TSTP Solution File: SET884+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET884+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 : n011.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 14:36:07 EDT 2023
% Result : Theorem 0.20s 0.57s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 17
% Syntax : Number of formulae : 33 ( 6 unt; 13 typ; 0 def)
% Number of atoms : 79 ( 42 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 97 ( 38 ~; 37 |; 16 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 2 ( 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 : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 50 ( 0 sgn; 35 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_24,type,
singleton: $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 ).
tff(decl_34,type,
esk8_0: $i ).
fof(t25_zfmisc_1,conjecture,
! [X1,X2,X3] :
~ ( subset(singleton(X1),unordered_pair(X2,X3))
& X1 != X2
& X1 != X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_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(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( subset(singleton(X1),unordered_pair(X2,X3))
& X1 != X2
& X1 != X3 ),
inference(assume_negation,[status(cth)],[t25_zfmisc_1]) ).
fof(c_0_5,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])])])])])]) ).
fof(c_0_6,negated_conjecture,
( subset(singleton(esk6_0),unordered_pair(esk7_0,esk8_0))
& esk6_0 != esk7_0
& esk6_0 != esk8_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_7,plain,
! [X9,X10,X11,X12,X13,X14] :
( ( ~ in(X11,X10)
| X11 = X9
| X10 != singleton(X9) )
& ( X12 != X9
| in(X12,X10)
| X10 != singleton(X9) )
& ( ~ in(esk1_2(X13,X14),X14)
| esk1_2(X13,X14) != X13
| X14 = singleton(X13) )
& ( in(esk1_2(X13,X14),X14)
| esk1_2(X13,X14) = X13
| X14 = singleton(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_tarski])])])])])]) ).
fof(c_0_8,plain,
! [X16,X17,X18,X19,X20,X21,X22,X23] :
( ( ~ in(X19,X18)
| X19 = X16
| X19 = X17
| X18 != unordered_pair(X16,X17) )
& ( X20 != X16
| in(X20,X18)
| X18 != unordered_pair(X16,X17) )
& ( X20 != X17
| in(X20,X18)
| X18 != unordered_pair(X16,X17) )
& ( esk2_3(X21,X22,X23) != X21
| ~ in(esk2_3(X21,X22,X23),X23)
| X23 = unordered_pair(X21,X22) )
& ( esk2_3(X21,X22,X23) != X22
| ~ in(esk2_3(X21,X22,X23),X23)
| X23 = unordered_pair(X21,X22) )
& ( in(esk2_3(X21,X22,X23),X23)
| esk2_3(X21,X22,X23) = X21
| esk2_3(X21,X22,X23) = X22
| X23 = unordered_pair(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_tarski])])])])])]) ).
cnf(c_0_9,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
subset(singleton(esk6_0),unordered_pair(esk7_0,esk8_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( X1 = X3
| X1 = X4
| ~ in(X1,X2)
| X2 != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
( in(X1,unordered_pair(esk7_0,esk8_0))
| ~ in(X1,singleton(esk6_0)) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_11])]) ).
cnf(c_0_15,plain,
( X1 = X2
| X1 = X3
| ~ in(X1,unordered_pair(X3,X2)) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
in(esk6_0,unordered_pair(esk7_0,esk8_0)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,negated_conjecture,
esk6_0 != esk7_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_18,negated_conjecture,
esk6_0 != esk8_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET884+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
% 0.14/0.34 % Computer : n011.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 15:50:24 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.20/0.57 % Version : CSE_E---1.5
% 0.20/0.57 % Problem : theBenchmark.p
% 0.20/0.57 % Proof found
% 0.20/0.57 % SZS status Theorem for theBenchmark.p
% 0.20/0.57 % SZS output start Proof
% See solution above
% 0.20/0.58 % Total time : 0.009000 s
% 0.20/0.58 % SZS output end Proof
% 0.20/0.58 % Total time : 0.011000 s
%------------------------------------------------------------------------------