TSTP Solution File: SWC410+1 by Enigma---0.5.1
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%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : SWC410+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n032.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 : 600s
% DateTime : Tue Jul 19 20:15:31 EDT 2022
% Result : Theorem 12.55s 2.87s
% Output : CNFRefutation 12.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 17
% Syntax : Number of formulae : 110 ( 19 unt; 0 def)
% Number of atoms : 476 ( 152 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 596 ( 230 ~; 266 |; 50 &)
% ( 5 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 141 ( 0 sgn 72 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X2,X5)
| memberP(X1,X5) ) )
| ( nil != X3
& nil = X4 )
| ( neq(X4,nil)
& ( ~ neq(X3,nil)
| ? [X6] :
( ssList(X6)
& X4 != X6
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& tl(X3) = X7
& app(X7,X8) = X6
& ? [X9] :
( ssItem(X9)
& cons(X9,nil) = X8
& hd(X3) = X9
& neq(nil,X3) )
& neq(nil,X3) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax85,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax85) ).
fof(ax13,axiom,
! [X1] :
( ssList(X1)
=> ( duplicatefreeP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
=> X2 != X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax13) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax37,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(cons(X2,X3),X1)
<=> ( X1 = X2
| memberP(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(ax72,axiom,
duplicatefreeP(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax72) ).
fof(ax36,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(app(X2,X3),X1)
<=> ( memberP(X2,X1)
| memberP(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax36) ).
fof(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(c_0_17,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X2,X5)
| memberP(X1,X5) ) )
| ( nil != X3
& nil = X4 )
| ( neq(X4,nil)
& ( ~ neq(X3,nil)
| ? [X6] :
( ssList(X6)
& X4 != X6
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& tl(X3) = X7
& app(X7,X8) = X6
& ? [X9] :
( ssItem(X9)
& cons(X9,nil) = X8
& hd(X3) = X9
& neq(nil,X3) )
& neq(nil,X3) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_18,negated_conjecture,
! [X259,X260,X261,X262] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ssItem(esk52_0)
& memberP(esk49_0,esk52_0)
& ~ memberP(esk48_0,esk52_0)
& ( nil = esk50_0
| nil != esk51_0 )
& ( neq(esk50_0,nil)
| ~ neq(esk51_0,nil) )
& ( ~ ssList(X259)
| esk51_0 = X259
| ~ ssList(X260)
| ~ ssList(X261)
| tl(esk50_0) != X260
| app(X260,X261) != X259
| ~ ssItem(X262)
| cons(X262,nil) != X261
| hd(esk50_0) != X262
| ~ 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)],[inference(fof_simplification,[status(thm)],[c_0_17])])])])])]) ).
cnf(c_0_19,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_18]) ).
fof(c_0_20,plain,
! [X133,X134] :
( ~ ssList(X133)
| ~ ssList(X134)
| ssList(app(X133,X134)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
cnf(c_0_21,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_19]) ).
cnf(c_0_22,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_23,plain,
! [X130] :
( ~ ssList(X130)
| nil = X130
| ssList(tl(X130)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).
cnf(c_0_24,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,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)
| ~ neq(esk51_0,nil)
| ~ ssItem(hd(esk50_0)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_21])])])]),c_0_22]) ).
cnf(c_0_27,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_29,plain,
! [X112,X113] :
( ( ~ neq(X112,X113)
| X112 != X113
| ~ ssList(X113)
| ~ ssList(X112) )
& ( X112 = X113
| neq(X112,X113)
| ~ ssList(X113)
| ~ ssList(X112) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
cnf(c_0_30,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)
| ~ neq(esk51_0,nil)
| ~ ssItem(hd(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
cnf(c_0_31,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_32,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_33,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_34,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_35,negated_conjecture,
( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
| esk50_0 = nil
| ~ ssList(cons(hd(esk50_0),nil))
| ~ neq(esk51_0,nil)
| ~ ssItem(hd(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_28]),c_0_32])]) ).
cnf(c_0_36,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
( nil = esk50_0
| nil != esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_38,plain,
! [X127] :
( ~ ssList(X127)
| nil = X127
| ssItem(hd(X127)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).
cnf(c_0_39,negated_conjecture,
( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
| esk50_0 = nil
| ~ ssList(cons(hd(esk50_0),nil))
| ~ ssItem(hd(esk50_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_31]),c_0_32]),c_0_36])]),c_0_37]) ).
cnf(c_0_40,plain,
( nil = X1
| ssItem(hd(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_41,plain,
! [X114,X115] :
( ~ ssList(X114)
| ~ ssItem(X115)
| ssList(cons(X115,X114)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
fof(c_0_42,plain,
! [X216] :
( ~ ssList(X216)
| nil = X216
| cons(hd(X216),tl(X216)) = X216 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).
fof(c_0_43,plain,
! [X233,X234] :
( ~ ssList(X233)
| ~ ssList(X234)
| nil = X233
| tl(app(X233,X234)) = app(tl(X233),X234) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax86])])]) ).
fof(c_0_44,plain,
! [X228,X229] :
( ( nil = X229
| nil != app(X228,X229)
| ~ ssList(X229)
| ~ ssList(X228) )
& ( nil = X228
| nil != app(X228,X229)
| ~ ssList(X229)
| ~ ssList(X228) )
& ( nil != X229
| nil != X228
| nil = app(X228,X229)
| ~ ssList(X229)
| ~ ssList(X228) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
cnf(c_0_45,negated_conjecture,
( app(tl(esk50_0),cons(hd(esk50_0),nil)) = 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_39,c_0_40]),c_0_28])]) ).
cnf(c_0_46,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_47,plain,
( nil = X1
| cons(hd(X1),tl(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_48,plain,
( nil = X1
| tl(app(X1,X2)) = app(tl(X1),X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_49,plain,
( nil = X1
| nil != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_50,negated_conjecture,
( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
| esk50_0 = nil
| ~ ssItem(hd(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_32])]) ).
cnf(c_0_51,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_47,c_0_48]),c_0_22]),c_0_49]) ).
cnf(c_0_52,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(spm,[status(thm)],[c_0_50,c_0_40]),c_0_28])]) ).
cnf(c_0_53,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_51,c_0_52]),c_0_28])]) ).
cnf(c_0_54,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_53,c_0_46]),c_0_32])]) ).
fof(c_0_55,plain,
! [X231,X232] :
( ~ ssList(X231)
| ~ ssList(X232)
| nil = X231
| hd(app(X231,X232)) = hd(X231) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax85])])]) ).
cnf(c_0_56,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_54,c_0_40]),c_0_28])]) ).
cnf(c_0_57,plain,
( nil = X1
| hd(app(X1,X2)) = hd(X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_58,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_56,c_0_57]),c_0_28])]) ).
fof(c_0_59,plain,
! [X92,X93,X94,X95,X96,X97] :
( ( ~ duplicatefreeP(X92)
| ~ ssItem(X93)
| ~ ssItem(X94)
| ~ ssList(X95)
| ~ ssList(X96)
| ~ ssList(X97)
| app(app(X95,cons(X93,X96)),cons(X94,X97)) != X92
| X93 != X94
| ~ ssList(X92) )
& ( ssItem(esk35_1(X92))
| duplicatefreeP(X92)
| ~ ssList(X92) )
& ( ssItem(esk36_1(X92))
| duplicatefreeP(X92)
| ~ ssList(X92) )
& ( ssList(esk37_1(X92))
| duplicatefreeP(X92)
| ~ ssList(X92) )
& ( ssList(esk38_1(X92))
| duplicatefreeP(X92)
| ~ ssList(X92) )
& ( ssList(esk39_1(X92))
| duplicatefreeP(X92)
| ~ ssList(X92) )
& ( app(app(esk37_1(X92),cons(esk35_1(X92),esk38_1(X92))),cons(esk36_1(X92),esk39_1(X92))) = X92
| duplicatefreeP(X92)
| ~ ssList(X92) )
& ( esk35_1(X92) = esk36_1(X92)
| duplicatefreeP(X92)
| ~ ssList(X92) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax13])])])])]) ).
cnf(c_0_60,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_58,c_0_46]),c_0_32])]) ).
cnf(c_0_61,plain,
( ~ duplicatefreeP(X1)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
| X2 != X3
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
fof(c_0_62,plain,
! [X138] :
( ~ ssList(X138)
| app(nil,X138) = X138 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
cnf(c_0_63,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_60,c_0_40]),c_0_28])]) ).
cnf(c_0_64,plain,
( ~ duplicatefreeP(app(app(X1,cons(X2,X3)),cons(X2,X4)))
| ~ ssList(app(app(X1,cons(X2,X3)),cons(X2,X4)))
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_61])]) ).
cnf(c_0_65,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_66,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_22,c_0_63]),c_0_28])]) ).
cnf(c_0_67,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_57,c_0_63]),c_0_28])]) ).
fof(c_0_68,plain,
! [X157,X158,X159] :
( ( ~ memberP(cons(X158,X159),X157)
| X157 = X158
| memberP(X159,X157)
| ~ ssList(X159)
| ~ ssItem(X158)
| ~ ssItem(X157) )
& ( X157 != X158
| memberP(cons(X158,X159),X157)
| ~ ssList(X159)
| ~ ssItem(X158)
| ~ ssItem(X157) )
& ( ~ memberP(X159,X157)
| memberP(cons(X158,X159),X157)
| ~ ssList(X159)
| ~ ssItem(X158)
| ~ ssItem(X157) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])]) ).
cnf(c_0_69,negated_conjecture,
memberP(esk49_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_70,plain,
( ~ duplicatefreeP(app(cons(X1,X2),cons(X1,X3)))
| ~ ssList(app(cons(X1,X2),cons(X1,X3)))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_32])]),c_0_46]) ).
cnf(c_0_71,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_66,c_0_46]),c_0_32])]) ).
cnf(c_0_72,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_67,c_0_46]),c_0_32])]) ).
cnf(c_0_73,plain,
( memberP(cons(X3,X1),X2)
| ~ memberP(X1,X2)
| ~ ssList(X1)
| ~ ssItem(X3)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_74,negated_conjecture,
memberP(esk51_0,esk52_0),
inference(rw,[status(thm)],[c_0_69,c_0_34]) ).
cnf(c_0_75,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_76,plain,
( nil = X1
| ~ duplicatefreeP(app(X1,cons(hd(X1),X2)))
| ~ ssList(app(X1,cons(hd(X1),X2)))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_47]),c_0_40]),c_0_27]) ).
cnf(c_0_77,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_71,c_0_40]),c_0_28])]) ).
cnf(c_0_78,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_72,c_0_40]),c_0_28])]) ).
cnf(c_0_79,negated_conjecture,
( memberP(cons(X1,esk51_0),esk52_0)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_36]),c_0_75])]) ).
cnf(c_0_80,negated_conjecture,
( esk50_0 = nil
| ~ duplicatefreeP(cons(hd(esk50_0),esk51_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_63]),c_0_32]),c_0_28])]),c_0_77]) ).
cnf(c_0_81,negated_conjecture,
( cons(hd(esk50_0),esk51_0) = nil
| esk50_0 = nil
| ssItem(hd(esk50_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_78]),c_0_77]) ).
cnf(c_0_82,plain,
duplicatefreeP(nil),
inference(split_conjunct,[status(thm)],[ax72]) ).
cnf(c_0_83,negated_conjecture,
( esk50_0 = nil
| memberP(app(esk50_0,cons(hd(esk50_0),nil)),esk52_0)
| ~ ssItem(hd(app(esk50_0,cons(hd(esk50_0),nil)))) ),
inference(spm,[status(thm)],[c_0_79,c_0_56]) ).
cnf(c_0_84,negated_conjecture,
( esk50_0 = nil
| ssItem(hd(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82])]) ).
fof(c_0_85,plain,
! [X154,X155,X156] :
( ( ~ memberP(app(X155,X156),X154)
| memberP(X155,X154)
| memberP(X156,X154)
| ~ ssList(X156)
| ~ ssList(X155)
| ~ ssItem(X154) )
& ( ~ memberP(X155,X154)
| memberP(app(X155,X156),X154)
| ~ ssList(X156)
| ~ ssList(X155)
| ~ ssItem(X154) )
& ( ~ memberP(X156,X154)
| memberP(app(X155,X156),X154)
| ~ ssList(X156)
| ~ ssList(X155)
| ~ ssItem(X154) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax36])])])]) ).
cnf(c_0_86,negated_conjecture,
( esk50_0 = nil
| memberP(app(esk50_0,cons(hd(esk50_0),nil)),esk52_0)
| ~ ssList(cons(hd(esk50_0),nil)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_57]),c_0_28])]),c_0_84]) ).
cnf(c_0_87,negated_conjecture,
~ memberP(esk48_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_88,plain,
( memberP(X1,X3)
| memberP(X2,X3)
| ~ memberP(app(X1,X2),X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_89,negated_conjecture,
( esk50_0 = nil
| memberP(app(esk50_0,cons(hd(esk50_0),nil)),esk52_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_46]),c_0_32])]),c_0_84]) ).
cnf(c_0_90,negated_conjecture,
~ memberP(esk50_0,esk52_0),
inference(rw,[status(thm)],[c_0_87,c_0_25]) ).
cnf(c_0_91,plain,
( memberP(cons(X2,X3),X1)
| X1 != X2
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_92,negated_conjecture,
( esk50_0 = nil
| memberP(cons(hd(esk50_0),nil),esk52_0)
| ~ ssList(cons(hd(esk50_0),nil)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_28]),c_0_75])]),c_0_90]) ).
cnf(c_0_93,plain,
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(er,[status(thm)],[c_0_91]) ).
cnf(c_0_94,plain,
( X3 = X1
| memberP(X2,X3)
| ~ memberP(cons(X1,X2),X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_95,negated_conjecture,
( esk50_0 = nil
| memberP(cons(hd(esk50_0),nil),esk52_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_46]),c_0_32])]),c_0_84]) ).
fof(c_0_96,plain,
! [X160] :
( ~ ssItem(X160)
| ~ memberP(nil,X160) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax38])])]) ).
cnf(c_0_97,plain,
( nil = X1
| memberP(X1,hd(X1))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_47]),c_0_40]),c_0_27]) ).
cnf(c_0_98,negated_conjecture,
( hd(esk50_0) = esk52_0
| esk50_0 = nil
| memberP(nil,esk52_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_32]),c_0_75])]),c_0_84]) ).
cnf(c_0_99,negated_conjecture,
( neq(esk50_0,nil)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_100,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_101,negated_conjecture,
( esk50_0 = nil
| memberP(nil,esk52_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_28])]),c_0_90]) ).
cnf(c_0_102,plain,
( ~ neq(X1,X2)
| X1 != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_103,negated_conjecture,
( esk51_0 = nil
| neq(esk50_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_31]),c_0_32]),c_0_36])]) ).
cnf(c_0_104,negated_conjecture,
esk50_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_75])]) ).
cnf(c_0_105,plain,
( ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(er,[status(thm)],[c_0_102]) ).
cnf(c_0_106,negated_conjecture,
( esk51_0 = nil
| neq(nil,nil) ),
inference(rw,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_107,negated_conjecture,
esk51_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_32])]) ).
cnf(c_0_108,negated_conjecture,
~ memberP(nil,esk52_0),
inference(rw,[status(thm)],[c_0_90,c_0_104]) ).
cnf(c_0_109,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_107]),c_0_108]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SWC410+1 : TPTP v8.1.0. Released v2.4.0.
% 0.00/0.10 % Command : enigmatic-eprover.py %s %d 1
% 0.09/0.30 % Computer : n032.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 600
% 0.09/0.30 % DateTime : Sun Jun 12 00:33:27 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.15/0.38 # ENIGMATIC: Selected SinE mode:
% 0.15/0.39 # Parsing /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.39 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.15/0.39 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.15/0.39 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 12.55/2.87 # ENIGMATIC: Solved by autoschedule:
% 12.55/2.87 # No SInE strategy applied
% 12.55/2.87 # Trying AutoSched0 for 150 seconds
% 12.55/2.87 # AutoSched0-Mode selected heuristic G_E___207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 12.55/2.87 # and selection function SelectNewComplexAHP.
% 12.55/2.87 #
% 12.55/2.87 # Preprocessing time : 0.028 s
% 12.55/2.87 # Presaturation interreduction done
% 12.55/2.87
% 12.55/2.87 # Proof found!
% 12.55/2.87 # SZS status Theorem
% 12.55/2.87 # SZS output start CNFRefutation
% See solution above
% 12.55/2.87 # Training examples: 0 positive, 0 negative
% 12.55/2.87
% 12.55/2.87 # -------------------------------------------------
% 12.55/2.87 # User time : 0.747 s
% 12.55/2.87 # System time : 0.020 s
% 12.55/2.87 # Total time : 0.767 s
% 12.55/2.87 # Maximum resident set size: 7120 pages
% 12.55/2.87
%------------------------------------------------------------------------------