TSTP Solution File: SET903+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET903+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 : 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 14:36:11 EDT 2023
% Result : Theorem 0.20s 0.58s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 27 ( 7 unt; 9 typ; 0 def)
% Number of atoms : 76 ( 75 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 91 ( 33 ~; 36 |; 22 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 3 >; 1 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 26 ( 4 sgn; 12 !; 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,
esk1_0: $i ).
tff(decl_27,type,
esk2_0: $i ).
tff(decl_28,type,
esk3_0: $i ).
tff(decl_29,type,
esk4_0: $i ).
tff(decl_30,type,
esk5_0: $i ).
fof(t43_zfmisc_1,axiom,
! [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/sandbox2/benchmark/theBenchmark.p',t43_zfmisc_1) ).
fof(t44_zfmisc_1,conjecture,
! [X1,X2,X3] :
~ ( singleton(X1) = set_union2(X2,X3)
& X2 != X3
& X2 != empty_set
& X3 != empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_zfmisc_1) ).
fof(c_0_2,plain,
! [X13,X14,X15] :
( ( X14 = singleton(X13)
| X14 = empty_set
| X14 = singleton(X13)
| singleton(X13) != set_union2(X14,X15) )
& ( X15 = empty_set
| X14 = empty_set
| X14 = singleton(X13)
| singleton(X13) != set_union2(X14,X15) )
& ( X14 = singleton(X13)
| X15 = singleton(X13)
| X14 = singleton(X13)
| singleton(X13) != set_union2(X14,X15) )
& ( X15 = empty_set
| X15 = singleton(X13)
| X14 = singleton(X13)
| singleton(X13) != set_union2(X14,X15) )
& ( X14 = singleton(X13)
| X14 = empty_set
| X15 = singleton(X13)
| singleton(X13) != set_union2(X14,X15) )
& ( X15 = empty_set
| X14 = empty_set
| X15 = singleton(X13)
| singleton(X13) != set_union2(X14,X15) )
& ( X14 = singleton(X13)
| X15 = singleton(X13)
| X15 = singleton(X13)
| singleton(X13) != set_union2(X14,X15) )
& ( X15 = empty_set
| X15 = singleton(X13)
| X15 = singleton(X13)
| singleton(X13) != set_union2(X14,X15) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t43_zfmisc_1])])]) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( singleton(X1) = set_union2(X2,X3)
& X2 != X3
& X2 != empty_set
& X3 != empty_set ),
inference(assume_negation,[status(cth)],[t44_zfmisc_1]) ).
cnf(c_0_4,plain,
( X1 = empty_set
| X1 = singleton(X2)
| X1 = singleton(X2)
| singleton(X2) != set_union2(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
fof(c_0_5,negated_conjecture,
( singleton(esk3_0) = set_union2(esk4_0,esk5_0)
& esk4_0 != esk5_0
& esk4_0 != empty_set
& esk5_0 != empty_set ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
cnf(c_0_6,plain,
( X1 = empty_set
| X1 = singleton(X2)
| singleton(X2) != set_union2(X3,X1) ),
inference(cn,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
singleton(esk3_0) = set_union2(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
esk5_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
( singleton(X1) = esk5_0
| singleton(X1) != singleton(esk3_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8]) ).
cnf(c_0_10,plain,
( X1 = singleton(X2)
| X1 = empty_set
| X1 = singleton(X2)
| singleton(X2) != set_union2(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_11,negated_conjecture,
singleton(esk3_0) = esk5_0,
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_12,plain,
( X1 = empty_set
| X1 = singleton(X2)
| singleton(X2) != set_union2(X1,X3) ),
inference(cn,[status(thm)],[c_0_10]) ).
cnf(c_0_13,negated_conjecture,
set_union2(esk4_0,esk5_0) = esk5_0,
inference(rw,[status(thm)],[c_0_7,c_0_11]) ).
cnf(c_0_14,negated_conjecture,
esk4_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_15,negated_conjecture,
( singleton(X1) = esk4_0
| singleton(X1) != esk5_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_16,negated_conjecture,
esk4_0 != esk5_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_17,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_11]),c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET903+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n001.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 09:07:45 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.57 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
% 0.20/0.59 % Total time : 0.007000 s
% 0.20/0.59 % SZS output end Proof
% 0.20/0.59 % Total time : 0.009000 s
%------------------------------------------------------------------------------