TSTP Solution File: NUM404+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM404+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n002.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 0.21s 0.67s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 41
% Syntax : Number of formulae : 80 ( 5 unt; 33 typ; 0 def)
% Number of atoms : 146 ( 9 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 162 ( 63 ~; 59 |; 23 &)
% ( 6 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 18 >; 4 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 15 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn; 46 !; 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,
subset: ( $i * $i ) > $o ).
tff(decl_31,type,
element: ( $i * $i ) > $o ).
tff(decl_32,type,
empty_set: $i ).
tff(decl_33,type,
relation_empty_yielding: $i > $o ).
tff(decl_34,type,
relation_non_empty: $i > $o ).
tff(decl_35,type,
powerset: $i > $i ).
tff(decl_36,type,
esk1_1: $i > $i ).
tff(decl_37,type,
esk2_1: $i > $i ).
tff(decl_38,type,
esk3_1: $i > $i ).
tff(decl_39,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_40,type,
esk5_1: $i > $i ).
tff(decl_41,type,
esk6_0: $i ).
tff(decl_42,type,
esk7_0: $i ).
tff(decl_43,type,
esk8_0: $i ).
tff(decl_44,type,
esk9_0: $i ).
tff(decl_45,type,
esk10_0: $i ).
tff(decl_46,type,
esk11_0: $i ).
tff(decl_47,type,
esk12_0: $i ).
tff(decl_48,type,
esk13_0: $i ).
tff(decl_49,type,
esk14_0: $i ).
tff(decl_50,type,
esk15_0: $i ).
tff(decl_51,type,
esk16_0: $i ).
tff(decl_52,type,
esk17_0: $i ).
tff(decl_53,type,
esk18_0: $i ).
tff(decl_54,type,
esk19_0: $i ).
fof(t37_ordinal1,conjecture,
! [X1] :
~ ! [X2] :
( in(X2,X1)
<=> ordinal(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_ordinal1) ).
fof(t23_ordinal1,axiom,
! [X1,X2] :
( ordinal(X2)
=> ( in(X1,X2)
=> ordinal(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_ordinal1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(d3_ordinal1,axiom,
! [X1] :
( epsilon_connected(X1)
<=> ! [X2,X3] :
~ ( in(X2,X1)
& in(X3,X1)
& ~ in(X2,X3)
& X2 != X3
& ~ in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_ordinal1) ).
fof(t24_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(d2_ordinal1,axiom,
! [X1] :
( epsilon_transitive(X1)
<=> ! [X2] :
( in(X2,X1)
=> subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(cc2_ordinal1,axiom,
! [X1] :
( ( epsilon_transitive(X1)
& epsilon_connected(X1) )
=> ordinal(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(c_0_8,negated_conjecture,
~ ! [X1] :
~ ! [X2] :
( in(X2,X1)
<=> ordinal(X2) ),
inference(assume_negation,[status(cth)],[t37_ordinal1]) ).
fof(c_0_9,plain,
! [X47,X48] :
( ~ ordinal(X48)
| ~ in(X47,X48)
| ordinal(X47) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_ordinal1])]) ).
fof(c_0_10,plain,
! [X22,X23,X24,X25,X26] :
( ( ~ subset(X22,X23)
| ~ in(X24,X22)
| in(X24,X23) )
& ( in(esk4_2(X25,X26),X25)
| subset(X25,X26) )
& ( ~ in(esk4_2(X25,X26),X26)
| subset(X25,X26) ) ),
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)],[d3_tarski])])])])])]) ).
fof(c_0_11,negated_conjecture,
! [X54] :
( ( ~ in(X54,esk19_0)
| ordinal(X54) )
& ( ~ ordinal(X54)
| in(X54,esk19_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
cnf(c_0_12,plain,
( ordinal(X2)
| ~ ordinal(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( in(esk4_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X1] :
( epsilon_connected(X1)
<=> ! [X2,X3] :
~ ( in(X2,X1)
& in(X3,X1)
& ~ in(X2,X3)
& X2 != X3
& ~ in(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[d3_ordinal1]) ).
fof(c_0_15,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_16,negated_conjecture,
( in(X1,esk19_0)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( subset(X1,X2)
| ordinal(esk4_2(X1,X2))
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_18,plain,
! [X12,X13,X14] :
( ( ~ epsilon_transitive(X12)
| ~ in(X13,X12)
| subset(X13,X12) )
& ( in(esk1_1(X14),X14)
| epsilon_transitive(X14) )
& ( ~ subset(esk1_1(X14),X14)
| epsilon_transitive(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)],[d2_ordinal1])])])])])]) ).
fof(c_0_19,plain,
! [X16,X17,X18,X19] :
( ( ~ epsilon_connected(X16)
| ~ in(X17,X16)
| ~ in(X18,X16)
| in(X17,X18)
| X17 = X18
| in(X18,X17) )
& ( in(esk2_1(X19),X19)
| epsilon_connected(X19) )
& ( in(esk3_1(X19),X19)
| epsilon_connected(X19) )
& ( ~ in(esk2_1(X19),esk3_1(X19))
| epsilon_connected(X19) )
& ( esk2_1(X19) != esk3_1(X19)
| epsilon_connected(X19) )
& ( ~ in(esk3_1(X19),esk2_1(X19))
| epsilon_connected(X19) ) ),
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)],[c_0_14])])])])])]) ).
fof(c_0_20,plain,
! [X49,X50] :
( ~ ordinal(X49)
| ~ ordinal(X50)
| in(X49,X50)
| X49 = X50
| in(X50,X49) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
cnf(c_0_21,plain,
( subset(X1,X2)
| ~ in(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_22,negated_conjecture,
( subset(X1,X2)
| in(esk4_2(X1,X2),esk19_0)
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,negated_conjecture,
( ordinal(X1)
| ~ in(X1,esk19_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_24,plain,
( in(esk1_1(X1),X1)
| epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( epsilon_connected(X1)
| ~ in(esk3_1(X1),esk2_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( in(X1,X2)
| X1 = X2
| in(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
( epsilon_connected(X1)
| ~ in(esk2_1(X1),esk3_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,plain,
( epsilon_connected(X1)
| esk2_1(X1) != esk3_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,plain,
( in(esk2_1(X1),X1)
| epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_30,plain,
( in(esk3_1(X1),X1)
| epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_31,plain,
! [X10] :
( ~ epsilon_transitive(X10)
| ~ epsilon_connected(X10)
| ordinal(X10) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_ordinal1])]) ).
cnf(c_0_32,plain,
( epsilon_transitive(X1)
| ~ subset(esk1_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_33,negated_conjecture,
( subset(X1,esk19_0)
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_34,negated_conjecture,
( epsilon_transitive(esk19_0)
| ordinal(esk1_1(esk19_0)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_35,plain,
( epsilon_connected(X1)
| ~ ordinal(esk2_1(X1))
| ~ ordinal(esk3_1(X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28]) ).
cnf(c_0_36,negated_conjecture,
( epsilon_connected(esk19_0)
| ordinal(esk2_1(esk19_0)) ),
inference(spm,[status(thm)],[c_0_23,c_0_29]) ).
cnf(c_0_37,negated_conjecture,
( epsilon_connected(esk19_0)
| ordinal(esk3_1(esk19_0)) ),
inference(spm,[status(thm)],[c_0_23,c_0_30]) ).
fof(c_0_38,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
cnf(c_0_39,plain,
( ordinal(X1)
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_40,negated_conjecture,
epsilon_transitive(esk19_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_41,negated_conjecture,
epsilon_connected(esk19_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
fof(c_0_42,plain,
! [X4,X5] :
( ~ in(X4,X5)
| ~ in(X5,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])]) ).
cnf(c_0_43,negated_conjecture,
ordinal(esk19_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]) ).
cnf(c_0_44,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_45,negated_conjecture,
in(esk19_0,esk19_0),
inference(spm,[status(thm)],[c_0_16,c_0_43]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_45])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM404+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n002.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 : Fri Aug 25 12:14:17 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.57 start to proof: theBenchmark
% 0.21/0.67 % Version : CSE_E---1.5
% 0.21/0.67 % Problem : theBenchmark.p
% 0.21/0.67 % Proof found
% 0.21/0.67 % SZS status Theorem for theBenchmark.p
% 0.21/0.67 % SZS output start Proof
% See solution above
% 0.21/0.68 % Total time : 0.092000 s
% 0.21/0.68 % SZS output end Proof
% 0.21/0.68 % Total time : 0.095000 s
%------------------------------------------------------------------------------