TSTP Solution File: SET813+4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET813+4 : 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 : n005.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 14:35:39 EDT 2023
% Result : Theorem 0.16s 0.58s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 39
% Syntax : Number of formulae : 51 ( 3 unt; 35 typ; 0 def)
% Number of atoms : 39 ( 4 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 37 ( 14 ~; 13 |; 5 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 60 ( 31 >; 29 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 27 ( 27 usr; 4 con; 0-3 aty)
% Number of variables : 26 ( 1 sgn; 16 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
subset: ( $i * $i ) > $o ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
equal_set: ( $i * $i ) > $o ).
tff(decl_25,type,
power_set: $i > $i ).
tff(decl_26,type,
intersection: ( $i * $i ) > $i ).
tff(decl_27,type,
union: ( $i * $i ) > $i ).
tff(decl_28,type,
empty_set: $i ).
tff(decl_29,type,
difference: ( $i * $i ) > $i ).
tff(decl_30,type,
singleton: $i > $i ).
tff(decl_31,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_32,type,
sum: $i > $i ).
tff(decl_33,type,
product: $i > $i ).
tff(decl_34,type,
on: $i ).
tff(decl_35,type,
set: $i > $o ).
tff(decl_36,type,
member_predicate: $i ).
tff(decl_37,type,
strict_well_order: ( $i * $i ) > $o ).
tff(decl_38,type,
strict_order: ( $i * $i ) > $o ).
tff(decl_39,type,
least: ( $i * $i * $i ) > $o ).
tff(decl_40,type,
apply: ( $i * $i * $i ) > $o ).
tff(decl_41,type,
initial_segment: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
suc: $i > $i ).
tff(decl_43,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_44,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_45,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_46,type,
esk4_1: $i > $i ).
tff(decl_47,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_48,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_51,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_53,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk13_2: ( $i * $i ) > $i ).
tff(decl_56,type,
esk14_0: $i ).
fof(thV12,conjecture,
! [X1] :
( member(X1,on)
=> member(X1,suc(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thV12) ).
fof(successor,axiom,
! [X1,X3] :
( member(X3,suc(X1))
<=> member(X3,union(X1,singleton(X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+4.ax',successor) ).
fof(union,axiom,
! [X3,X1,X2] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',union) ).
fof(singleton,axiom,
! [X3,X1] :
( member(X3,singleton(X1))
<=> X3 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',singleton) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( member(X1,on)
=> member(X1,suc(X1)) ),
inference(assume_negation,[status(cth)],[thV12]) ).
fof(c_0_5,plain,
! [X90,X91] :
( ( ~ member(X91,suc(X90))
| member(X91,union(X90,singleton(X90))) )
& ( ~ member(X91,union(X90,singleton(X90)))
| member(X91,suc(X90)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[successor])]) ).
fof(c_0_6,plain,
! [X22,X23,X24] :
( ( ~ member(X22,union(X23,X24))
| member(X22,X23)
| member(X22,X24) )
& ( ~ member(X22,X23)
| member(X22,union(X23,X24)) )
& ( ~ member(X22,X24)
| member(X22,union(X23,X24)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union])])]) ).
fof(c_0_7,plain,
! [X29,X30] :
( ( ~ member(X29,singleton(X30))
| X29 = X30 )
& ( X29 != X30
| member(X29,singleton(X30)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[singleton])]) ).
fof(c_0_8,negated_conjecture,
( member(esk14_0,on)
& ~ member(esk14_0,suc(esk14_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_9,plain,
( member(X1,suc(X2))
| ~ member(X1,union(X2,singleton(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( member(X1,singleton(X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
~ member(esk14_0,suc(esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( member(X1,suc(X2))
| ~ member(X1,singleton(X2)) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
member(X1,singleton(X1)),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SET813+4 : TPTP v8.1.2. Released v3.2.0.
% 0.09/0.11 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sat Aug 26 13:01:38 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.16/0.56 start to proof: theBenchmark
% 0.16/0.58 % Version : CSE_E---1.5
% 0.16/0.58 % Problem : theBenchmark.p
% 0.16/0.58 % Proof found
% 0.16/0.58 % SZS status Theorem for theBenchmark.p
% 0.16/0.58 % SZS output start Proof
% See solution above
% 0.16/0.59 % Total time : 0.019000 s
% 0.16/0.59 % SZS output end Proof
% 0.16/0.59 % Total time : 0.022000 s
%------------------------------------------------------------------------------