TSTP Solution File: SET796+4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET796+4 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n008.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 14:35:35 EDT 2023
% Result : Theorem 22.07s 22.12s
% Output : CNFRefutation 22.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 53
% Syntax : Number of formulae : 85 ( 9 unt; 47 typ; 0 def)
% Number of atoms : 404 ( 27 equ)
% Maximal formula atoms : 256 ( 10 avg)
% Number of connectives : 478 ( 112 ~; 247 |; 99 &)
% ( 6 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 77 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 101 ( 42 >; 59 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-4 aty)
% Number of functors : 32 ( 32 usr; 5 con; 0-4 aty)
% Number of variables : 122 ( 3 sgn; 69 !; 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,
order: ( $i * $i ) > $o ).
tff(decl_35,type,
apply: ( $i * $i * $i ) > $o ).
tff(decl_36,type,
total_order: ( $i * $i ) > $o ).
tff(decl_37,type,
upper_bound: ( $i * $i * $i ) > $o ).
tff(decl_38,type,
lower_bound: ( $i * $i * $i ) > $o ).
tff(decl_39,type,
greatest: ( $i * $i * $i ) > $o ).
tff(decl_40,type,
least: ( $i * $i * $i ) > $o ).
tff(decl_41,type,
max: ( $i * $i * $i ) > $o ).
tff(decl_42,type,
min: ( $i * $i * $i ) > $o ).
tff(decl_43,type,
least_upper_bound: ( $i * $i * $i * $i ) > $o ).
tff(decl_44,type,
greatest_lower_bound: ( $i * $i * $i * $i ) > $o ).
tff(decl_45,type,
epred1_2: ( $i * $i ) > $o ).
tff(decl_46,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_47,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_48,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_51,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_52,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_53,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_54,type,
esk9_3: ( $i * $i * $i ) > $i ).
tff(decl_55,type,
esk10_3: ( $i * $i * $i ) > $i ).
tff(decl_56,type,
esk11_3: ( $i * $i * $i ) > $i ).
tff(decl_57,type,
esk12_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_58,type,
esk13_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_59,type,
esk14_0: $i ).
tff(decl_60,type,
esk15_0: $i ).
tff(decl_61,type,
esk16_0: $i ).
tff(decl_62,type,
esk17_0: $i ).
tff(decl_63,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_64,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_65,type,
esk20_2: ( $i * $i ) > $i ).
tff(decl_66,type,
esk21_2: ( $i * $i ) > $i ).
tff(decl_67,type,
esk22_2: ( $i * $i ) > $i ).
tff(decl_68,type,
esk23_2: ( $i * $i ) > $i ).
fof(lower_bound,axiom,
! [X6,X4,X8] :
( lower_bound(X8,X6,X4)
<=> ! [X3] :
( member(X3,X4)
=> apply(X6,X8,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',lower_bound) ).
fof(greatest_lower_bound,axiom,
! [X1,X3,X6,X4] :
( greatest_lower_bound(X1,X3,X6,X4)
<=> ( member(X1,X3)
& lower_bound(X1,X6,X3)
& ! [X8] :
( ( member(X8,X4)
& lower_bound(X8,X6,X3) )
=> apply(X6,X8,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',greatest_lower_bound) ).
fof(unordered_pair,axiom,
! [X3,X1,X2] :
( member(X3,unordered_pair(X1,X2))
<=> ( X3 = X1
| X3 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',unordered_pair) ).
fof(thIV8,conjecture,
! [X6,X4,X1,X2] :
( ( order(X6,X4)
& member(X1,X4)
& member(X2,X4)
& apply(X6,X1,X2) )
=> greatest_lower_bound(X1,unordered_pair(X1,X2),X6,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV8) ).
fof(order,axiom,
! [X6,X4] :
( order(X6,X4)
<=> ( ! [X3] :
( member(X3,X4)
=> apply(X6,X3,X3) )
& ! [X3,X5] :
( ( member(X3,X4)
& member(X5,X4) )
=> ( ( apply(X6,X3,X5)
& apply(X6,X5,X3) )
=> X3 = X5 ) )
& ! [X3,X5,X7] :
( ( member(X3,X4)
& member(X5,X4)
& member(X7,X4) )
=> ( ( apply(X6,X3,X5)
& apply(X6,X5,X7) )
=> apply(X6,X3,X7) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',order) ).
fof(c_0_5,plain,
! [X64,X65,X66,X67,X68,X69,X70] :
( ( ~ lower_bound(X66,X64,X65)
| ~ member(X67,X65)
| apply(X64,X66,X67) )
& ( member(esk7_3(X68,X69,X70),X69)
| lower_bound(X70,X68,X69) )
& ( ~ apply(X68,X70,esk7_3(X68,X69,X70))
| lower_bound(X70,X68,X69) ) ),
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)],[lower_bound])])])])])]) ).
fof(c_0_6,plain,
! [X114,X115,X116,X117,X118,X119,X120,X121,X122] :
( ( member(X114,X115)
| ~ greatest_lower_bound(X114,X115,X116,X117) )
& ( lower_bound(X114,X116,X115)
| ~ greatest_lower_bound(X114,X115,X116,X117) )
& ( ~ member(X118,X117)
| ~ lower_bound(X118,X116,X115)
| apply(X116,X118,X114)
| ~ greatest_lower_bound(X114,X115,X116,X117) )
& ( member(esk13_4(X119,X120,X121,X122),X122)
| ~ member(X119,X120)
| ~ lower_bound(X119,X121,X120)
| greatest_lower_bound(X119,X120,X121,X122) )
& ( lower_bound(esk13_4(X119,X120,X121,X122),X121,X120)
| ~ member(X119,X120)
| ~ lower_bound(X119,X121,X120)
| greatest_lower_bound(X119,X120,X121,X122) )
& ( ~ apply(X121,esk13_4(X119,X120,X121,X122),X119)
| ~ member(X119,X120)
| ~ lower_bound(X119,X121,X120)
| greatest_lower_bound(X119,X120,X121,X122) ) ),
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)],[greatest_lower_bound])])])])])]) ).
fof(c_0_7,plain,
! [X31,X32,X33] :
( ( ~ member(X31,unordered_pair(X32,X33))
| X31 = X32
| X31 = X33 )
& ( X31 != X32
| member(X31,unordered_pair(X32,X33)) )
& ( X31 != X33
| member(X31,unordered_pair(X32,X33)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unordered_pair])])]) ).
fof(c_0_8,plain,
! [X4,X6] :
( epred1_2(X6,X4)
<=> ( ! [X3] :
( member(X3,X4)
=> apply(X6,X3,X3) )
& ! [X3,X5] :
( ( member(X3,X4)
& member(X5,X4) )
=> ( ( apply(X6,X3,X5)
& apply(X6,X5,X3) )
=> X3 = X5 ) )
& ! [X3,X5,X7] :
( ( member(X3,X4)
& member(X5,X4)
& member(X7,X4) )
=> ( ( apply(X6,X3,X5)
& apply(X6,X5,X7) )
=> apply(X6,X3,X7) ) ) ) ),
introduced(definition) ).
fof(c_0_9,negated_conjecture,
~ ! [X6,X4,X1,X2] :
( ( order(X6,X4)
& member(X1,X4)
& member(X2,X4)
& apply(X6,X1,X2) )
=> greatest_lower_bound(X1,unordered_pair(X1,X2),X6,X4) ),
inference(assume_negation,[status(cth)],[thIV8]) ).
cnf(c_0_10,plain,
( apply(X2,X1,X4)
| ~ lower_bound(X1,X2,X3)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,plain,
( lower_bound(esk13_4(X1,X2,X3,X4),X3,X2)
| greatest_lower_bound(X1,X2,X3,X4)
| ~ member(X1,X2)
| ~ lower_bound(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( member(esk7_3(X1,X2,X3),X2)
| lower_bound(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_14,axiom,
! [X6,X4] :
( order(X6,X4)
<=> epred1_2(X6,X4) ),
inference(apply_def,[status(thm)],[order,c_0_8]) ).
fof(c_0_15,negated_conjecture,
( order(esk14_0,esk15_0)
& member(esk16_0,esk15_0)
& member(esk17_0,esk15_0)
& apply(esk14_0,esk16_0,esk17_0)
& ~ greatest_lower_bound(esk16_0,unordered_pair(esk16_0,esk17_0),esk14_0,esk15_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_16,plain,
( greatest_lower_bound(X2,X3,X1,X4)
| ~ apply(X1,esk13_4(X2,X3,X1,X4),X2)
| ~ member(X2,X3)
| ~ lower_bound(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,plain,
( greatest_lower_bound(X1,X2,X3,X4)
| apply(X3,esk13_4(X1,X2,X3,X4),X5)
| ~ lower_bound(X1,X3,X2)
| ~ member(X5,X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_18,plain,
( member(X1,unordered_pair(X2,X3))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,plain,
( lower_bound(X2,X1,X3)
| ~ apply(X1,X2,esk7_3(X1,X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_20,plain,
( esk7_3(X1,unordered_pair(X2,X3),X4) = X3
| esk7_3(X1,unordered_pair(X2,X3),X4) = X2
| lower_bound(X4,X1,unordered_pair(X2,X3)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_21,plain,
! [X46,X47] :
( ( ~ order(X46,X47)
| epred1_2(X46,X47) )
& ( ~ epred1_2(X46,X47)
| order(X46,X47) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])]) ).
cnf(c_0_22,negated_conjecture,
~ greatest_lower_bound(esk16_0,unordered_pair(esk16_0,esk17_0),esk14_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
( greatest_lower_bound(X1,X2,X3,X4)
| ~ lower_bound(X1,X3,X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,plain,
member(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( esk7_3(X1,unordered_pair(X2,X3),X4) = X3
| lower_bound(X4,X1,unordered_pair(X2,X3))
| ~ apply(X1,X4,X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_26,plain,
! [X128,X129,X130,X131,X132,X133,X134,X135,X136,X137] :
( ( ~ member(X130,X128)
| apply(X129,X130,X130)
| ~ epred1_2(X129,X128) )
& ( ~ member(X131,X128)
| ~ member(X132,X128)
| ~ apply(X129,X131,X132)
| ~ apply(X129,X132,X131)
| X131 = X132
| ~ epred1_2(X129,X128) )
& ( ~ member(X133,X128)
| ~ member(X134,X128)
| ~ member(X135,X128)
| ~ apply(X129,X133,X134)
| ~ apply(X129,X134,X135)
| apply(X129,X133,X135)
| ~ epred1_2(X129,X128) )
& ( member(esk21_2(X136,X137),X136)
| member(esk19_2(X136,X137),X136)
| member(esk18_2(X136,X137),X136)
| epred1_2(X137,X136) )
& ( member(esk22_2(X136,X137),X136)
| member(esk19_2(X136,X137),X136)
| member(esk18_2(X136,X137),X136)
| epred1_2(X137,X136) )
& ( member(esk23_2(X136,X137),X136)
| member(esk19_2(X136,X137),X136)
| member(esk18_2(X136,X137),X136)
| epred1_2(X137,X136) )
& ( apply(X137,esk21_2(X136,X137),esk22_2(X136,X137))
| member(esk19_2(X136,X137),X136)
| member(esk18_2(X136,X137),X136)
| epred1_2(X137,X136) )
& ( apply(X137,esk22_2(X136,X137),esk23_2(X136,X137))
| member(esk19_2(X136,X137),X136)
| member(esk18_2(X136,X137),X136)
| epred1_2(X137,X136) )
& ( ~ apply(X137,esk21_2(X136,X137),esk23_2(X136,X137))
| member(esk19_2(X136,X137),X136)
| member(esk18_2(X136,X137),X136)
| epred1_2(X137,X136) )
& ( member(esk21_2(X136,X137),X136)
| member(esk20_2(X136,X137),X136)
| member(esk18_2(X136,X137),X136)
| epred1_2(X137,X136) )
& ( member(esk22_2(X136,X137),X136)
| member(esk20_2(X136,X137),X136)
| member(esk18_2(X136,X137),X136)
| epred1_2(X137,X136) )
& ( member(esk23_2(X136,X137),X136)
| member(esk20_2(X136,X137),X136)
| member(esk18_2(X136,X137),X136)
| epred1_2(X137,X136) )
& ( apply(X137,esk21_2(X136,X137),esk22_2(X136,X137))
| member(esk20_2(X136,X137),X136)
| member(esk18_2(X136,X137),X136)
| epred1_2(X137,X136) )
& ( apply(X137,esk22_2(X136,X137),esk23_2(X136,X137))
| member(esk20_2(X136,X137),X136)
| member(esk18_2(X136,X137),X136)
| epred1_2(X137,X136) )
& ( ~ apply(X137,esk21_2(X136,X137),esk23_2(X136,X137))
| member(esk20_2(X136,X137),X136)
| member(esk18_2(X136,X137),X136)
| epred1_2(X137,X136) )
& ( member(esk21_2(X136,X137),X136)
| apply(X137,esk19_2(X136,X137),esk20_2(X136,X137))
| member(esk18_2(X136,X137),X136)
| epred1_2(X137,X136) )
& ( member(esk22_2(X136,X137),X136)
| apply(X137,esk19_2(X136,X137),esk20_2(X136,X137))
| member(esk18_2(X136,X137),X136)
| epred1_2(X137,X136) )
& ( member(esk23_2(X136,X137),X136)
| apply(X137,esk19_2(X136,X137),esk20_2(X136,X137))
| member(esk18_2(X136,X137),X136)
| epred1_2(X137,X136) )
& ( apply(X137,esk21_2(X136,X137),esk22_2(X136,X137))
| apply(X137,esk19_2(X136,X137),esk20_2(X136,X137))
| member(esk18_2(X136,X137),X136)
| epred1_2(X137,X136) )
& ( apply(X137,esk22_2(X136,X137),esk23_2(X136,X137))
| apply(X137,esk19_2(X136,X137),esk20_2(X136,X137))
| member(esk18_2(X136,X137),X136)
| epred1_2(X137,X136) )
& ( ~ apply(X137,esk21_2(X136,X137),esk23_2(X136,X137))
| apply(X137,esk19_2(X136,X137),esk20_2(X136,X137))
| member(esk18_2(X136,X137),X136)
| epred1_2(X137,X136) )
& ( member(esk21_2(X136,X137),X136)
| apply(X137,esk20_2(X136,X137),esk19_2(X136,X137))
| member(esk18_2(X136,X137),X136)
| epred1_2(X137,X136) )
& ( member(esk22_2(X136,X137),X136)
| apply(X137,esk20_2(X136,X137),esk19_2(X136,X137))
| member(esk18_2(X136,X137),X136)
| epred1_2(X137,X136) )
& ( member(esk23_2(X136,X137),X136)
| apply(X137,esk20_2(X136,X137),esk19_2(X136,X137))
| member(esk18_2(X136,X137),X136)
| epred1_2(X137,X136) )
& ( apply(X137,esk21_2(X136,X137),esk22_2(X136,X137))
| apply(X137,esk20_2(X136,X137),esk19_2(X136,X137))
| member(esk18_2(X136,X137),X136)
| epred1_2(X137,X136) )
& ( apply(X137,esk22_2(X136,X137),esk23_2(X136,X137))
| apply(X137,esk20_2(X136,X137),esk19_2(X136,X137))
| member(esk18_2(X136,X137),X136)
| epred1_2(X137,X136) )
& ( ~ apply(X137,esk21_2(X136,X137),esk23_2(X136,X137))
| apply(X137,esk20_2(X136,X137),esk19_2(X136,X137))
| member(esk18_2(X136,X137),X136)
| epred1_2(X137,X136) )
& ( member(esk21_2(X136,X137),X136)
| esk19_2(X136,X137) != esk20_2(X136,X137)
| member(esk18_2(X136,X137),X136)
| epred1_2(X137,X136) )
& ( member(esk22_2(X136,X137),X136)
| esk19_2(X136,X137) != esk20_2(X136,X137)
| member(esk18_2(X136,X137),X136)
| epred1_2(X137,X136) )
& ( member(esk23_2(X136,X137),X136)
| esk19_2(X136,X137) != esk20_2(X136,X137)
| member(esk18_2(X136,X137),X136)
| epred1_2(X137,X136) )
& ( apply(X137,esk21_2(X136,X137),esk22_2(X136,X137))
| esk19_2(X136,X137) != esk20_2(X136,X137)
| member(esk18_2(X136,X137),X136)
| epred1_2(X137,X136) )
& ( apply(X137,esk22_2(X136,X137),esk23_2(X136,X137))
| esk19_2(X136,X137) != esk20_2(X136,X137)
| member(esk18_2(X136,X137),X136)
| epred1_2(X137,X136) )
& ( ~ apply(X137,esk21_2(X136,X137),esk23_2(X136,X137))
| esk19_2(X136,X137) != esk20_2(X136,X137)
| member(esk18_2(X136,X137),X136)
| epred1_2(X137,X136) )
& ( member(esk21_2(X136,X137),X136)
| member(esk19_2(X136,X137),X136)
| ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
| epred1_2(X137,X136) )
& ( member(esk22_2(X136,X137),X136)
| member(esk19_2(X136,X137),X136)
| ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
| epred1_2(X137,X136) )
& ( member(esk23_2(X136,X137),X136)
| member(esk19_2(X136,X137),X136)
| ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
| epred1_2(X137,X136) )
& ( apply(X137,esk21_2(X136,X137),esk22_2(X136,X137))
| member(esk19_2(X136,X137),X136)
| ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
| epred1_2(X137,X136) )
& ( apply(X137,esk22_2(X136,X137),esk23_2(X136,X137))
| member(esk19_2(X136,X137),X136)
| ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
| epred1_2(X137,X136) )
& ( ~ apply(X137,esk21_2(X136,X137),esk23_2(X136,X137))
| member(esk19_2(X136,X137),X136)
| ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
| epred1_2(X137,X136) )
& ( member(esk21_2(X136,X137),X136)
| member(esk20_2(X136,X137),X136)
| ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
| epred1_2(X137,X136) )
& ( member(esk22_2(X136,X137),X136)
| member(esk20_2(X136,X137),X136)
| ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
| epred1_2(X137,X136) )
& ( member(esk23_2(X136,X137),X136)
| member(esk20_2(X136,X137),X136)
| ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
| epred1_2(X137,X136) )
& ( apply(X137,esk21_2(X136,X137),esk22_2(X136,X137))
| member(esk20_2(X136,X137),X136)
| ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
| epred1_2(X137,X136) )
& ( apply(X137,esk22_2(X136,X137),esk23_2(X136,X137))
| member(esk20_2(X136,X137),X136)
| ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
| epred1_2(X137,X136) )
& ( ~ apply(X137,esk21_2(X136,X137),esk23_2(X136,X137))
| member(esk20_2(X136,X137),X136)
| ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
| epred1_2(X137,X136) )
& ( member(esk21_2(X136,X137),X136)
| apply(X137,esk19_2(X136,X137),esk20_2(X136,X137))
| ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
| epred1_2(X137,X136) )
& ( member(esk22_2(X136,X137),X136)
| apply(X137,esk19_2(X136,X137),esk20_2(X136,X137))
| ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
| epred1_2(X137,X136) )
& ( member(esk23_2(X136,X137),X136)
| apply(X137,esk19_2(X136,X137),esk20_2(X136,X137))
| ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
| epred1_2(X137,X136) )
& ( apply(X137,esk21_2(X136,X137),esk22_2(X136,X137))
| apply(X137,esk19_2(X136,X137),esk20_2(X136,X137))
| ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
| epred1_2(X137,X136) )
& ( apply(X137,esk22_2(X136,X137),esk23_2(X136,X137))
| apply(X137,esk19_2(X136,X137),esk20_2(X136,X137))
| ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
| epred1_2(X137,X136) )
& ( ~ apply(X137,esk21_2(X136,X137),esk23_2(X136,X137))
| apply(X137,esk19_2(X136,X137),esk20_2(X136,X137))
| ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
| epred1_2(X137,X136) )
& ( member(esk21_2(X136,X137),X136)
| apply(X137,esk20_2(X136,X137),esk19_2(X136,X137))
| ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
| epred1_2(X137,X136) )
& ( member(esk22_2(X136,X137),X136)
| apply(X137,esk20_2(X136,X137),esk19_2(X136,X137))
| ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
| epred1_2(X137,X136) )
& ( member(esk23_2(X136,X137),X136)
| apply(X137,esk20_2(X136,X137),esk19_2(X136,X137))
| ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
| epred1_2(X137,X136) )
& ( apply(X137,esk21_2(X136,X137),esk22_2(X136,X137))
| apply(X137,esk20_2(X136,X137),esk19_2(X136,X137))
| ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
| epred1_2(X137,X136) )
& ( apply(X137,esk22_2(X136,X137),esk23_2(X136,X137))
| apply(X137,esk20_2(X136,X137),esk19_2(X136,X137))
| ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
| epred1_2(X137,X136) )
& ( ~ apply(X137,esk21_2(X136,X137),esk23_2(X136,X137))
| apply(X137,esk20_2(X136,X137),esk19_2(X136,X137))
| ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
| epred1_2(X137,X136) )
& ( member(esk21_2(X136,X137),X136)
| esk19_2(X136,X137) != esk20_2(X136,X137)
| ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
| epred1_2(X137,X136) )
& ( member(esk22_2(X136,X137),X136)
| esk19_2(X136,X137) != esk20_2(X136,X137)
| ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
| epred1_2(X137,X136) )
& ( member(esk23_2(X136,X137),X136)
| esk19_2(X136,X137) != esk20_2(X136,X137)
| ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
| epred1_2(X137,X136) )
& ( apply(X137,esk21_2(X136,X137),esk22_2(X136,X137))
| esk19_2(X136,X137) != esk20_2(X136,X137)
| ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
| epred1_2(X137,X136) )
& ( apply(X137,esk22_2(X136,X137),esk23_2(X136,X137))
| esk19_2(X136,X137) != esk20_2(X136,X137)
| ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
| epred1_2(X137,X136) )
& ( ~ apply(X137,esk21_2(X136,X137),esk23_2(X136,X137))
| esk19_2(X136,X137) != esk20_2(X136,X137)
| ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
| epred1_2(X137,X136) ) ),
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_27,plain,
( epred1_2(X1,X2)
| ~ order(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,negated_conjecture,
order(esk14_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_29,negated_conjecture,
~ lower_bound(esk16_0,esk14_0,unordered_pair(esk16_0,esk17_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_30,plain,
( lower_bound(X1,X2,unordered_pair(X3,X4))
| ~ apply(X2,X1,X4)
| ~ apply(X2,X1,X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_25]) ).
cnf(c_0_31,negated_conjecture,
apply(esk14_0,esk16_0,esk17_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_32,plain,
( apply(X3,X1,X1)
| ~ member(X1,X2)
| ~ epred1_2(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,negated_conjecture,
epred1_2(esk14_0,esk15_0),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,negated_conjecture,
~ apply(esk14_0,esk16_0,esk16_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_35,plain,
( apply(esk14_0,X1,X1)
| ~ member(X1,esk15_0) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
member(esk16_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_37,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET796+4 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.17/0.33 % Computer : n008.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Sat Aug 26 16:32:48 EDT 2023
% 0.17/0.34 % CPUTime :
% 0.20/0.52 start to proof: theBenchmark
% 22.07/22.12 % Version : CSE_E---1.5
% 22.07/22.12 % Problem : theBenchmark.p
% 22.07/22.12 % Proof found
% 22.07/22.12 % SZS status Theorem for theBenchmark.p
% 22.07/22.12 % SZS output start Proof
% See solution above
% 22.07/22.13 % Total time : 21.599000 s
% 22.07/22.13 % SZS output end Proof
% 22.07/22.13 % Total time : 21.604000 s
%------------------------------------------------------------------------------