TSTP Solution File: SET810+4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET810+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 14:35:38 EDT 2023
% Result : Theorem 3.24s 3.38s
% Output : CNFRefutation 3.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 42
% Syntax : Number of formulae : 65 ( 5 unt; 36 typ; 0 def)
% Number of atoms : 201 ( 0 equ)
% Maximal formula atoms : 84 ( 6 avg)
% Number of connectives : 237 ( 65 ~; 106 |; 53 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 60 ( 31 >; 29 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 28 ( 28 usr; 5 con; 0-3 aty)
% Number of variables : 73 ( 0 sgn; 47 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
subset: ( $i * $i ) > $o ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
equal_set: ( $i * $i ) > $o ).
tff(decl_25,type,
power_set: $i > $i ).
tff(decl_26,type,
intersection: ( $i * $i ) > $i ).
tff(decl_27,type,
union: ( $i * $i ) > $i ).
tff(decl_28,type,
empty_set: $i ).
tff(decl_29,type,
difference: ( $i * $i ) > $i ).
tff(decl_30,type,
singleton: $i > $i ).
tff(decl_31,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_32,type,
sum: $i > $i ).
tff(decl_33,type,
product: $i > $i ).
tff(decl_34,type,
on: $i ).
tff(decl_35,type,
set: $i > $o ).
tff(decl_36,type,
member_predicate: $i ).
tff(decl_37,type,
strict_well_order: ( $i * $i ) > $o ).
tff(decl_38,type,
strict_order: ( $i * $i ) > $o ).
tff(decl_39,type,
least: ( $i * $i * $i ) > $o ).
tff(decl_40,type,
apply: ( $i * $i * $i ) > $o ).
tff(decl_41,type,
initial_segment: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
suc: $i > $i ).
tff(decl_43,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_44,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_45,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_46,type,
esk4_1: $i > $i ).
tff(decl_47,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_48,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_51,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_53,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk13_2: ( $i * $i ) > $i ).
tff(decl_56,type,
esk14_0: $i ).
tff(decl_57,type,
esk15_0: $i ).
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(ordinal_number,axiom,
! [X1] :
( member(X1,on)
<=> ( set(X1)
& strict_well_order(member_predicate,X1)
& ! [X3] :
( member(X3,X1)
=> subset(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+4.ax',ordinal_number) ).
fof(thV3,conjecture,
! [X1,X2] :
( ( member(X1,on)
& member(X2,on) )
=> ~ ( member(X1,X2)
& member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thV3) ).
fof(strict_order,axiom,
! [X6,X4] :
( strict_order(X6,X4)
<=> ( ! [X3,X5] :
( ( member(X3,X4)
& member(X5,X4) )
=> ~ ( apply(X6,X3,X5)
& apply(X6,X5,X3) ) )
& ! [X3,X5,X8] :
( ( member(X3,X4)
& member(X5,X4)
& member(X8,X4) )
=> ( ( apply(X6,X3,X5)
& apply(X6,X5,X8) )
=> apply(X6,X3,X8) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+4.ax',strict_order) ).
fof(rel_member,axiom,
! [X3,X5] :
( apply(member_predicate,X3,X5)
<=> member(X3,X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+4.ax',rel_member) ).
fof(strict_well_order,axiom,
! [X6,X4] :
( strict_well_order(X6,X4)
<=> ( strict_order(X6,X4)
& ! [X1] :
( ( subset(X1,X4)
& ? [X3] : member(X3,X1) )
=> ? [X5] : least(X5,X6,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+4.ax',strict_well_order) ).
fof(c_0_6,plain,
! [X9,X10,X11,X12,X13] :
( ( ~ subset(X9,X10)
| ~ member(X11,X9)
| member(X11,X10) )
& ( member(esk1_2(X12,X13),X12)
| subset(X12,X13) )
& ( ~ member(esk1_2(X12,X13),X13)
| subset(X12,X13) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[subset])])])])])]) ).
fof(c_0_7,plain,
! [X46,X47,X48] :
( ( set(X46)
| ~ member(X46,on) )
& ( strict_well_order(member_predicate,X46)
| ~ member(X46,on) )
& ( ~ member(X47,X46)
| subset(X47,X46)
| ~ member(X46,on) )
& ( member(esk4_1(X48),X48)
| ~ set(X48)
| ~ strict_well_order(member_predicate,X48)
| member(X48,on) )
& ( ~ subset(esk4_1(X48),X48)
| ~ set(X48)
| ~ strict_well_order(member_predicate,X48)
| member(X48,on) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[ordinal_number])])])])])]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2] :
( ( member(X1,on)
& member(X2,on) )
=> ~ ( member(X1,X2)
& member(X2,X1) ) ),
inference(assume_negation,[status(cth)],[thV3]) ).
cnf(c_0_9,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( subset(X1,X2)
| ~ member(X1,X2)
| ~ member(X2,on) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,negated_conjecture,
( member(esk14_0,on)
& member(esk15_0,on)
& member(esk14_0,esk15_0)
& member(esk15_0,esk14_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
cnf(c_0_12,plain,
( member(X1,X2)
| ~ member(X2,on)
| ~ member(X1,X3)
| ~ member(X3,X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,negated_conjecture,
member(esk14_0,on),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_14,plain,
! [X70,X71,X72,X73,X74,X75,X76,X77,X78] :
( ( ~ member(X72,X71)
| ~ member(X73,X71)
| ~ apply(X70,X72,X73)
| ~ apply(X70,X73,X72)
| ~ strict_order(X70,X71) )
& ( ~ member(X74,X71)
| ~ member(X75,X71)
| ~ member(X76,X71)
| ~ apply(X70,X74,X75)
| ~ apply(X70,X75,X76)
| apply(X70,X74,X76)
| ~ strict_order(X70,X71) )
& ( member(esk11_2(X77,X78),X78)
| member(esk9_2(X77,X78),X78)
| strict_order(X77,X78) )
& ( member(esk12_2(X77,X78),X78)
| member(esk9_2(X77,X78),X78)
| strict_order(X77,X78) )
& ( member(esk13_2(X77,X78),X78)
| member(esk9_2(X77,X78),X78)
| strict_order(X77,X78) )
& ( apply(X77,esk11_2(X77,X78),esk12_2(X77,X78))
| member(esk9_2(X77,X78),X78)
| strict_order(X77,X78) )
& ( apply(X77,esk12_2(X77,X78),esk13_2(X77,X78))
| member(esk9_2(X77,X78),X78)
| strict_order(X77,X78) )
& ( ~ apply(X77,esk11_2(X77,X78),esk13_2(X77,X78))
| member(esk9_2(X77,X78),X78)
| strict_order(X77,X78) )
& ( member(esk11_2(X77,X78),X78)
| member(esk10_2(X77,X78),X78)
| strict_order(X77,X78) )
& ( member(esk12_2(X77,X78),X78)
| member(esk10_2(X77,X78),X78)
| strict_order(X77,X78) )
& ( member(esk13_2(X77,X78),X78)
| member(esk10_2(X77,X78),X78)
| strict_order(X77,X78) )
& ( apply(X77,esk11_2(X77,X78),esk12_2(X77,X78))
| member(esk10_2(X77,X78),X78)
| strict_order(X77,X78) )
& ( apply(X77,esk12_2(X77,X78),esk13_2(X77,X78))
| member(esk10_2(X77,X78),X78)
| strict_order(X77,X78) )
& ( ~ apply(X77,esk11_2(X77,X78),esk13_2(X77,X78))
| member(esk10_2(X77,X78),X78)
| strict_order(X77,X78) )
& ( member(esk11_2(X77,X78),X78)
| apply(X77,esk9_2(X77,X78),esk10_2(X77,X78))
| strict_order(X77,X78) )
& ( member(esk12_2(X77,X78),X78)
| apply(X77,esk9_2(X77,X78),esk10_2(X77,X78))
| strict_order(X77,X78) )
& ( member(esk13_2(X77,X78),X78)
| apply(X77,esk9_2(X77,X78),esk10_2(X77,X78))
| strict_order(X77,X78) )
& ( apply(X77,esk11_2(X77,X78),esk12_2(X77,X78))
| apply(X77,esk9_2(X77,X78),esk10_2(X77,X78))
| strict_order(X77,X78) )
& ( apply(X77,esk12_2(X77,X78),esk13_2(X77,X78))
| apply(X77,esk9_2(X77,X78),esk10_2(X77,X78))
| strict_order(X77,X78) )
& ( ~ apply(X77,esk11_2(X77,X78),esk13_2(X77,X78))
| apply(X77,esk9_2(X77,X78),esk10_2(X77,X78))
| strict_order(X77,X78) )
& ( member(esk11_2(X77,X78),X78)
| apply(X77,esk10_2(X77,X78),esk9_2(X77,X78))
| strict_order(X77,X78) )
& ( member(esk12_2(X77,X78),X78)
| apply(X77,esk10_2(X77,X78),esk9_2(X77,X78))
| strict_order(X77,X78) )
& ( member(esk13_2(X77,X78),X78)
| apply(X77,esk10_2(X77,X78),esk9_2(X77,X78))
| strict_order(X77,X78) )
& ( apply(X77,esk11_2(X77,X78),esk12_2(X77,X78))
| apply(X77,esk10_2(X77,X78),esk9_2(X77,X78))
| strict_order(X77,X78) )
& ( apply(X77,esk12_2(X77,X78),esk13_2(X77,X78))
| apply(X77,esk10_2(X77,X78),esk9_2(X77,X78))
| strict_order(X77,X78) )
& ( ~ apply(X77,esk11_2(X77,X78),esk13_2(X77,X78))
| apply(X77,esk10_2(X77,X78),esk9_2(X77,X78))
| strict_order(X77,X78) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[strict_order])])])])])]) ).
fof(c_0_15,plain,
! [X68,X69] :
( ( ~ apply(member_predicate,X68,X69)
| member(X68,X69) )
& ( ~ member(X68,X69)
| apply(member_predicate,X68,X69) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rel_member])]) ).
fof(c_0_16,plain,
! [X50,X51,X52,X53,X55,X56,X59] :
( ( strict_order(X50,X51)
| ~ strict_well_order(X50,X51) )
& ( ~ subset(X52,X51)
| ~ member(X53,X52)
| least(esk5_3(X50,X51,X52),X50,X52)
| ~ strict_well_order(X50,X51) )
& ( subset(esk6_2(X55,X56),X56)
| ~ strict_order(X55,X56)
| strict_well_order(X55,X56) )
& ( member(esk7_2(X55,X56),esk6_2(X55,X56))
| ~ strict_order(X55,X56)
| strict_well_order(X55,X56) )
& ( ~ least(X59,X55,esk6_2(X55,X56))
| ~ strict_order(X55,X56)
| strict_well_order(X55,X56) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[strict_well_order])])])])])]) ).
cnf(c_0_17,negated_conjecture,
( member(X1,esk14_0)
| ~ member(X2,esk14_0)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,negated_conjecture,
member(esk15_0,esk14_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
( ~ member(X1,X2)
| ~ member(X3,X2)
| ~ apply(X4,X1,X3)
| ~ apply(X4,X3,X1)
| ~ strict_order(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( apply(member_predicate,X1,X2)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
( strict_order(X1,X2)
| ~ strict_well_order(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( strict_well_order(member_predicate,X1)
| ~ member(X1,on) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_23,negated_conjecture,
( member(X1,esk14_0)
| ~ member(X1,esk15_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,negated_conjecture,
member(esk14_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_25,plain,
( ~ apply(member_predicate,X1,X2)
| ~ strict_order(member_predicate,X3)
| ~ member(X2,X3)
| ~ member(X1,X3)
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
( strict_order(member_predicate,X1)
| ~ member(X1,on) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,negated_conjecture,
member(esk14_0,esk14_0),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_25,c_0_26,c_0_20,c_0_27,c_0_13]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET810+4 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.15/0.35 % Computer : n018.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat Aug 26 11:23:29 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 3.24/3.38 % Version : CSE_E---1.5
% 3.24/3.38 % Problem : theBenchmark.p
% 3.24/3.38 % Proof found
% 3.24/3.38 % SZS status Theorem for theBenchmark.p
% 3.24/3.38 % SZS output start Proof
% See solution above
% 3.24/3.39 % Total time : 2.792000 s
% 3.24/3.39 % SZS output end Proof
% 3.24/3.39 % Total time : 2.796000 s
%------------------------------------------------------------------------------