TSTP Solution File: SET766+4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET766+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n022.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 14:35:29 EDT 2023
% Result : Theorem 0.21s 0.58s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 46
% Syntax : Number of formulae : 63 ( 6 unt; 42 typ; 0 def)
% Number of atoms : 276 ( 0 equ)
% Maximal formula atoms : 207 ( 13 avg)
% Number of connectives : 327 ( 72 ~; 169 |; 70 &)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 65 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 75 ( 38 >; 37 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 33 ( 33 usr; 4 con; 0-3 aty)
% Number of variables : 55 ( 0 sgn; 44 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
subset: ( $i * $i ) > $o ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
equal_set: ( $i * $i ) > $o ).
tff(decl_25,type,
power_set: $i > $i ).
tff(decl_26,type,
intersection: ( $i * $i ) > $i ).
tff(decl_27,type,
union: ( $i * $i ) > $i ).
tff(decl_28,type,
empty_set: $i ).
tff(decl_29,type,
difference: ( $i * $i ) > $i ).
tff(decl_30,type,
singleton: $i > $i ).
tff(decl_31,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_32,type,
sum: $i > $i ).
tff(decl_33,type,
product: $i > $i ).
tff(decl_34,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_35,type,
partition: ( $i * $i ) > $o ).
tff(decl_36,type,
equivalence: ( $i * $i ) > $o ).
tff(decl_37,type,
apply: ( $i * $i * $i ) > $o ).
tff(decl_38,type,
equivalence_class: ( $i * $i * $i ) > $i ).
tff(decl_39,type,
pre_order: ( $i * $i ) > $o ).
tff(decl_40,type,
epred1_2: ( $i * $i ) > $o ).
tff(decl_41,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_42,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_43,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_44,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_45,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_47,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_48,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_51,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_53,type,
esk13_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk15_0: $i ).
tff(decl_56,type,
esk16_0: $i ).
tff(decl_57,type,
esk17_0: $i ).
tff(decl_58,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_59,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_60,type,
esk20_2: ( $i * $i ) > $i ).
tff(decl_61,type,
esk21_2: ( $i * $i ) > $i ).
tff(decl_62,type,
esk22_2: ( $i * $i ) > $i ).
tff(decl_63,type,
esk23_2: ( $i * $i ) > $i ).
fof(equivalence,axiom,
! [X1,X7] :
( equivalence(X7,X1)
<=> ( ! [X3] :
( member(X3,X1)
=> apply(X7,X3,X3) )
& ! [X3,X5] :
( ( member(X3,X1)
& member(X5,X1) )
=> ( apply(X7,X3,X5)
=> apply(X7,X5,X3) ) )
& ! [X3,X5,X6] :
( ( member(X3,X1)
& member(X5,X1)
& member(X6,X1) )
=> ( ( apply(X7,X3,X5)
& apply(X7,X5,X6) )
=> apply(X7,X3,X6) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+2.ax',equivalence) ).
fof(thIII02,conjecture,
! [X4,X7,X1] :
( ( equivalence(X7,X4)
& member(X1,X4) )
=> member(X1,equivalence_class(X1,X4,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIII02) ).
fof(equivalence_class,axiom,
! [X7,X4,X1,X3] :
( member(X3,equivalence_class(X1,X4,X7))
<=> ( member(X3,X4)
& apply(X7,X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+2.ax',equivalence_class) ).
fof(c_0_3,plain,
! [X1,X7] :
( epred1_2(X7,X1)
<=> ( ! [X3] :
( member(X3,X1)
=> apply(X7,X3,X3) )
& ! [X3,X5] :
( ( member(X3,X1)
& member(X5,X1) )
=> ( apply(X7,X3,X5)
=> apply(X7,X5,X3) ) )
& ! [X3,X5,X6] :
( ( member(X3,X1)
& member(X5,X1)
& member(X6,X1) )
=> ( ( apply(X7,X3,X5)
& apply(X7,X5,X6) )
=> apply(X7,X3,X6) ) ) ) ),
introduced(definition) ).
fof(c_0_4,axiom,
! [X1,X7] :
( equivalence(X7,X1)
<=> epred1_2(X7,X1) ),
inference(apply_def,[status(thm)],[equivalence,c_0_3]) ).
fof(c_0_5,negated_conjecture,
~ ! [X4,X7,X1] :
( ( equivalence(X7,X4)
& member(X1,X4) )
=> member(X1,equivalence_class(X1,X4,X7)) ),
inference(assume_negation,[status(cth)],[thIII02]) ).
fof(c_0_6,plain,
! [X67,X68] :
( ( ~ equivalence(X68,X67)
| epred1_2(X68,X67) )
& ( ~ epred1_2(X68,X67)
| equivalence(X68,X67) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])]) ).
fof(c_0_7,negated_conjecture,
( equivalence(esk16_0,esk15_0)
& member(esk17_0,esk15_0)
& ~ member(esk17_0,equivalence_class(esk17_0,esk15_0,esk16_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_8,plain,
! [X88,X89,X90,X91,X92,X93,X94,X95,X96,X97] :
( ( ~ member(X90,X88)
| apply(X89,X90,X90)
| ~ epred1_2(X89,X88) )
& ( ~ member(X91,X88)
| ~ member(X92,X88)
| ~ apply(X89,X91,X92)
| apply(X89,X92,X91)
| ~ epred1_2(X89,X88) )
& ( ~ member(X93,X88)
| ~ member(X94,X88)
| ~ member(X95,X88)
| ~ apply(X89,X93,X94)
| ~ apply(X89,X94,X95)
| apply(X89,X93,X95)
| ~ epred1_2(X89,X88) )
& ( member(esk21_2(X96,X97),X96)
| member(esk19_2(X96,X97),X96)
| member(esk18_2(X96,X97),X96)
| epred1_2(X97,X96) )
& ( member(esk22_2(X96,X97),X96)
| member(esk19_2(X96,X97),X96)
| member(esk18_2(X96,X97),X96)
| epred1_2(X97,X96) )
& ( member(esk23_2(X96,X97),X96)
| member(esk19_2(X96,X97),X96)
| member(esk18_2(X96,X97),X96)
| epred1_2(X97,X96) )
& ( apply(X97,esk21_2(X96,X97),esk22_2(X96,X97))
| member(esk19_2(X96,X97),X96)
| member(esk18_2(X96,X97),X96)
| epred1_2(X97,X96) )
& ( apply(X97,esk22_2(X96,X97),esk23_2(X96,X97))
| member(esk19_2(X96,X97),X96)
| member(esk18_2(X96,X97),X96)
| epred1_2(X97,X96) )
& ( ~ apply(X97,esk21_2(X96,X97),esk23_2(X96,X97))
| member(esk19_2(X96,X97),X96)
| member(esk18_2(X96,X97),X96)
| epred1_2(X97,X96) )
& ( member(esk21_2(X96,X97),X96)
| member(esk20_2(X96,X97),X96)
| member(esk18_2(X96,X97),X96)
| epred1_2(X97,X96) )
& ( member(esk22_2(X96,X97),X96)
| member(esk20_2(X96,X97),X96)
| member(esk18_2(X96,X97),X96)
| epred1_2(X97,X96) )
& ( member(esk23_2(X96,X97),X96)
| member(esk20_2(X96,X97),X96)
| member(esk18_2(X96,X97),X96)
| epred1_2(X97,X96) )
& ( apply(X97,esk21_2(X96,X97),esk22_2(X96,X97))
| member(esk20_2(X96,X97),X96)
| member(esk18_2(X96,X97),X96)
| epred1_2(X97,X96) )
& ( apply(X97,esk22_2(X96,X97),esk23_2(X96,X97))
| member(esk20_2(X96,X97),X96)
| member(esk18_2(X96,X97),X96)
| epred1_2(X97,X96) )
& ( ~ apply(X97,esk21_2(X96,X97),esk23_2(X96,X97))
| member(esk20_2(X96,X97),X96)
| member(esk18_2(X96,X97),X96)
| epred1_2(X97,X96) )
& ( member(esk21_2(X96,X97),X96)
| apply(X97,esk19_2(X96,X97),esk20_2(X96,X97))
| member(esk18_2(X96,X97),X96)
| epred1_2(X97,X96) )
& ( member(esk22_2(X96,X97),X96)
| apply(X97,esk19_2(X96,X97),esk20_2(X96,X97))
| member(esk18_2(X96,X97),X96)
| epred1_2(X97,X96) )
& ( member(esk23_2(X96,X97),X96)
| apply(X97,esk19_2(X96,X97),esk20_2(X96,X97))
| member(esk18_2(X96,X97),X96)
| epred1_2(X97,X96) )
& ( apply(X97,esk21_2(X96,X97),esk22_2(X96,X97))
| apply(X97,esk19_2(X96,X97),esk20_2(X96,X97))
| member(esk18_2(X96,X97),X96)
| epred1_2(X97,X96) )
& ( apply(X97,esk22_2(X96,X97),esk23_2(X96,X97))
| apply(X97,esk19_2(X96,X97),esk20_2(X96,X97))
| member(esk18_2(X96,X97),X96)
| epred1_2(X97,X96) )
& ( ~ apply(X97,esk21_2(X96,X97),esk23_2(X96,X97))
| apply(X97,esk19_2(X96,X97),esk20_2(X96,X97))
| member(esk18_2(X96,X97),X96)
| epred1_2(X97,X96) )
& ( member(esk21_2(X96,X97),X96)
| ~ apply(X97,esk20_2(X96,X97),esk19_2(X96,X97))
| member(esk18_2(X96,X97),X96)
| epred1_2(X97,X96) )
& ( member(esk22_2(X96,X97),X96)
| ~ apply(X97,esk20_2(X96,X97),esk19_2(X96,X97))
| member(esk18_2(X96,X97),X96)
| epred1_2(X97,X96) )
& ( member(esk23_2(X96,X97),X96)
| ~ apply(X97,esk20_2(X96,X97),esk19_2(X96,X97))
| member(esk18_2(X96,X97),X96)
| epred1_2(X97,X96) )
& ( apply(X97,esk21_2(X96,X97),esk22_2(X96,X97))
| ~ apply(X97,esk20_2(X96,X97),esk19_2(X96,X97))
| member(esk18_2(X96,X97),X96)
| epred1_2(X97,X96) )
& ( apply(X97,esk22_2(X96,X97),esk23_2(X96,X97))
| ~ apply(X97,esk20_2(X96,X97),esk19_2(X96,X97))
| member(esk18_2(X96,X97),X96)
| epred1_2(X97,X96) )
& ( ~ apply(X97,esk21_2(X96,X97),esk23_2(X96,X97))
| ~ apply(X97,esk20_2(X96,X97),esk19_2(X96,X97))
| member(esk18_2(X96,X97),X96)
| epred1_2(X97,X96) )
& ( member(esk21_2(X96,X97),X96)
| member(esk19_2(X96,X97),X96)
| ~ apply(X97,esk18_2(X96,X97),esk18_2(X96,X97))
| epred1_2(X97,X96) )
& ( member(esk22_2(X96,X97),X96)
| member(esk19_2(X96,X97),X96)
| ~ apply(X97,esk18_2(X96,X97),esk18_2(X96,X97))
| epred1_2(X97,X96) )
& ( member(esk23_2(X96,X97),X96)
| member(esk19_2(X96,X97),X96)
| ~ apply(X97,esk18_2(X96,X97),esk18_2(X96,X97))
| epred1_2(X97,X96) )
& ( apply(X97,esk21_2(X96,X97),esk22_2(X96,X97))
| member(esk19_2(X96,X97),X96)
| ~ apply(X97,esk18_2(X96,X97),esk18_2(X96,X97))
| epred1_2(X97,X96) )
& ( apply(X97,esk22_2(X96,X97),esk23_2(X96,X97))
| member(esk19_2(X96,X97),X96)
| ~ apply(X97,esk18_2(X96,X97),esk18_2(X96,X97))
| epred1_2(X97,X96) )
& ( ~ apply(X97,esk21_2(X96,X97),esk23_2(X96,X97))
| member(esk19_2(X96,X97),X96)
| ~ apply(X97,esk18_2(X96,X97),esk18_2(X96,X97))
| epred1_2(X97,X96) )
& ( member(esk21_2(X96,X97),X96)
| member(esk20_2(X96,X97),X96)
| ~ apply(X97,esk18_2(X96,X97),esk18_2(X96,X97))
| epred1_2(X97,X96) )
& ( member(esk22_2(X96,X97),X96)
| member(esk20_2(X96,X97),X96)
| ~ apply(X97,esk18_2(X96,X97),esk18_2(X96,X97))
| epred1_2(X97,X96) )
& ( member(esk23_2(X96,X97),X96)
| member(esk20_2(X96,X97),X96)
| ~ apply(X97,esk18_2(X96,X97),esk18_2(X96,X97))
| epred1_2(X97,X96) )
& ( apply(X97,esk21_2(X96,X97),esk22_2(X96,X97))
| member(esk20_2(X96,X97),X96)
| ~ apply(X97,esk18_2(X96,X97),esk18_2(X96,X97))
| epred1_2(X97,X96) )
& ( apply(X97,esk22_2(X96,X97),esk23_2(X96,X97))
| member(esk20_2(X96,X97),X96)
| ~ apply(X97,esk18_2(X96,X97),esk18_2(X96,X97))
| epred1_2(X97,X96) )
& ( ~ apply(X97,esk21_2(X96,X97),esk23_2(X96,X97))
| member(esk20_2(X96,X97),X96)
| ~ apply(X97,esk18_2(X96,X97),esk18_2(X96,X97))
| epred1_2(X97,X96) )
& ( member(esk21_2(X96,X97),X96)
| apply(X97,esk19_2(X96,X97),esk20_2(X96,X97))
| ~ apply(X97,esk18_2(X96,X97),esk18_2(X96,X97))
| epred1_2(X97,X96) )
& ( member(esk22_2(X96,X97),X96)
| apply(X97,esk19_2(X96,X97),esk20_2(X96,X97))
| ~ apply(X97,esk18_2(X96,X97),esk18_2(X96,X97))
| epred1_2(X97,X96) )
& ( member(esk23_2(X96,X97),X96)
| apply(X97,esk19_2(X96,X97),esk20_2(X96,X97))
| ~ apply(X97,esk18_2(X96,X97),esk18_2(X96,X97))
| epred1_2(X97,X96) )
& ( apply(X97,esk21_2(X96,X97),esk22_2(X96,X97))
| apply(X97,esk19_2(X96,X97),esk20_2(X96,X97))
| ~ apply(X97,esk18_2(X96,X97),esk18_2(X96,X97))
| epred1_2(X97,X96) )
& ( apply(X97,esk22_2(X96,X97),esk23_2(X96,X97))
| apply(X97,esk19_2(X96,X97),esk20_2(X96,X97))
| ~ apply(X97,esk18_2(X96,X97),esk18_2(X96,X97))
| epred1_2(X97,X96) )
& ( ~ apply(X97,esk21_2(X96,X97),esk23_2(X96,X97))
| apply(X97,esk19_2(X96,X97),esk20_2(X96,X97))
| ~ apply(X97,esk18_2(X96,X97),esk18_2(X96,X97))
| epred1_2(X97,X96) )
& ( member(esk21_2(X96,X97),X96)
| ~ apply(X97,esk20_2(X96,X97),esk19_2(X96,X97))
| ~ apply(X97,esk18_2(X96,X97),esk18_2(X96,X97))
| epred1_2(X97,X96) )
& ( member(esk22_2(X96,X97),X96)
| ~ apply(X97,esk20_2(X96,X97),esk19_2(X96,X97))
| ~ apply(X97,esk18_2(X96,X97),esk18_2(X96,X97))
| epred1_2(X97,X96) )
& ( member(esk23_2(X96,X97),X96)
| ~ apply(X97,esk20_2(X96,X97),esk19_2(X96,X97))
| ~ apply(X97,esk18_2(X96,X97),esk18_2(X96,X97))
| epred1_2(X97,X96) )
& ( apply(X97,esk21_2(X96,X97),esk22_2(X96,X97))
| ~ apply(X97,esk20_2(X96,X97),esk19_2(X96,X97))
| ~ apply(X97,esk18_2(X96,X97),esk18_2(X96,X97))
| epred1_2(X97,X96) )
& ( apply(X97,esk22_2(X96,X97),esk23_2(X96,X97))
| ~ apply(X97,esk20_2(X96,X97),esk19_2(X96,X97))
| ~ apply(X97,esk18_2(X96,X97),esk18_2(X96,X97))
| epred1_2(X97,X96) )
& ( ~ apply(X97,esk21_2(X96,X97),esk23_2(X96,X97))
| ~ apply(X97,esk20_2(X96,X97),esk19_2(X96,X97))
| ~ apply(X97,esk18_2(X96,X97),esk18_2(X96,X97))
| epred1_2(X97,X96) ) ),
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_3])])])])])]) ).
cnf(c_0_9,plain,
( epred1_2(X1,X2)
| ~ equivalence(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
equivalence(esk16_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( apply(X3,X1,X1)
| ~ member(X1,X2)
| ~ epred1_2(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
epred1_2(esk16_0,esk15_0),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_13,plain,
! [X69,X70,X71,X72] :
( ( member(X72,X70)
| ~ member(X72,equivalence_class(X71,X70,X69)) )
& ( apply(X69,X71,X72)
| ~ member(X72,equivalence_class(X71,X70,X69)) )
& ( ~ member(X72,X70)
| ~ apply(X69,X71,X72)
| member(X72,equivalence_class(X71,X70,X69)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equivalence_class])])]) ).
cnf(c_0_14,plain,
( apply(esk16_0,X1,X1)
| ~ member(X1,esk15_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,negated_conjecture,
member(esk17_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,plain,
( member(X1,equivalence_class(X4,X2,X3))
| ~ member(X1,X2)
| ~ apply(X3,X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
apply(esk16_0,esk17_0,esk17_0),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
( member(esk17_0,equivalence_class(esk17_0,X1,esk16_0))
| ~ member(esk17_0,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,negated_conjecture,
~ member(esk17_0,equivalence_class(esk17_0,esk15_0,esk16_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_15]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET766+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n022.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 : Sat Aug 26 11:21:25 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.55 start to proof: theBenchmark
% 0.21/0.58 % Version : CSE_E---1.5
% 0.21/0.58 % Problem : theBenchmark.p
% 0.21/0.58 % Proof found
% 0.21/0.58 % SZS status Theorem for theBenchmark.p
% 0.21/0.58 % SZS output start Proof
% See solution above
% 0.21/0.59 % Total time : 0.023000 s
% 0.21/0.59 % SZS output end Proof
% 0.21/0.59 % Total time : 0.026000 s
%------------------------------------------------------------------------------