TSTP Solution File: SEU238+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU238+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n019.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 16:23:41 EDT 2023
% Result : Theorem 0.85s 0.93s
% Output : CNFRefutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 45
% Syntax : Number of formulae : 97 ( 14 unt; 35 typ; 0 def)
% Number of atoms : 215 ( 25 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 264 ( 111 ~; 100 |; 32 &)
% ( 4 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 20 >; 6 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 15 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn; 38 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
proper_subset: ( $i * $i ) > $o ).
tff(decl_24,type,
empty: $i > $o ).
tff(decl_25,type,
function: $i > $o ).
tff(decl_26,type,
ordinal: $i > $o ).
tff(decl_27,type,
epsilon_transitive: $i > $o ).
tff(decl_28,type,
epsilon_connected: $i > $o ).
tff(decl_29,type,
relation: $i > $o ).
tff(decl_30,type,
one_to_one: $i > $o ).
tff(decl_31,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_32,type,
ordinal_subset: ( $i * $i ) > $o ).
tff(decl_33,type,
succ: $i > $i ).
tff(decl_34,type,
singleton: $i > $i ).
tff(decl_35,type,
subset: ( $i * $i ) > $o ).
tff(decl_36,type,
element: ( $i * $i ) > $o ).
tff(decl_37,type,
empty_set: $i ).
tff(decl_38,type,
relation_empty_yielding: $i > $o ).
tff(decl_39,type,
powerset: $i > $i ).
tff(decl_40,type,
being_limit_ordinal: $i > $o ).
tff(decl_41,type,
esk1_1: $i > $i ).
tff(decl_42,type,
esk2_0: $i ).
tff(decl_43,type,
esk3_0: $i ).
tff(decl_44,type,
esk4_0: $i ).
tff(decl_45,type,
esk5_0: $i ).
tff(decl_46,type,
esk6_0: $i ).
tff(decl_47,type,
esk7_0: $i ).
tff(decl_48,type,
esk8_0: $i ).
tff(decl_49,type,
esk9_0: $i ).
tff(decl_50,type,
esk10_0: $i ).
tff(decl_51,type,
esk11_0: $i ).
tff(decl_52,type,
esk12_0: $i ).
tff(decl_53,type,
esk13_0: $i ).
tff(decl_54,type,
esk14_1: $i > $i ).
tff(decl_55,type,
esk15_0: $i ).
tff(decl_56,type,
esk16_0: $i ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(t10_ordinal1,axiom,
! [X1] : in(X1,succ(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(d1_ordinal1,axiom,
! [X1] : succ(X1) = set_union2(X1,singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(t41_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ( being_limit_ordinal(X1)
<=> ! [X2] :
( ordinal(X2)
=> ( in(X2,X1)
=> in(succ(X2),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_ordinal1) ).
fof(fc3_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ( ~ empty(succ(X1))
& epsilon_transitive(succ(X1))
& epsilon_connected(succ(X1))
& ordinal(succ(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_ordinal1) ).
fof(t42_ordinal1,conjecture,
! [X1] :
( ordinal(X1)
=> ( ~ ( ~ being_limit_ordinal(X1)
& ! [X2] :
( ordinal(X2)
=> X1 != succ(X2) ) )
& ~ ( ? [X2] :
( ordinal(X2)
& X1 = succ(X2) )
& being_limit_ordinal(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_ordinal1) ).
fof(t33_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( in(X1,X2)
<=> ordinal_subset(succ(X1),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_ordinal1) ).
fof(redefinition_r1_ordinal1,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
<=> subset(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(d8_xboole_0,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( subset(X1,X2)
& X1 != X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(t21_ordinal1,axiom,
! [X1] :
( epsilon_transitive(X1)
=> ! [X2] :
( ordinal(X2)
=> ( proper_subset(X1,X2)
=> in(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_ordinal1) ).
fof(c_0_10,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(c_0_11,plain,
! [X50] : in(X50,succ(X50)),
inference(variable_rename,[status(thm)],[t10_ordinal1]) ).
fof(c_0_12,plain,
! [X18] : succ(X18) = set_union2(X18,singleton(X18)),
inference(variable_rename,[status(thm)],[d1_ordinal1]) ).
fof(c_0_13,plain,
! [X4,X5] :
( ~ in(X4,X5)
| ~ in(X5,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])]) ).
cnf(c_0_14,plain,
in(X1,succ(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
succ(X1) = set_union2(X1,singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,plain,
! [X62,X63] :
( ( ~ being_limit_ordinal(X62)
| ~ ordinal(X63)
| ~ in(X63,X62)
| in(succ(X63),X62)
| ~ ordinal(X62) )
& ( ordinal(esk14_1(X62))
| being_limit_ordinal(X62)
| ~ ordinal(X62) )
& ( in(esk14_1(X62),X62)
| being_limit_ordinal(X62)
| ~ ordinal(X62) )
& ( ~ in(succ(esk14_1(X62)),X62)
| being_limit_ordinal(X62)
| ~ ordinal(X62) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t41_ordinal1])])])])]) ).
fof(c_0_17,plain,
! [X1] :
( ordinal(X1)
=> ( ~ empty(succ(X1))
& epsilon_transitive(succ(X1))
& epsilon_connected(succ(X1))
& ordinal(succ(X1)) ) ),
inference(fof_simplification,[status(thm)],[fc3_ordinal1]) ).
cnf(c_0_18,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
in(X1,set_union2(X1,singleton(X1))),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
( in(succ(X2),X1)
| ~ being_limit_ordinal(X1)
| ~ ordinal(X2)
| ~ in(X2,X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_21,plain,
! [X28] :
( ( ~ empty(succ(X28))
| ~ ordinal(X28) )
& ( epsilon_transitive(succ(X28))
| ~ ordinal(X28) )
& ( epsilon_connected(succ(X28))
| ~ ordinal(X28) )
& ( ordinal(succ(X28))
| ~ ordinal(X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
fof(c_0_22,negated_conjecture,
~ ! [X1] :
( ordinal(X1)
=> ( ~ ( ~ being_limit_ordinal(X1)
& ! [X2] :
( ordinal(X2)
=> X1 != succ(X2) ) )
& ~ ( ? [X2] :
( ordinal(X2)
& X1 = succ(X2) )
& being_limit_ordinal(X1) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t42_ordinal1])]) ).
fof(c_0_23,plain,
! [X58,X59] :
( ( ~ in(X58,X59)
| ordinal_subset(succ(X58),X59)
| ~ ordinal(X59)
| ~ ordinal(X58) )
& ( ~ ordinal_subset(succ(X58),X59)
| in(X58,X59)
| ~ ordinal(X59)
| ~ ordinal(X58) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_ordinal1])])])]) ).
cnf(c_0_24,plain,
~ in(set_union2(X1,singleton(X1)),X1),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
( in(set_union2(X2,singleton(X2)),X1)
| ~ ordinal(X2)
| ~ ordinal(X1)
| ~ being_limit_ordinal(X1)
| ~ in(X2,X1) ),
inference(rw,[status(thm)],[c_0_20,c_0_15]) ).
cnf(c_0_26,plain,
( ordinal(succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_27,negated_conjecture,
! [X66] :
( ordinal(esk15_0)
& ( ordinal(esk16_0)
| ~ being_limit_ordinal(esk15_0) )
& ( esk15_0 = succ(esk16_0)
| ~ being_limit_ordinal(esk15_0) )
& ( being_limit_ordinal(esk15_0)
| ~ being_limit_ordinal(esk15_0) )
& ( ordinal(esk16_0)
| ~ ordinal(X66)
| esk15_0 != succ(X66) )
& ( esk15_0 = succ(esk16_0)
| ~ ordinal(X66)
| esk15_0 != succ(X66) )
& ( being_limit_ordinal(esk15_0)
| ~ ordinal(X66)
| esk15_0 != succ(X66) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])])]) ).
fof(c_0_28,plain,
! [X45,X46] :
( ( ~ ordinal_subset(X45,X46)
| subset(X45,X46)
| ~ ordinal(X45)
| ~ ordinal(X46) )
& ( ~ subset(X45,X46)
| ordinal_subset(X45,X46)
| ~ ordinal(X45)
| ~ ordinal(X46) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r1_ordinal1])])]) ).
cnf(c_0_29,plain,
( ordinal_subset(succ(X1),X2)
| ~ in(X1,X2)
| ~ ordinal(X2)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( ~ being_limit_ordinal(X1)
| ~ ordinal(X1)
| ~ in(X1,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,plain,
( ordinal(set_union2(X1,singleton(X1)))
| ~ ordinal(X1) ),
inference(rw,[status(thm)],[c_0_26,c_0_15]) ).
cnf(c_0_32,negated_conjecture,
( esk15_0 = succ(esk16_0)
| ~ being_limit_ordinal(esk15_0) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_33,plain,
! [X19,X20] :
( ( subset(X19,X20)
| ~ proper_subset(X19,X20) )
& ( X19 != X20
| ~ proper_subset(X19,X20) )
& ( ~ subset(X19,X20)
| X19 = X20
| proper_subset(X19,X20) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_xboole_0])])]) ).
cnf(c_0_34,plain,
( subset(X1,X2)
| ~ ordinal_subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,plain,
( ordinal_subset(set_union2(X1,singleton(X1)),X2)
| ~ ordinal(X2)
| ~ ordinal(X1)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_29,c_0_15]) ).
cnf(c_0_36,plain,
( ~ being_limit_ordinal(set_union2(X1,singleton(X1)))
| ~ ordinal(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_25]),c_0_19])]),c_0_31]) ).
cnf(c_0_37,negated_conjecture,
( esk15_0 = set_union2(esk16_0,singleton(esk16_0))
| ~ being_limit_ordinal(esk15_0) ),
inference(rw,[status(thm)],[c_0_32,c_0_15]) ).
cnf(c_0_38,negated_conjecture,
( ordinal(esk16_0)
| ~ being_limit_ordinal(esk15_0) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_39,plain,
( ordinal(esk14_1(X1))
| being_limit_ordinal(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_40,negated_conjecture,
ordinal(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_41,plain,
( X1 = X2
| proper_subset(X1,X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_42,plain,
( subset(set_union2(X1,singleton(X1)),X2)
| ~ ordinal(X2)
| ~ ordinal(X1)
| ~ in(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_31]) ).
cnf(c_0_43,plain,
( in(esk14_1(X1),X1)
| being_limit_ordinal(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_44,negated_conjecture,
~ being_limit_ordinal(esk15_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_45,negated_conjecture,
( being_limit_ordinal(esk15_0)
| ordinal(esk14_1(esk15_0)) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
fof(c_0_46,plain,
! [X54,X55] :
( ~ epsilon_transitive(X54)
| ~ ordinal(X55)
| ~ proper_subset(X54,X55)
| in(X54,X55) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_ordinal1])])]) ).
cnf(c_0_47,plain,
( set_union2(X1,singleton(X1)) = X2
| proper_subset(set_union2(X1,singleton(X1)),X2)
| ~ ordinal(X2)
| ~ ordinal(X1)
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,negated_conjecture,
in(esk14_1(esk15_0),esk15_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_40]),c_0_44]) ).
cnf(c_0_49,negated_conjecture,
ordinal(esk14_1(esk15_0)),
inference(sr,[status(thm)],[c_0_45,c_0_44]) ).
cnf(c_0_50,plain,
( in(X1,X2)
| ~ epsilon_transitive(X1)
| ~ ordinal(X2)
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_51,negated_conjecture,
( set_union2(esk14_1(esk15_0),singleton(esk14_1(esk15_0))) = esk15_0
| proper_subset(set_union2(esk14_1(esk15_0),singleton(esk14_1(esk15_0))),esk15_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_40]),c_0_49])]) ).
cnf(c_0_52,plain,
( epsilon_transitive(succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_53,plain,
( being_limit_ordinal(X1)
| ~ in(succ(esk14_1(X1)),X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_54,negated_conjecture,
( set_union2(esk14_1(esk15_0),singleton(esk14_1(esk15_0))) = esk15_0
| in(set_union2(esk14_1(esk15_0),singleton(esk14_1(esk15_0))),esk15_0)
| ~ epsilon_transitive(set_union2(esk14_1(esk15_0),singleton(esk14_1(esk15_0)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_40])]) ).
cnf(c_0_55,plain,
( epsilon_transitive(set_union2(X1,singleton(X1)))
| ~ ordinal(X1) ),
inference(rw,[status(thm)],[c_0_52,c_0_15]) ).
cnf(c_0_56,negated_conjecture,
( being_limit_ordinal(esk15_0)
| ~ ordinal(X1)
| esk15_0 != succ(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_57,plain,
( being_limit_ordinal(X1)
| ~ ordinal(X1)
| ~ in(set_union2(esk14_1(X1),singleton(esk14_1(X1))),X1) ),
inference(rw,[status(thm)],[c_0_53,c_0_15]) ).
cnf(c_0_58,negated_conjecture,
( set_union2(esk14_1(esk15_0),singleton(esk14_1(esk15_0))) = esk15_0
| in(set_union2(esk14_1(esk15_0),singleton(esk14_1(esk15_0))),esk15_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_49])]) ).
cnf(c_0_59,negated_conjecture,
( being_limit_ordinal(esk15_0)
| esk15_0 != set_union2(X1,singleton(X1))
| ~ ordinal(X1) ),
inference(rw,[status(thm)],[c_0_56,c_0_15]) ).
cnf(c_0_60,negated_conjecture,
set_union2(esk14_1(esk15_0),singleton(esk14_1(esk15_0))) = esk15_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_40])]),c_0_44]) ).
cnf(c_0_61,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_49])]),c_0_44]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU238+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 12:40:13 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.57 start to proof: theBenchmark
% 0.85/0.93 % Version : CSE_E---1.5
% 0.85/0.93 % Problem : theBenchmark.p
% 0.85/0.93 % Proof found
% 0.85/0.93 % SZS status Theorem for theBenchmark.p
% 0.85/0.93 % SZS output start Proof
% See solution above
% 0.85/0.93 % Total time : 0.347000 s
% 0.85/0.93 % SZS output end Proof
% 0.85/0.93 % Total time : 0.351000 s
%------------------------------------------------------------------------------