TSTP Solution File: SET878+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET878+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 : n027.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 14:36:06 EDT 2023
% Result : Theorem 0.20s 0.60s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 14
% Syntax : Number of formulae : 27 ( 11 unt; 10 typ; 0 def)
% Number of atoms : 44 ( 30 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 46 ( 19 ~; 19 |; 5 &)
% ( 2 <=>; 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 : 11 ( 6 >; 5 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 34 ( 2 sgn; 24 !; 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_3: ( $i * $i * $i ) > $i ).
tff(decl_28,type,
esk2_0: $i ).
tff(decl_29,type,
esk3_0: $i ).
tff(decl_30,type,
esk4_0: $i ).
tff(decl_31,type,
esk5_0: $i ).
fof(t19_zfmisc_1,conjecture,
! [X1,X2] : set_intersection2(singleton(X1),unordered_pair(X1,X2)) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_zfmisc_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(l32_zfmisc_1,axiom,
! [X1,X2] :
( in(X1,X2)
=> set_intersection2(X2,singleton(X1)) = singleton(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_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(c_0_4,negated_conjecture,
~ ! [X1,X2] : set_intersection2(singleton(X1),unordered_pair(X1,X2)) = singleton(X1),
inference(assume_negation,[status(cth)],[t19_zfmisc_1]) ).
fof(c_0_5,negated_conjecture,
set_intersection2(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)) != singleton(esk4_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_6,plain,
! [X9,X10] : set_intersection2(X9,X10) = set_intersection2(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_0_7,negated_conjecture,
set_intersection2(singleton(esk4_0),unordered_pair(esk4_0,esk5_0)) != singleton(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X21,X22] :
( ~ in(X21,X22)
| set_intersection2(X22,singleton(X21)) = singleton(X21) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_zfmisc_1])]) ).
fof(c_0_10,plain,
! [X11,X12,X13,X14,X15,X16,X17,X18] :
( ( ~ in(X14,X13)
| X14 = X11
| X14 = X12
| X13 != unordered_pair(X11,X12) )
& ( X15 != X11
| in(X15,X13)
| X13 != unordered_pair(X11,X12) )
& ( X15 != X12
| in(X15,X13)
| X13 != unordered_pair(X11,X12) )
& ( esk1_3(X16,X17,X18) != X16
| ~ in(esk1_3(X16,X17,X18),X18)
| X18 = unordered_pair(X16,X17) )
& ( esk1_3(X16,X17,X18) != X17
| ~ in(esk1_3(X16,X17,X18),X18)
| X18 = unordered_pair(X16,X17) )
& ( in(esk1_3(X16,X17,X18),X18)
| esk1_3(X16,X17,X18) = X16
| esk1_3(X16,X17,X18) = X17
| X18 = unordered_pair(X16,X17) ) ),
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_11,negated_conjecture,
set_intersection2(unordered_pair(esk4_0,esk5_0),singleton(esk4_0)) != singleton(esk4_0),
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,plain,
( set_intersection2(X2,singleton(X1)) = singleton(X1)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
~ in(esk4_0,unordered_pair(esk4_0,esk5_0)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
in(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_13])]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET878+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
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 10:07:20 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.59 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 : 0.007000 s
% 0.20/0.60 % SZS output end Proof
% 0.20/0.60 % Total time : 0.009000 s
%------------------------------------------------------------------------------