_2(singleton(empty_set),empty_set),empty_set)
| partition(singleton(empty_set),empty_set) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_16]),c_0_16]) ).
cnf(c_0_64,plain,
( ~ partition(X2,X3)
| ~ member(X1,X2)
| subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_65,plain,
partition(singleton(empty_set),empty_set),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_58]),c_0_59])]) ).
cnf(c_0_66,plain,
( ~ member(X1,singleton(empty_set))
| subset(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_67,plain,
( ~ member(X1,singleton(empty_set))
| subset(singleton(X1),X2)
| subset(esk8_2(singleton(X1),X2),empty_set) ),
inference(spm,[status(thm)],[c_0_66,c_0_27]) ).
cnf(c_0_68,plain,
( ~ member(X1,singleton(empty_set))
| ~ member(X3,esk8_2(singleton(X1),X2))
| subset(singleton(X1),X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_67]),c_0_16]) ).
cnf(c_0_69,plain,
( ~ member(X3,X1)
| ~ member(X1,singleton(empty_set))
| subset(singleton(X1),X2) ),
inference(spm,[status(thm)],[c_0_68,c_0_11]) ).
cnf(c_0_70,plain,
( ~ member(X2,singleton(empty_set))
| subset(singleton(X2),X3)
| member(esk6_2(X1,X2),X1)
| member(esk3_2(X1,X2),X1)
| partition(X1,X2) ),
inference(spm,[status(thm)],[c_0_69,c_0_43]) ).
cnf(c_0_71,plain,
( ~ member(X2,singleton(empty_set))
| subset(singleton(X2),X3)
| member(esk5_2(X1,X2),X1)
| member(esk3_2(X1,X2),X1)
| partition(X1,X2) ),
inference(spm,[status(thm)],[c_0_69,c_0_17]) ).
cnf(c_0_72,plain,
( subset(singleton(empty_set),X2)
| member(esk3_2(X1,empty_set),X1)
| member(esk6_2(X1,empty_set),X1)
| partition(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_70,c_0_29]) ).
cnf(c_0_73,plain,
( subset(singleton(empty_set),X2)
| member(esk3_2(X1,empty_set),X1)
| member(esk5_2(X1,empty_set),X1)
| partition(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_71,c_0_29]) ).
cnf(c_0_74,plain,
( ~ member(X2,singleton(empty_set))
| member(X2,X3)
| member(esk6_2(X1,empty_set),X1)
| member(esk3_2(X1,empty_set),X1)
| partition(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_14,c_0_72]) ).
cnf(c_0_75,plain,
( ~ member(X2,singleton(empty_set))
| member(X2,X3)
| member(esk5_2(X1,empty_set),X1)
| member(esk3_2(X1,empty_set),X1)
| partition(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_14,c_0_73]) ).
cnf(c_0_76,plain,
( member(empty_set,X2)
| member(esk3_2(X1,empty_set),X1)
| member(esk6_2(X1,empty_set),X1)
| partition(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_74,c_0_29]) ).
cnf(c_0_77,plain,
( member(empty_set,X2)
| member(esk3_2(X1,empty_set),X1)
| member(esk5_2(X1,empty_set),X1)
| partition(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_75,c_0_29]) ).
cnf(c_0_78,plain,
( member(esk6_2(X2,empty_set),X2)
| member(esk3_2(X2,empty_set),X2)
| partition(X2,empty_set)
| empty_set = X1 ),
inference(spm,[status(thm)],[c_0_7,c_0_76]) ).
cnf(c_0_79,plain,
( member(esk5_2(X2,empty_set),X2)
| member(esk3_2(X2,empty_set),X2)
| partition(X2,empty_set)
| empty_set = X1 ),
inference(spm,[status(thm)],[c_0_7,c_0_77]) ).
cnf(c_0_80,plain,
( member(esk3_2(X1,empty_set),X1)
| member(esk6_2(X1,empty_set),X1)
| partition(X1,empty_set) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_78]),c_0_16]) ).
cnf(c_0_81,plain,
( member(esk3_2(X1,empty_set),X1)
| member(esk5_2(X1,empty_set),X1)
| partition(X1,empty_set) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_79]),c_0_16]) ).
cnf(c_0_82,plain,
( member(esk3_2(singleton(X1),empty_set),singleton(X1))
| partition(singleton(X1),empty_set)
| esk6_2(singleton(X1),empty_set) = X1 ),
inference(spm,[status(thm)],[c_0_7,c_0_80]) ).
cnf(c_0_83,plain,
( member(esk3_2(singleton(X1),empty_set),singleton(X1))
| partition(singleton(X1),empty_set)
| esk5_2(singleton(X1),empty_set) = X1 ),
inference(spm,[status(thm)],[c_0_7,c_0_81]) ).
cnf(c_0_84,plain,
( partition(singleton(X1),empty_set)
| esk3_2(singleton(X1),empty_set) = X1
| esk6_2(singleton(X1),empty_set) = X1 ),
inference(spm,[status(thm)],[c_0_7,c_0_82]) ).
cnf(c_0_85,plain,
( partition(singleton(X1),empty_set)
| esk3_2(singleton(X1),empty_set) = X1
| esk5_2(singleton(X1),empty_set) = X1 ),
inference(spm,[status(thm)],[c_0_7,c_0_83]) ).
cnf(c_0_86,plain,
( ~ subset(esk3_2(X1,X2),X2)
| partition(X1,X2)
| member(esk4_2(X1,X2),X2)
| member(esk6_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_87,plain,
( partition(singleton(X1),empty_set)
| esk3_2(singleton(X1),empty_set) = X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_84]),c_0_16]),c_0_85]),c_0_7]) ).
cnf(c_0_88,plain,
( ~ subset(esk3_2(X1,X2),X2)
| esk5_2(X1,X2) != esk6_2(X1,X2)
| partition(X1,X2)
| member(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_89,plain,
( ~ subset(X1,empty_set)
| member(esk6_2(singleton(X1),empty_set),singleton(X1))
| partition(singleton(X1),empty_set) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_16]) ).
cnf(c_0_90,plain,
( ~ subset(X1,empty_set)
| member(esk5_2(singleton(X1),empty_set),singleton(X1))
| partition(singleton(X1),empty_set) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_87]),c_0_16]) ).
cnf(c_0_91,plain,
( ~ subset(X1,empty_set)
| esk6_2(singleton(X1),empty_set) != esk5_2(singleton(X1),empty_set)
| partition(singleton(X1),empty_set) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_87]),c_0_16]) ).
cnf(c_0_92,plain,
( ~ subset(X1,empty_set)
| partition(singleton(X1),empty_set)
| esk6_2(singleton(X1),empty_set) = X1 ),
inference(spm,[status(thm)],[c_0_7,c_0_89]) ).
cnf(c_0_93,plain,
( ~ subset(X1,empty_set)
| partition(singleton(X1),empty_set)
| esk5_2(singleton(X1),empty_set) = X1 ),
inference(spm,[status(thm)],[c_0_7,c_0_90]) ).
cnf(c_0_94,plain,
( ~ subset(X1,empty_set)
| partition(singleton(X1),empty_set) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93]) ).
cnf(c_0_95,plain,
( ~ subset(X2,empty_set)
| ~ member(X1,singleton(X2))
| subset(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_64,c_0_94]) ).
cnf(c_0_96,plain,
( ~ member(X2,singleton(X1))
| member(esk3_2(singleton(X1),X2),singleton(X1))
| partition(singleton(X1),X2)
| esk5_2(singleton(X1),X2) = X1 ),
inference(spm,[status(thm)],[c_0_7,c_0_35]) ).
cnf(c_0_97,plain,
( ~ member(X2,singleton(X1))
| member(esk3_2(singleton(X1),X2),singleton(X1))
| partition(singleton(X1),X2)
| esk6_2(singleton(X1),X2) = X1 ),
inference(spm,[status(thm)],[c_0_7,c_0_45]) ).
cnf(c_0_98,plain,
( ~ subset(X1,empty_set)
| subset(esk6_2(singleton(X1),X1),empty_set)
| member(esk3_2(singleton(X1),X1),singleton(X1))
| partition(singleton(X1),X1) ),
inference(spm,[status(thm)],[c_0_95,c_0_51]) ).
cnf(c_0_99,plain,
( ~ subset(X1,empty_set)
| ~ member(X3,X2)
| ~ partition(singleton(X1),X2)
| subset(esk2_3(singleton(X1),X2,X3),empty_set) ),
inference(spm,[status(thm)],[c_0_95,c_0_22]) ).
cnf(c_0_100,plain,
( ~ member(X1,X3)
| ~ member(X2,singleton(X1))
| member(esk3_2(singleton(X1),X2),X3)
| partition(singleton(X1),X2)
| esk5_2(singleton(X1),X2) = X1 ),
inference(spm,[status(thm)],[c_0_18,c_0_96]) ).
cnf(c_0_101,plain,
( ~ member(X1,X3)
| ~ member(X2,singleton(X1))
| member(esk3_2(singleton(X1),X2),X3)
| partition(singleton(X1),X2)
| esk6_2(singleton(X1),X2) = X1 ),
inference(spm,[status(thm)],[c_0_18,c_0_97]) ).
cnf(c_0_102,plain,
( ~ subset(X1,empty_set)
| subset(esk6_2(singleton(X1),X1),empty_set)
| partition(singleton(X1),X1)
| esk3_2(singleton(X1),X1) = X1 ),
inference(spm,[status(thm)],[c_0_7,c_0_98]) ).
cnf(c_0_103,plain,
( ~ subset(X1,empty_set)
| ~ member(X4,X2)
| ~ member(X3,esk2_3(singleton(X1),X2,X4))
| ~ partition(singleton(X1),X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_99]),c_0_16]) ).
cnf(c_0_104,plain,
( ~ partition(X2,X3)
| ~ member(X1,X3)
| member(X1,esk2_3(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_105,plain,
( ~ member(X1,X2)
| member(esk3_2(singleton(X1),X1),X2)
| partition(singleton(X1),X1)
| esk5_2(singleton(X1),X1) = X1 ),
inference(spm,[status(thm)],[c_0_100,c_0_29]) ).
cnf(c_0_106,plain,
( ~ member(X1,X2)
| member(esk3_2(singleton(X1),X1),X2)
| partition(singleton(X1),X1)
| esk6_2(singleton(X1),X1) = X1 ),
inference(spm,[status(thm)],[c_0_101,c_0_29]) ).
cnf(c_0_107,plain,
( ~ subset(X1,empty_set)
| ~ member(X2,esk6_2(singleton(X1),X1))
| partition(singleton(X1),X1)
| esk3_2(singleton(X1),X1) = X1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_102]),c_0_16]) ).
cnf(c_0_108,plain,
( ~ member(X2,singleton(X1))
| partition(singleton(X1),X2)
| esk3_2(singleton(X1),X2) = X1
| esk6_2(singleton(X1),X2) = X1 ),
inference(spm,[status(thm)],[c_0_7,c_0_97]) ).
cnf(c_0_109,plain,
( ~ subset(X1,empty_set)
| ~ member(X3,X2)
| ~ partition(singleton(X1),X2) ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_110,plain,
( member(esk3_2(singleton(X1),X1),singleton(X1))
| partition(singleton(X1),X1)
| esk5_2(singleton(X1),X1) = X1 ),
inference(spm,[status(thm)],[c_0_105,c_0_29]) ).
cnf(c_0_111,plain,
( member(esk3_2(singleton(X1),X1),singleton(X1))
| partition(singleton(X1),X1)
| esk6_2(singleton(X1),X1) = X1 ),
inference(spm,[status(thm)],[c_0_106,c_0_29]) ).
cnf(c_0_112,plain,
( ~ subset(X1,empty_set)
| ~ member(X2,X1)
| esk3_2(singleton(X1),X1) = X1 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_29])]),c_0_109]) ).
cnf(c_0_113,plain,
( ~ subset(X1,empty_set)
| subset(esk3_2(singleton(X1),X1),empty_set)
| partition(singleton(X1),X1)
| esk5_2(singleton(X1),X1) = X1 ),
inference(spm,[status(thm)],[c_0_95,c_0_110]) ).
cnf(c_0_114,plain,
( ~ subset(X1,empty_set)
| subset(esk3_2(singleton(X1),X1),empty_set)
| partition(singleton(X1),X1)
| esk6_2(singleton(X1),X1) = X1 ),
inference(spm,[status(thm)],[c_0_95,c_0_111]) ).
cnf(c_0_115,plain,
( ~ subset(X1,empty_set)
| subset(esk5_2(singleton(X1),X1),empty_set)
| member(esk3_2(singleton(X1),X1),singleton(X1))
| partition(singleton(X1),X1) ),
inference(spm,[status(thm)],[c_0_95,c_0_41]) ).
cnf(c_0_116,plain,
( ~ subset(X1,empty_set)
| partition(singleton(X1),X1)
| esk3_2(singleton(X1),X1) = X1 ),
inference(spm,[status(thm)],[c_0_112,c_0_56]) ).
cnf(c_0_117,plain,
( ~ subset(X1,empty_set)
| ~ member(X2,esk3_2(singleton(X1),X1))
| partition(singleton(X1),X1)
| esk5_2(singleton(X1),X1) = X1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_113]),c_0_16]) ).
cnf(c_0_118,plain,
( ~ subset(X1,empty_set)
| ~ member(X2,esk3_2(singleton(X1),X1))
| partition(singleton(X1),X1)
| esk6_2(singleton(X1),X1) = X1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_114]),c_0_16]) ).
cnf(c_0_119,plain,
( ~ subset(X1,empty_set)
| subset(esk3_2(singleton(X1),X1),empty_set)
| subset(esk5_2(singleton(X1),X1),empty_set)
| partition(singleton(X1),X1) ),
inference(spm,[status(thm)],[c_0_95,c_0_115]) ).
cnf(c_0_120,plain,
( ~ subset(X1,empty_set)
| member(esk4_2(singleton(X1),X1),X1)
| member(esk5_2(singleton(X1),X1),singleton(X1))
| partition(singleton(X1),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_116]),c_0_59])]) ).
cnf(c_0_121,plain,
( ~ subset(X1,empty_set)
| ~ member(X2,X1)
| esk5_2(singleton(X1),X1) = X1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_116]),c_0_109]) ).
cnf(c_0_122,plain,
( ~ subset(X1,empty_set)
| member(esk4_2(singleton(X1),X1),X1)
| member(esk6_2(singleton(X1),X1),singleton(X1))
| partition(singleton(X1),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_116]),c_0_59])]) ).
cnf(c_0_123,plain,
( ~ subset(X1,empty_set)
| ~ member(X2,X1)
| esk6_2(singleton(X1),X1) = X1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_116]),c_0_109]) ).
cnf(c_0_124,plain,
( ~ subset(X1,empty_set)
| ~ member(X2,esk5_2(singleton(X1),X1))
| subset(esk3_2(singleton(X1),X1),empty_set)
| partition(singleton(X1),X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_119]),c_0_16]) ).
cnf(c_0_125,plain,
( ~ subset(X1,empty_set)
| partition(singleton(X1),X1)
| esk5_2(singleton(X1),X1) = X1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_120]),c_0_121]) ).
cnf(c_0_126,plain,
( ~ subset(X1,empty_set)
| esk6_2(singleton(X1),X1) != esk5_2(singleton(X1),X1)
| member(esk4_2(singleton(X1),X1),X1)
| partition(singleton(X1),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_116]),c_0_59])]) ).
cnf(c_0_127,plain,
( ~ subset(X1,empty_set)
| partition(singleton(X1),X1)
| esk6_2(singleton(X1),X1) = X1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_122]),c_0_123]) ).
cnf(c_0_128,plain,
( ~ subset(X1,empty_set)
| ~ member(X2,X1)
| subset(esk3_2(singleton(X1),X1),empty_set) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_109]) ).
cnf(c_0_129,plain,
( ~ subset(X1,empty_set)
| member(esk4_2(singleton(X1),X1),X1)
| partition(singleton(X1),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_125]) ).
cnf(c_0_130,plain,
( ~ subset(X1,empty_set)
| subset(esk3_2(singleton(X1),X1),empty_set)
| partition(singleton(X1),X1) ),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
fof(c_0_131,negated_conjecture,
~ ! [X4] :
( X4 != empty_set
=> partition(singleton(X4),X4) ),
inference(assume_negation,[status(cth)],[set_partitions_itself]) ).
cnf(c_0_132,plain,
( ~ subset(X1,empty_set)
| ~ member(X2,esk3_2(singleton(X1),X1))
| partition(singleton(X1),X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_130]),c_0_16]) ).
cnf(c_0_133,plain,
( subset(singleton(X1),X2)
| partition(singleton(X1),X1)
| esk3_2(singleton(X1),X1) = X1
| esk5_2(singleton(X1),X1) = esk8_2(singleton(X1),X2) ),
inference(spm,[status(thm)],[c_0_7,c_0_44]) ).
cnf(c_0_134,plain,
( subset(singleton(X1),X2)
| member(esk3_2(singleton(X1),X1),singleton(X1))
| partition(singleton(X1),X1)
| esk6_2(singleton(X1),X1) = esk8_2(singleton(X1),X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_51]) ).
fof(c_0_135,negated_conjecture,
~ ! [X4] :
( X4 != empty_set
=> partition(singleton(X4),X4) ),
inference(fof_simplification,[status(thm)],[c_0_131]) ).
cnf(c_0_136,plain,
( ~ subset(esk3_2(X1,X2),X2)
| ~ member(esk4_2(X1,X2),X3)
| ~ member(X3,X1)
| esk5_2(X1,X2) != esk6_2(X1,X2)
| partition(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_137,plain,
( ~ subset(X1,empty_set)
| subset(esk3_2(singleton(X1),X1),X2)
| partition(singleton(X1),X1) ),
inference(spm,[status(thm)],[c_0_132,c_0_8]) ).
cnf(c_0_138,plain,
( subset(singleton(X1),X2)
| member(esk5_2(singleton(X1),X1),singleton(X1))
| partition(singleton(X1),X1)
| esk3_2(singleton(X1),X1) = X1 ),
inference(spm,[status(thm)],[c_0_8,c_0_133]) ).
cnf(c_0_139,plain,
( subset(singleton(X1),X2)
| partition(singleton(X1),X1)
| esk3_2(singleton(X1),X1) = X1
| esk6_2(singleton(X1),X1) = esk8_2(singleton(X1),X2) ),
inference(spm,[status(thm)],[c_0_7,c_0_134]) ).
fof(c_0_140,negated_conjecture,
( ~ partition(singleton(esk1_0),esk1_0)
& esk1_0 != empty_set ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_135])])])]) ).
cnf(c_0_141,plain,
( ~ subset(X1,empty_set)
| esk6_2(singleton(X1),X1) != esk5_2(singleton(X1),X1)
| partition(singleton(X1),X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_129]),c_0_29])]),c_0_137]) ).
cnf(c_0_142,plain,
( ~ member(X2,singleton(X1))
| member(X2,X3)
| member(esk5_2(singleton(X1),X1),singleton(X1))
| partition(singleton(X1),X1)
| esk3_2(singleton(X1),X1) = X1 ),
inference(spm,[status(thm)],[c_0_14,c_0_138]) ).
cnf(c_0_143,plain,
( ~ member(esk6_2(singleton(X1),X1),X2)
| subset(singleton(X1),X2)
| partition(singleton(X1),X1)
| esk3_2(singleton(X1),X1) = X1 ),
inference(spm,[status(thm)],[c_0_10,c_0_139]) ).
cnf(c_0_144,negated_conjecture,
~ partition(singleton(esk1_0),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_140]) ).
cnf(c_0_145,plain,
( ~ subset(X1,empty_set)
| partition(singleton(X1),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_127]),c_0_125]) ).
cnf(c_0_146,plain,
( member(X1,X2)
| member(esk5_2(singleton(X1),X1),singleton(X1))
| partition(singleton(X1),X1)
| esk3_2(singleton(X1),X1) = X1 ),
inference(spm,[status(thm)],[c_0_142,c_0_29]) ).
cnf(c_0_147,plain,
( subset(singleton(X1),singleton(esk6_2(singleton(X1),X1)))
| partition(singleton(X1),X1)
| esk3_2(singleton(X1),X1) = X1 ),
inference(spm,[status(thm)],[c_0_143,c_0_29]) ).
cnf(c_0_148,negated_conjecture,
~ subset(esk1_0,empty_set),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_149,plain,
( member(esk5_2(singleton(X1),X1),singleton(X1))
| partition(singleton(X1),X1)
| X1 = X2
| esk3_2(singleton(X1),X1) = X1 ),
inference(spm,[status(thm)],[c_0_7,c_0_146]) ).
cnf(c_0_150,plain,
( ~ member(X2,singleton(X1))
| member(X2,singleton(esk6_2(singleton(X1),X1)))
| partition(singleton(X1),X1)
| esk3_2(singleton(X1),X1) = X1 ),
inference(spm,[status(thm)],[c_0_14,c_0_147]) ).
cnf(c_0_151,negated_conjecture,
( ~ subset(X1,empty_set)
| member(esk5_2(singleton(esk1_0),esk1_0),singleton(esk1_0))
| esk3_2(singleton(esk1_0),esk1_0) = esk1_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_144]) ).
cnf(c_0_152,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[c_0_16,c_0_8]) ).
cnf(c_0_153,plain,
( ~ member(X2,singleton(X1))
| partition(singleton(X1),X1)
| X2 = esk6_2(singleton(X1),X1)
| esk3_2(singleton(X1),X1) = X1 ),
inference(spm,[status(thm)],[c_0_7,c_0_150]) ).
cnf(c_0_154,negated_conjecture,
( member(esk5_2(singleton(esk1_0),esk1_0),singleton(esk1_0))
| esk3_2(singleton(esk1_0),esk1_0) = esk1_0 ),
inference(spm,[status(thm)],[c_0_151,c_0_152]) ).
cnf(c_0_155,negated_conjecture,
( esk3_2(singleton(esk1_0),esk1_0) = esk1_0
| esk6_2(singleton(esk1_0),esk1_0) = esk5_2(singleton(esk1_0),esk1_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_154]),c_0_144]) ).
cnf(c_0_156,plain,
( ~ member(esk4_2(X1,X2),X3)
| ~ member(X3,X1)
| esk5_2(X1,X2) != esk6_2(X1,X2)
| partition(X1,X2)
| member(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_157,negated_conjecture,
( member(esk4_2(singleton(esk1_0),esk1_0),esk1_0)
| esk3_2(singleton(esk1_0),esk1_0) = esk1_0 ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_155]),c_0_144]),c_0_7]) ).
cnf(c_0_158,negated_conjecture,
esk3_2(singleton(esk1_0),esk1_0) = esk1_0,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_157]),c_0_29])]),c_0_144]),c_0_155]),c_0_7]) ).
cnf(c_0_159,negated_conjecture,
( member(esk4_2(singleton(esk1_0),esk1_0),esk1_0)
| member(esk6_2(singleton(esk1_0),esk1_0),singleton(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_158]),c_0_59])]),c_0_144]) ).
cnf(c_0_160,negated_conjecture,
( member(esk4_2(singleton(esk1_0),esk1_0),esk1_0)
| member(esk5_2(singleton(esk1_0),esk1_0),singleton(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_158]),c_0_59])]),c_0_144]) ).
cnf(c_0_161,plain,
( ~ subset(esk3_2(X1,X2),X2)
| ~ member(esk4_2(X1,X2),X3)
| ~ member(X3,X1)
| partition(X1,X2)
| member(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_162,negated_conjecture,
( esk6_2(singleton(esk1_0),esk1_0) != esk5_2(singleton(esk1_0),esk1_0)
| member(esk4_2(singleton(esk1_0),esk1_0),esk1_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_158]),c_0_59])]),c_0_144]) ).
cnf(c_0_163,negated_conjecture,
( member(esk4_2(singleton(esk1_0),esk1_0),esk1_0)
| esk6_2(singleton(esk1_0),esk1_0) = esk1_0 ),
inference(spm,[status(thm)],[c_0_7,c_0_159]) ).
cnf(c_0_164,negated_conjecture,
( member(esk4_2(singleton(esk1_0),esk1_0),esk1_0)
| esk5_2(singleton(esk1_0),esk1_0) = esk1_0 ),
inference(spm,[status(thm)],[c_0_7,c_0_160]) ).
cnf(c_0_165,negated_conjecture,
( ~ member(X1,singleton(esk1_0))
| ~ member(esk4_2(singleton(esk1_0),esk1_0),X1)
| member(esk5_2(singleton(esk1_0),esk1_0),singleton(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_158]),c_0_59])]),c_0_144]) ).
cnf(c_0_166,negated_conjecture,
member(esk4_2(singleton(esk1_0),esk1_0),esk1_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_163]),c_0_164]) ).
cnf(c_0_167,plain,
( ~ subset(esk3_2(X1,X2),X2)
| ~ member(esk4_2(X1,X2),X3)
| ~ member(X3,X1)
| partition(X1,X2)
| member(esk6_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_168,negated_conjecture,
member(esk5_2(singleton(esk1_0),esk1_0),singleton(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_29])]) ).
cnf(c_0_169,negated_conjecture,
( ~ member(X1,singleton(esk1_0))
| ~ member(esk4_2(singleton(esk1_0),esk1_0),X1)
| member(esk6_2(singleton(esk1_0),esk1_0),singleton(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_158]),c_0_59])]),c_0_144]) ).
cnf(c_0_170,negated_conjecture,
esk6_2(singleton(esk1_0),esk1_0) != esk5_2(singleton(esk1_0),esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_166]),c_0_29]),c_0_158]),c_0_59])]),c_0_144]) ).
cnf(c_0_171,negated_conjecture,
esk5_2(singleton(esk1_0),esk1_0) = esk1_0,
inference(spm,[status(thm)],[c_0_7,c_0_168]) ).
cnf(c_0_172,negated_conjecture,
member(esk6_2(singleton(esk1_0),esk1_0),singleton(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_166]),c_0_29])]) ).
cnf(c_0_173,negated_conjecture,
esk6_2(singleton(esk1_0),esk1_0) != esk1_0,
inference(rw,[status(thm)],[c_0_170,c_0_171]) ).
cnf(c_0_174,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_172]),c_0_173]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV521+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 07:24:12 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.46 Running first-order theorem proving
% 0.13/0.46 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 46.04/8.49 % Version: 3.5.1
% 46.04/8.49 % Preprocessing class: FSMSSMSSSSSNFFN.
% 46.04/8.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 46.04/8.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 46.04/8.49 % Starting new_bool_3 with 300s (1) cores
% 46.04/8.49 % Starting new_bool_1 with 300s (1) cores
% 46.04/8.49 % Starting sh5l with 300s (1) cores
% 46.04/8.49 % new_bool_3 with pid 1212908 completed with status 0
% 46.04/8.49 % Result found by new_bool_3
% 46.04/8.49 % Preprocessing class: FSMSSMSSSSSNFFN.
% 46.04/8.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 46.04/8.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 46.04/8.49 % Starting new_bool_3 with 300s (1) cores
% 46.04/8.49 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 46.04/8.49 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 46.04/8.49 % Search class: FGUSF-FFMF32-SFFFFFNN
% 46.04/8.49 % partial match(1): FGHSF-FFMF32-SFFFFFNN
% 46.04/8.49 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 46.04/8.49 % Starting SubtermCWHack with 31s (1) cores
% 46.04/8.49 % SubtermCWHack with pid 1212913 completed with status 0
% 46.04/8.49 % Result found by SubtermCWHack
% 46.04/8.49 % Preprocessing class: FSMSSMSSSSSNFFN.
% 46.04/8.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 46.04/8.49 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 46.04/8.49 % Starting new_bool_3 with 300s (1) cores
% 46.04/8.49 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 46.04/8.49 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 46.04/8.49 % Search class: FGUSF-FFMF32-SFFFFFNN
% 46.04/8.49 % partial match(1): FGHSF-FFMF32-SFFFFFNN
% 46.04/8.49 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 46.04/8.49 % Starting SubtermCWHack with 31s (1) cores
% 46.04/8.49 % Preprocessing time : 0.002 s
% 46.04/8.49
% 46.04/8.49 % Proof found!
% 46.04/8.49 % SZS status Theorem
% 46.04/8.49 % SZS output start CNFRefutation
% See solution above
% 46.04/8.49 % Parsed axioms : 20
% 46.04/8.49 % Removed by relevancy pruning/SinE : 15
% 46.04/8.49 % Initial clauses : 32
% 46.04/8.49 % Removed in clause preprocessing : 0
% 46.04/8.49 % Initial clauses in saturation : 32
% 46.04/8.49 % Processed clauses : 8671
% 46.04/8.49 % ...of these trivial : 17
% 46.04/8.49 % ...subsumed : 6525
% 46.04/8.49 % ...remaining for further processing : 2129
% 46.04/8.49 % Other redundant clauses eliminated : 9
% 46.04/8.49 % Clauses deleted for lack of memory : 0
% 46.04/8.49 % Backward-subsumed : 606
% 46.04/8.49 % Backward-rewritten : 138
% 46.04/8.49 % Generated clauses : 235626
% 46.04/8.49 % ...of the previous two non-redundant : 223362
% 46.04/8.49 % ...aggressively subsumed : 0
% 46.04/8.49 % Contextual simplify-reflections : 109
% 46.04/8.49 % Paramodulations : 235604
% 46.04/8.49 % Factorizations : 13
% 46.04/8.49 % NegExts : 0
% 46.04/8.49 % Equation resolutions : 9
% 46.04/8.49 % Disequality decompositions : 0
% 46.04/8.49 % Total rewrite steps : 34042
% 46.04/8.49 % ...of those cached : 33800
% 46.04/8.49 % Propositional unsat checks : 0
% 46.04/8.49 % Propositional check models : 0
% 46.04/8.49 % Propositional check unsatisfiable : 0
% 46.04/8.49 % Propositional clauses : 0
% 46.04/8.49 % Propositional clauses after purity: 0
% 46.04/8.49 % Propositional unsat core size : 0
% 46.04/8.49 % Propositional preprocessing time : 0.000
% 46.04/8.49 % Propositional encoding time : 0.000
% 46.04/8.49 % Propositional solver time : 0.000
% 46.04/8.49 % Success case prop preproc time : 0.000
% 46.04/8.49 % Success case prop encoding time : 0.000
% 46.04/8.49 % Success case prop solver time : 0.000
% 46.04/8.49 % Current number of processed clauses : 1384
% 46.04/8.49 % Positive orientable unit clauses : 13
% 46.04/8.49 % Positive unorientable unit clauses: 0
% 46.04/8.49 % Negative unit clauses : 9
% 46.04/8.49 % Non-unit-clauses : 1362
% 46.04/8.49 % Current number of unprocessed clauses: 210785
% 46.04/8.49 % ...number of literals in the above : 1727935
% 46.04/8.49 % Current number of archived formulas : 0
% 46.04/8.49 % Current number of archived clauses : 744
% 46.04/8.49 % Clause-clause subsumption calls (NU) : 621924
% 46.04/8.49 % Rec. Clause-clause subsumption calls : 86729
% 46.04/8.49 % Non-unit clause-clause subsumptions : 5667
% 46.04/8.49 % Unit Clause-clause subsumption calls : 3415
% 46.04/8.49 % Rewrite failures with RHS unbound : 0
% 46.04/8.49 % BW rewrite match attempts : 14
% 46.04/8.49 % BW rewrite match successes : 12
% 46.04/8.49 % Condensation attempts : 0
% 46.04/8.49 % Condensation successes : 0
% 46.04/8.49 % Termbank termtop insertions : 9806985
% 46.04/8.49 % Search garbage collected termcells : 640
% 46.04/8.49
% 46.04/8.49 % -------------------------------------------------
% 46.04/8.49 % User time : 7.582 s
% 46.04/8.49 % System time : 0.241 s
% 46.04/8.49 % Total time : 7.823 s
% 46.04/8.49 % Maximum resident set size: 3668 pages
% 46.04/8.49
% 46.04/8.49 % -------------------------------------------------
% 46.04/8.49 % User time : 7.586 s
% 46.04/8.49 % System time : 0.243 s
% 46.04/8.49 % Total time : 7.829 s
% 46.04/8.49 % Maximum resident set size: 4864 pages
% 46.04/8.49 % E exiting
%------------------------------------------------------------------------------