%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET806+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n029.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 : 600s
% DateTime : Tue Jul 19 00:54:29 EDT 2022
% Result : Theorem 0.23s 1.42s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 72 ( 9 unt; 0 def)
% Number of atoms : 442 ( 0 equ)
% Maximal formula atoms : 207 ( 6 avg)
% Number of connectives : 499 ( 129 ~; 284 |; 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 : 147 ( 11 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rel_equal_set,hypothesis,
! [X3,X5] :
( apply(equal_set_predicate,X3,X5)
<=> equal_set(X3,X5) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',rel_equal_set) ).
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(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(thIII13,conjecture,
! [X4] : equivalence(equal_set_predicate,power_set(X4)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',thIII13) ).
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(c_0_5,hypothesis,
! [X6,X7,X6,X7] :
( ( ~ apply(equal_set_predicate,X6,X7)
| equal_set(X6,X7) )
& ( ~ equal_set(X6,X7)
| apply(equal_set_predicate,X6,X7) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rel_equal_set])])])]) ).
fof(c_0_6,plain,
! [X3,X4,X3,X4] :
( ( subset(X3,X4)
| ~ equal_set(X3,X4) )
& ( subset(X4,X3)
| ~ equal_set(X3,X4) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| equal_set(X3,X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])])])]) ).
fof(c_0_7,plain,
! [X4,X5,X6,X4,X5] :
( ( ~ subset(X4,X5)
| ~ member(X6,X4)
| member(X6,X5) )
& ( member(esk2_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ member(esk2_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subset])])])])])])]) ).
cnf(c_0_8,hypothesis,
( apply(equal_set_predicate,X1,X2)
| ~ equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( equal_set(X1,X2)
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( subset(X1,X2)
| ~ equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,hypothesis,
( equal_set(X1,X2)
| ~ apply(equal_set_predicate,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,plain,
( subset(X2,X1)
| ~ equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_13,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) ).
cnf(c_0_14,plain,
( subset(X1,X2)
| ~ member(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,plain,
( subset(X1,X2)
| member(esk2_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,hypothesis,
( apply(equal_set_predicate,X1,X2)
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_17,hypothesis,
( subset(X1,X2)
| ~ apply(equal_set_predicate,X1,X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_18,hypothesis,
( subset(X1,X2)
| ~ apply(equal_set_predicate,X2,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
fof(c_0_19,plain,
! [X8,X9,X10,X11,X12,X13,X14,X15,X8,X9] :
( ( ~ member(X10,X8)
| apply(X9,X10,X10)
| ~ epred1_2(X9,X8) )
& ( ~ member(X11,X8)
| ~ member(X12,X8)
| ~ apply(X9,X11,X12)
| apply(X9,X12,X11)
| ~ epred1_2(X9,X8) )
& ( ~ member(X13,X8)
| ~ member(X14,X8)
| ~ member(X15,X8)
| ~ apply(X9,X13,X14)
| ~ apply(X9,X14,X15)
| apply(X9,X13,X15)
| ~ epred1_2(X9,X8) )
& ( member(esk6_2(X8,X9),X8)
| member(esk4_2(X8,X9),X8)
| member(esk3_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk7_2(X8,X9),X8)
| member(esk4_2(X8,X9),X8)
| member(esk3_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk8_2(X8,X9),X8)
| member(esk4_2(X8,X9),X8)
| member(esk3_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( apply(X9,esk6_2(X8,X9),esk7_2(X8,X9))
| member(esk4_2(X8,X9),X8)
| member(esk3_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( apply(X9,esk7_2(X8,X9),esk8_2(X8,X9))
| member(esk4_2(X8,X9),X8)
| member(esk3_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( ~ apply(X9,esk6_2(X8,X9),esk8_2(X8,X9))
| member(esk4_2(X8,X9),X8)
| member(esk3_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk6_2(X8,X9),X8)
| member(esk5_2(X8,X9),X8)
| member(esk3_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk7_2(X8,X9),X8)
| member(esk5_2(X8,X9),X8)
| member(esk3_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk8_2(X8,X9),X8)
| member(esk5_2(X8,X9),X8)
| member(esk3_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( apply(X9,esk6_2(X8,X9),esk7_2(X8,X9))
| member(esk5_2(X8,X9),X8)
| member(esk3_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( apply(X9,esk7_2(X8,X9),esk8_2(X8,X9))
| member(esk5_2(X8,X9),X8)
| member(esk3_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( ~ apply(X9,esk6_2(X8,X9),esk8_2(X8,X9))
| member(esk5_2(X8,X9),X8)
| member(esk3_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk6_2(X8,X9),X8)
| apply(X9,esk4_2(X8,X9),esk5_2(X8,X9))
| member(esk3_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk7_2(X8,X9),X8)
| apply(X9,esk4_2(X8,X9),esk5_2(X8,X9))
| member(esk3_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk8_2(X8,X9),X8)
| apply(X9,esk4_2(X8,X9),esk5_2(X8,X9))
| member(esk3_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( apply(X9,esk6_2(X8,X9),esk7_2(X8,X9))
| apply(X9,esk4_2(X8,X9),esk5_2(X8,X9))
| member(esk3_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( apply(X9,esk7_2(X8,X9),esk8_2(X8,X9))
| apply(X9,esk4_2(X8,X9),esk5_2(X8,X9))
| member(esk3_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( ~ apply(X9,esk6_2(X8,X9),esk8_2(X8,X9))
| apply(X9,esk4_2(X8,X9),esk5_2(X8,X9))
| member(esk3_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk6_2(X8,X9),X8)
| ~ apply(X9,esk5_2(X8,X9),esk4_2(X8,X9))
| member(esk3_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk7_2(X8,X9),X8)
| ~ apply(X9,esk5_2(X8,X9),esk4_2(X8,X9))
| member(esk3_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk8_2(X8,X9),X8)
| ~ apply(X9,esk5_2(X8,X9),esk4_2(X8,X9))
| member(esk3_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( apply(X9,esk6_2(X8,X9),esk7_2(X8,X9))
| ~ apply(X9,esk5_2(X8,X9),esk4_2(X8,X9))
| member(esk3_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( apply(X9,esk7_2(X8,X9),esk8_2(X8,X9))
| ~ apply(X9,esk5_2(X8,X9),esk4_2(X8,X9))
| member(esk3_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( ~ apply(X9,esk6_2(X8,X9),esk8_2(X8,X9))
| ~ apply(X9,esk5_2(X8,X9),esk4_2(X8,X9))
| member(esk3_2(X8,X9),X8)
| epred1_2(X9,X8) )
& ( member(esk6_2(X8,X9),X8)
| member(esk4_2(X8,X9),X8)
| ~ apply(X9,esk3_2(X8,X9),esk3_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk7_2(X8,X9),X8)
| member(esk4_2(X8,X9),X8)
| ~ apply(X9,esk3_2(X8,X9),esk3_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk8_2(X8,X9),X8)
| member(esk4_2(X8,X9),X8)
| ~ apply(X9,esk3_2(X8,X9),esk3_2(X8,X9))
| epred1_2(X9,X8) )
& ( apply(X9,esk6_2(X8,X9),esk7_2(X8,X9))
| member(esk4_2(X8,X9),X8)
| ~ apply(X9,esk3_2(X8,X9),esk3_2(X8,X9))
| epred1_2(X9,X8) )
& ( apply(X9,esk7_2(X8,X9),esk8_2(X8,X9))
| member(esk4_2(X8,X9),X8)
| ~ apply(X9,esk3_2(X8,X9),esk3_2(X8,X9))
| epred1_2(X9,X8) )
& ( ~ apply(X9,esk6_2(X8,X9),esk8_2(X8,X9))
| member(esk4_2(X8,X9),X8)
| ~ apply(X9,esk3_2(X8,X9),esk3_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk6_2(X8,X9),X8)
| member(esk5_2(X8,X9),X8)
| ~ apply(X9,esk3_2(X8,X9),esk3_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk7_2(X8,X9),X8)
| member(esk5_2(X8,X9),X8)
| ~ apply(X9,esk3_2(X8,X9),esk3_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk8_2(X8,X9),X8)
| member(esk5_2(X8,X9),X8)
| ~ apply(X9,esk3_2(X8,X9),esk3_2(X8,X9))
| epred1_2(X9,X8) )
& ( apply(X9,esk6_2(X8,X9),esk7_2(X8,X9))
| member(esk5_2(X8,X9),X8)
| ~ apply(X9,esk3_2(X8,X9),esk3_2(X8,X9))
| epred1_2(X9,X8) )
& ( apply(X9,esk7_2(X8,X9),esk8_2(X8,X9))
| member(esk5_2(X8,X9),X8)
| ~ apply(X9,esk3_2(X8,X9),esk3_2(X8,X9))
| epred1_2(X9,X8) )
& ( ~ apply(X9,esk6_2(X8,X9),esk8_2(X8,X9))
| member(esk5_2(X8,X9),X8)
| ~ apply(X9,esk3_2(X8,X9),esk3_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk6_2(X8,X9),X8)
| apply(X9,esk4_2(X8,X9),esk5_2(X8,X9))
| ~ apply(X9,esk3_2(X8,X9),esk3_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk7_2(X8,X9),X8)
| apply(X9,esk4_2(X8,X9),esk5_2(X8,X9))
| ~ apply(X9,esk3_2(X8,X9),esk3_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk8_2(X8,X9),X8)
| apply(X9,esk4_2(X8,X9),esk5_2(X8,X9))
| ~ apply(X9,esk3_2(X8,X9),esk3_2(X8,X9))
| epred1_2(X9,X8) )
& ( apply(X9,esk6_2(X8,X9),esk7_2(X8,X9))
| apply(X9,esk4_2(X8,X9),esk5_2(X8,X9))
| ~ apply(X9,esk3_2(X8,X9),esk3_2(X8,X9))
| epred1_2(X9,X8) )
& ( apply(X9,esk7_2(X8,X9),esk8_2(X8,X9))
| apply(X9,esk4_2(X8,X9),esk5_2(X8,X9))
| ~ apply(X9,esk3_2(X8,X9),esk3_2(X8,X9))
| epred1_2(X9,X8) )
& ( ~ apply(X9,esk6_2(X8,X9),esk8_2(X8,X9))
| apply(X9,esk4_2(X8,X9),esk5_2(X8,X9))
| ~ apply(X9,esk3_2(X8,X9),esk3_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk6_2(X8,X9),X8)
| ~ apply(X9,esk5_2(X8,X9),esk4_2(X8,X9))
| ~ apply(X9,esk3_2(X8,X9),esk3_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk7_2(X8,X9),X8)
| ~ apply(X9,esk5_2(X8,X9),esk4_2(X8,X9))
| ~ apply(X9,esk3_2(X8,X9),esk3_2(X8,X9))
| epred1_2(X9,X8) )
& ( member(esk8_2(X8,X9),X8)
| ~ apply(X9,esk5_2(X8,X9),esk4_2(X8,X9))
| ~ apply(X9,esk3_2(X8,X9),esk3_2(X8,X9))
| epred1_2(X9,X8) )
& ( apply(X9,esk6_2(X8,X9),esk7_2(X8,X9))
| ~ apply(X9,esk5_2(X8,X9),esk4_2(X8,X9))
| ~ apply(X9,esk3_2(X8,X9),esk3_2(X8,X9))
| epred1_2(X9,X8) )
& ( apply(X9,esk7_2(X8,X9),esk8_2(X8,X9))
| ~ apply(X9,esk5_2(X8,X9),esk4_2(X8,X9))
| ~ apply(X9,esk3_2(X8,X9),esk3_2(X8,X9))
| epred1_2(X9,X8) )
& ( ~ apply(X9,esk6_2(X8,X9),esk8_2(X8,X9))
| ~ apply(X9,esk5_2(X8,X9),esk4_2(X8,X9))
| ~ apply(X9,esk3_2(X8,X9),esk3_2(X8,X9))
| epred1_2(X9,X8) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])])])])]) ).
cnf(c_0_20,plain,
subset(X1,X1),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,hypothesis,
( apply(equal_set_predicate,X1,X2)
| ~ apply(equal_set_predicate,X2,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_23,plain,
( epred1_2(X1,X2)
| apply(X1,esk4_2(X2,X1),esk5_2(X2,X1))
| apply(X1,esk7_2(X2,X1),esk8_2(X2,X1))
| ~ apply(X1,esk3_2(X2,X1),esk3_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
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_16,c_0_20]),c_0_20])]) ).
cnf(c_0_25,plain,
( epred1_2(X1,X2)
| apply(X1,esk7_2(X2,X1),esk8_2(X2,X1))
| ~ apply(X1,esk3_2(X2,X1),esk3_2(X2,X1))
| ~ apply(X1,esk5_2(X2,X1),esk4_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,hypothesis,
( member(X1,X2)
| ~ apply(equal_set_predicate,X2,X3)
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_18]) ).
cnf(c_0_27,plain,
( epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| apply(equal_set_predicate,esk8_2(X1,equal_set_predicate),esk7_2(X1,equal_set_predicate)) ),
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,plain,
( epred1_2(X1,X2)
| apply(X1,esk4_2(X2,X1),esk5_2(X2,X1))
| apply(X1,esk6_2(X2,X1),esk7_2(X2,X1))
| ~ apply(X1,esk3_2(X2,X1),esk3_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,plain,
( epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk8_2(X1,equal_set_predicate),esk7_2(X1,equal_set_predicate))
| ~ apply(equal_set_predicate,esk5_2(X1,equal_set_predicate),esk4_2(X1,equal_set_predicate)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_25]),c_0_24])]) ).
cnf(c_0_30,plain,
( epred1_2(X1,X2)
| apply(X1,esk6_2(X2,X1),esk7_2(X2,X1))
| ~ apply(X1,esk3_2(X2,X1),esk3_2(X2,X1))
| ~ apply(X1,esk5_2(X2,X1),esk4_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_31,hypothesis,
( epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| member(X2,esk8_2(X1,equal_set_predicate))
| ~ member(X2,esk7_2(X1,equal_set_predicate)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
( epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| apply(equal_set_predicate,esk7_2(X1,equal_set_predicate),esk6_2(X1,equal_set_predicate)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_28]),c_0_24])]) ).
cnf(c_0_33,hypothesis,
( epred1_2(equal_set_predicate,X1)
| 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)) ),
inference(spm,[status(thm)],[c_0_26,c_0_29]) ).
cnf(c_0_34,plain,
( epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk7_2(X1,equal_set_predicate),esk6_2(X1,equal_set_predicate))
| ~ apply(equal_set_predicate,esk5_2(X1,equal_set_predicate),esk4_2(X1,equal_set_predicate)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_30]),c_0_24])]) ).
cnf(c_0_35,hypothesis,
( epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| subset(X2,esk8_2(X1,equal_set_predicate))
| ~ member(esk2_2(X2,esk8_2(X1,equal_set_predicate)),esk7_2(X1,equal_set_predicate)) ),
inference(spm,[status(thm)],[c_0_14,c_0_31]) ).
cnf(c_0_36,hypothesis,
( epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| member(X2,esk7_2(X1,equal_set_predicate))
| ~ member(X2,esk6_2(X1,equal_set_predicate)) ),
inference(spm,[status(thm)],[c_0_26,c_0_32]) ).
cnf(c_0_37,plain,
( epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| member(X2,esk7_2(X1,equal_set_predicate))
| ~ member(X2,esk8_2(X1,equal_set_predicate)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_23]),c_0_24])]) ).
cnf(c_0_38,hypothesis,
( epred1_2(equal_set_predicate,X1)
| subset(X2,esk8_2(X1,equal_set_predicate))
| ~ apply(equal_set_predicate,esk5_2(X1,equal_set_predicate),esk4_2(X1,equal_set_predicate))
| ~ member(esk2_2(X2,esk8_2(X1,equal_set_predicate)),esk7_2(X1,equal_set_predicate)) ),
inference(spm,[status(thm)],[c_0_14,c_0_33]) ).
cnf(c_0_39,hypothesis,
( epred1_2(equal_set_predicate,X1)
| 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)) ),
inference(spm,[status(thm)],[c_0_26,c_0_34]) ).
cnf(c_0_40,plain,
( epred1_2(equal_set_predicate,X1)
| 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)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_25]),c_0_24])]) ).
cnf(c_0_41,hypothesis,
( epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| subset(X2,esk8_2(X1,equal_set_predicate))
| ~ member(esk2_2(X2,esk8_2(X1,equal_set_predicate)),esk6_2(X1,equal_set_predicate)) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,plain,
( epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| member(X2,esk6_2(X1,equal_set_predicate))
| ~ member(X2,esk7_2(X1,equal_set_predicate)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_28]),c_0_24])]) ).
cnf(c_0_43,plain,
( epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| member(esk2_2(esk8_2(X1,equal_set_predicate),X2),esk7_2(X1,equal_set_predicate))
| subset(esk8_2(X1,equal_set_predicate),X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_15]) ).
cnf(c_0_44,hypothesis,
( epred1_2(equal_set_predicate,X1)
| subset(X2,esk8_2(X1,equal_set_predicate))
| ~ apply(equal_set_predicate,esk5_2(X1,equal_set_predicate),esk4_2(X1,equal_set_predicate))
| ~ member(esk2_2(X2,esk8_2(X1,equal_set_predicate)),esk6_2(X1,equal_set_predicate)) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_45,plain,
( epred1_2(equal_set_predicate,X1)
| 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)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_30]),c_0_24])]) ).
cnf(c_0_46,plain,
( epred1_2(equal_set_predicate,X1)
| member(esk2_2(esk8_2(X1,equal_set_predicate),X2),esk7_2(X1,equal_set_predicate))
| subset(esk8_2(X1,equal_set_predicate),X2)
| ~ apply(equal_set_predicate,esk5_2(X1,equal_set_predicate),esk4_2(X1,equal_set_predicate)) ),
inference(spm,[status(thm)],[c_0_40,c_0_15]) ).
cnf(c_0_47,hypothesis,
( epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| subset(esk6_2(X1,equal_set_predicate),esk8_2(X1,equal_set_predicate)) ),
inference(spm,[status(thm)],[c_0_41,c_0_15]) ).
cnf(c_0_48,plain,
( epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| member(esk2_2(esk8_2(X1,equal_set_predicate),X2),esk6_2(X1,equal_set_predicate))
| subset(esk8_2(X1,equal_set_predicate),X2) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,hypothesis,
( epred1_2(equal_set_predicate,X1)
| subset(esk6_2(X1,equal_set_predicate),esk8_2(X1,equal_set_predicate))
| ~ apply(equal_set_predicate,esk5_2(X1,equal_set_predicate),esk4_2(X1,equal_set_predicate)) ),
inference(spm,[status(thm)],[c_0_44,c_0_15]) ).
cnf(c_0_50,plain,
( epred1_2(equal_set_predicate,X1)
| member(esk2_2(esk8_2(X1,equal_set_predicate),X2),esk6_2(X1,equal_set_predicate))
| subset(esk8_2(X1,equal_set_predicate),X2)
| ~ apply(equal_set_predicate,esk5_2(X1,equal_set_predicate),esk4_2(X1,equal_set_predicate)) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,hypothesis,
( epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| apply(equal_set_predicate,esk8_2(X1,equal_set_predicate),esk6_2(X1,equal_set_predicate))
| ~ subset(esk8_2(X1,equal_set_predicate),esk6_2(X1,equal_set_predicate)) ),
inference(spm,[status(thm)],[c_0_16,c_0_47]) ).
cnf(c_0_52,plain,
( epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| subset(esk8_2(X1,equal_set_predicate),esk6_2(X1,equal_set_predicate)) ),
inference(spm,[status(thm)],[c_0_14,c_0_48]) ).
cnf(c_0_53,hypothesis,
( epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk8_2(X1,equal_set_predicate),esk6_2(X1,equal_set_predicate))
| ~ apply(equal_set_predicate,esk5_2(X1,equal_set_predicate),esk4_2(X1,equal_set_predicate))
| ~ subset(esk8_2(X1,equal_set_predicate),esk6_2(X1,equal_set_predicate)) ),
inference(spm,[status(thm)],[c_0_16,c_0_49]) ).
cnf(c_0_54,plain,
( epred1_2(equal_set_predicate,X1)
| subset(esk8_2(X1,equal_set_predicate),esk6_2(X1,equal_set_predicate))
| ~ apply(equal_set_predicate,esk5_2(X1,equal_set_predicate),esk4_2(X1,equal_set_predicate)) ),
inference(spm,[status(thm)],[c_0_14,c_0_50]) ).
fof(c_0_55,negated_conjecture,
~ ! [X4] : equivalence(equal_set_predicate,power_set(X4)),
inference(assume_negation,[status(cth)],[thIII13]) ).
fof(c_0_56,axiom,
! [X1,X7] :
( equivalence(X7,X1)
<=> epred1_2(X7,X1) ),
inference(apply_def,[status(thm)],[equivalence,c_0_13]) ).
cnf(c_0_57,hypothesis,
( epred1_2(equal_set_predicate,X1)
| 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)) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_58,hypothesis,
( epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk8_2(X1,equal_set_predicate),esk6_2(X1,equal_set_predicate))
| ~ apply(equal_set_predicate,esk5_2(X1,equal_set_predicate),esk4_2(X1,equal_set_predicate)) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
fof(c_0_59,negated_conjecture,
~ equivalence(equal_set_predicate,power_set(esk1_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])]) ).
fof(c_0_60,plain,
! [X8,X9,X8,X9] :
( ( ~ equivalence(X9,X8)
| epred1_2(X9,X8) )
& ( ~ epred1_2(X9,X8)
| equivalence(X9,X8) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_56])])])]) ).
cnf(c_0_61,plain,
( epred1_2(X1,X2)
| apply(X1,esk4_2(X2,X1),esk5_2(X2,X1))
| ~ apply(X1,esk3_2(X2,X1),esk3_2(X2,X1))
| ~ apply(X1,esk6_2(X2,X1),esk8_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_62,hypothesis,
( epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate))
| apply(equal_set_predicate,esk6_2(X1,equal_set_predicate),esk8_2(X1,equal_set_predicate)) ),
inference(spm,[status(thm)],[c_0_22,c_0_57]) ).
cnf(c_0_63,plain,
( epred1_2(X1,X2)
| ~ 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)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_64,hypothesis,
( epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk6_2(X1,equal_set_predicate),esk8_2(X1,equal_set_predicate))
| ~ apply(equal_set_predicate,esk5_2(X1,equal_set_predicate),esk4_2(X1,equal_set_predicate)) ),
inference(spm,[status(thm)],[c_0_22,c_0_58]) ).
cnf(c_0_65,negated_conjecture,
~ equivalence(equal_set_predicate,power_set(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_66,plain,
( equivalence(X1,X2)
| ~ epred1_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_67,plain,
( epred1_2(equal_set_predicate,X1)
| apply(equal_set_predicate,esk4_2(X1,equal_set_predicate),esk5_2(X1,equal_set_predicate)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_24])]) ).
cnf(c_0_68,plain,
( epred1_2(equal_set_predicate,X1)
| ~ apply(equal_set_predicate,esk5_2(X1,equal_set_predicate),esk4_2(X1,equal_set_predicate)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_24])]) ).
cnf(c_0_69,negated_conjecture,
~ epred1_2(equal_set_predicate,power_set(esk1_0)),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_70,hypothesis,
epred1_2(equal_set_predicate,X1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_67]),c_0_68]) ).
cnf(c_0_71,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET806+4 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 9 16:40:00 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.23/1.42 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.23/1.42 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.23/1.42 # Preprocessing time : 0.016 s
% 0.23/1.42
% 0.23/1.42 # Proof found!
% 0.23/1.42 # SZS status Theorem
% 0.23/1.42 # SZS output start CNFRefutation
% See solution above
% 0.23/1.42 # Proof object total steps : 72
% 0.23/1.42 # Proof object clause steps : 58
% 0.23/1.42 # Proof object formula steps : 14
% 0.23/1.42 # Proof object conjectures : 6
% 0.23/1.42 # Proof object clause conjectures : 3
% 0.23/1.42 # Proof object formula conjectures : 3
% 0.23/1.42 # Proof object initial clauses used : 16
% 0.23/1.42 # Proof object initial formulas used : 5
% 0.23/1.42 # Proof object generating inferences : 41
% 0.23/1.42 # Proof object simplifying inferences : 26
% 0.23/1.42 # Training examples: 0 positive, 0 negative
% 0.23/1.42 # Parsed axioms : 18
% 0.23/1.42 # Removed by relevancy pruning/SinE : 12
% 0.23/1.42 # Initial clauses : 64
% 0.23/1.42 # Removed in clause preprocessing : 0
% 0.23/1.42 # Initial clauses in saturation : 64
% 0.23/1.42 # Processed clauses : 1097
% 0.23/1.42 # ...of these trivial : 0
% 0.23/1.42 # ...subsumed : 477
% 0.23/1.42 # ...remaining for further processing : 620
% 0.23/1.42 # Other redundant clauses eliminated : 0
% 0.23/1.42 # Clauses deleted for lack of memory : 0
% 0.23/1.42 # Backward-subsumed : 211
% 0.23/1.42 # Backward-rewritten : 183
% 0.23/1.42 # Generated clauses : 12041
% 0.23/1.42 # ...of the previous two non-trivial : 11531
% 0.23/1.42 # Contextual simplify-reflections : 319
% 0.23/1.42 # Paramodulations : 12041
% 0.23/1.42 # Factorizations : 0
% 0.23/1.42 # Equation resolutions : 0
% 0.23/1.42 # Current number of processed clauses : 226
% 0.23/1.42 # Positive orientable unit clauses : 4
% 0.23/1.42 # Positive unorientable unit clauses: 0
% 0.23/1.42 # Negative unit clauses : 1
% 0.23/1.42 # Non-unit-clauses : 221
% 0.23/1.42 # Current number of unprocessed clauses: 1327
% 0.23/1.42 # ...number of literals in the above : 9572
% 0.23/1.42 # Current number of archived formulas : 0
% 0.23/1.42 # Current number of archived clauses : 394
% 0.23/1.42 # Clause-clause subsumption calls (NU) : 106413
% 0.23/1.42 # Rec. Clause-clause subsumption calls : 22638
% 0.23/1.42 # Non-unit clause-clause subsumptions : 1007
% 0.23/1.42 # Unit Clause-clause subsumption calls : 323
% 0.23/1.42 # Rewrite failures with RHS unbound : 0
% 0.23/1.42 # BW rewrite match attempts : 54
% 0.23/1.42 # BW rewrite match successes : 47
% 0.23/1.42 # Condensation attempts : 0
% 0.23/1.42 # Condensation successes : 0
% 0.23/1.42 # Termbank termtop insertions : 567163
% 0.23/1.42
% 0.23/1.42 # -------------------------------------------------
% 0.23/1.42 # User time : 0.351 s
% 0.23/1.42 # System time : 0.007 s
% 0.23/1.42 # Total time : 0.358 s
% 0.23/1.42 # Maximum resident set size: 13928 pages
% 0.23/23.41 eprover: CPU time limit exceeded, terminating
% 0.23/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.43 eprover: No such file or directory
% 0.23/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.43 eprover: No such file or directory
% 0.23/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.43 eprover: No such file or directory
% 0.23/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.44 eprover: No such file or directory
% 0.23/23.44 eprover: CPU time limit exceeded, terminating
% 0.23/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.44 eprover: No such file or directory
% 0.23/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.45 eprover: No such file or directory
% 0.23/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.45 eprover: No such file or directory
% 0.23/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.45 eprover: No such file or directory
% 0.23/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.46 eprover: No such file or directory
% 0.23/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.46 eprover: No such file or directory
% 0.23/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.46 eprover: No such file or directory
% 0.23/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.46 eprover: No such file or directory
% 0.23/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.46 eprover: No such file or directory
% 0.23/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.46 eprover: No such file or directory
% 0.23/23.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.47 eprover: No such file or directory
% 0.23/23.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.47 eprover: No such file or directory
% 0.23/23.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.48 eprover: No such file or directory
% 0.23/23.49 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.49 eprover: No such file or directory
% 0.23/23.49 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.49 eprover: No such file or directory
% 0.23/23.50 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.50 eprover: No such file or directory
% 0.23/23.50 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.50 eprover: No such file or directory
% 0.23/23.51 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.51 eprover: No such file or directory
%------------------------------------------------------------------------------