TSTP Solution File: SET902+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET902+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 : n028.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 14:36:11 EDT 2023
% Result : Theorem 0.19s 0.58s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of formulae : 43 ( 18 unt; 10 typ; 0 def)
% Number of atoms : 70 ( 58 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 69 ( 32 ~; 19 |; 17 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 4 >; 2 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 33 ( 4 sgn; 23 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_23,type,
empty_set: $i ).
tff(decl_24,type,
empty: $i > $o ).
tff(decl_25,type,
singleton: $i > $i ).
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(t7_xboole_1,axiom,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_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(t43_zfmisc_1,conjecture,
! [X1,X2,X3] :
~ ( singleton(X1) = set_union2(X2,X3)
& ~ ( X2 = singleton(X1)
& X3 = singleton(X1) )
& ~ ( X2 = empty_set
& X3 = singleton(X1) )
& ~ ( X2 = singleton(X1)
& X3 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_zfmisc_1) ).
fof(l4_zfmisc_1,axiom,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(idempotence_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(l1_zfmisc_1,axiom,
! [X1] : singleton(X1) != empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(c_0_6,plain,
! [X20,X21] : subset(X20,set_union2(X20,X21)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
fof(c_0_7,plain,
! [X4,X5] : set_union2(X4,X5) = set_union2(X5,X4),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( singleton(X1) = set_union2(X2,X3)
& ~ ( X2 = singleton(X1)
& X3 = singleton(X1) )
& ~ ( X2 = empty_set
& X3 = singleton(X1) )
& ~ ( X2 = singleton(X1)
& X3 = empty_set ) ),
inference(assume_negation,[status(cth)],[t43_zfmisc_1]) ).
cnf(c_0_9,plain,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,negated_conjecture,
( singleton(esk3_0) = set_union2(esk4_0,esk5_0)
& ( esk4_0 != singleton(esk3_0)
| esk5_0 != singleton(esk3_0) )
& ( esk4_0 != empty_set
| esk5_0 != singleton(esk3_0) )
& ( esk4_0 != singleton(esk3_0)
| esk5_0 != empty_set ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_12,plain,
! [X12,X13] :
( ( ~ subset(X12,singleton(X13))
| X12 = empty_set
| X12 = singleton(X13) )
& ( X12 != empty_set
| subset(X12,singleton(X13)) )
& ( X12 != singleton(X13)
| subset(X12,singleton(X13)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l4_zfmisc_1])])]) ).
cnf(c_0_13,plain,
subset(X1,set_union2(X2,X1)),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
singleton(esk3_0) = set_union2(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( X1 = empty_set
| X1 = singleton(X2)
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
subset(esk5_0,singleton(esk3_0)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,negated_conjecture,
subset(esk4_0,singleton(esk3_0)),
inference(spm,[status(thm)],[c_0_9,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( esk4_0 != empty_set
| esk5_0 != singleton(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,negated_conjecture,
( singleton(esk3_0) = esk5_0
| esk5_0 = empty_set ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
( esk4_0 != singleton(esk3_0)
| esk5_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,negated_conjecture,
( singleton(esk3_0) = esk4_0
| esk4_0 = empty_set ),
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_22,negated_conjecture,
( esk4_0 != singleton(esk3_0)
| esk5_0 != singleton(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_23,negated_conjecture,
( esk5_0 = empty_set
| esk4_0 != empty_set ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( esk4_0 = empty_set
| esk5_0 != empty_set ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
( esk4_0 = empty_set
| esk5_0 != esk4_0 ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
fof(c_0_26,plain,
! [X10] : set_union2(X10,X10) = X10,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
fof(c_0_27,plain,
! [X11] : singleton(X11) != empty_set,
inference(variable_rename,[status(thm)],[l1_zfmisc_1]) ).
cnf(c_0_28,negated_conjecture,
( set_union2(empty_set,esk4_0) = singleton(esk3_0)
| esk4_0 != empty_set ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_23]),c_0_10]) ).
cnf(c_0_29,negated_conjecture,
esk4_0 = empty_set,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_19]),c_0_24]),c_0_25]) ).
cnf(c_0_30,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_29])]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET902+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
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 10:30:07 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.58 % Version : CSE_E---1.5
% 0.19/0.58 % Problem : theBenchmark.p
% 0.19/0.58 % Proof found
% 0.19/0.58 % SZS status Theorem for theBenchmark.p
% 0.19/0.58 % SZS output start Proof
% See solution above
% 0.19/0.59 % Total time : 0.006000 s
% 0.19/0.59 % SZS output end Proof
% 0.19/0.59 % Total time : 0.009000 s
%------------------------------------------------------------------------------