TSTP Solution File: SET934+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET934+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n007.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 14:36:21 EDT 2023
% Result : Theorem 153.20s 153.16s
% Output : CNFRefutation 153.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 19
% Syntax : Number of formulae : 67 ( 18 unt; 12 typ; 0 def)
% Number of atoms : 139 ( 18 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 135 ( 51 ~; 66 |; 11 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 8 >; 7 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 148 ( 10 sgn; 47 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_24,type,
powerset: $i > $i ).
tff(decl_25,type,
subset: ( $i * $i ) > $o ).
tff(decl_26,type,
empty: $i > $o ).
tff(decl_27,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_28,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_30,type,
esk4_0: $i ).
tff(decl_31,type,
esk5_0: $i ).
tff(decl_32,type,
esk6_0: $i ).
tff(decl_33,type,
esk7_0: $i ).
fof(d1_zfmisc_1,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(t1_xboole_1,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(t7_xboole_1,axiom,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(t81_zfmisc_1,conjecture,
! [X1,X2] : subset(set_union2(powerset(X1),powerset(X2)),powerset(set_union2(X1,X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_zfmisc_1) ).
fof(c_0_7,plain,
! [X9,X10,X11,X12,X13,X14] :
( ( ~ in(X11,X10)
| subset(X11,X9)
| X10 != powerset(X9) )
& ( ~ subset(X12,X9)
| in(X12,X10)
| X10 != powerset(X9) )
& ( ~ in(esk1_2(X13,X14),X14)
| ~ subset(esk1_2(X13,X14),X13)
| X14 = powerset(X13) )
& ( in(esk1_2(X13,X14),X14)
| subset(esk1_2(X13,X14),X13)
| X14 = powerset(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)],[d1_zfmisc_1])])])])])]) ).
fof(c_0_8,plain,
! [X25,X26,X27,X28,X29] :
( ( ~ subset(X25,X26)
| ~ in(X27,X25)
| in(X27,X26) )
& ( in(esk3_2(X28,X29),X28)
| subset(X28,X29) )
& ( ~ in(esk3_2(X28,X29),X29)
| subset(X28,X29) ) ),
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)],[d3_tarski])])])])])]) ).
cnf(c_0_9,plain,
( in(X1,X3)
| ~ subset(X1,X2)
| X3 != powerset(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X39,X40,X41] :
( ~ subset(X39,X40)
| ~ subset(X40,X41)
| subset(X39,X41) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).
fof(c_0_11,plain,
! [X42,X43] : subset(X42,set_union2(X42,X43)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
fof(c_0_12,plain,
! [X16,X17,X18,X19,X20,X21,X22,X23] :
( ( ~ in(X19,X18)
| in(X19,X16)
| in(X19,X17)
| X18 != set_union2(X16,X17) )
& ( ~ in(X20,X16)
| in(X20,X18)
| X18 != set_union2(X16,X17) )
& ( ~ in(X20,X17)
| in(X20,X18)
| X18 != set_union2(X16,X17) )
& ( ~ in(esk2_3(X21,X22,X23),X21)
| ~ in(esk2_3(X21,X22,X23),X23)
| X23 = set_union2(X21,X22) )
& ( ~ in(esk2_3(X21,X22,X23),X22)
| ~ in(esk2_3(X21,X22,X23),X23)
| X23 = set_union2(X21,X22) )
& ( in(esk2_3(X21,X22,X23),X23)
| in(esk2_3(X21,X22,X23),X21)
| in(esk2_3(X21,X22,X23),X22)
| X23 = set_union2(X21,X22) ) ),
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)],[d2_xboole_0])])])])])]) ).
fof(c_0_13,plain,
! [X7,X8] : set_union2(X7,X8) = set_union2(X8,X7),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_0_14,plain,
( subset(X1,X2)
| ~ in(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
( in(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( subset(X1,X3)
| ~ in(X1,X2)
| X2 != powerset(X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_22,plain,
( subset(X1,powerset(X2))
| ~ subset(esk3_2(X1,powerset(X2)),X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_23,plain,
( subset(X1,set_union2(X2,X3))
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,plain,
( subset(X1,X2)
| ~ in(X1,powerset(X2)) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( in(esk3_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_26,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X3,X2)) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
subset(X1,set_union2(X2,X1)),
inference(spm,[status(thm)],[c_0_17,c_0_20]) ).
cnf(c_0_28,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_17]) ).
cnf(c_0_29,plain,
( subset(X1,powerset(set_union2(X2,X3)))
| ~ subset(esk3_2(X1,powerset(set_union2(X2,X3))),X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,plain,
( subset(esk3_2(powerset(X1),X2),X1)
| subset(powerset(X1),X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,plain,
( subset(set_union2(X1,X2),X3)
| in(esk3_2(set_union2(X1,X2),X3),X1)
| in(esk3_2(set_union2(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_32,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_27]) ).
cnf(c_0_33,plain,
( subset(X1,set_union2(X2,X3))
| ~ in(esk3_2(X1,set_union2(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_28]) ).
cnf(c_0_34,plain,
subset(powerset(X1),powerset(set_union2(X1,X2))),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
( subset(X1,set_union2(X2,X3))
| ~ subset(X1,X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_27]) ).
cnf(c_0_36,plain,
( subset(set_union2(X1,X2),X2)
| in(esk3_2(set_union2(X1,X2),X2),X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_31]) ).
cnf(c_0_37,plain,
( subset(X1,set_union2(X2,X3))
| ~ in(esk3_2(X1,set_union2(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_32]) ).
cnf(c_0_38,plain,
( subset(set_union2(X1,X2),set_union2(X2,X3))
| in(esk3_2(set_union2(X1,X2),set_union2(X2,X3)),X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_31]) ).
cnf(c_0_39,plain,
( in(X1,powerset(set_union2(X2,X3)))
| ~ in(X1,powerset(X2)) ),
inference(spm,[status(thm)],[c_0_21,c_0_34]) ).
cnf(c_0_40,plain,
( subset(X1,powerset(set_union2(X2,X3)))
| ~ subset(esk3_2(X1,powerset(set_union2(X2,X3))),X3) ),
inference(spm,[status(thm)],[c_0_22,c_0_35]) ).
cnf(c_0_41,plain,
( subset(esk3_2(set_union2(powerset(X1),X2),X2),X1)
| subset(set_union2(powerset(X1),X2),X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_36]) ).
cnf(c_0_42,plain,
subset(set_union2(X1,X2),set_union2(X2,X1)),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,plain,
( subset(X1,set_union2(powerset(set_union2(X2,X3)),X4))
| ~ in(esk3_2(X1,set_union2(powerset(set_union2(X2,X3)),X4)),powerset(X2)) ),
inference(spm,[status(thm)],[c_0_33,c_0_39]) ).
cnf(c_0_44,plain,
( subset(set_union2(X1,X2),set_union2(X3,X2))
| in(esk3_2(set_union2(X1,X2),set_union2(X3,X2)),X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_31]) ).
fof(c_0_45,negated_conjecture,
~ ! [X1,X2] : subset(set_union2(powerset(X1),powerset(X2)),powerset(set_union2(X1,X2))),
inference(assume_negation,[status(cth)],[t81_zfmisc_1]) ).
cnf(c_0_46,plain,
subset(set_union2(powerset(X1),powerset(set_union2(X2,X1))),powerset(set_union2(X2,X1))),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,plain,
( subset(X1,set_union2(X2,X3))
| ~ subset(X1,set_union2(X3,X2)) ),
inference(spm,[status(thm)],[c_0_16,c_0_42]) ).
cnf(c_0_48,plain,
subset(set_union2(powerset(X1),X2),set_union2(powerset(set_union2(X1,X3)),X2)),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
fof(c_0_49,negated_conjecture,
~ subset(set_union2(powerset(esk6_0),powerset(esk7_0)),powerset(set_union2(esk6_0,esk7_0))),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])]) ).
cnf(c_0_50,plain,
( subset(X1,powerset(set_union2(X2,X3)))
| ~ subset(X1,set_union2(powerset(X3),powerset(set_union2(X2,X3)))) ),
inference(spm,[status(thm)],[c_0_16,c_0_46]) ).
cnf(c_0_51,plain,
subset(set_union2(powerset(X1),X2),set_union2(X2,powerset(set_union2(X1,X3)))),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_52,negated_conjecture,
~ subset(set_union2(powerset(esk6_0),powerset(esk7_0)),powerset(set_union2(esk6_0,esk7_0))),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_53,plain,
subset(set_union2(powerset(X1),powerset(X2)),powerset(set_union2(X1,X2))),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_53])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET934+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n007.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 : 300
% 0.13/0.34 % DateTime : Sat Aug 26 16:23:41 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 153.20/153.16 % Version : CSE_E---1.5
% 153.20/153.16 % Problem : theBenchmark.p
% 153.20/153.16 % Proof found
% 153.20/153.16 % SZS status Theorem for theBenchmark.p
% 153.20/153.16 % SZS output start Proof
% See solution above
% 153.20/153.17 % Total time : 152.600000 s
% 153.20/153.17 % SZS output end Proof
% 153.20/153.17 % Total time : 152.611000 s
%------------------------------------------------------------------------------