TSTP Solution File: SET887+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET887+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 : n031.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 14:36:09 EDT 2023
% Result : Theorem 0.20s 0.56s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 19
% Syntax : Number of formulae : 55 ( 10 unt; 14 typ; 0 def)
% Number of atoms : 128 ( 94 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 138 ( 51 ~; 62 |; 19 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 7 >; 5 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 72 ( 9 sgn; 39 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_24,type,
empty_set: $i ).
tff(decl_25,type,
empty: $i > $o ).
tff(decl_26,type,
subset: ( $i * $i ) > $o ).
tff(decl_27,type,
singleton: $i > $i ).
tff(decl_28,type,
esk1_1: $i > $i ).
tff(decl_29,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_30,type,
esk3_0: $i ).
tff(decl_31,type,
esk4_0: $i ).
tff(decl_32,type,
esk5_0: $i ).
tff(decl_33,type,
esk6_0: $i ).
tff(decl_34,type,
esk7_0: $i ).
tff(decl_35,type,
esk8_0: $i ).
fof(t28_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
~ ( subset(unordered_pair(X1,X2),unordered_pair(X3,X4))
& X1 != X3
& X1 != X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_zfmisc_1) ).
fof(l46_zfmisc_1,axiom,
! [X1,X2,X3] :
( subset(X1,unordered_pair(X2,X3))
<=> ~ ( X1 != empty_set
& X1 != singleton(X2)
& X1 != singleton(X3)
& X1 != unordered_pair(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l46_zfmisc_1) ).
fof(t8_zfmisc_1,axiom,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3,X4] :
~ ( subset(unordered_pair(X1,X2),unordered_pair(X3,X4))
& X1 != X3
& X1 != X4 ),
inference(assume_negation,[status(cth)],[t28_zfmisc_1]) ).
fof(c_0_6,plain,
! [X22,X23,X24] :
( ( ~ subset(X22,unordered_pair(X23,X24))
| X22 = empty_set
| X22 = singleton(X23)
| X22 = singleton(X24)
| X22 = unordered_pair(X23,X24) )
& ( X22 != empty_set
| subset(X22,unordered_pair(X23,X24)) )
& ( X22 != singleton(X23)
| subset(X22,unordered_pair(X23,X24)) )
& ( X22 != singleton(X24)
| subset(X22,unordered_pair(X23,X24)) )
& ( X22 != unordered_pair(X23,X24)
| subset(X22,unordered_pair(X23,X24)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l46_zfmisc_1])])]) ).
fof(c_0_7,negated_conjecture,
( subset(unordered_pair(esk5_0,esk6_0),unordered_pair(esk7_0,esk8_0))
& esk5_0 != esk7_0
& esk5_0 != esk8_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_8,plain,
! [X36,X37,X38] :
( singleton(X36) != unordered_pair(X37,X38)
| X36 = X37 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_zfmisc_1])]) ).
cnf(c_0_9,plain,
( X1 = empty_set
| X1 = singleton(X2)
| X1 = singleton(X3)
| X1 = unordered_pair(X2,X3)
| ~ subset(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
subset(unordered_pair(esk5_0,esk6_0),unordered_pair(esk7_0,esk8_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
( unordered_pair(esk7_0,esk8_0) = unordered_pair(esk5_0,esk6_0)
| singleton(esk7_0) = unordered_pair(esk5_0,esk6_0)
| singleton(esk8_0) = unordered_pair(esk5_0,esk6_0)
| unordered_pair(esk5_0,esk6_0) = empty_set ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,negated_conjecture,
( unordered_pair(esk7_0,esk8_0) = unordered_pair(esk5_0,esk6_0)
| singleton(esk7_0) = unordered_pair(esk5_0,esk6_0)
| unordered_pair(esk5_0,esk6_0) = empty_set
| esk8_0 = X1
| unordered_pair(esk5_0,esk6_0) != unordered_pair(X1,X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,negated_conjecture,
esk5_0 != esk8_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_15,plain,
! [X13,X14,X15,X16,X17,X18,X19,X20] :
( ( ~ in(X16,X15)
| X16 = X13
| X16 = X14
| X15 != unordered_pair(X13,X14) )
& ( X17 != X13
| in(X17,X15)
| X15 != unordered_pair(X13,X14) )
& ( X17 != X14
| in(X17,X15)
| X15 != unordered_pair(X13,X14) )
& ( esk2_3(X18,X19,X20) != X18
| ~ in(esk2_3(X18,X19,X20),X20)
| X20 = unordered_pair(X18,X19) )
& ( esk2_3(X18,X19,X20) != X19
| ~ in(esk2_3(X18,X19,X20),X20)
| X20 = unordered_pair(X18,X19) )
& ( in(esk2_3(X18,X19,X20),X20)
| esk2_3(X18,X19,X20) = X18
| esk2_3(X18,X19,X20) = X19
| X20 = unordered_pair(X18,X19) ) ),
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_tarski])])])])])]) ).
cnf(c_0_16,negated_conjecture,
( unordered_pair(esk7_0,esk8_0) = unordered_pair(esk5_0,esk6_0)
| singleton(esk7_0) = unordered_pair(esk5_0,esk6_0)
| unordered_pair(esk5_0,esk6_0) = empty_set ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_13]),c_0_14]) ).
cnf(c_0_17,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,negated_conjecture,
( unordered_pair(esk7_0,esk8_0) = unordered_pair(esk5_0,esk6_0)
| unordered_pair(esk5_0,esk6_0) = empty_set
| esk7_0 = X1
| unordered_pair(esk5_0,esk6_0) != unordered_pair(X1,X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
esk5_0 != esk7_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_20,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
cnf(c_0_21,plain,
( X1 = X3
| X1 = X4
| ~ in(X1,X2)
| X2 != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
in(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_17])]) ).
cnf(c_0_23,negated_conjecture,
( unordered_pair(esk7_0,esk8_0) = unordered_pair(esk5_0,esk6_0)
| unordered_pair(esk5_0,esk6_0) = empty_set ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_18]),c_0_19]) ).
fof(c_0_24,plain,
! [X9,X10,X11] :
( ( X9 != empty_set
| ~ in(X10,X9) )
& ( in(esk1_1(X11),X11)
| X11 = empty_set ) ),
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_20])])])])]) ).
cnf(c_0_25,plain,
( X1 = X2
| X1 = X3
| ~ in(X1,unordered_pair(X3,X2)) ),
inference(er,[status(thm)],[c_0_21]) ).
cnf(c_0_26,negated_conjecture,
( unordered_pair(esk5_0,esk6_0) = empty_set
| in(esk7_0,unordered_pair(esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,negated_conjecture,
( unordered_pair(esk5_0,esk6_0) = empty_set
| esk6_0 = esk7_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_19]) ).
cnf(c_0_29,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_30,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_31,negated_conjecture,
esk6_0 = esk7_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_28]),c_0_29]) ).
cnf(c_0_32,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_30])]) ).
cnf(c_0_33,negated_conjecture,
( unordered_pair(esk7_0,esk8_0) = unordered_pair(esk5_0,esk7_0)
| unordered_pair(esk5_0,esk7_0) = empty_set ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_31]),c_0_31]) ).
cnf(c_0_34,negated_conjecture,
( unordered_pair(esk5_0,esk7_0) = empty_set
| in(esk8_0,unordered_pair(esk5_0,esk7_0)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_35,negated_conjecture,
( unordered_pair(esk5_0,esk7_0) = empty_set
| esk8_0 = esk7_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_34]),c_0_14]) ).
cnf(c_0_36,negated_conjecture,
esk8_0 = esk7_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_35]),c_0_29]) ).
cnf(c_0_37,negated_conjecture,
( unordered_pair(esk7_0,esk7_0) = unordered_pair(esk5_0,esk7_0)
| unordered_pair(esk5_0,esk7_0) = empty_set ),
inference(rw,[status(thm)],[c_0_33,c_0_36]) ).
cnf(c_0_38,negated_conjecture,
( unordered_pair(esk5_0,esk7_0) = empty_set
| X1 = esk7_0
| ~ in(X1,unordered_pair(esk5_0,esk7_0)) ),
inference(spm,[status(thm)],[c_0_25,c_0_37]) ).
cnf(c_0_39,negated_conjecture,
unordered_pair(esk5_0,esk7_0) = empty_set,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_22]),c_0_19]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_39]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET887+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n031.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 13:31:08 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.54 start to proof: theBenchmark
% 0.20/0.56 % Version : CSE_E---1.5
% 0.20/0.56 % Problem : theBenchmark.p
% 0.20/0.56 % Proof found
% 0.20/0.56 % SZS status Theorem for theBenchmark.p
% 0.20/0.56 % SZS output start Proof
% See solution above
% 0.20/0.56 % Total time : 0.009000 s
% 0.20/0.56 % SZS output end Proof
% 0.20/0.56 % Total time : 0.012000 s
%------------------------------------------------------------------------------