TSTP Solution File: SET909+1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET909+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 : n015.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 14:36:13 EDT 2023
% Result : Theorem 0.21s 0.58s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 18
% Syntax : Number of formulae : 36 ( 12 unt; 13 typ; 0 def)
% Number of atoms : 78 ( 40 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 91 ( 36 ~; 38 |; 11 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 7 >; 7 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 60 ( 7 sgn; 41 !; 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_union2: ( $i * $i ) > $i ).
tff(decl_25,type,
empty_set: $i ).
tff(decl_26,type,
empty: $i > $o ).
tff(decl_27,type,
esk1_1: $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(t50_zfmisc_1,conjecture,
! [X1,X2,X3] : set_union2(unordered_pair(X1,X2),X3) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_zfmisc_1) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
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_5,negated_conjecture,
~ ! [X1,X2,X3] : set_union2(unordered_pair(X1,X2),X3) != empty_set,
inference(assume_negation,[status(cth)],[t50_zfmisc_1]) ).
fof(c_0_6,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_7,plain,
! [X24,X25,X26,X27,X28,X29,X30,X31] :
( ( ~ in(X27,X26)
| in(X27,X24)
| in(X27,X25)
| X26 != set_union2(X24,X25) )
& ( ~ in(X28,X24)
| in(X28,X26)
| X26 != set_union2(X24,X25) )
& ( ~ in(X28,X25)
| in(X28,X26)
| X26 != set_union2(X24,X25) )
& ( ~ in(esk3_3(X29,X30,X31),X29)
| ~ in(esk3_3(X29,X30,X31),X31)
| X31 = set_union2(X29,X30) )
& ( ~ in(esk3_3(X29,X30,X31),X30)
| ~ in(esk3_3(X29,X30,X31),X31)
| X31 = set_union2(X29,X30) )
& ( in(esk3_3(X29,X30,X31),X31)
| in(esk3_3(X29,X30,X31),X29)
| in(esk3_3(X29,X30,X31),X30)
| X31 = set_union2(X29,X30) ) ),
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_xboole_0])])])])])]) ).
fof(c_0_8,negated_conjecture,
set_union2(unordered_pair(esk6_0,esk7_0),esk8_0) = empty_set,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_9,plain,
! [X9,X10] : set_union2(X9,X10) = set_union2(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_10,plain,
! [X11,X12,X13] :
( ( X11 != empty_set
| ~ in(X12,X11) )
& ( in(esk1_1(X13),X13)
| X13 = 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_6])])])])]) ).
cnf(c_0_11,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
set_union2(unordered_pair(esk6_0,esk7_0),esk8_0) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,plain,
! [X15,X16,X17,X18,X19,X20,X21,X22] :
( ( ~ in(X18,X17)
| X18 = X15
| X18 = X16
| X17 != unordered_pair(X15,X16) )
& ( X19 != X15
| in(X19,X17)
| X17 != unordered_pair(X15,X16) )
& ( X19 != X16
| in(X19,X17)
| X17 != unordered_pair(X15,X16) )
& ( esk2_3(X20,X21,X22) != X20
| ~ in(esk2_3(X20,X21,X22),X22)
| X22 = unordered_pair(X20,X21) )
& ( esk2_3(X20,X21,X22) != X21
| ~ in(esk2_3(X20,X21,X22),X22)
| X22 = unordered_pair(X20,X21) )
& ( in(esk2_3(X20,X21,X22),X22)
| esk2_3(X20,X21,X22) = X20
| esk2_3(X20,X21,X22) = X21
| X22 = unordered_pair(X20,X21) ) ),
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,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
set_union2(esk8_0,unordered_pair(esk6_0,esk7_0)) = empty_set,
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,negated_conjecture,
~ in(X1,unordered_pair(esk6_0,esk7_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_21,plain,
in(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_19])]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_20,c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET909+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n015.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
% 0.14/0.35 % DateTime : Sat Aug 26 13:21:23 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.56 start to proof: theBenchmark
% 0.21/0.58 % Version : CSE_E---1.5
% 0.21/0.58 % Problem : theBenchmark.p
% 0.21/0.58 % Proof found
% 0.21/0.58 % SZS status Theorem for theBenchmark.p
% 0.21/0.58 % SZS output start Proof
% See solution above
% 0.21/0.58 % Total time : 0.010000 s
% 0.21/0.58 % SZS output end Proof
% 0.21/0.58 % Total time : 0.012000 s
%------------------------------------------------------------------------------