TSTP Solution File: SET907+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET907+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 : n001.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 0.20s 0.58s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 14
% Syntax : Number of formulae : 29 ( 8 unt; 10 typ; 0 def)
% Number of atoms : 42 ( 13 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 39 ( 16 ~; 12 |; 7 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 5 >; 4 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn; 20 !; 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: $i > $o ).
tff(decl_26,type,
subset: ( $i * $i ) > $o ).
tff(decl_27,type,
esk1_0: $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(t48_zfmisc_1,conjecture,
! [X1,X2,X3] :
( ( in(X1,X2)
& in(X3,X2) )
=> set_union2(unordered_pair(X1,X3),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_zfmisc_1) ).
fof(t12_xboole_1,axiom,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(t38_zfmisc_1,axiom,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3] :
( ( in(X1,X2)
& in(X3,X2) )
=> set_union2(unordered_pair(X1,X3),X2) = X2 ),
inference(assume_negation,[status(cth)],[t48_zfmisc_1]) ).
fof(c_0_5,plain,
! [X18,X19] :
( ~ subset(X18,X19)
| set_union2(X18,X19) = X19 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])]) ).
fof(c_0_6,plain,
! [X20,X21,X22] :
( ( in(X20,X22)
| ~ subset(unordered_pair(X20,X21),X22) )
& ( in(X21,X22)
| ~ subset(unordered_pair(X20,X21),X22) )
& ( ~ in(X20,X22)
| ~ in(X21,X22)
| subset(unordered_pair(X20,X21),X22) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t38_zfmisc_1])])]) ).
fof(c_0_7,negated_conjecture,
( in(esk3_0,esk4_0)
& in(esk5_0,esk4_0)
& set_union2(unordered_pair(esk3_0,esk5_0),esk4_0) != esk4_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_8,plain,
! [X8,X9] : set_union2(X8,X9) = set_union2(X9,X8),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_0_9,plain,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
( subset(unordered_pair(X1,X3),X2)
| ~ in(X1,X2)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
set_union2(unordered_pair(esk3_0,esk5_0),esk4_0) != esk4_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( set_union2(unordered_pair(X1,X2),X3) = X3
| ~ in(X2,X3)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
set_union2(esk4_0,unordered_pair(esk3_0,esk5_0)) != esk4_0,
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
( set_union2(X1,unordered_pair(X2,X3)) = X1
| ~ in(X3,X1)
| ~ in(X2,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,negated_conjecture,
in(esk5_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,negated_conjecture,
in(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_18,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET907+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
% 0.14/0.33 % Computer : n001.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Sat Aug 26 09:55:00 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.20/0.58 % Version : CSE_E---1.5
% 0.20/0.58 % Problem : theBenchmark.p
% 0.20/0.58 % Proof found
% 0.20/0.58 % SZS status Theorem for theBenchmark.p
% 0.20/0.58 % SZS output start Proof
% See solution above
% 0.20/0.58 % Total time : 0.008000 s
% 0.20/0.58 % SZS output end Proof
% 0.20/0.58 % Total time : 0.011000 s
%------------------------------------------------------------------------------