%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET806+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 02:15:26 PM UTC 2026
% Result : Theorem 0.16s 5.64s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 71 ( 9 unt; 0 def)
% Number of atoms : 429 ( 0 equ)
% Maximal formula atoms : 207 ( 6 avg)
% Number of connectives : 477 ( 119 ~; 272 |; 69 &)
% ( 6 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 65 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-2 aty)
% Number of variables : 146 ( 1 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(equal_set,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(rel_equal_set,hypothesis,
! [X3,X5] :
( apply(equal_set_predicate,X3,X5)
<=> equal_set(X3,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rel_equal_set) ).
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(thIII13,conjecture,
! [X4] : equivalence(equal_set_predicate,power_set(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII13) ).
fof(equivalence,axiom,
! [X1,X7] :
( equivalence(X7,X1)
<=> ( ! [X3,X5,X6] :
( ( member(X6,X1)
& member(X5,X1)
& member(X3,X1) )
=> ( ( apply(X7,X5,X6)
& apply(X7,X3,X5) )
=> apply(X7,X3,X6) ) )
& ! [X3,X5] :
( ( member(X5,X1)
& member(X3,X1) )
=> ( apply(X7,X3,X5)
=> apply(X7,X5,X3) ) )
& ! [X3] :
( member(X3,X1)
=> apply(X7,X3,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax',equivalence) ).
fof(c_0_5,plain,
! [X11,X12] :
( ( equal_set(X11,X12)
| ~ subset(X12,X11)
| ~ subset(X11,X12) )
& ( ~ equal_set(X11,X12)
| subset(X12,X11) )
& ( ~ equal_set(X11,X12)
| subset(X11,X12) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])])]) ).
fof(c_0_6,hypothesis,
! [X8,X9] :
( ( apply(equal_set_predicate,X8,X9)
| ~ equal_set(X8,X9) )
& ( equal_set(X8,X9)
| ~ apply(equal_set_predicate,X8,X9) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rel_equal_set])])]) ).
fof(c_0_7,plain,
! [X17,X18,X19,X20,X21] :
( ( subset(X20,X21)
| ~ member(esk2_2(X20,X21),X21) )
& ( subset(X20,X21)
| member(esk2_2(X20,X21),X20) )
& ( member(X19,X18)
| ~ member(X19,X17)
| ~ subset(X17,X18) ) ),
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_8,plain,
( ~ equal_set(X1,X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,hypothesis,
( ~ apply(equal_set_predicate,X1,X2)
| equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,plain,
! [X1,X7] :
( epred1_2(X7,X1)
<=> ( ! [X3,X5,X6] :
( ( member(X6,X1)
& member(X5,X1)
& member(X3,X1) )
=> ( ( apply(X7,X5,X6)
& apply(X7,X3,X5) )
=> apply(X7,X3,X6) ) )
& ! [X3,X5] :
( ( member(X5,X1)
& member(X3,X1) )
=> ( apply(X7,X3,X5)
=> apply(X7,X5,X3) ) )
& ! [X3] :
( member(X3,X1)
=> apply(X7,X3,X3) ) ) ),
introduced(definition) ).
cnf(c_0_11,hypothesis,
( ~ equal_set(X1,X2)
| apply(equal_set_predicate,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,plain,
( ~ member(esk2_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
( subset(X1,X2)
| member(esk2_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,plain,
( ~ equal_set(X2,X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_16,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,hypothesis,
( ~ apply(equal_set_predicate,X1,X2)
| subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
fof(c_0_18,plain,
! [X23,X24,X25,X26,X27,X28,X29,X30,X31,X32] :
( ( epred1_2(X32,X31)
| ~ apply(X32,esk3_2(X31,X32),esk3_2(X31,X32))
| ~ apply(X32,esk5_2(X31,X32),esk4_2(X31,X32))
| ~ apply(X32,esk6_2(X31,X32),esk8_2(X31,X32)) )
& ( epred1_2(X32,X31)
| ~ apply(X32,esk3_2(X31,X32),esk3_2(X31,X32))
| ~ apply(X32,esk5_2(X31,X32),esk4_2(X31,X32))
| apply(X32,esk7_2(X31,X32),esk8_2(X31,X32)) )
& ( epred1_2(X32,X31)
| ~ apply(X32,esk3_2(X31,X32),esk3_2(X31,X32))
| ~ apply(X32,esk5_2(X31,X32),esk4_2(X31,X32))
| apply(X32,esk6_2(X31,X32),esk7_2(X31,X32)) )
& ( epred1_2(X32,X31)
| ~ apply(X32,esk3_2(X31,X32),esk3_2(X31,X32))
| ~ apply(X32,esk5_2(X31,X32),esk4_2(X31,X32))
| member(esk8_2(X31,X32),X31) )
& ( epred1_2(X32,X31)
| ~ apply(X32,esk3_2(X31,X32),esk3_2(X31,X32))
| ~ apply(X32,esk5_2(X31,X32),esk4_2(X31,X32))
| member(esk7_2(X31,X32),X31) )
& ( epred1_2(X32,X31)
| ~ apply(X32,esk3_2(X31,X32),esk3_2(X31,X32))
| ~ apply(X32,esk5_2(X31,X32),esk4_2(X31,X32))
| member(esk6_2(X31,X32),X31) )
& ( epred1_2(X32,X31)
| ~ apply(X32,esk3_2(X31,X32),esk3_2(X31,X32))
| apply(X32,esk4_2(X31,X32),esk5_2(X31,X32))
| ~ apply(X32,esk6_2(X31,X32),esk8_2(X31,X32)) )
& ( epred1_2(X32,X31)
| ~ apply(X32,esk3_2(X31,X32),esk3_2(X31,X32))
| apply(X32,esk4_2(X31,X32),esk5_2(X31,X32))
| apply(X32,esk7_2(X31,X32),esk8_2(X31,X32)) )
& ( epred1_2(X32,X31)
| ~ apply(X32,esk3_2(X31,X32),esk3_2(X31,X32))
| apply(X32,esk4_2(X31,X32),esk5_2(X31,X32))
| apply(X32,esk6_2(X31,X32),esk7_2(X31,X32)) )
& ( epred1_2(X32,X31)
| ~ apply(X32,esk3_2(X31,X32),esk3_2(X31,X32))
| apply(X32,esk4_2(X31,X32),esk5_2(X31,X32))
| member(esk8_2(X31,X32),X31) )
& ( epred1_2(X32,X31)
| ~ apply(X32,esk3_2(X31,X32),esk3_2(X31,X32))
| apply(X32,esk4_2(X31,X32),esk5_2(X31,X32))
| member(esk7_2(X31,X32),X31) )
& ( epred1_2(X32,X31)
| ~ apply(X32,esk3_2(X31,X32),esk3_2(X31,X32))
| apply(X32,esk4_2(X31,X32),esk5_2(X31,X32))
| member(esk6_2(X31,X32),X31) )
& ( epred1_2(X32,X31)
| ~ apply(X32,esk3_2(X31,X32),esk3_2(X31,X32))
| member(esk5_2(X31,X32),X31)
| ~ apply(X32,esk6_2(X31,X32),esk8_2(X31,X32)) )
& ( epred1_2(X32,X31)
| ~ apply(X32,esk3_2(X31,X32),esk3_2(X31,X32))
| member(esk5_2(X31,X32),X31)
| apply(X32,esk7_2(X31,X32),esk8_2(X31,X32)) )
& ( epred1_2(X32,X31)
| ~ apply(X32,esk3_2(X31,X32),esk3_2(X31,X32))
| member(esk5_2(X31,X32),X31)
| apply(X32,esk6_2(X31,X32),esk7_2(X31,X32)) )
& ( epred1_2(X32,X31)
| ~ apply(X32,esk3_2(X31,X32),esk3_2(X31,X32))
| member(esk5_2(X31,X32),X31)
| member(esk8_2(X31,X32),X31) )
& ( epred1_2(X32,X31)
| ~ apply(X32,esk3_2(X31,X32),esk3_2(X31,X32))
| member(esk5_2(X31,X32),X31)
| member(esk7_2(X31,X32),X31) )
& ( epred1_2(X32,X31)
| ~ apply(X32,esk3_2(X31,X32),esk3_2(X31,X32))
| member(esk5_2(X31,X32),X31)
| member(esk6_2(X31,X32),X31) )
& ( epred1_2(X32,X31)
| ~ apply(X32,esk3_2(X31,X32),esk3_2(X31,X32))
| member(esk4_2(X31,X32),X31)
| ~ apply(X32,esk6_2(X31,X32),esk8_2(X31,X32)) )
& ( epred1_2(X32,X31)
| ~ apply(X32,esk3_2(X31,X32),esk3_2(X31,X32))
| member(esk4_2(X31,X32),X31)
| apply(X32,esk7_2(X31,X32),esk8_2(X31,X32)) )
& ( epred1_2(X32,X31)
| ~ apply(X32,esk3_2(X31,X32),esk3_2(X31,X32))
| member(esk4_2(X31,X32),X31)
| apply(X32,esk6_2(X31,X32),esk7_2(X31,X32)) )
& ( epred1_2(X32,X31)
| ~ apply(X32,esk3_2(X31,X32),esk3_2(X31,X32))
| member(esk4_2(X31,X32),X31)
| member(esk8_2(X31,X32),X31) )
& ( epred1_2(X32,X31)
| ~ apply(X32,esk3_2(X31,X32),esk3_2(X31,X32))
| member(esk4_2(X31,X32),X31)
| member(esk7_2(X31,X32),X31) )
& ( epred1_2(X32,X31)
| ~ apply(X32,esk3_2(X31,X32),esk3_2(X31,X32))
| member(esk4_2(X31,X32),X31)
| member(esk6_2(X31,X32),X31) )
& ( epred1_2(X32,X31)
| member(esk3_2(X31,X32),X31)
| ~ apply(X32,esk5_2(X31,X32),esk4_2(X31,X32))
| ~ apply(X32,esk6_2(X31,X32),esk8_2(X31,X32)) )
& ( epred1_2(X32,X31)
| member(esk3_2(X31,X32),X31)
| ~ apply(X32,esk5_2(X31,X32),esk4_2(X31,X32))
| apply(X32,esk7_2(X31,X32),esk8_2(X31,X32)) )
& ( epred1_2(X32,X31)
| member(esk3_2(X31,X32),X31)
| ~ apply(X32,esk5_2(X31,X32),esk4_2(X31,X32))
| apply(X32,esk6_2(X31,X32),esk7_2(X31,X32)) )
& ( epred1_2(X32,X31)
| member(esk3_2(X31,X32),X31)
| ~ apply(X32,esk5_2(X31,X32),esk4_2(X31,X32))
| member(esk8_2(X31,X32),X31) )
& ( epred1_2(X32,X31)
| member(esk3_2(X31,X32),X31)
| ~ apply(X32,esk5_2(X31,X32),esk4_2(X31,X32))
| member(esk7_2(X31,X32),X31) )
& ( epred1_2(X32,X31)
| member(esk3_2(X31,X32),X31)
| ~ apply(X32,esk5_2(X31,X32),esk4_2(X31,X32))
| member(esk6_2(X31,X32),X31) )
& ( epred1_2(X32,X31)
| member(esk3_2(X31,X32),X31)
| apply(X32,esk4_2(X31,X32),esk5_2(X31,X32))
| ~ apply(X32,esk6_2(X31,X32),esk8_2(X31,X32)) )
& ( epred1_2(X32,X31)
| member(esk3_2(X31,X32),X31)
| apply(X32,esk4_2(X31,X32),esk5_2(X31,X32))
| apply(X32,esk7_2(X31,X32),esk8_2(X31,X32)) )
& ( epred1_2(X32,X31)
| member(esk3_2(X31,X32),X31)
| apply(X32,esk4_2(X31,X32),esk5_2(X31,X32))
| apply(X32,esk6_2(X31,X32),esk7_2(X31,X32)) )
& ( epred1_2(X32,X31)
| member(esk3_2(X31,X32),X31)
| apply(X32,esk4_2(X31,X32),esk5_2(X31,X32))
| member(esk8_2(X31,X32),X31) )
& ( epred1_2(X32,X31)
| member(esk3_2(X31,X32),X31)
| apply(X32,esk4_2(X31,X32),esk5_2(X31,X32))
| member(esk7_2(X31,X32),X31) )
& ( epred1_2(X32,X31)
| member(esk3_2(X31,X32),X31)
| apply(X32,esk4_2(X31,X32),esk5_2(X31,X32))
| member(esk6_2(X31,X32),X31) )
& ( epred1_2(X32,X31)
| member(esk3_2(X31,X32),X31)
| member(esk5_2(X31,X32),X31)
| ~ apply(X32,esk6_2(X31,X32),esk8_2(X31,X32)) )
& ( epred1_2(X32,X31)
| member(esk3_2(X31,X32),X31)
| member(esk5_2(X31,X32),X31)
| apply(X32,esk7_2(X31,X32),esk8_2(X31,X32)) )
& ( epred1_2(X32,X31)
| member(esk3_2(X31,X32),X31)
| member(esk5_2(X31,X32),X31)
| apply(X32,esk6_2(X31,X32),esk7_2(X31,X32)) )
& ( epred1_2(X32,X31)
| member(esk3_2(X31,X32),X31)
| member(esk5_2(X31,X32),X31)
| member(esk8_2(X31,X32),X31) )
& ( epred1_2(X32,X31)
| member(esk3_2(X31,X32),X31)
| member(esk5_2(X31,X32),X31)
| member(esk7_2(X31,X32),X31) )
& ( epred1_2(X32,X31)
| member(esk3_2(X31,X32),X31)
| member(esk5_2(X31,X32),X31)
| member(esk6_2(X31,X32),X31) )
& ( epred1_2(X32,X31)
| member(esk3_2(X31,X32),X31)
| member(esk4_2(X31,X32),X31)
| ~ apply(X32,esk6_2(X31,X32),esk8_2(X31,X32)) )
& ( epred1_2(X32,X31)
| member(esk3_2(X31,X32),X31)
| member(esk4_2(X31,X32),X31)
| apply(X32,esk7_2(X31,X32),esk8_2(X31,X32)) )
& ( epred1_2(X32,X31)
| member(esk3_2(X31,X32),X31)
| member(esk4_2(X31,X32),X31)
| apply(X32,esk6_2(X31,X32),esk7_2(X31,X32)) )
& ( epred1_2(X32,X31)
| member(esk3_2(X31,X32),X31)
| member(esk4_2(X31,X32),X31)
| member(esk8_2(X31,X32),X31) )
& ( epred1_2(X32,X31)
| member(esk3_2(X31,X32),X31)
| member(esk4_2(X31,X32),X31)
| member(esk7_2(X31,X32),X31) )
& ( epred1_2(X32,X31)
| member(esk3_2(X31,X32),X31)
| member(esk4_2(X31,X32),X31)
| member(esk6_2(X31,X32),X31) )
& ( ~ epred1_2(X24,X23)
| apply(X24,X28,X30)
| ~ apply(X24,X29,X30)
| ~ apply(X24,X28,X29)
| ~ member(X30,X23)
| ~ member(X29,X23)
| ~ member(X28,X23) )
& ( ~ epred1_2(X24,X23)
| apply(X24,X27,X26)
| ~ apply(X24,X26,X27)
| ~ member(X27,X23)
| ~ member(X26,X23) )
& ( ~ epred1_2(X24,X23)
| apply(X24,X25,X25)
| ~ member(X25,X23) ) ),
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)],[c_0_10])])])])])])]) ).
cnf(c_0_19,hypothesis,
( ~ subset(X1,X2)
| ~ subset(X2,X1)
| apply(equal_set_predicate,X1,X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_20,plain,
subset(X1,X1),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_21,hypothesis,
( ~ apply(equal_set_predicate,X2,X1)
| subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_9]) ).
cnf(c_0_22,hypothesis,
( ~ member(X1,X3)
| ~ apply(equal_set_predicate,X3,X2)
| member(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,plain,
( ~ apply(X1,esk3_2(X2,X1),esk3_2(X2,X1))
| epred1_2(X1,X2)
| apply(X1,esk4_2(X2,X1),esk5_2(X2,X1))
| apply(X1,esk6_2(X2,X1),esk7_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,hypothesis,
apply(equal_set_predicate,X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_20])]) ).
cnf(c_0_25,hypothesis,
( ~ member(X1,X3)
| ~ apply(equal_set_predicate,X2,X3)
| member(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_21]) ).
cnf(c_0_26,plain,
( ~ apply(X1,esk3_2(X2,X1),esk3_2(X2,X1))
| epred1_2(X1,X2)
| apply(X1,esk4_2(X2,X1),esk5_2(X2,X1))
| apply(X1,esk7_2(X2,X1),esk8_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,hypothesis,
( ~ member(X2,esk6_2(X1,equal_set_predicate))
| member(X2,esk7_2(X1,equal_set_predicate))
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_28,hypothesis,
( ~ member(X2,esk8_2(X1,equal_set_predicate))
| member(X2,esk7_2(X1,equal_set_predicate))
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_24])]) ).
cnf(c_0_29,hypothesis,
( ~ member(X2,esk7_2(X1,equal_set_predicate))
| member(X2,esk8_2(X1,equal_set_predicate))
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_26]),c_0_24])]) ).
cnf(c_0_30,hypothesis,
( subset(esk6_2(X1,equal_set_predicate),X2)
| member(esk2_2(esk6_2(X1,equal_set_predicate),X2),esk7_2(X1,equal_set_predicate))
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_14]) ).
cnf(c_0_31,hypothesis,
( ~ member(X2,esk7_2(X1,equal_set_predicate))
| member(X2,esk6_2(X1,equal_set_predicate))
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_23]),c_0_24])]) ).
cnf(c_0_32,hypothesis,
( subset(esk8_2(X1,equal_set_predicate),X2)
| member(esk2_2(esk8_2(X1,equal_set_predicate),X2),esk7_2(X1,equal_set_predicate))
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_14]) ).
cnf(c_0_33,hypothesis,
( subset(esk6_2(X1,equal_set_predicate),X2)
| member(esk2_2(esk6_2(X1,equal_set_predicate),X2),esk8_2(X1,equal_set_predicate))
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,hypothesis,
( subset(esk8_2(X1,equal_set_predicate),X2)
| member(esk2_2(esk8_2(X1,equal_set_predicate),X2),esk6_2(X1,equal_set_predicate))
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,hypothesis,
( subset(esk6_2(X1,equal_set_predicate),esk8_2(X1,equal_set_predicate))
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_33]) ).
cnf(c_0_36,hypothesis,
( subset(esk8_2(X1,equal_set_predicate),esk6_2(X1,equal_set_predicate))
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_34]) ).
cnf(c_0_37,hypothesis,
( ~ apply(equal_set_predicate,X2,X1)
| apply(equal_set_predicate,X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_17]),c_0_21]) ).
cnf(c_0_38,hypothesis,
( apply(equal_set_predicate,esk8_2(X1,equal_set_predicate),esk6_2(X1,equal_set_predicate))
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_35]),c_0_36]) ).
cnf(c_0_39,plain,
( ~ apply(X1,esk3_2(X2,X1),esk3_2(X2,X1))
| ~ apply(X1,esk6_2(X2,X1),esk8_2(X2,X1))
| epred1_2(X1,X2)
| apply(X1,esk4_2(X2,X1),esk5_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_40,hypothesis,
( apply(equal_set_predicate,esk6_2(X1,equal_set_predicate),esk8_2(X1,equal_set_predicate))
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_41,plain,
( ~ apply(X1,esk3_2(X2,X1),esk3_2(X2,X1))
| ~ apply(X1,esk5_2(X2,X1),esk4_2(X2,X1))
| epred1_2(X1,X2)
| apply(X1,esk7_2(X2,X1),esk8_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_42,plain,
( apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_24])]) ).
cnf(c_0_43,hypothesis,
( ~ member(X2,esk7_2(X1,equal_set_predicate))
| ~ apply(equal_set_predicate,esk5_2(X1,equal_set_predicate),esk4_2(X1,equal_set_predicate))
| member(X2,esk8_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_41]),c_0_24])]) ).
cnf(c_0_44,hypothesis,
( apply(equal_set_predicate,esk5_2(X1,equal_set_predicate),esk4_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_42]) ).
cnf(c_0_45,plain,
( ~ apply(X1,esk3_2(X2,X1),esk3_2(X2,X1))
| ~ apply(X1,esk5_2(X2,X1),esk4_2(X2,X1))
| epred1_2(X1,X2)
| apply(X1,esk6_2(X2,X1),esk7_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_46,hypothesis,
( ~ member(X2,esk8_2(X1,equal_set_predicate))
| ~ apply(equal_set_predicate,esk5_2(X1,equal_set_predicate),esk4_2(X1,equal_set_predicate))
| member(X2,esk7_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_41]),c_0_24])]) ).
cnf(c_0_47,hypothesis,
( ~ member(X2,esk7_2(X1,equal_set_predicate))
| member(X2,esk8_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,hypothesis,
( ~ member(X2,esk6_2(X1,equal_set_predicate))
| ~ apply(equal_set_predicate,esk5_2(X1,equal_set_predicate),esk4_2(X1,equal_set_predicate))
| member(X2,esk7_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_45]),c_0_24])]) ).
cnf(c_0_49,hypothesis,
( ~ member(X2,esk7_2(X1,equal_set_predicate))
| ~ apply(equal_set_predicate,esk5_2(X1,equal_set_predicate),esk4_2(X1,equal_set_predicate))
| member(X2,esk6_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_45]),c_0_24])]) ).
cnf(c_0_50,hypothesis,
( ~ member(X2,esk8_2(X1,equal_set_predicate))
| member(X2,esk7_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_44]) ).
cnf(c_0_51,hypothesis,
( ~ member(esk2_2(X2,esk8_2(X1,equal_set_predicate)),esk7_2(X1,equal_set_predicate))
| subset(X2,esk8_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_47]) ).
cnf(c_0_52,hypothesis,
( ~ member(X2,esk6_2(X1,equal_set_predicate))
| member(X2,esk7_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_44]) ).
cnf(c_0_53,hypothesis,
( ~ member(X2,esk7_2(X1,equal_set_predicate))
| member(X2,esk6_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_44]) ).
cnf(c_0_54,hypothesis,
( subset(esk8_2(X1,equal_set_predicate),X2)
| member(esk2_2(esk8_2(X1,equal_set_predicate),X2),esk7_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_14]) ).
cnf(c_0_55,hypothesis,
( ~ member(esk2_2(X2,esk8_2(X1,equal_set_predicate)),esk6_2(X1,equal_set_predicate))
| subset(X2,esk8_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,hypothesis,
( subset(esk8_2(X1,equal_set_predicate),X2)
| member(esk2_2(esk8_2(X1,equal_set_predicate),X2),esk6_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
fof(c_0_57,negated_conjecture,
~ ! [X4] : equivalence(equal_set_predicate,power_set(X4)),
inference(assume_negation,[status(cth)],[thIII13]) ).
fof(c_0_58,axiom,
! [X1,X7] :
( equivalence(X7,X1)
<=> epred1_2(X7,X1) ),
inference(apply_def,[status(thm)],[equivalence,c_0_10]) ).
cnf(c_0_59,hypothesis,
( subset(esk6_2(X1,equal_set_predicate),esk8_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_14]) ).
cnf(c_0_60,hypothesis,
( subset(esk8_2(X1,equal_set_predicate),esk6_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_56]) ).
fof(c_0_61,negated_conjecture,
~ equivalence(equal_set_predicate,power_set(esk1_0)),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])])]) ).
fof(c_0_62,plain,
! [X13,X14] :
( ( equivalence(X14,X13)
| ~ epred1_2(X14,X13) )
& ( epred1_2(X14,X13)
| ~ equivalence(X14,X13) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_58])])]) ).
cnf(c_0_63,hypothesis,
( apply(equal_set_predicate,esk8_2(X1,equal_set_predicate),esk6_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_59]),c_0_60]) ).
cnf(c_0_64,negated_conjecture,
~ equivalence(equal_set_predicate,power_set(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_65,plain,
( ~ epred1_2(X1,X2)
| equivalence(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_66,plain,
( ~ apply(X1,esk3_2(X2,X1),esk3_2(X2,X1))
| ~ apply(X1,esk5_2(X2,X1),esk4_2(X2,X1))
| ~ apply(X1,esk6_2(X2,X1),esk8_2(X2,X1))
| epred1_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_67,hypothesis,
( apply(equal_set_predicate,esk6_2(X1,equal_set_predicate),esk8_2(X1,equal_set_predicate))
| epred1_2(equal_set_predicate,X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_63]) ).
cnf(c_0_68,negated_conjecture,
~ epred1_2(equal_set_predicate,power_set(esk1_0)),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_69,plain,
epred1_2(equal_set_predicate,X1),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_24])]),c_0_44]) ).
cnf(c_0_70,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_69])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET806+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/5.39 % Computer : n018.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Mon Sep 21 05:41:03 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/5.44 Running first-order theorem proving
% 0.16/5.44 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
% 0.16/5.64 % Version: 3.5.1
% 0.16/5.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/5.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/5.64 % Starting new_bool_3 with 300s (1) cores
% 0.16/5.64 % Starting new_bool_1 with 300s (1) cores
% 0.16/5.64 % Starting sh5l with 300s (1) cores
% 0.16/5.64 % new_bool_3 with pid 1079835 completed with status 0
% 0.16/5.64 % Result found by new_bool_3
% 0.16/5.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/5.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/5.64 % Starting new_bool_3 with 300s (1) cores
% 0.16/5.64 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/5.64 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/5.64 % Search class: FGUNF-FFMF21-SFFFFFNN
% 0.16/5.64 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/5.64 % Starting SubtermCWHack with 31s (1) cores
% 0.16/5.64 % SubtermCWHack with pid 1079838 completed with status 0
% 0.16/5.64 % Result found by SubtermCWHack
% 0.16/5.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/5.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/5.64 % Starting new_bool_3 with 300s (1) cores
% 0.16/5.64 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/5.64 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/5.64 % Search class: FGUNF-FFMF21-SFFFFFNN
% 0.16/5.64 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/5.64 % Starting SubtermCWHack with 31s (1) cores
% 0.16/5.64 % Preprocessing time : 0.002 s
% 0.16/5.64
% 0.16/5.64 % Proof found!
% 0.16/5.64 % SZS status Theorem
% 0.16/5.64 % SZS output start CNFRefutation
% See solution above
% 0.16/5.64 % Parsed axioms : 18
% 0.16/5.64 % Removed by relevancy pruning/SinE : 12
% 0.16/5.64 % Initial clauses : 64
% 0.16/5.64 % Removed in clause preprocessing : 0
% 0.16/5.64 % Initial clauses in saturation : 64
% 0.16/5.64 % Processed clauses : 972
% 0.16/5.64 % ...of these trivial : 0
% 0.16/5.64 % ...subsumed : 408
% 0.16/5.64 % ...remaining for further processing : 564
% 0.16/5.64 % Other redundant clauses eliminated : 0
% 0.16/5.64 % Clauses deleted for lack of memory : 0
% 0.16/5.64 % Backward-subsumed : 224
% 0.16/5.64 % Backward-rewritten : 193
% 0.16/5.64 % Generated clauses : 6580
% 0.16/5.64 % ...of the previous two non-redundant : 6472
% 0.16/5.64 % ...aggressively subsumed : 0
% 0.16/5.64 % Contextual simplify-reflections : 17
% 0.16/5.64 % Paramodulations : 6580
% 0.16/5.64 % Factorizations : 0
% 0.16/5.64 % NegExts : 0
% 0.16/5.64 % Equation resolutions : 0
% 0.16/5.64 % Disequality decompositions : 0
% 0.16/5.64 % Total rewrite steps : 182
% 0.16/5.64 % ...of those cached : 144
% 0.16/5.64 % Propositional unsat checks : 0
% 0.16/5.64 % Propositional check models : 0
% 0.16/5.64 % Propositional check unsatisfiable : 0
% 0.16/5.64 % Propositional clauses : 0
% 0.16/5.64 % Propositional clauses after purity: 0
% 0.16/5.64 % Propositional unsat core size : 0
% 0.16/5.64 % Propositional preprocessing time : 0.000
% 0.16/5.64 % Propositional encoding time : 0.000
% 0.16/5.64 % Propositional solver time : 0.000
% 0.16/5.64 % Success case prop preproc time : 0.000
% 0.16/5.64 % Success case prop encoding time : 0.000
% 0.16/5.64 % Success case prop solver time : 0.000
% 0.16/5.64 % Current number of processed clauses : 147
% 0.16/5.64 % Positive orientable unit clauses : 3
% 0.16/5.64 % Positive unorientable unit clauses: 0
% 0.16/5.64 % Negative unit clauses : 1
% 0.16/5.64 % Non-unit-clauses : 143
% 0.16/5.64 % Current number of unprocessed clauses: 4892
% 0.16/5.64 % ...number of literals in the above : 25538
% 0.16/5.64 % Current number of archived formulas : 0
% 0.16/5.64 % Current number of archived clauses : 417
% 0.16/5.64 % Clause-clause subsumption calls (NU) : 63222
% 0.16/5.64 % Rec. Clause-clause subsumption calls : 14106
% 0.16/5.64 % Non-unit clause-clause subsumptions : 649
% 0.16/5.64 % Unit Clause-clause subsumption calls : 111
% 0.16/5.64 % Rewrite failures with RHS unbound : 0
% 0.16/5.64 % BW rewrite match attempts : 25
% 0.16/5.64 % BW rewrite match successes : 20
% 0.16/5.64 % Condensation attempts : 0
% 0.16/5.64 % Condensation successes : 0
% 0.16/5.64 % Termbank termtop insertions : 221553
% 0.16/5.64 % Search garbage collected termcells : 789
% 0.16/5.64
% 0.16/5.64 % -------------------------------------------------
% 0.16/5.64 % User time : 0.161 s
% 0.16/5.64 % System time : 0.013 s
% 0.16/5.64 % Total time : 0.174 s
% 0.16/5.64 % Maximum resident set size: 3612 pages
% 0.16/5.64
% 0.16/5.64 % -------------------------------------------------
% 0.16/5.64 % User time : 0.165 s
% 0.16/5.64 % System time : 0.016 s
% 0.16/5.64 % Total time : 0.181 s
% 0.16/5.64 % Maximum resident set size: 4608 pages
% 0.16/5.64 % E exiting
%------------------------------------------------------------------------------