TSTP Solution File: SET076+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET076+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n018.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 14:32:48 EDT 2023
% Result : Theorem 17.59s 17.68s
% Output : CNFRefutation 17.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 44
% Syntax : Number of formulae : 59 ( 4 unt; 41 typ; 0 def)
% Number of atoms : 55 ( 12 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 53 ( 16 ~; 22 |; 10 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 47 ( 31 >; 16 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 36 ( 36 usr; 10 con; 0-3 aty)
% Number of variables : 35 ( 0 sgn; 20 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
subclass: ( $i * $i ) > $o ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
universal_class: $i ).
tff(decl_25,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_26,type,
singleton: $i > $i ).
tff(decl_27,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_28,type,
cross_product: ( $i * $i ) > $i ).
tff(decl_29,type,
first: $i > $i ).
tff(decl_30,type,
second: $i > $i ).
tff(decl_31,type,
element_relation: $i ).
tff(decl_32,type,
intersection: ( $i * $i ) > $i ).
tff(decl_33,type,
complement: $i > $i ).
tff(decl_34,type,
restrict: ( $i * $i * $i ) > $i ).
tff(decl_35,type,
null_class: $i ).
tff(decl_36,type,
domain_of: $i > $i ).
tff(decl_37,type,
rotate: $i > $i ).
tff(decl_38,type,
flip: $i > $i ).
tff(decl_39,type,
union: ( $i * $i ) > $i ).
tff(decl_40,type,
successor: $i > $i ).
tff(decl_41,type,
successor_relation: $i ).
tff(decl_42,type,
inverse: $i > $i ).
tff(decl_43,type,
range_of: $i > $i ).
tff(decl_44,type,
image: ( $i * $i ) > $i ).
tff(decl_45,type,
inductive: $i > $o ).
tff(decl_46,type,
sum_class: $i > $i ).
tff(decl_47,type,
power_class: $i > $i ).
tff(decl_48,type,
compose: ( $i * $i ) > $i ).
tff(decl_49,type,
identity_relation: $i ).
tff(decl_50,type,
function: $i > $o ).
tff(decl_51,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_52,type,
apply: ( $i * $i ) > $i ).
tff(decl_53,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk2_0: $i ).
tff(decl_55,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_56,type,
esk4_1: $i > $i ).
tff(decl_57,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_58,type,
esk6_1: $i > $i ).
tff(decl_59,type,
esk7_0: $i ).
tff(decl_60,type,
esk8_0: $i ).
tff(decl_61,type,
esk9_0: $i ).
tff(decl_62,type,
esk10_0: $i ).
fof(unordered_pair_defn,axiom,
! [X3,X1,X2] :
( member(X3,unordered_pair(X1,X2))
<=> ( member(X3,universal_class)
& ( X3 = X1
| X3 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).
fof(subclass_defn,axiom,
! [X1,X2] :
( subclass(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',subclass_defn) ).
fof(unordered_pair_is_subset,conjecture,
! [X1,X2,X5] :
( ( member(X1,X5)
& member(X2,X5) )
=> subclass(unordered_pair(X1,X2),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_is_subset) ).
fof(c_0_3,plain,
! [X19,X20,X21] :
( ( member(X19,universal_class)
| ~ member(X19,unordered_pair(X20,X21)) )
& ( X19 = X20
| X19 = X21
| ~ member(X19,unordered_pair(X20,X21)) )
& ( X19 != X20
| ~ member(X19,universal_class)
| member(X19,unordered_pair(X20,X21)) )
& ( X19 != X21
| ~ member(X19,universal_class)
| member(X19,unordered_pair(X20,X21)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unordered_pair_defn])])]) ).
fof(c_0_4,plain,
! [X10,X11,X12,X13,X14] :
( ( ~ subclass(X10,X11)
| ~ member(X12,X10)
| member(X12,X11) )
& ( member(esk1_2(X13,X14),X13)
| subclass(X13,X14) )
& ( ~ member(esk1_2(X13,X14),X14)
| subclass(X13,X14) ) ),
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)],[subclass_defn])])])])])]) ).
cnf(c_0_5,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,plain,
( member(esk1_2(X1,X2),X1)
| subclass(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2,X5] :
( ( member(X1,X5)
& member(X2,X5) )
=> subclass(unordered_pair(X1,X2),X5) ),
inference(assume_negation,[status(cth)],[unordered_pair_is_subset]) ).
cnf(c_0_8,plain,
( subclass(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,plain,
( esk1_2(unordered_pair(X1,X2),X3) = X2
| esk1_2(unordered_pair(X1,X2),X3) = X1
| subclass(unordered_pair(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
fof(c_0_10,negated_conjecture,
( member(esk8_0,esk10_0)
& member(esk9_0,esk10_0)
& ~ subclass(unordered_pair(esk8_0,esk9_0),esk10_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_11,plain,
( esk1_2(unordered_pair(X1,X2),X3) = X2
| subclass(unordered_pair(X1,X2),X3)
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,negated_conjecture,
member(esk8_0,esk10_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,negated_conjecture,
( esk1_2(unordered_pair(esk8_0,X1),esk10_0) = X1
| subclass(unordered_pair(esk8_0,X1),esk10_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,negated_conjecture,
( subclass(unordered_pair(esk8_0,X1),esk10_0)
| ~ member(X1,esk10_0) ),
inference(spm,[status(thm)],[c_0_8,c_0_13]) ).
cnf(c_0_15,negated_conjecture,
member(esk9_0,esk10_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
~ subclass(unordered_pair(esk8_0,esk9_0),esk10_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET076+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.34 % CPULimit : 300
% 0.19/0.34 % WCLimit : 300
% 0.19/0.34 % DateTime : Sat Aug 26 15:39:45 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 17.59/17.68 % Version : CSE_E---1.5
% 17.59/17.68 % Problem : theBenchmark.p
% 17.59/17.68 % Proof found
% 17.59/17.68 % SZS status Theorem for theBenchmark.p
% 17.59/17.68 % SZS output start Proof
% See solution above
% 17.59/17.68 % Total time : 17.110000 s
% 17.59/17.68 % SZS output end Proof
% 17.59/17.68 % Total time : 17.115000 s
%------------------------------------------------------------------------------