TSTP Solution File: SEU156+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU156+2 : 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 : n012.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 16:22:52 EDT 2023
% Result : Theorem 0.18s 0.57s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 43
% Syntax : Number of formulae : 91 ( 25 unt; 34 typ; 0 def)
% Number of atoms : 134 ( 107 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 124 ( 47 ~; 56 |; 13 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 54 ( 27 >; 27 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 7 con; 0-3 aty)
% Number of variables : 111 ( 9 sgn; 59 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
proper_subset: ( $i * $i ) > $o ).
tff(decl_24,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_25,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_26,type,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_27,type,
subset: ( $i * $i ) > $o ).
tff(decl_28,type,
singleton: $i > $i ).
tff(decl_29,type,
empty_set: $i ).
tff(decl_30,type,
powerset: $i > $i ).
tff(decl_31,type,
union: $i > $i ).
tff(decl_32,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_33,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_34,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_35,type,
empty: $i > $o ).
tff(decl_36,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_37,type,
esk2_1: $i > $i ).
tff(decl_38,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_39,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_40,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_41,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_42,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_43,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_44,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_45,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_46,type,
esk11_3: ( $i * $i * $i ) > $i ).
tff(decl_47,type,
esk12_0: $i ).
tff(decl_48,type,
esk13_0: $i ).
tff(decl_49,type,
esk14_2: ( $i * $i ) > $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_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk20_2: ( $i * $i ) > $i ).
fof(t33_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(t10_zfmisc_1,lemma,
! [X1,X2,X3,X4] :
~ ( unordered_pair(X1,X2) = unordered_pair(X3,X4)
& X1 != X3
& X1 != X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(t8_zfmisc_1,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(t9_zfmisc_1,lemma,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X2 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfmisc_1) ).
fof(c_0_9,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ),
inference(assume_negation,[status(cth)],[t33_zfmisc_1]) ).
fof(c_0_10,plain,
! [X88,X89] : ordered_pair(X88,X89) = unordered_pair(unordered_pair(X88,X89),singleton(X88)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_11,lemma,
! [X190] : unordered_pair(X190,X190) = singleton(X190),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_12,negated_conjecture,
( ordered_pair(esk15_0,esk16_0) = ordered_pair(esk17_0,esk18_0)
& ( esk15_0 != esk17_0
| esk16_0 != esk18_0 ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_13,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
ordered_pair(esk15_0,esk16_0) = ordered_pair(esk17_0,esk18_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_17,plain,
! [X9,X10] : unordered_pair(X9,X10) = unordered_pair(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(c_0_18,lemma,
! [X126,X127,X128,X129] :
( unordered_pair(X126,X127) != unordered_pair(X128,X129)
| X126 = X128
| X126 = X129 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t10_zfmisc_1])]) ).
cnf(c_0_19,negated_conjecture,
unordered_pair(unordered_pair(esk17_0,esk18_0),unordered_pair(esk17_0,esk17_0)) = unordered_pair(unordered_pair(esk15_0,esk16_0),unordered_pair(esk15_0,esk15_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]) ).
cnf(c_0_20,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_21,plain,
! [X35,X36,X37,X38,X39,X40,X41,X42] :
( ( ~ in(X38,X37)
| X38 = X35
| X38 = X36
| X37 != unordered_pair(X35,X36) )
& ( X39 != X35
| in(X39,X37)
| X37 != unordered_pair(X35,X36) )
& ( X39 != X36
| in(X39,X37)
| X37 != unordered_pair(X35,X36) )
& ( esk4_3(X40,X41,X42) != X40
| ~ in(esk4_3(X40,X41,X42),X42)
| X42 = unordered_pair(X40,X41) )
& ( esk4_3(X40,X41,X42) != X41
| ~ in(esk4_3(X40,X41,X42),X42)
| X42 = unordered_pair(X40,X41) )
& ( in(esk4_3(X40,X41,X42),X42)
| esk4_3(X40,X41,X42) = X40
| esk4_3(X40,X41,X42) = X41
| X42 = unordered_pair(X40,X41) ) ),
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_tarski])])])])])]) ).
fof(c_0_22,plain,
! [X17,X18,X19,X20,X21,X22] :
( ( ~ in(X19,X18)
| X19 = X17
| X18 != singleton(X17) )
& ( X20 != X17
| in(X20,X18)
| X18 != singleton(X17) )
& ( ~ in(esk1_2(X21,X22),X22)
| esk1_2(X21,X22) != X21
| X22 = singleton(X21) )
& ( in(esk1_2(X21,X22),X22)
| esk1_2(X21,X22) = X21
| X22 = singleton(X21) ) ),
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_23,lemma,
( X1 = X3
| X1 = X4
| unordered_pair(X1,X2) != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,negated_conjecture,
unordered_pair(unordered_pair(esk15_0,esk15_0),unordered_pair(esk15_0,esk16_0)) = unordered_pair(unordered_pair(esk17_0,esk17_0),unordered_pair(esk17_0,esk18_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_20]) ).
cnf(c_0_25,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,negated_conjecture,
( X1 = unordered_pair(esk15_0,esk15_0)
| X1 = unordered_pair(esk15_0,esk16_0)
| unordered_pair(X1,X2) != unordered_pair(unordered_pair(esk17_0,esk17_0),unordered_pair(esk17_0,esk18_0)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
fof(c_0_29,lemma,
! [X205,X206,X207] :
( singleton(X205) != unordered_pair(X206,X207)
| X205 = X206 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_zfmisc_1])]) ).
cnf(c_0_30,plain,
( X1 = X3
| X1 = X4
| ~ in(X1,X2)
| X2 != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_31,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_25])]) ).
cnf(c_0_32,plain,
( X1 = X3
| X2 != unordered_pair(X3,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_26,c_0_14]) ).
cnf(c_0_33,plain,
in(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_27])]) ).
cnf(c_0_34,negated_conjecture,
( unordered_pair(esk15_0,esk16_0) = unordered_pair(esk17_0,esk17_0)
| unordered_pair(esk15_0,esk15_0) = unordered_pair(esk17_0,esk17_0) ),
inference(er,[status(thm)],[c_0_28]) ).
cnf(c_0_35,lemma,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,plain,
( X1 = X2
| X1 = X3
| ~ in(X1,unordered_pair(X3,X2)) ),
inference(er,[status(thm)],[c_0_30]) ).
cnf(c_0_37,negated_conjecture,
in(unordered_pair(esk15_0,esk16_0),unordered_pair(unordered_pair(esk17_0,esk17_0),unordered_pair(esk17_0,esk18_0))),
inference(spm,[status(thm)],[c_0_31,c_0_24]) ).
cnf(c_0_38,plain,
( X1 = X2
| ~ in(X1,unordered_pair(X2,X2)) ),
inference(er,[status(thm)],[c_0_32]) ).
cnf(c_0_39,negated_conjecture,
( unordered_pair(esk15_0,esk15_0) = unordered_pair(esk17_0,esk17_0)
| in(esk15_0,unordered_pair(esk17_0,esk17_0)) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,lemma,
( X1 = X2
| unordered_pair(X1,X1) != unordered_pair(X2,X3) ),
inference(rw,[status(thm)],[c_0_35,c_0_14]) ).
cnf(c_0_41,negated_conjecture,
( unordered_pair(esk15_0,esk16_0) = unordered_pair(esk17_0,esk18_0)
| unordered_pair(esk15_0,esk16_0) = unordered_pair(esk17_0,esk17_0) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,negated_conjecture,
esk15_0 = esk17_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
fof(c_0_43,lemma,
! [X208,X209,X210] :
( singleton(X208) != unordered_pair(X209,X210)
| X209 = X210 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t9_zfmisc_1])]) ).
cnf(c_0_44,negated_conjecture,
( unordered_pair(esk17_0,esk16_0) = unordered_pair(esk17_0,esk17_0)
| unordered_pair(esk17_0,esk16_0) = unordered_pair(esk17_0,esk18_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42]),c_0_42]) ).
cnf(c_0_45,negated_conjecture,
( esk15_0 != esk17_0
| esk16_0 != esk18_0 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_46,lemma,
( X2 = X3
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_47,negated_conjecture,
( unordered_pair(esk17_0,esk16_0) = unordered_pair(esk17_0,esk17_0)
| in(esk16_0,unordered_pair(esk17_0,esk18_0)) ),
inference(spm,[status(thm)],[c_0_31,c_0_44]) ).
cnf(c_0_48,negated_conjecture,
esk16_0 != esk18_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_42])]) ).
cnf(c_0_49,lemma,
( X2 = X3
| unordered_pair(X1,X1) != unordered_pair(X2,X3) ),
inference(rw,[status(thm)],[c_0_46,c_0_14]) ).
cnf(c_0_50,negated_conjecture,
esk16_0 = esk17_0,
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_47]),c_0_48]),c_0_49]) ).
cnf(c_0_51,negated_conjecture,
unordered_pair(unordered_pair(esk17_0,esk17_0),unordered_pair(esk17_0,esk18_0)) = unordered_pair(unordered_pair(esk17_0,esk17_0),unordered_pair(esk17_0,esk17_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_50]),c_0_42]),c_0_42]),c_0_42]) ).
cnf(c_0_52,negated_conjecture,
in(unordered_pair(esk17_0,esk18_0),unordered_pair(unordered_pair(esk17_0,esk17_0),unordered_pair(esk17_0,esk17_0))),
inference(spm,[status(thm)],[c_0_31,c_0_51]) ).
cnf(c_0_53,negated_conjecture,
unordered_pair(esk17_0,esk18_0) = unordered_pair(esk17_0,esk17_0),
inference(spm,[status(thm)],[c_0_38,c_0_52]) ).
cnf(c_0_54,negated_conjecture,
in(esk18_0,unordered_pair(esk17_0,esk17_0)),
inference(spm,[status(thm)],[c_0_31,c_0_53]) ).
cnf(c_0_55,negated_conjecture,
esk18_0 != esk17_0,
inference(rw,[status(thm)],[c_0_48,c_0_50]) ).
cnf(c_0_56,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_54]),c_0_55]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU156+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.33 % Computer : n012.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Wed Aug 23 15:57:42 EDT 2023
% 0.14/0.33 % CPUTime :
% 0.18/0.54 start to proof: theBenchmark
% 0.18/0.57 % Version : CSE_E---1.5
% 0.18/0.57 % Problem : theBenchmark.p
% 0.18/0.57 % Proof found
% 0.18/0.57 % SZS status Theorem for theBenchmark.p
% 0.18/0.57 % SZS output start Proof
% See solution above
% 0.18/0.58 % Total time : 0.021000 s
% 0.18/0.58 % SZS output end Proof
% 0.18/0.58 % Total time : 0.024000 s
%------------------------------------------------------------------------------