TSTP Solution File: SET906+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET906+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 14:36:12 EDT 2023
% Result : Theorem 0.21s 0.59s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 19
% Syntax : Number of formulae : 40 ( 12 unt; 13 typ; 0 def)
% Number of atoms : 91 ( 33 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 99 ( 35 ~; 43 |; 13 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 8 >; 9 *; 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 : 70 ( 5 sgn; 46 !; 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,
subset: ( $i * $i ) > $o ).
tff(decl_26,type,
empty: $i > $o ).
tff(decl_27,type,
esk1_3: ( $i * $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(t47_zfmisc_1,conjecture,
! [X1,X2,X3] :
( subset(set_union2(unordered_pair(X1,X2),X3),X3)
=> in(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_zfmisc_1) ).
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(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(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(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(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(set_union2(unordered_pair(X1,X2),X3),X3)
=> in(X1,X3) ),
inference(assume_negation,[status(cth)],[t47_zfmisc_1]) ).
fof(c_0_7,negated_conjecture,
( subset(set_union2(unordered_pair(esk6_0,esk7_0),esk8_0),esk8_0)
& ~ in(esk6_0,esk8_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_8,plain,
! [X9,X10] : set_union2(X9,X10) = set_union2(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_9,plain,
! [X29,X30,X31,X32,X33] :
( ( ~ subset(X29,X30)
| ~ in(X31,X29)
| in(X31,X30) )
& ( in(esk3_2(X32,X33),X32)
| subset(X32,X33) )
& ( ~ in(esk3_2(X32,X33),X33)
| subset(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_tarski])])])])])]) ).
cnf(c_0_10,negated_conjecture,
subset(set_union2(unordered_pair(esk6_0,esk7_0),esk8_0),esk8_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X20,X21,X22,X23,X24,X25,X26,X27] :
( ( ~ in(X23,X22)
| in(X23,X20)
| in(X23,X21)
| X22 != set_union2(X20,X21) )
& ( ~ in(X24,X20)
| in(X24,X22)
| X22 != set_union2(X20,X21) )
& ( ~ in(X24,X21)
| in(X24,X22)
| X22 != set_union2(X20,X21) )
& ( ~ in(esk2_3(X25,X26,X27),X25)
| ~ in(esk2_3(X25,X26,X27),X27)
| X27 = set_union2(X25,X26) )
& ( ~ in(esk2_3(X25,X26,X27),X26)
| ~ in(esk2_3(X25,X26,X27),X27)
| X27 = set_union2(X25,X26) )
& ( in(esk2_3(X25,X26,X27),X27)
| in(esk2_3(X25,X26,X27),X25)
| in(esk2_3(X25,X26,X27),X26)
| X27 = set_union2(X25,X26) ) ),
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_13,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_14,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
subset(set_union2(esk8_0,unordered_pair(esk6_0,esk7_0)),esk8_0),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_18,plain,
! [X7,X8] : unordered_pair(X7,X8) = unordered_pair(X8,X7),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_19,negated_conjecture,
( in(X1,esk8_0)
| ~ in(X1,set_union2(esk8_0,unordered_pair(esk6_0,esk7_0))) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_17])]) ).
cnf(c_0_22,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( in(X1,esk8_0)
| ~ in(X1,unordered_pair(esk6_0,esk7_0)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
in(X1,unordered_pair(X1,X2)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
~ in(esk6_0,esk8_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET906+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
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 14:16:24 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.57 start to proof: theBenchmark
% 0.21/0.59 % Version : CSE_E---1.5
% 0.21/0.59 % Problem : theBenchmark.p
% 0.21/0.59 % Proof found
% 0.21/0.59 % SZS status Theorem for theBenchmark.p
% 0.21/0.59 % SZS output start Proof
% See solution above
% 0.21/0.59 % Total time : 0.007000 s
% 0.21/0.59 % SZS output end Proof
% 0.21/0.59 % Total time : 0.010000 s
%------------------------------------------------------------------------------