TSTP Solution File: NUM401+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM401+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 : n024.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 10:37:12 EDT 2023
% Result : Theorem 0.20s 0.62s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 48
% Syntax : Number of formulae : 96 ( 15 unt; 37 typ; 0 def)
% Number of atoms : 195 ( 41 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 219 ( 83 ~; 92 |; 24 &)
% ( 9 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 29 ( 21 >; 8 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 16 con; 0-3 aty)
% Number of variables : 88 ( 3 sgn; 53 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
empty: $i > $o ).
tff(decl_24,type,
function: $i > $o ).
tff(decl_25,type,
ordinal: $i > $o ).
tff(decl_26,type,
epsilon_transitive: $i > $o ).
tff(decl_27,type,
epsilon_connected: $i > $o ).
tff(decl_28,type,
relation: $i > $o ).
tff(decl_29,type,
one_to_one: $i > $o ).
tff(decl_30,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_31,type,
ordinal_subset: ( $i * $i ) > $o ).
tff(decl_32,type,
subset: ( $i * $i ) > $o ).
tff(decl_33,type,
succ: $i > $i ).
tff(decl_34,type,
singleton: $i > $i ).
tff(decl_35,type,
element: ( $i * $i ) > $o ).
tff(decl_36,type,
empty_set: $i ).
tff(decl_37,type,
relation_empty_yielding: $i > $o ).
tff(decl_38,type,
relation_non_empty: $i > $o ).
tff(decl_39,type,
powerset: $i > $i ).
tff(decl_40,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_41,type,
esk2_1: $i > $i ).
tff(decl_42,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_43,type,
esk4_1: $i > $i ).
tff(decl_44,type,
esk5_0: $i ).
tff(decl_45,type,
esk6_0: $i ).
tff(decl_46,type,
esk7_0: $i ).
tff(decl_47,type,
esk8_0: $i ).
tff(decl_48,type,
esk9_0: $i ).
tff(decl_49,type,
esk10_0: $i ).
tff(decl_50,type,
esk11_0: $i ).
tff(decl_51,type,
esk12_0: $i ).
tff(decl_52,type,
esk13_0: $i ).
tff(decl_53,type,
esk14_0: $i ).
tff(decl_54,type,
esk15_0: $i ).
tff(decl_55,type,
esk16_0: $i ).
tff(decl_56,type,
esk17_0: $i ).
tff(decl_57,type,
esk18_0: $i ).
tff(decl_58,type,
esk19_0: $i ).
fof(t34_ordinal1,conjecture,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( in(X1,succ(X2))
<=> ordinal_subset(X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_ordinal1) ).
fof(d1_ordinal1,axiom,
! [X1] : succ(X1) = set_union2(X1,singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(redefinition_r1_ordinal1,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
<=> subset(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(d2_ordinal1,axiom,
! [X1] :
( epsilon_transitive(X1)
<=> ! [X2] :
( in(X2,X1)
=> subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(t24_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(cc1_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(t10_ordinal1,axiom,
! [X1] : in(X1,succ(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(c_0_11,negated_conjecture,
~ ! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( in(X1,succ(X2))
<=> ordinal_subset(X1,X2) ) ) ),
inference(assume_negation,[status(cth)],[t34_ordinal1]) ).
fof(c_0_12,negated_conjecture,
( ordinal(esk18_0)
& ordinal(esk19_0)
& ( ~ in(esk18_0,succ(esk19_0))
| ~ ordinal_subset(esk18_0,esk19_0) )
& ( in(esk18_0,succ(esk19_0))
| ordinal_subset(esk18_0,esk19_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_13,plain,
! [X19] : succ(X19) = set_union2(X19,singleton(X19)),
inference(variable_rename,[status(thm)],[d1_ordinal1]) ).
cnf(c_0_14,negated_conjecture,
( ~ in(esk18_0,succ(esk19_0))
| ~ ordinal_subset(esk18_0,esk19_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,plain,
succ(X1) = set_union2(X1,singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_16,plain,
! [X64,X65] :
( ( ~ ordinal_subset(X64,X65)
| subset(X64,X65)
| ~ ordinal(X64)
| ~ ordinal(X65) )
& ( ~ subset(X64,X65)
| ordinal_subset(X64,X65)
| ~ ordinal(X64)
| ~ ordinal(X65) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r1_ordinal1])])]) ).
cnf(c_0_17,negated_conjecture,
( in(esk18_0,succ(esk19_0))
| ordinal_subset(esk18_0,esk19_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
( ~ ordinal_subset(esk18_0,esk19_0)
| ~ in(esk18_0,set_union2(esk19_0,singleton(esk19_0))) ),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
( ordinal_subset(X1,X2)
| ~ subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,negated_conjecture,
ordinal(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,negated_conjecture,
ordinal(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_22,plain,
! [X27,X28,X29] :
( ( ~ epsilon_transitive(X27)
| ~ in(X28,X27)
| subset(X28,X27) )
& ( in(esk2_1(X29),X29)
| epsilon_transitive(X29) )
& ( ~ subset(esk2_1(X29),X29)
| epsilon_transitive(X29) ) ),
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)],[d2_ordinal1])])])])])]) ).
fof(c_0_23,plain,
! [X17,X18] :
( ( subset(X17,X18)
| X17 != X18 )
& ( subset(X18,X17)
| X17 != X18 )
& ( ~ subset(X17,X18)
| ~ subset(X18,X17)
| X17 = X18 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
cnf(c_0_24,plain,
( subset(X1,X2)
| ~ ordinal_subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,negated_conjecture,
( ordinal_subset(esk18_0,esk19_0)
| in(esk18_0,set_union2(esk19_0,singleton(esk19_0))) ),
inference(rw,[status(thm)],[c_0_17,c_0_15]) ).
fof(c_0_26,plain,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[t24_ordinal1]) ).
cnf(c_0_27,negated_conjecture,
( ~ subset(esk18_0,esk19_0)
| ~ in(esk18_0,set_union2(esk19_0,singleton(esk19_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]) ).
cnf(c_0_28,plain,
( subset(X2,X1)
| ~ epsilon_transitive(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_29,plain,
! [X8] :
( ( epsilon_transitive(X8)
| ~ ordinal(X8) )
& ( epsilon_connected(X8)
| ~ ordinal(X8) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_ordinal1])])]) ).
fof(c_0_30,plain,
! [X31,X32,X33,X34,X35,X36,X37,X38] :
( ( ~ in(X34,X33)
| in(X34,X31)
| in(X34,X32)
| X33 != set_union2(X31,X32) )
& ( ~ in(X35,X31)
| in(X35,X33)
| X33 != set_union2(X31,X32) )
& ( ~ in(X35,X32)
| in(X35,X33)
| X33 != set_union2(X31,X32) )
& ( ~ in(esk3_3(X36,X37,X38),X36)
| ~ in(esk3_3(X36,X37,X38),X38)
| X38 = set_union2(X36,X37) )
& ( ~ in(esk3_3(X36,X37,X38),X37)
| ~ in(esk3_3(X36,X37,X38),X38)
| X38 = set_union2(X36,X37) )
& ( in(esk3_3(X36,X37,X38),X38)
| in(esk3_3(X36,X37,X38),X36)
| in(esk3_3(X36,X37,X38),X37)
| X38 = set_union2(X36,X37) ) ),
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)],[d2_xboole_0])])])])])]) ).
cnf(c_0_31,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,negated_conjecture,
( subset(esk18_0,esk19_0)
| in(esk18_0,set_union2(esk19_0,singleton(esk19_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_20]),c_0_21])]) ).
fof(c_0_33,plain,
! [X74,X75] :
( ~ ordinal(X74)
| ~ ordinal(X75)
| in(X74,X75)
| X74 = X75
| in(X75,X74) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])]) ).
cnf(c_0_34,negated_conjecture,
( ~ epsilon_transitive(esk19_0)
| ~ in(esk18_0,set_union2(esk19_0,singleton(esk19_0)))
| ~ in(esk18_0,esk19_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,negated_conjecture,
( esk18_0 = esk19_0
| in(esk18_0,set_union2(esk19_0,singleton(esk19_0)))
| ~ subset(esk19_0,esk18_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_38,plain,
( in(X1,X2)
| X1 = X2
| in(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_39,negated_conjecture,
( ~ in(esk18_0,set_union2(esk19_0,singleton(esk19_0)))
| ~ in(esk18_0,esk19_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_20])]) ).
cnf(c_0_40,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_36]) ).
cnf(c_0_41,negated_conjecture,
( esk18_0 = esk19_0
| in(esk18_0,set_union2(esk19_0,singleton(esk19_0)))
| ~ epsilon_transitive(esk18_0)
| ~ in(esk19_0,esk18_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_28]) ).
cnf(c_0_42,negated_conjecture,
( X1 = esk19_0
| in(X1,esk19_0)
| in(esk19_0,X1)
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_20]) ).
cnf(c_0_43,negated_conjecture,
~ in(esk18_0,esk19_0),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
fof(c_0_44,plain,
! [X20,X21,X22,X23,X24,X25] :
( ( ~ in(X22,X21)
| X22 = X20
| X21 != singleton(X20) )
& ( X23 != X20
| in(X23,X21)
| X21 != singleton(X20) )
& ( ~ in(esk1_2(X24,X25),X25)
| esk1_2(X24,X25) != X24
| X25 = singleton(X24) )
& ( in(esk1_2(X24,X25),X25)
| esk1_2(X24,X25) = X24
| X25 = singleton(X24) ) ),
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)],[d1_tarski])])])])])]) ).
cnf(c_0_45,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_46,negated_conjecture,
( esk18_0 = esk19_0
| in(esk18_0,set_union2(esk19_0,singleton(esk19_0)))
| ~ in(esk19_0,esk18_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_35]),c_0_21])]) ).
cnf(c_0_47,negated_conjecture,
( esk18_0 = esk19_0
| in(esk19_0,esk18_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_21]),c_0_43]) ).
cnf(c_0_48,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_49,plain,
! [X69] : in(X69,succ(X69)),
inference(variable_rename,[status(thm)],[t10_ordinal1]) ).
cnf(c_0_50,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X3,X2)) ),
inference(er,[status(thm)],[c_0_45]) ).
cnf(c_0_51,negated_conjecture,
( esk18_0 = esk19_0
| in(esk18_0,set_union2(esk19_0,singleton(esk19_0))) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_48]) ).
fof(c_0_53,plain,
! [X68] : subset(X68,X68),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_54,plain,
in(X1,succ(X1)),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_55,negated_conjecture,
esk18_0 = esk19_0,
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_43]),c_0_52]) ).
cnf(c_0_56,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_57,plain,
in(X1,set_union2(X1,singleton(X1))),
inference(rw,[status(thm)],[c_0_54,c_0_15]) ).
cnf(c_0_58,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_55]),c_0_56]),c_0_55]),c_0_57])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM401+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n024.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 15:29:09 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.20/0.62 % Version : CSE_E---1.5
% 0.20/0.62 % Problem : theBenchmark.p
% 0.20/0.62 % Proof found
% 0.20/0.62 % SZS status Theorem for theBenchmark.p
% 0.20/0.62 % SZS output start Proof
% See solution above
% 0.20/0.63 % Total time : 0.054000 s
% 0.20/0.63 % SZS output end Proof
% 0.20/0.63 % Total time : 0.058000 s
%------------------------------------------------------------------------------