TSTP Solution File: SWC421+1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWC421+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n010.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 20:22:28 EDT 2023
% Result : Theorem 2.57s 2.77s
% Output : CNFRefutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 102
% Syntax : Number of formulae : 265 ( 15 unt; 75 typ; 0 def)
% Number of atoms : 722 ( 267 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 898 ( 366 ~; 403 |; 62 &)
% ( 6 <=>; 61 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 85 ( 68 >; 17 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-2 aty)
% Number of functors : 56 ( 56 usr; 7 con; 0-2 aty)
% Number of variables : 272 ( 0 sgn; 112 !; 19 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
ssItem: $i > $o ).
tff(decl_23,type,
neq: ( $i * $i ) > $o ).
tff(decl_24,type,
ssList: $i > $o ).
tff(decl_25,type,
memberP: ( $i * $i ) > $o ).
tff(decl_26,type,
cons: ( $i * $i ) > $i ).
tff(decl_27,type,
app: ( $i * $i ) > $i ).
tff(decl_28,type,
singletonP: $i > $o ).
tff(decl_29,type,
nil: $i ).
tff(decl_30,type,
frontsegP: ( $i * $i ) > $o ).
tff(decl_31,type,
rearsegP: ( $i * $i ) > $o ).
tff(decl_32,type,
segmentP: ( $i * $i ) > $o ).
tff(decl_33,type,
cyclefreeP: $i > $o ).
tff(decl_34,type,
leq: ( $i * $i ) > $o ).
tff(decl_35,type,
totalorderP: $i > $o ).
tff(decl_36,type,
strictorderP: $i > $o ).
tff(decl_37,type,
lt: ( $i * $i ) > $o ).
tff(decl_38,type,
totalorderedP: $i > $o ).
tff(decl_39,type,
strictorderedP: $i > $o ).
tff(decl_40,type,
duplicatefreeP: $i > $o ).
tff(decl_41,type,
equalelemsP: $i > $o ).
tff(decl_42,type,
hd: $i > $i ).
tff(decl_43,type,
tl: $i > $i ).
tff(decl_44,type,
geq: ( $i * $i ) > $o ).
tff(decl_45,type,
gt: ( $i * $i ) > $o ).
tff(decl_46,type,
esk1_0: $i ).
tff(decl_47,type,
esk2_0: $i ).
tff(decl_48,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk5_1: $i > $i ).
tff(decl_51,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_53,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk10_1: $i > $i ).
tff(decl_56,type,
esk11_1: $i > $i ).
tff(decl_57,type,
esk12_1: $i > $i ).
tff(decl_58,type,
esk13_1: $i > $i ).
tff(decl_59,type,
esk14_1: $i > $i ).
tff(decl_60,type,
esk15_1: $i > $i ).
tff(decl_61,type,
esk16_1: $i > $i ).
tff(decl_62,type,
esk17_1: $i > $i ).
tff(decl_63,type,
esk18_1: $i > $i ).
tff(decl_64,type,
esk19_1: $i > $i ).
tff(decl_65,type,
esk20_1: $i > $i ).
tff(decl_66,type,
esk21_1: $i > $i ).
tff(decl_67,type,
esk22_1: $i > $i ).
tff(decl_68,type,
esk23_1: $i > $i ).
tff(decl_69,type,
esk24_1: $i > $i ).
tff(decl_70,type,
esk25_1: $i > $i ).
tff(decl_71,type,
esk26_1: $i > $i ).
tff(decl_72,type,
esk27_1: $i > $i ).
tff(decl_73,type,
esk28_1: $i > $i ).
tff(decl_74,type,
esk29_1: $i > $i ).
tff(decl_75,type,
esk30_1: $i > $i ).
tff(decl_76,type,
esk31_1: $i > $i ).
tff(decl_77,type,
esk32_1: $i > $i ).
tff(decl_78,type,
esk33_1: $i > $i ).
tff(decl_79,type,
esk34_1: $i > $i ).
tff(decl_80,type,
esk35_1: $i > $i ).
tff(decl_81,type,
esk36_1: $i > $i ).
tff(decl_82,type,
esk37_1: $i > $i ).
tff(decl_83,type,
esk38_1: $i > $i ).
tff(decl_84,type,
esk39_1: $i > $i ).
tff(decl_85,type,
esk40_1: $i > $i ).
tff(decl_86,type,
esk41_1: $i > $i ).
tff(decl_87,type,
esk42_1: $i > $i ).
tff(decl_88,type,
esk43_1: $i > $i ).
tff(decl_89,type,
esk44_1: $i > $i ).
tff(decl_90,type,
esk45_1: $i > $i ).
tff(decl_91,type,
esk46_1: $i > $i ).
tff(decl_92,type,
esk47_1: $i > $i ).
tff(decl_93,type,
esk48_0: $i ).
tff(decl_94,type,
esk49_0: $i ).
tff(decl_95,type,
esk50_0: $i ).
tff(decl_96,type,
esk51_0: $i ).
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X2
& app(app(X7,cons(X5,nil)),X6) = X1 ) ) )
| ( nil != X3
& nil = X4 )
| ( neq(X4,nil)
& ( ~ neq(X3,nil)
| ? [X8] :
( ssList(X8)
& X4 != X8
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& tl(X3) = X9
& app(X9,X10) = X8
& ? [X11] :
( ssItem(X11)
& cons(X11,nil) = X10
& hd(X3) = X11
& neq(nil,X3) )
& neq(nil,X3) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(ax86,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax86) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax85,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax85) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(ax4,axiom,
! [X1] :
( ssList(X1)
=> ( singletonP(X1)
<=> ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax4) ).
fof(ax25,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> tl(cons(X2,X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax25) ).
fof(ax5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(ax23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax23) ).
fof(ax27,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax27) ).
fof(ax18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(ax44,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( frontsegP(cons(X1,X3),cons(X2,X4))
<=> ( X1 = X2
& frontsegP(X3,X4) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax44) ).
fof(ax20,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax20) ).
fof(ax81,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(ax6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X3,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax6) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax82,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax51,axiom,
! [X1] :
( ssList(X1)
=> rearsegP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax51) ).
fof(ax79,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X3,X2) = app(X1,X2)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax79) ).
fof(c_0_27,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X2
& app(app(X7,cons(X5,nil)),X6) = X1 ) ) )
| ( nil != X3
& nil = X4 )
| ( neq(X4,nil)
& ( ~ neq(X3,nil)
| ? [X8] :
( ssList(X8)
& X4 != X8
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& tl(X3) = X9
& app(X9,X10) = X8
& ? [X11] :
( ssItem(X11)
& cons(X11,nil) = X10
& hd(X3) = X11
& neq(nil,X3) )
& neq(nil,X3) ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_28,negated_conjecture,
! [X260,X261,X262,X263,X264,X265,X266] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& neq(esk49_0,nil)
& ( ~ ssItem(X260)
| ~ ssList(X261)
| ~ ssList(X262)
| app(app(X261,cons(X260,nil)),X262) != esk49_0
| app(app(X262,cons(X260,nil)),X261) != esk48_0 )
& ( nil = esk50_0
| nil != esk51_0 )
& ( neq(esk50_0,nil)
| ~ neq(esk51_0,nil) )
& ( ~ ssList(X263)
| esk51_0 = X263
| ~ ssList(X264)
| ~ ssList(X265)
| tl(esk50_0) != X264
| app(X264,X265) != X263
| ~ ssItem(X266)
| cons(X266,nil) != X265
| hd(esk50_0) != X266
| ~ neq(nil,esk50_0)
| ~ neq(nil,esk50_0)
| ~ neq(esk51_0,nil) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])])]) ).
cnf(c_0_29,negated_conjecture,
( esk51_0 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| tl(esk50_0) != X2
| app(X2,X3) != X1
| ~ ssItem(X4)
| cons(X4,nil) != X3
| hd(esk50_0) != X4
| ~ neq(nil,esk50_0)
| ~ neq(nil,esk50_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_30,negated_conjecture,
neq(esk49_0,nil),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_31,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_32,plain,
! [X135,X136] :
( ~ ssList(X135)
| ~ ssList(X136)
| ssList(app(X135,X136)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
cnf(c_0_33,negated_conjecture,
( esk51_0 = X1
| hd(esk50_0) != X4
| tl(esk50_0) != X2
| app(X2,X3) != X1
| cons(X4,nil) != X3
| ~ ssItem(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(nil,esk50_0)
| ~ neq(esk51_0,nil) ),
inference(cn,[status(thm)],[c_0_29]) ).
cnf(c_0_34,negated_conjecture,
neq(esk51_0,nil),
inference(rw,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_36,plain,
! [X132] :
( ~ ssList(X132)
| nil = X132
| ssList(tl(X132)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).
cnf(c_0_37,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_39,negated_conjecture,
( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
| ~ ssList(cons(hd(esk50_0),nil))
| ~ ssList(tl(esk50_0))
| ~ neq(nil,esk50_0)
| ~ ssItem(hd(esk50_0)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])])])])])]),c_0_35]) ).
cnf(c_0_40,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_41,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
fof(c_0_42,plain,
! [X116,X117] :
( ~ ssList(X116)
| ~ ssItem(X117)
| ssList(cons(X117,X116)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
cnf(c_0_43,negated_conjecture,
( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
| esk50_0 = nil
| ~ ssList(cons(hd(esk50_0),nil))
| ~ neq(nil,esk50_0)
| ~ ssItem(hd(esk50_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,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_45,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_46,plain,
! [X129] :
( ~ ssList(X129)
| nil = X129
| ssItem(hd(X129)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).
fof(c_0_47,plain,
! [X218] :
( ~ ssList(X218)
| nil = X218
| cons(hd(X218),tl(X218)) = X218 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).
fof(c_0_48,plain,
! [X235,X236] :
( ~ ssList(X235)
| ~ ssList(X236)
| nil = X235
| tl(app(X235,X236)) = app(tl(X235),X236) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax86])])]) ).
fof(c_0_49,plain,
! [X230,X231] :
( ( nil = X231
| nil != app(X230,X231)
| ~ ssList(X231)
| ~ ssList(X230) )
& ( nil = X230
| nil != app(X230,X231)
| ~ ssList(X231)
| ~ ssList(X230) )
& ( nil != X231
| nil != X230
| nil = app(X230,X231)
| ~ ssList(X231)
| ~ ssList(X230) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
cnf(c_0_50,negated_conjecture,
( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
| esk50_0 = nil
| ~ neq(nil,esk50_0)
| ~ ssItem(hd(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).
cnf(c_0_51,plain,
( nil = X1
| ssItem(hd(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
fof(c_0_52,plain,
! [X114,X115] :
( ( ~ neq(X114,X115)
| X114 != X115
| ~ ssList(X115)
| ~ ssList(X114) )
& ( X114 = X115
| neq(X114,X115)
| ~ ssList(X115)
| ~ ssList(X114) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
cnf(c_0_53,plain,
( nil = X1
| cons(hd(X1),tl(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_54,plain,
( nil = X1
| tl(app(X1,X2)) = app(tl(X1),X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_55,plain,
( nil = X1
| nil != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_56,negated_conjecture,
( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
| esk50_0 = nil
| ~ neq(nil,esk50_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_41])]) ).
cnf(c_0_57,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_58,plain,
( cons(hd(app(X1,X2)),app(tl(X1),X2)) = app(X1,X2)
| nil = X1
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_35]),c_0_55]) ).
cnf(c_0_59,negated_conjecture,
( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_41]),c_0_45])]) ).
cnf(c_0_60,negated_conjecture,
( cons(hd(app(esk50_0,cons(hd(esk50_0),nil))),esk51_0) = app(esk50_0,cons(hd(esk50_0),nil))
| esk50_0 = nil
| ~ ssList(cons(hd(esk50_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_41])]) ).
cnf(c_0_61,negated_conjecture,
( cons(hd(app(esk50_0,cons(hd(esk50_0),nil))),esk51_0) = app(esk50_0,cons(hd(esk50_0),nil))
| esk50_0 = nil
| ~ ssItem(hd(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_44]),c_0_45])]) ).
fof(c_0_62,plain,
! [X233,X234] :
( ~ ssList(X233)
| ~ ssList(X234)
| nil = X233
| hd(app(X233,X234)) = hd(X233) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax85])])]) ).
cnf(c_0_63,negated_conjecture,
( cons(hd(app(esk50_0,cons(hd(esk50_0),nil))),esk51_0) = app(esk50_0,cons(hd(esk50_0),nil))
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_51]),c_0_41])]) ).
cnf(c_0_64,plain,
( nil = X1
| hd(app(X1,X2)) = hd(X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
fof(c_0_65,plain,
! [X127,X128] :
( ~ ssList(X127)
| ~ ssItem(X128)
| nil != cons(X128,X127) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])]) ).
cnf(c_0_66,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_67,negated_conjecture,
( app(esk50_0,cons(hd(esk50_0),nil)) = cons(hd(esk50_0),esk51_0)
| esk50_0 = nil
| ~ ssList(cons(hd(esk50_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_41])]) ).
cnf(c_0_68,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| nil != cons(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_69,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_66,c_0_31]) ).
cnf(c_0_70,negated_conjecture,
( app(esk50_0,cons(hd(esk50_0),nil)) = cons(hd(esk50_0),esk51_0)
| esk50_0 = nil
| ~ ssItem(hd(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_44]),c_0_45])]) ).
cnf(c_0_71,negated_conjecture,
( esk50_0 = nil
| app(esk50_0,cons(hd(esk50_0),nil)) != nil
| ~ ssItem(hd(app(esk50_0,cons(hd(esk50_0),nil)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_63]),c_0_69])]) ).
fof(c_0_72,plain,
! [X22,X24] :
( ( ssItem(esk5_1(X22))
| ~ singletonP(X22)
| ~ ssList(X22) )
& ( cons(esk5_1(X22),nil) = X22
| ~ singletonP(X22)
| ~ ssList(X22) )
& ( ~ ssItem(X24)
| cons(X24,nil) != X22
| singletonP(X22)
| ~ ssList(X22) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])])])]) ).
cnf(c_0_73,negated_conjecture,
( app(esk50_0,cons(hd(esk50_0),nil)) = cons(hd(esk50_0),esk51_0)
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_51]),c_0_41])]) ).
cnf(c_0_74,negated_conjecture,
( esk50_0 = nil
| app(esk50_0,cons(hd(esk50_0),nil)) != nil
| ~ ssList(cons(hd(esk50_0),nil))
| ~ ssItem(hd(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_64]),c_0_41])]) ).
fof(c_0_75,plain,
! [X133,X134] :
( ~ ssList(X133)
| ~ ssItem(X134)
| tl(cons(X134,X133)) = X133 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])]) ).
cnf(c_0_76,plain,
( singletonP(X2)
| ~ ssItem(X1)
| cons(X1,nil) != X2
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
fof(c_0_77,plain,
! [X25,X26,X28] :
( ( ssList(esk6_2(X25,X26))
| ~ frontsegP(X25,X26)
| ~ ssList(X26)
| ~ ssList(X25) )
& ( app(X26,esk6_2(X25,X26)) = X25
| ~ frontsegP(X25,X26)
| ~ ssList(X26)
| ~ ssList(X25) )
& ( ~ ssList(X28)
| app(X26,X28) != X25
| frontsegP(X25,X26)
| ~ ssList(X26)
| ~ ssList(X25) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax5])])])])]) ).
cnf(c_0_78,negated_conjecture,
( hd(cons(hd(esk50_0),esk51_0)) = hd(esk50_0)
| esk50_0 = nil
| ~ ssList(cons(hd(esk50_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_73]),c_0_41])]) ).
cnf(c_0_79,negated_conjecture,
( esk50_0 = nil
| ssList(cons(hd(esk50_0),esk51_0))
| ~ ssList(cons(hd(esk50_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_73]),c_0_41])]) ).
cnf(c_0_80,negated_conjecture,
( esk50_0 = nil
| app(esk50_0,cons(hd(esk50_0),nil)) != nil
| ~ ssItem(hd(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_44]),c_0_45])]) ).
fof(c_0_81,plain,
! [X130,X131] :
( ~ ssList(X130)
| ~ ssItem(X131)
| hd(cons(X131,X130)) = X131 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])]) ).
cnf(c_0_82,plain,
( tl(cons(X2,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_83,plain,
( cons(esk5_1(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_84,plain,
( ssItem(esk5_1(X1))
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_85,plain,
( singletonP(cons(X1,nil))
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(er,[status(thm)],[c_0_76]) ).
cnf(c_0_86,plain,
( frontsegP(X3,X2)
| ~ ssList(X1)
| app(X2,X1) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_87,negated_conjecture,
( hd(cons(hd(esk50_0),esk51_0)) = hd(esk50_0)
| esk50_0 = nil
| ~ ssItem(hd(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_44]),c_0_45])]) ).
cnf(c_0_88,negated_conjecture,
( esk50_0 = nil
| ssList(cons(hd(esk50_0),esk51_0))
| ~ ssItem(hd(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_44]),c_0_45])]) ).
cnf(c_0_89,negated_conjecture,
( esk50_0 = nil
| app(esk50_0,cons(hd(esk50_0),nil)) != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_51]),c_0_41])]) ).
fof(c_0_90,plain,
! [X137,X138,X139] :
( ~ ssList(X137)
| ~ ssList(X138)
| ~ ssItem(X139)
| cons(X139,app(X138,X137)) = app(cons(X139,X138),X137) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])]) ).
fof(c_0_91,plain,
! [X118,X119] :
( ~ ssList(X118)
| ~ ssItem(X119)
| cons(X119,X118) != X118 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])]) ).
cnf(c_0_92,plain,
( hd(cons(X2,X1)) = X2
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_93,plain,
( tl(X1) = nil
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_45])]),c_0_84]) ).
cnf(c_0_94,plain,
( singletonP(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_44]),c_0_45])]) ).
fof(c_0_95,plain,
! [X172,X173,X174,X175] :
( ( X172 = X173
| ~ frontsegP(cons(X172,X174),cons(X173,X175))
| ~ ssList(X175)
| ~ ssList(X174)
| ~ ssItem(X173)
| ~ ssItem(X172) )
& ( frontsegP(X174,X175)
| ~ frontsegP(cons(X172,X174),cons(X173,X175))
| ~ ssList(X175)
| ~ ssList(X174)
| ~ ssItem(X173)
| ~ ssItem(X172) )
& ( X172 != X173
| ~ frontsegP(X174,X175)
| frontsegP(cons(X172,X174),cons(X173,X175))
| ~ ssList(X175)
| ~ ssList(X174)
| ~ ssItem(X173)
| ~ ssItem(X172) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax44])])])]) ).
fof(c_0_96,plain,
! [X124] :
( ( ssList(esk44_1(X124))
| nil = X124
| ~ ssList(X124) )
& ( ssItem(esk45_1(X124))
| nil = X124
| ~ ssList(X124) )
& ( cons(esk45_1(X124),esk44_1(X124)) = X124
| nil = X124
| ~ ssList(X124) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])]) ).
cnf(c_0_97,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_86]),c_0_35]) ).
cnf(c_0_98,negated_conjecture,
( hd(cons(hd(esk50_0),esk51_0)) = hd(esk50_0)
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_51]),c_0_41])]) ).
cnf(c_0_99,negated_conjecture,
( esk50_0 = nil
| ssList(cons(hd(esk50_0),esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_51]),c_0_41])]) ).
cnf(c_0_100,negated_conjecture,
( esk50_0 = nil
| cons(hd(esk50_0),esk51_0) != nil ),
inference(spm,[status(thm)],[c_0_89,c_0_73]) ).
cnf(c_0_101,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_102,plain,
( nil = app(X2,X1)
| nil != X1
| nil != X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_103,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,X1) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_104,plain,
( cons(X1,tl(cons(X1,X2))) = cons(X1,X2)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_92]),c_0_44]),c_0_68]) ).
cnf(c_0_105,plain,
( tl(cons(X1,nil)) = nil
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_106,plain,
( X1 = X2
| ~ frontsegP(cons(X1,X3),cons(X2,X4))
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_107,plain,
( cons(esk45_1(X1),esk44_1(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_108,plain,
( ssItem(esk45_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_109,plain,
( ssList(esk44_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_110,negated_conjecture,
( esk50_0 = nil
| frontsegP(cons(hd(esk50_0),esk51_0),esk50_0)
| ~ ssList(cons(hd(esk50_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_73]),c_0_41])]) ).
cnf(c_0_111,negated_conjecture,
( esk50_0 = nil
| ssItem(hd(esk50_0)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_98]),c_0_99]),c_0_100]) ).
cnf(c_0_112,plain,
( esk5_1(X1) = hd(X1)
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_83]),c_0_45])]),c_0_84]) ).
fof(c_0_113,plain,
! [X225,X226] :
( ~ ssList(X225)
| ~ ssItem(X226)
| cons(X226,X225) = app(cons(X226,nil),X225) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
cnf(c_0_114,plain,
( ssList(cons(X1,app(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_101]),c_0_44]) ).
cnf(c_0_115,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_102])]),c_0_45])]) ).
cnf(c_0_116,plain,
( tl(cons(X1,X2)) != cons(X1,X2)
| ~ ssList(tl(cons(X1,X2)))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_117,plain,
( tl(cons(X1,nil)) = nil
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_44]),c_0_45])]) ).
cnf(c_0_118,plain,
( X1 = esk45_1(X2)
| nil = X2
| ~ frontsegP(cons(X1,X3),X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_108]),c_0_109]) ).
cnf(c_0_119,negated_conjecture,
( esk50_0 = nil
| frontsegP(cons(hd(esk50_0),esk51_0),esk50_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_44]),c_0_45])]),c_0_111]) ).
cnf(c_0_120,plain,
( ssItem(hd(X1))
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_84,c_0_112]) ).
cnf(c_0_121,plain,
( cons(hd(X1),tl(app(X1,X2))) = app(X1,X2)
| nil = X1
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_64]),c_0_35]),c_0_55]) ).
cnf(c_0_122,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_123,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_45])]) ).
cnf(c_0_124,plain,
( cons(X1,nil) != nil
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_45])]) ).
cnf(c_0_125,plain,
( cons(esk45_1(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_107]),c_0_108]),c_0_109]) ).
cnf(c_0_126,negated_conjecture,
( esk45_1(esk50_0) = hd(esk50_0)
| esk50_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_69]),c_0_41])]),c_0_111]) ).
fof(c_0_127,plain,
! [X29,X30,X32] :
( ( ssList(esk7_2(X29,X30))
| ~ rearsegP(X29,X30)
| ~ ssList(X30)
| ~ ssList(X29) )
& ( app(esk7_2(X29,X30),X30) = X29
| ~ rearsegP(X29,X30)
| ~ ssList(X30)
| ~ ssList(X29) )
& ( ~ ssList(X32)
| app(X32,X30) != X29
| rearsegP(X29,X30)
| ~ ssList(X30)
| ~ ssList(X29) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])])])])]) ).
fof(c_0_128,plain,
! [X232] :
( ~ ssList(X232)
| app(X232,nil) = X232 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
fof(c_0_129,plain,
! [X227,X228,X229] :
( ~ ssList(X227)
| ~ ssList(X228)
| ~ ssList(X229)
| app(app(X227,X228),X229) = app(X227,app(X228,X229)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).
fof(c_0_130,plain,
! [X140] :
( ~ ssList(X140)
| app(nil,X140) = X140 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
cnf(c_0_131,plain,
( ssItem(hd(cons(X1,nil)))
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[c_0_120,c_0_94]) ).
cnf(c_0_132,plain,
( cons(hd(cons(X1,nil)),tl(cons(X1,X2))) = cons(X1,X2)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_123]),c_0_124]) ).
cnf(c_0_133,negated_conjecture,
( cons(hd(esk50_0),tl(esk50_0)) = esk50_0
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_41])]) ).
cnf(c_0_134,plain,
( rearsegP(X3,X2)
| ~ ssList(X1)
| app(X1,X2) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_135,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
cnf(c_0_136,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_137,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_130]) ).
cnf(c_0_138,plain,
( cons(hd(cons(X1,X2)),X2) = cons(X1,X2)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_82]),c_0_44]),c_0_68]) ).
cnf(c_0_139,plain,
( ssItem(hd(cons(X1,nil)))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_44]),c_0_45])]) ).
cnf(c_0_140,negated_conjecture,
( cons(hd(cons(hd(esk50_0),nil)),tl(esk50_0)) = esk50_0
| esk50_0 = nil
| ~ ssList(tl(esk50_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_111]) ).
cnf(c_0_141,plain,
( ssList(esk7_2(X1,X2))
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_142,plain,
( rearsegP(app(X1,X2),X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_134]),c_0_35]) ).
cnf(c_0_143,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_45])]),c_0_35]) ).
cnf(c_0_144,plain,
( app(nil,app(X1,X2)) = app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_45])]) ).
cnf(c_0_145,plain,
( cons(hd(cons(X1,nil)),X2) = app(cons(X1,nil),X2)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_138]),c_0_45])]),c_0_139]) ).
cnf(c_0_146,negated_conjecture,
( cons(hd(cons(hd(esk50_0),nil)),tl(esk50_0)) = esk50_0
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_40]),c_0_41])]) ).
fof(c_0_147,plain,
! [X187] :
( ~ ssList(X187)
| rearsegP(X187,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax51])]) ).
cnf(c_0_148,plain,
( ssList(esk7_2(app(X1,X2),X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_35]) ).
cnf(c_0_149,plain,
( app(X1,nil) = app(nil,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_45])]) ).
cnf(c_0_150,negated_conjecture,
( app(cons(hd(esk50_0),nil),tl(esk50_0)) = esk50_0
| esk50_0 = nil
| ~ ssList(tl(esk50_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_111]) ).
fof(c_0_151,plain,
! [X219,X220,X221] :
( ~ ssList(X219)
| ~ ssList(X220)
| ~ ssList(X221)
| app(X221,X220) != app(X219,X220)
| X221 = X219 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])]) ).
cnf(c_0_152,plain,
( app(esk7_2(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_153,plain,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_147]) ).
cnf(c_0_154,plain,
( ssList(app(X1,app(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_136]),c_0_35]) ).
cnf(c_0_155,plain,
( ssList(esk7_2(app(nil,X1),nil))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_45])]) ).
cnf(c_0_156,negated_conjecture,
( app(cons(hd(esk50_0),nil),tl(esk50_0)) = esk50_0
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_40]),c_0_41])]) ).
cnf(c_0_157,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X3,X2) != app(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_151]) ).
cnf(c_0_158,plain,
( app(esk7_2(X1,nil),nil) = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_45])]) ).
cnf(c_0_159,plain,
( ssList(app(X1,nil))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_115]),c_0_45])]) ).
cnf(c_0_160,plain,
( ssList(esk7_2(app(X1,nil),nil))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_155,c_0_149]) ).
cnf(c_0_161,negated_conjecture,
( app(nil,esk50_0) = esk50_0
| esk50_0 = nil
| ~ ssList(cons(hd(esk50_0),nil))
| ~ ssList(tl(esk50_0)) ),
inference(spm,[status(thm)],[c_0_144,c_0_156]) ).
cnf(c_0_162,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != esk49_0
| app(app(X3,cons(X1,nil)),X2) != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_163,plain,
( esk7_2(app(X1,nil),nil) = X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_45])])]),c_0_159]),c_0_160]) ).
cnf(c_0_164,negated_conjecture,
( app(nil,esk50_0) = esk50_0
| esk50_0 = nil
| ~ ssList(cons(hd(esk50_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_40]),c_0_41])]) ).
cnf(c_0_165,negated_conjecture,
( app(app(X1,cons(X2,nil)),X3) != esk50_0
| app(app(X3,cons(X2,nil)),X1) != esk51_0
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_162,c_0_38]),c_0_31]) ).
cnf(c_0_166,plain,
( ssList(esk7_2(X1,nil))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_153]),c_0_45])]) ).
cnf(c_0_167,plain,
( esk7_2(app(nil,X1),nil) = X1
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_163,c_0_149]) ).
cnf(c_0_168,negated_conjecture,
( app(nil,esk50_0) = esk50_0
| esk50_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_44]),c_0_45])]),c_0_111]) ).
cnf(c_0_169,negated_conjecture,
( app(app(X1,X2),X3) != esk50_0
| app(app(X3,X2),X1) != esk51_0
| ~ singletonP(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_83]),c_0_84]) ).
cnf(c_0_170,plain,
( app(tl(esk7_2(X1,nil)),nil) = tl(X1)
| esk7_2(X1,nil) = nil
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_158]),c_0_45])]),c_0_166]) ).
cnf(c_0_171,negated_conjecture,
( esk7_2(esk50_0,nil) = esk50_0
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_168]),c_0_41])]) ).
cnf(c_0_172,negated_conjecture,
( cons(hd(cons(hd(esk50_0),esk51_0)),esk51_0) = cons(hd(esk50_0),esk51_0)
| esk50_0 = nil ),
inference(spm,[status(thm)],[c_0_63,c_0_73]) ).
cnf(c_0_173,negated_conjecture,
( app(app(X1,X2),nil) != esk51_0
| app(X2,X1) != esk50_0
| ~ singletonP(X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_137]),c_0_45])]) ).
cnf(c_0_174,plain,
( nil = X1
| ssList(app(tl(X1),X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_54]),c_0_35]),c_0_55]) ).
cnf(c_0_175,negated_conjecture,
( app(tl(esk50_0),nil) = tl(esk50_0)
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_171]),c_0_41])]) ).
cnf(c_0_176,negated_conjecture,
( tl(cons(hd(esk50_0),esk51_0)) = esk51_0
| esk50_0 = nil
| ~ ssItem(hd(cons(hd(esk50_0),esk51_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_172]),c_0_69])]) ).
cnf(c_0_177,negated_conjecture,
( app(app(X1,cons(X2,nil)),nil) != esk51_0
| cons(X2,X1) != esk50_0
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_122]),c_0_123]),c_0_94]) ).
cnf(c_0_178,negated_conjecture,
( esk50_0 = nil
| ssList(tl(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_175]),c_0_45]),c_0_41])]) ).
cnf(c_0_179,plain,
( app(tl(X1),nil) = tl(X1)
| nil = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_135]),c_0_45])]) ).
cnf(c_0_180,negated_conjecture,
( tl(cons(hd(esk50_0),esk51_0)) = esk51_0
| esk50_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_92]),c_0_69])]),c_0_111]) ).
cnf(c_0_181,negated_conjecture,
( neq(esk50_0,nil)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_182,negated_conjecture,
( esk50_0 = nil
| app(app(tl(esk50_0),cons(hd(esk50_0),nil)),nil) != esk51_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_133]),c_0_111]),c_0_178]) ).
cnf(c_0_183,negated_conjecture,
( app(esk51_0,nil) = esk51_0
| esk50_0 = nil ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_180]),c_0_99]),c_0_100]) ).
cnf(c_0_184,plain,
( ~ neq(X1,X2)
| X1 != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_185,negated_conjecture,
neq(esk50_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_181,c_0_34])]) ).
cnf(c_0_186,negated_conjecture,
esk50_0 = nil,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_59]),c_0_183]) ).
cnf(c_0_187,plain,
( ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(er,[status(thm)],[c_0_184]) ).
cnf(c_0_188,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[c_0_185,c_0_186]) ).
cnf(c_0_189,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_188]),c_0_45])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC421+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 14:20:49 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.56 start to proof: theBenchmark
% 2.57/2.77 % Version : CSE_E---1.5
% 2.57/2.77 % Problem : theBenchmark.p
% 2.57/2.77 % Proof found
% 2.57/2.77 % SZS status Theorem for theBenchmark.p
% 2.57/2.77 % SZS output start Proof
% See solution above
% 2.57/2.78 % Total time : 2.197000 s
% 2.57/2.78 % SZS output end Proof
% 2.57/2.78 % Total time : 2.201000 s
%------------------------------------------------------------------------------