TSTP Solution File: SEU164+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU164+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n014.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 16:22:58 EDT 2023
% Result : Theorem 0.19s 0.76s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 43 ( 9 unt; 13 typ; 0 def)
% Number of atoms : 98 ( 29 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 105 ( 37 ~; 51 |; 11 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 12 >; 10 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 1 con; 0-3 aty)
% Number of variables : 66 ( 1 sgn; 33 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
singleton: $i > $i ).
tff(decl_24,type,
powerset: $i > $i ).
tff(decl_25,type,
subset: ( $i * $i ) > $o ).
tff(decl_26,type,
union: $i > $i ).
tff(decl_27,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_28,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_29,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_30,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_31,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_32,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_33,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_34,type,
esk8_0: $i ).
fof(d4_tarski,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
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(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
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(t99_zfmisc_1,conjecture,
! [X1] : union(powerset(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(c_0_5,plain,
! [X27,X28,X29,X31,X32,X33,X34,X36] :
( ( in(X29,esk4_3(X27,X28,X29))
| ~ in(X29,X28)
| X28 != union(X27) )
& ( in(esk4_3(X27,X28,X29),X27)
| ~ in(X29,X28)
| X28 != union(X27) )
& ( ~ in(X31,X32)
| ~ in(X32,X27)
| in(X31,X28)
| X28 != union(X27) )
& ( ~ in(esk5_2(X33,X34),X34)
| ~ in(esk5_2(X33,X34),X36)
| ~ in(X36,X33)
| X34 = union(X33) )
& ( in(esk5_2(X33,X34),esk6_2(X33,X34))
| in(esk5_2(X33,X34),X34)
| X34 = union(X33) )
& ( in(esk6_2(X33,X34),X33)
| in(esk5_2(X33,X34),X34)
| X34 = union(X33) ) ),
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)],[d4_tarski])])])])])]) ).
fof(c_0_6,plain,
! [X14,X15,X16,X17,X18,X19] :
( ( ~ in(X16,X15)
| subset(X16,X14)
| X15 != powerset(X14) )
& ( ~ subset(X17,X14)
| in(X17,X15)
| X15 != powerset(X14) )
& ( ~ in(esk2_2(X18,X19),X19)
| ~ subset(esk2_2(X18,X19),X18)
| X19 = powerset(X18) )
& ( in(esk2_2(X18,X19),X19)
| subset(esk2_2(X18,X19),X18)
| X19 = powerset(X18) ) ),
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])])])])])]) ).
cnf(c_0_7,plain,
( X2 = union(X1)
| ~ in(esk5_2(X1,X2),X2)
| ~ in(esk5_2(X1,X2),X3)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( in(esk6_2(X1,X2),X1)
| in(esk5_2(X1,X2),X2)
| X2 = union(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( in(X1,X3)
| ~ subset(X1,X2)
| X3 != powerset(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( X1 = union(X2)
| in(esk6_2(X2,X1),X2)
| ~ in(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_8]) ).
cnf(c_0_11,plain,
( in(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(er,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X40] : subset(X40,X40),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_13,plain,
( subset(X1,X3)
| ~ in(X1,X2)
| X2 != powerset(X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,plain,
( X1 = union(powerset(X2))
| in(esk6_2(powerset(X2),X1),powerset(X2))
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,plain,
! [X21,X22,X23,X24,X25] :
( ( ~ subset(X21,X22)
| ~ in(X23,X21)
| in(X23,X22) )
& ( in(esk3_2(X24,X25),X24)
| subset(X24,X25) )
& ( ~ in(esk3_2(X24,X25),X25)
| subset(X24,X25) ) ),
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_17,plain,
( subset(X1,X2)
| ~ in(X1,powerset(X2)) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( union(powerset(X1)) = X1
| in(esk6_2(powerset(X1),X1),powerset(X1)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
( union(powerset(X1)) = X1
| subset(esk6_2(powerset(X1),X1),X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
( union(powerset(X1)) = X1
| in(X2,X1)
| ~ in(X2,esk6_2(powerset(X1),X1)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,plain,
( in(esk5_2(X1,X2),esk6_2(X1,X2))
| in(esk5_2(X1,X2),X2)
| X2 = union(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_23,negated_conjecture,
~ ! [X1] : union(powerset(X1)) = X1,
inference(assume_negation,[status(cth)],[t99_zfmisc_1]) ).
cnf(c_0_24,plain,
( union(powerset(X1)) = X1
| in(esk5_2(powerset(X1),X1),X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_25,negated_conjecture,
union(powerset(esk8_0)) != esk8_0,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])]) ).
cnf(c_0_26,plain,
( union(powerset(X1)) = X1
| ~ in(X1,powerset(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_24]),c_0_24]) ).
cnf(c_0_27,negated_conjecture,
union(powerset(esk8_0)) != esk8_0,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_28,plain,
union(powerset(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_11]),c_0_15])]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU164+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.16/0.34 % Computer : n014.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Wed Aug 23 22:15:19 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.19/0.76 % Version : CSE_E---1.5
% 0.19/0.76 % Problem : theBenchmark.p
% 0.19/0.76 % Proof found
% 0.19/0.76 % SZS status Theorem for theBenchmark.p
% 0.19/0.76 % SZS output start Proof
% See solution above
% 0.19/0.76 % Total time : 0.186000 s
% 0.19/0.76 % SZS output end Proof
% 0.19/0.76 % Total time : 0.189000 s
%------------------------------------------------------------------------------