TSTP Solution File: SEU154+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU154+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n031.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 16:22:51 EDT 2023
% Result : Theorem 0.21s 0.64s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 31
% Syntax : Number of formulae : 50 ( 10 unt; 27 typ; 0 def)
% Number of atoms : 62 ( 19 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 69 ( 30 ~; 19 |; 16 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 44 ( 22 >; 22 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 5 con; 0-3 aty)
% Number of variables : 41 ( 0 sgn; 26 !; 2 ?; 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,
set_difference: ( $i * $i ) > $i ).
tff(decl_32,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_33,type,
empty: $i > $o ).
tff(decl_34,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_35,type,
esk2_1: $i > $i ).
tff(decl_36,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_37,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_38,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_39,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_40,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_41,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
esk9_0: $i ).
tff(decl_43,type,
esk10_0: $i ).
tff(decl_44,type,
esk11_0: $i ).
tff(decl_45,type,
esk12_0: $i ).
tff(decl_46,type,
esk13_2: ( $i * $i ) > $i ).
tff(decl_47,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_48,type,
esk15_2: ( $i * $i ) > $i ).
fof(l28_zfmisc_1,conjecture,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
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(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(t3_xboole_0,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[l28_zfmisc_1])]) ).
fof(c_0_5,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])])])])])]) ).
fof(c_0_6,lemma,
! [X169] : unordered_pair(X169,X169) = singleton(X169),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_7,negated_conjecture,
( ~ in(esk9_0,esk10_0)
& ~ disjoint(singleton(esk9_0),esk10_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_8,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[t3_xboole_0]) ).
cnf(c_0_9,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
~ disjoint(singleton(esk9_0),esk10_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,lemma,
! [X144,X145,X147,X148,X149] :
( ( in(esk14_2(X144,X145),X144)
| disjoint(X144,X145) )
& ( in(esk14_2(X144,X145),X145)
| disjoint(X144,X145) )
& ( ~ in(X149,X147)
| ~ in(X149,X148)
| ~ disjoint(X147,X148) ) ),
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_8])])])])])]) ).
cnf(c_0_13,plain,
( X1 = X3
| X2 != unordered_pair(X3,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
~ disjoint(unordered_pair(esk9_0,esk9_0),esk10_0),
inference(rw,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_15,lemma,
( in(esk14_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,lemma,
( in(esk14_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( X1 = X2
| ~ in(X1,unordered_pair(X2,X2)) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
in(esk14_2(unordered_pair(esk9_0,esk9_0),esk10_0),unordered_pair(esk9_0,esk9_0)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
in(esk14_2(unordered_pair(esk9_0,esk9_0),esk10_0),esk10_0),
inference(spm,[status(thm)],[c_0_14,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
esk14_2(unordered_pair(esk9_0,esk9_0),esk10_0) = esk9_0,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
~ in(esk9_0,esk10_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU154+2 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n031.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 20:53:20 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.61 start to proof: theBenchmark
% 0.21/0.64 % Version : CSE_E---1.5
% 0.21/0.64 % Problem : theBenchmark.p
% 0.21/0.64 % Proof found
% 0.21/0.64 % SZS status Theorem for theBenchmark.p
% 0.21/0.64 % SZS output start Proof
% See solution above
% 0.21/0.65 % Total time : 0.022000 s
% 0.21/0.65 % SZS output end Proof
% 0.21/0.65 % Total time : 0.025000 s
%------------------------------------------------------------------------------