TSTP Solution File: SET919+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET919+1 : 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 14:36:16 EDT 2023
% Result : Theorem 0.20s 0.60s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 18
% Syntax : Number of formulae : 52 ( 10 unt; 13 typ; 0 def)
% Number of atoms : 136 ( 70 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 154 ( 57 ~; 71 |; 18 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 8 >; 8 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 83 ( 6 sgn; 43 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_24,type,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_25,type,
singleton: $i > $i ).
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_3: ( $i * $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 ).
tff(decl_34,type,
esk8_0: $i ).
fof(t60_zfmisc_1,conjecture,
! [X1,X2,X3] :
( in(X1,X2)
=> ( ( in(X3,X2)
& X1 != X3 )
| set_intersection2(unordered_pair(X1,X3),X2) = singleton(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_zfmisc_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
( in(X1,X2)
=> ( ( in(X3,X2)
& X1 != X3 )
| set_intersection2(unordered_pair(X1,X3),X2) = singleton(X1) ) ),
inference(assume_negation,[status(cth)],[t60_zfmisc_1]) ).
fof(c_0_6,negated_conjecture,
( in(esk6_0,esk7_0)
& ( ~ in(esk8_0,esk7_0)
| esk6_0 = esk8_0 )
& set_intersection2(unordered_pair(esk6_0,esk8_0),esk7_0) != singleton(esk6_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_7,plain,
! [X9,X10] : set_intersection2(X9,X10) = set_intersection2(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_8,plain,
! [X27,X28,X29,X30,X31,X32,X33,X34] :
( ( in(X30,X27)
| ~ in(X30,X29)
| X29 != set_intersection2(X27,X28) )
& ( in(X30,X28)
| ~ in(X30,X29)
| X29 != set_intersection2(X27,X28) )
& ( ~ in(X31,X27)
| ~ in(X31,X28)
| in(X31,X29)
| X29 != set_intersection2(X27,X28) )
& ( ~ in(esk3_3(X32,X33,X34),X34)
| ~ in(esk3_3(X32,X33,X34),X32)
| ~ in(esk3_3(X32,X33,X34),X33)
| X34 = set_intersection2(X32,X33) )
& ( in(esk3_3(X32,X33,X34),X32)
| in(esk3_3(X32,X33,X34),X34)
| X34 = set_intersection2(X32,X33) )
& ( in(esk3_3(X32,X33,X34),X33)
| in(esk3_3(X32,X33,X34),X34)
| X34 = set_intersection2(X32,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)],[d3_xboole_0])])])])])]) ).
cnf(c_0_9,negated_conjecture,
set_intersection2(unordered_pair(esk6_0,esk8_0),esk7_0) != singleton(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X11,X12,X13,X14,X15,X16] :
( ( ~ in(X13,X12)
| X13 = X11
| X12 != singleton(X11) )
& ( X14 != X11
| in(X14,X12)
| X12 != singleton(X11) )
& ( ~ in(esk1_2(X15,X16),X16)
| esk1_2(X15,X16) != X15
| X16 = singleton(X15) )
& ( in(esk1_2(X15,X16),X16)
| esk1_2(X15,X16) = X15
| X16 = singleton(X15) ) ),
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_tarski])])])])])]) ).
fof(c_0_12,plain,
! [X18,X19,X20,X21,X22,X23,X24,X25] :
( ( ~ in(X21,X20)
| X21 = X18
| X21 = X19
| X20 != unordered_pair(X18,X19) )
& ( X22 != X18
| in(X22,X20)
| X20 != unordered_pair(X18,X19) )
& ( X22 != X19
| in(X22,X20)
| X20 != unordered_pair(X18,X19) )
& ( esk2_3(X23,X24,X25) != X23
| ~ in(esk2_3(X23,X24,X25),X25)
| X25 = unordered_pair(X23,X24) )
& ( esk2_3(X23,X24,X25) != X24
| ~ in(esk2_3(X23,X24,X25),X25)
| X25 = unordered_pair(X23,X24) )
& ( in(esk2_3(X23,X24,X25),X25)
| esk2_3(X23,X24,X25) = X23
| esk2_3(X23,X24,X25) = X24
| X25 = unordered_pair(X23,X24) ) ),
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_13,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
singleton(esk6_0) != set_intersection2(esk7_0,unordered_pair(esk6_0,esk8_0)),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,plain,
( in(esk1_2(X1,X2),X2)
| esk1_2(X1,X2) = X1
| X2 = singleton(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( X1 = X3
| X1 = X4
| ~ in(X1,X2)
| X2 != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
( esk1_2(esk6_0,set_intersection2(esk7_0,unordered_pair(esk6_0,esk8_0))) = esk6_0
| in(esk1_2(esk6_0,set_intersection2(esk7_0,unordered_pair(esk6_0,esk8_0))),set_intersection2(esk7_0,unordered_pair(esk6_0,esk8_0))) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15])]) ).
cnf(c_0_19,plain,
( X1 = X2
| X1 = X3
| ~ in(X1,unordered_pair(X3,X2)) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_20,negated_conjecture,
( esk1_2(esk6_0,set_intersection2(esk7_0,unordered_pair(esk6_0,esk8_0))) = esk6_0
| in(esk1_2(esk6_0,set_intersection2(esk7_0,unordered_pair(esk6_0,esk8_0))),unordered_pair(esk6_0,esk8_0)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
( esk1_2(esk6_0,set_intersection2(esk7_0,unordered_pair(esk6_0,esk8_0))) = esk8_0
| esk1_2(esk6_0,set_intersection2(esk7_0,unordered_pair(esk6_0,esk8_0))) = esk6_0 ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_23,plain,
( X2 = singleton(X1)
| ~ in(esk1_2(X1,X2),X2)
| esk1_2(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_24,negated_conjecture,
( esk1_2(esk6_0,set_intersection2(esk7_0,unordered_pair(esk6_0,esk8_0))) = esk6_0
| esk8_0 != esk6_0 ),
inference(ef,[status(thm)],[c_0_21]) ).
cnf(c_0_25,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_26,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_27,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_28,negated_conjecture,
( esk8_0 != esk6_0
| ~ in(esk6_0,set_intersection2(esk7_0,unordered_pair(esk6_0,esk8_0))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_14]) ).
cnf(c_0_29,plain,
( in(X1,set_intersection2(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_25]) ).
cnf(c_0_30,plain,
in(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_26])]) ).
cnf(c_0_31,negated_conjecture,
in(esk6_0,esk7_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_32,negated_conjecture,
( esk1_2(esk6_0,set_intersection2(esk7_0,unordered_pair(esk6_0,esk8_0))) = esk6_0
| in(esk1_2(esk6_0,set_intersection2(esk7_0,unordered_pair(esk6_0,esk8_0))),esk7_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_18]) ).
cnf(c_0_33,negated_conjecture,
esk8_0 != esk6_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31])]) ).
cnf(c_0_34,negated_conjecture,
( esk1_2(esk6_0,set_intersection2(esk7_0,unordered_pair(esk6_0,esk8_0))) = esk6_0
| in(esk8_0,esk7_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_21]),c_0_33]) ).
cnf(c_0_35,negated_conjecture,
( in(esk8_0,esk7_0)
| ~ in(esk6_0,set_intersection2(esk7_0,unordered_pair(esk6_0,esk8_0))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_34]),c_0_14]) ).
cnf(c_0_36,negated_conjecture,
( esk6_0 = esk8_0
| ~ in(esk8_0,esk7_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_37,negated_conjecture,
in(esk8_0,esk7_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_29]),c_0_30]),c_0_31])]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET919+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 08:56:59 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 0.20/0.60 % Version : CSE_E---1.5
% 0.20/0.60 % Problem : theBenchmark.p
% 0.20/0.60 % Proof found
% 0.20/0.60 % SZS status Theorem for theBenchmark.p
% 0.20/0.60 % SZS output start Proof
% See solution above
% 0.20/0.60 % Total time : 0.012000 s
% 0.20/0.60 % SZS output end Proof
% 0.20/0.60 % Total time : 0.014000 s
%------------------------------------------------------------------------------