%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC072+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:42:52 PM UTC 2026
% Result : Theorem 5.88s 6.19s
% Output : CNFRefutation 5.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 26
% Syntax : Number of formulae : 177 ( 36 unt; 0 def)
% Number of atoms : 668 ( 206 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 823 ( 332 ~; 335 |; 77 &)
% ( 7 <=>; 72 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-2 aty)
% Number of variables : 254 ( 0 sgn 119 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax23) ).
fof(ax4,axiom,
! [X1] :
( ssList(X1)
=> ( singletonP(X1)
<=> ? [X2] :
( cons(X2,nil) = X1
& ssItem(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax4) ).
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ( neq(X4,nil)
& ? [X6] :
( ? [X7] :
( ? [X8] :
( neq(nil,X4)
& ? [X9] :
( neq(nil,X4)
& hd(X4) = X9
& cons(X9,nil) = X8
& ssItem(X9) )
& app(X7,X8) = X6
& tl(X4) = X7
& ssList(X8) )
& ssList(X7) )
& X3 != X6
& ssList(X6) ) )
| ( nil = X1
& nil = X2 )
| ( nil = X4
& nil != X3 )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| X1 != X3
| X2 != X4
| ~ ssList(X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
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(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).
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/sandbox/benchmark/Axioms/SWC001+0.ax',ax27) ).
fof(ax5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( app(X2,X3) = X1
& ssList(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(ax44,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( frontsegP(cons(X1,X3),cons(X2,X4))
<=> ( frontsegP(X3,X4)
& X1 = X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax44) ).
fof(ax20,axiom,
! [X1] :
( ssList(X1)
=> ( ? [X2] :
( ? [X3] :
( cons(X3,X2) = X1
& ssItem(X3) )
& ssList(X2) )
| nil = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax20) ).
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(ax25,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> tl(cons(X2,X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax25) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax56,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( segmentP(X1,X2)
=> segmentP(app(app(X3,X1),X4),X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax56) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X1,X2)
<=> ? [X3] :
( app(X3,X2) = X1
& ssList(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax6) ).
fof(ax81,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X1
& nil = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax80,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X2,X3) = app(X2,X1)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax80) ).
fof(ax42,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax42) ).
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/sandbox/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(c_0_26,plain,
! [X128,X129] :
( hd(cons(X129,X128)) = X129
| ~ ssItem(X129)
| ~ ssList(X128) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])])]) ).
fof(c_0_27,plain,
! [X20,X22] :
( ( ~ ssList(X20)
| singletonP(X20)
| cons(X22,nil) != X20
| ~ ssItem(X22) )
& ( ~ ssList(X20)
| ~ singletonP(X20)
| cons(esk5_1(X20),nil) = X20 )
& ( ~ ssList(X20)
| ~ singletonP(X20)
| ssItem(esk5_1(X20)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])])])])]) ).
fof(c_0_28,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ( neq(X4,nil)
& ? [X6] :
( ? [X7] :
( ? [X8] :
( neq(nil,X4)
& ? [X9] :
( neq(nil,X4)
& hd(X4) = X9
& cons(X9,nil) = X8
& ssItem(X9) )
& app(X7,X8) = X6
& tl(X4) = X7
& ssList(X8) )
& ssList(X7) )
& X3 != X6
& ssList(X6) ) )
| ( nil = X1
& nil = X2 )
| ( nil = X4
& nil != X3 )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| X1 != X3
| X2 != X4
| ~ ssList(X4) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
cnf(c_0_29,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| hd(cons(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_30,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(esk5_1(X1),nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_32,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| ssItem(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
( ~ ssList(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| singletonP(X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_34,plain,
! [X114,X115] :
( ssList(cons(X115,X114))
| ~ ssItem(X115)
| ~ ssList(X114) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
fof(c_0_35,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ( neq(X4,nil)
& ? [X6] :
( ? [X7] :
( ? [X8] :
( neq(nil,X4)
& ? [X9] :
( neq(nil,X4)
& hd(X4) = X9
& cons(X9,nil) = X8
& ssItem(X9) )
& app(X7,X8) = X6
& tl(X4) = X7
& ssList(X8) )
& ssList(X7) )
& X3 != X6
& ssList(X6) ) )
| ( nil = X1
& nil = X2 )
| ( nil = X4
& nil != X3 )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| X1 != X3
| X2 != X4
| ~ ssList(X4) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
cnf(c_0_36,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| esk5_1(X1) = hd(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]),c_0_32]) ).
cnf(c_0_37,plain,
( ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| singletonP(cons(X1,nil)) ),
inference(er,[status(thm)],[c_0_33]) ).
cnf(c_0_38,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_39,negated_conjecture,
! [X258,X259,X260,X261,X262] :
( ( ~ neq(esk51_0,nil)
| ~ neq(nil,esk51_0)
| ~ neq(nil,esk51_0)
| hd(esk51_0) != X262
| cons(X262,nil) != X261
| ~ ssItem(X262)
| app(X260,X261) != X259
| tl(esk51_0) != X260
| ~ ssList(X261)
| ~ ssList(X260)
| esk50_0 = X259
| ~ ssList(X259) )
& ( nil != esk48_0
| nil != esk49_0 )
& ( nil != esk51_0
| nil = esk50_0 )
& ( ~ segmentP(esk48_0,X258)
| ~ segmentP(esk49_0,X258)
| ~ neq(X258,nil)
| ~ ssList(X258) )
& esk48_0 = esk50_0
& esk49_0 = esk51_0
& ssList(esk51_0)
& ssList(esk50_0)
& ssList(esk49_0)
& ssList(esk48_0) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])])])]) ).
cnf(c_0_40,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(hd(X1),nil) = X1 ),
inference(spm,[status(thm)],[c_0_30,c_0_36]) ).
cnf(c_0_41,plain,
( ~ ssItem(X1)
| singletonP(cons(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_31])]) ).
cnf(c_0_42,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| ssItem(hd(X1)) ),
inference(spm,[status(thm)],[c_0_32,c_0_36]) ).
cnf(c_0_43,negated_conjecture,
( ~ neq(esk51_0,nil)
| ~ neq(nil,esk51_0)
| ~ neq(nil,esk51_0)
| hd(esk51_0) != X4
| cons(X4,nil) != X3
| ~ ssItem(X4)
| app(X2,X3) != X1
| tl(esk51_0) != X2
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| esk50_0 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_44,plain,
! [X133,X134] :
( ssList(app(X133,X134))
| ~ ssList(X134)
| ~ ssList(X133) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
fof(c_0_45,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax24]) ).
cnf(c_0_46,negated_conjecture,
( nil != esk51_0
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_47,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_48,plain,
( ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| cons(hd(cons(X1,nil)),nil) = cons(X1,nil) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_49,plain,
( ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ssItem(hd(cons(X1,nil))) ),
inference(spm,[status(thm)],[c_0_42,c_0_41]) ).
cnf(c_0_50,negated_conjecture,
( ~ neq(esk51_0,nil)
| ~ neq(nil,esk51_0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X4)
| cons(X4,nil) != X3
| app(X2,X3) != X1
| tl(esk51_0) != X2
| hd(esk51_0) != X4
| esk50_0 = X1 ),
inference(cn,[status(thm)],[c_0_43]) ).
cnf(c_0_51,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_52,plain,
! [X130] :
( ssList(tl(X130))
| nil = X130
| ~ ssList(X130) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])]) ).
cnf(c_0_53,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_54,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_55,negated_conjecture,
( nil != esk48_0
| nil != esk49_0 ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_56,negated_conjecture,
( esk51_0 != nil
| esk48_0 = nil ),
inference(rw,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_57,plain,
( ~ ssItem(X1)
| cons(hd(cons(X1,nil)),nil) = cons(X1,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_38]),c_0_31])]) ).
cnf(c_0_58,plain,
( ~ ssItem(X1)
| ssItem(hd(cons(X1,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_38]),c_0_31])]) ).
fof(c_0_59,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
cnf(c_0_60,negated_conjecture,
( ~ ssItem(hd(esk51_0))
| ~ neq(esk51_0,nil)
| ~ neq(nil,esk51_0)
| ~ ssList(tl(esk51_0))
| ~ ssList(cons(hd(esk51_0),nil))
| app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk48_0 ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_47])])])])]),c_0_51]) ).
cnf(c_0_61,plain,
( ~ ssList(X1)
| ssList(tl(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_62,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_63,negated_conjecture,
esk51_0 != nil,
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_54]),c_0_56]) ).
cnf(c_0_64,plain,
( ~ ssItem(X1)
| ssList(cons(X1,nil)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_57]),c_0_31])]),c_0_58]) ).
fof(c_0_65,plain,
! [X112,X113] :
( ( ~ ssList(X112)
| ~ ssList(X113)
| neq(X112,X113)
| X112 = X113 )
& ( ~ ssList(X112)
| ~ ssList(X113)
| X112 != X113
| ~ neq(X112,X113) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])])])])]) ).
fof(c_0_66,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
inference(fof_simplification,[status(thm)],[ax78]) ).
fof(c_0_67,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax22]) ).
cnf(c_0_68,negated_conjecture,
( ~ ssItem(hd(esk51_0))
| ~ neq(esk51_0,nil)
| ~ neq(nil,esk51_0)
| app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk48_0 ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62])]),c_0_63]),c_0_64]) ).
cnf(c_0_69,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
fof(c_0_70,plain,
! [X135,X136,X137] :
( cons(X137,app(X136,X135)) = app(cons(X137,X136),X135)
| ~ ssItem(X137)
| ~ ssList(X136)
| ~ ssList(X135) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])])]) ).
fof(c_0_71,plain,
! [X216] :
( cons(hd(X216),tl(X216)) = X216
| nil = X216
| ~ ssList(X216) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_66])])]) ).
fof(c_0_72,plain,
! [X127] :
( ssItem(hd(X127))
| nil = X127
| ~ ssList(X127) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_67])])]) ).
cnf(c_0_73,negated_conjecture,
( ~ ssItem(hd(esk51_0))
| ~ neq(esk51_0,nil)
| app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk48_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_62]),c_0_31])]),c_0_63]) ).
cnf(c_0_74,plain,
( ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_75,plain,
( ~ ssList(X1)
| cons(hd(X1),tl(X1)) = X1
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_76,plain,
( ~ ssList(X1)
| ssItem(hd(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_77,negated_conjecture,
( ~ ssItem(hd(esk51_0))
| app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk48_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_69]),c_0_31]),c_0_62])]),c_0_63]) ).
cnf(c_0_78,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil = X1
| cons(hd(X1),app(tl(X1),X2)) = app(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]),c_0_61]) ).
cnf(c_0_79,negated_conjecture,
app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk48_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_76]),c_0_62])]),c_0_63]) ).
fof(c_0_80,plain,
! [X23,X24,X26] :
( ( ~ ssList(X23)
| ~ ssList(X24)
| frontsegP(X23,X24)
| app(X24,X26) != X23
| ~ ssList(X26) )
& ( ~ ssList(X23)
| ~ ssList(X24)
| ~ frontsegP(X23,X24)
| app(X24,esk6_2(X23,X24)) = X23 )
& ( ~ ssList(X23)
| ~ ssList(X24)
| ~ frontsegP(X23,X24)
| ssList(esk6_2(X23,X24)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_81,negated_conjecture,
( ~ ssList(cons(hd(esk51_0),nil))
| app(esk51_0,cons(hd(esk51_0),nil)) = cons(hd(esk51_0),esk48_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_62])]),c_0_63]) ).
cnf(c_0_82,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| app(X2,X1) != X3
| ~ ssList(X1)
| frontsegP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_83,negated_conjecture,
( ~ ssItem(hd(esk51_0))
| app(esk51_0,cons(hd(esk51_0),nil)) = cons(hd(esk51_0),esk48_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_38]),c_0_31])]) ).
cnf(c_0_84,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| frontsegP(app(X1,X2),X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_82]),c_0_51]) ).
cnf(c_0_85,negated_conjecture,
app(esk51_0,cons(hd(esk51_0),nil)) = cons(hd(esk51_0),esk48_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_76]),c_0_62])]),c_0_63]) ).
fof(c_0_86,plain,
! [X170,X171,X172,X173] :
( ( ~ ssItem(X170)
| ~ ssItem(X171)
| ~ ssList(X172)
| ~ ssList(X173)
| frontsegP(cons(X170,X172),cons(X171,X173))
| ~ frontsegP(X172,X173)
| X170 != X171 )
& ( ~ ssItem(X170)
| ~ ssItem(X171)
| ~ ssList(X172)
| ~ ssList(X173)
| ~ frontsegP(cons(X170,X172),cons(X171,X173))
| frontsegP(X172,X173) )
& ( ~ ssItem(X170)
| ~ ssItem(X171)
| ~ ssList(X172)
| ~ ssList(X173)
| ~ frontsegP(cons(X170,X172),cons(X171,X173))
| X170 = X171 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax44])])])])]) ).
fof(c_0_87,plain,
! [X122] :
( ( ~ ssList(X122)
| nil = X122
| cons(esk45_1(X122),esk44_1(X122)) = X122 )
& ( ~ ssList(X122)
| nil = X122
| ssItem(esk45_1(X122)) )
& ( ~ ssList(X122)
| nil = X122
| ssList(esk44_1(X122)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])])]) ).
cnf(c_0_88,negated_conjecture,
( ~ ssList(cons(hd(esk51_0),nil))
| frontsegP(cons(hd(esk51_0),esk48_0),esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_62])]) ).
fof(c_0_89,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
inference(fof_simplification,[status(thm)],[ax86]) ).
fof(c_0_90,plain,
! [X131,X132] :
( tl(cons(X132,X131)) = X131
| ~ ssItem(X132)
| ~ ssList(X131) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])])]) ).
cnf(c_0_91,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ frontsegP(cons(X1,X3),cons(X2,X4))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_92,plain,
( ~ ssList(X1)
| nil = X1
| cons(esk45_1(X1),esk44_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_93,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(esk45_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_94,plain,
( ~ ssList(X1)
| nil = X1
| ssList(esk44_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_95,negated_conjecture,
( ~ ssItem(hd(esk51_0))
| frontsegP(cons(hd(esk51_0),esk48_0),esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_38]),c_0_31])]) ).
fof(c_0_96,plain,
! [X233,X234] :
( tl(app(X233,X234)) = app(tl(X233),X234)
| nil = X233
| ~ ssList(X234)
| ~ ssList(X233) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_89])])])]) ).
fof(c_0_97,plain,
! [X230] :
( app(X230,nil) = X230
| ~ ssList(X230) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).
cnf(c_0_98,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| tl(cons(X2,X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_99,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(cons(X1,X3),X2)
| nil = X2
| X1 = esk45_1(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93]),c_0_94]) ).
cnf(c_0_100,negated_conjecture,
frontsegP(cons(hd(esk51_0),esk48_0),esk51_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_76]),c_0_62])]),c_0_63]) ).
cnf(c_0_101,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_102,plain,
! [X193,X194,X195,X196] :
( segmentP(app(app(X195,X193),X196),X194)
| ~ segmentP(X193,X194)
| ~ ssList(X196)
| ~ ssList(X195)
| ~ ssList(X194)
| ~ ssList(X193) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax56])])])]) ).
fof(c_0_103,plain,
! [X192] :
( segmentP(X192,X192)
| ~ ssList(X192) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])])]) ).
cnf(c_0_104,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X1,X2)) = app(tl(X1),X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_105,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_106,plain,
( ~ ssList(X1)
| nil = X1
| esk44_1(X1) = tl(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_92]),c_0_93]),c_0_94]) ).
cnf(c_0_107,negated_conjecture,
( ~ ssItem(hd(esk51_0))
| esk45_1(esk51_0) = hd(esk51_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_101]),c_0_62])]),c_0_63]) ).
cnf(c_0_108,plain,
( ~ segmentP(X1,X2)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| segmentP(app(app(X3,X1),X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_109,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
fof(c_0_110,plain,
! [X138] :
( app(nil,X138) = X138
| ~ ssList(X138) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
fof(c_0_111,plain,
! [X27,X28,X30] :
( ( ~ ssList(X27)
| ~ ssList(X28)
| rearsegP(X27,X28)
| app(X30,X28) != X27
| ~ ssList(X30) )
& ( ~ ssList(X27)
| ~ ssList(X28)
| ~ rearsegP(X27,X28)
| app(esk7_2(X27,X28),X28) = X27 )
& ( ~ ssList(X27)
| ~ ssList(X28)
| ~ rearsegP(X27,X28)
| ssList(esk7_2(X27,X28)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])])])])])]) ).
cnf(c_0_112,plain,
( ~ ssList(X1)
| nil = X1
| app(tl(X1),nil) = tl(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_31])]) ).
cnf(c_0_113,plain,
( ~ ssList(X1)
| nil = X1
| cons(esk45_1(X1),tl(X1)) = X1 ),
inference(spm,[status(thm)],[c_0_92,c_0_106]) ).
cnf(c_0_114,negated_conjecture,
esk45_1(esk51_0) = hd(esk51_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_76]),c_0_62])]),c_0_63]) ).
cnf(c_0_115,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| segmentP(app(app(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_116,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_117,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| app(X1,X2) != X3
| ~ ssList(X1)
| rearsegP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
fof(c_0_118,plain,
! [X223,X224] :
( cons(X224,X223) = app(cons(X224,nil),X223)
| ~ ssItem(X224)
| ~ ssList(X223) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
fof(c_0_119,plain,
! [X228,X229] :
( ( ~ ssList(X228)
| ~ ssList(X229)
| nil = app(X228,X229)
| nil != X228
| nil != X229 )
& ( ~ ssList(X228)
| ~ ssList(X229)
| nil != app(X228,X229)
| nil = X228 )
& ( ~ ssList(X228)
| ~ ssList(X229)
| nil != app(X228,X229)
| nil = X229 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])])]) ).
cnf(c_0_120,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),tl(X1)) = app(X1,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_112]),c_0_31])]) ).
cnf(c_0_121,negated_conjecture,
cons(hd(esk51_0),tl(esk51_0)) = esk51_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_62])]),c_0_63]) ).
cnf(c_0_122,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| segmentP(app(X1,X2),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_31])]) ).
cnf(c_0_123,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| rearsegP(app(X1,X2),X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_117]),c_0_51]) ).
cnf(c_0_124,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_125,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != app(X1,X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_126,negated_conjecture,
app(esk51_0,nil) = esk51_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_62])]),c_0_63]) ).
cnf(c_0_127,negated_conjecture,
( ~ ssList(tl(esk51_0))
| ~ ssList(cons(hd(esk51_0),nil))
| segmentP(esk48_0,tl(esk51_0)) ),
inference(spm,[status(thm)],[c_0_122,c_0_79]) ).
cnf(c_0_128,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(cons(X1,nil))
| rearsegP(cons(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_129,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ssList(app(tl(X1),X2))
| nil = X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_104]),c_0_51]),c_0_125]) ).
cnf(c_0_130,negated_conjecture,
app(tl(esk51_0),nil) = tl(esk51_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_126]),c_0_31]),c_0_62])]),c_0_63]) ).
cnf(c_0_131,negated_conjecture,
( ~ ssList(cons(hd(esk51_0),nil))
| segmentP(esk48_0,tl(esk51_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_61]),c_0_62])]),c_0_63]) ).
cnf(c_0_132,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| rearsegP(cons(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_38]),c_0_31])]) ).
cnf(c_0_133,negated_conjecture,
ssItem(hd(esk51_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_114]),c_0_62])]),c_0_63]) ).
cnf(c_0_134,negated_conjecture,
ssList(tl(esk51_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_31]),c_0_62])]),c_0_63]) ).
fof(c_0_135,plain,
! [X220,X221,X222] :
( X222 = X220
| app(X221,X222) != app(X221,X220)
| ~ ssList(X222)
| ~ ssList(X221)
| ~ ssList(X220) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])])]) ).
cnf(c_0_136,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X2,X1)
| app(X1,esk6_2(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_137,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ssList(esk6_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_138,negated_conjecture,
( ~ segmentP(esk48_0,X1)
| ~ segmentP(esk49_0,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_139,negated_conjecture,
( ~ ssItem(hd(esk51_0))
| segmentP(esk48_0,tl(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_38]),c_0_31])]) ).
cnf(c_0_140,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| app(esk7_2(X1,X2),X2) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_141,negated_conjecture,
rearsegP(esk51_0,tl(esk51_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_121]),c_0_133])]),c_0_134])]) ).
cnf(c_0_142,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| ssList(esk7_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
fof(c_0_143,plain,
! [X166] :
( frontsegP(X166,X166)
| ~ ssList(X166) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax42])])]) ).
cnf(c_0_144,plain,
( app(X2,X3) != app(X2,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_135]) ).
cnf(c_0_145,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| app(X1,esk6_2(app(X1,X2),X1)) = app(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_84]),c_0_51]) ).
cnf(c_0_146,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(esk6_2(app(X1,X2),X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_84]),c_0_51]) ).
cnf(c_0_147,negated_conjecture,
( ~ neq(X1,nil)
| ~ ssList(X1)
| ~ segmentP(esk51_0,X1)
| ~ segmentP(esk48_0,X1) ),
inference(rw,[status(thm)],[c_0_138,c_0_54]) ).
cnf(c_0_148,negated_conjecture,
segmentP(esk48_0,tl(esk51_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_76]),c_0_62])]),c_0_63]) ).
cnf(c_0_149,negated_conjecture,
app(esk7_2(esk51_0,tl(esk51_0)),tl(esk51_0)) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_134]),c_0_62])]) ).
cnf(c_0_150,negated_conjecture,
ssList(esk7_2(esk51_0,tl(esk51_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_141]),c_0_134]),c_0_62])]) ).
cnf(c_0_151,plain,
( ~ ssList(X1)
| frontsegP(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_143]) ).
cnf(c_0_152,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X2,X1) != X2
| X1 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_105]),c_0_31])]) ).
cnf(c_0_153,negated_conjecture,
app(esk51_0,esk6_2(esk51_0,esk51_0)) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_126]),c_0_62]),c_0_31])]) ).
cnf(c_0_154,negated_conjecture,
ssList(esk6_2(esk51_0,esk51_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_126]),c_0_62]),c_0_31])]) ).
cnf(c_0_155,negated_conjecture,
( ~ neq(tl(esk51_0),nil)
| ~ ssList(tl(esk51_0))
| ~ segmentP(esk51_0,tl(esk51_0)) ),
inference(spm,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_156,negated_conjecture,
( ~ ssList(X1)
| segmentP(app(esk51_0,X1),tl(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_149]),c_0_150]),c_0_134])]) ).
cnf(c_0_157,plain,
( ~ ssList(X1)
| app(X1,esk6_2(X1,X1)) = X1 ),
inference(spm,[status(thm)],[c_0_136,c_0_151]) ).
cnf(c_0_158,negated_conjecture,
esk6_2(esk51_0,esk51_0) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_62]),c_0_154])]) ).
cnf(c_0_159,negated_conjecture,
( ~ neq(tl(esk51_0),nil)
| ~ segmentP(esk51_0,tl(esk51_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_61]),c_0_62])]),c_0_63]) ).
cnf(c_0_160,negated_conjecture,
segmentP(esk51_0,tl(esk51_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_157]),c_0_158]),c_0_31]),c_0_62])]) ).
cnf(c_0_161,negated_conjecture,
~ neq(tl(esk51_0),nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_159,c_0_160])]) ).
cnf(c_0_162,negated_conjecture,
tl(esk51_0) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_69]),c_0_31]),c_0_134])]) ).
fof(c_0_163,plain,
! [X225,X226,X227] :
( app(app(X225,X226),X227) = app(X225,app(X226,X227))
| ~ ssList(X227)
| ~ ssList(X226)
| ~ ssList(X225) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).
cnf(c_0_164,negated_conjecture,
( ~ ssList(cons(hd(esk51_0),nil))
| tl(cons(hd(esk51_0),esk48_0)) = esk48_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_85]),c_0_79]),c_0_62])]),c_0_63]) ).
cnf(c_0_165,negated_conjecture,
cons(hd(esk51_0),nil) = esk51_0,
inference(rw,[status(thm)],[c_0_121,c_0_162]) ).
cnf(c_0_166,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X1,X2),X3) = app(X1,app(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_163]) ).
cnf(c_0_167,negated_conjecture,
tl(cons(hd(esk51_0),esk48_0)) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_164,c_0_165]),c_0_62])]) ).
cnf(c_0_168,negated_conjecture,
cons(hd(esk51_0),esk48_0) = app(esk51_0,esk51_0),
inference(rw,[status(thm)],[c_0_85,c_0_165]) ).
cnf(c_0_169,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(nil,app(X1,X2)) = app(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_116]),c_0_31])]) ).
cnf(c_0_170,negated_conjecture,
tl(app(esk51_0,esk51_0)) = esk48_0,
inference(rw,[status(thm)],[c_0_167,c_0_168]) ).
cnf(c_0_171,negated_conjecture,
app(nil,esk51_0) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_126]),c_0_31]),c_0_62])]) ).
cnf(c_0_172,negated_conjecture,
( ~ neq(esk48_0,nil)
| ~ segmentP(esk51_0,esk48_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_109]),c_0_101])]) ).
cnf(c_0_173,negated_conjecture,
esk48_0 = esk51_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_170]),c_0_162]),c_0_171]),c_0_62])]),c_0_63]) ).
cnf(c_0_174,negated_conjecture,
segmentP(esk51_0,esk51_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_126]),c_0_31]),c_0_62])]) ).
cnf(c_0_175,negated_conjecture,
~ neq(esk51_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_172,c_0_173]),c_0_174]),c_0_173])]) ).
cnf(c_0_176,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_69]),c_0_31]),c_0_62])]),c_0_63]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC072+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/5.37 % Computer : n002.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 21 07:56:22 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/5.41 Running first-order theorem proving
% 0.14/5.41 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.88/6.19 % Version: 3.5.1
% 5.88/6.19 % Preprocessing class: FSLSSMSSSSSNFFN.
% 5.88/6.19 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.88/6.19 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 5.88/6.19 % Starting new_bool_3 with 300s (1) cores
% 5.88/6.19 % Starting new_bool_1 with 300s (1) cores
% 5.88/6.19 % Starting sh5l with 300s (1) cores
% 5.88/6.19 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2812037 completed with status 0
% 5.88/6.19 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 5.88/6.19 % Preprocessing class: FSLSSMSSSSSNFFN.
% 5.88/6.19 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.88/6.19 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 5.88/6.19 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.88/6.19 % No SInE strategy applied
% 5.88/6.19 % Search class: FGHSF-FSLM21-MFFFFFNN
% 5.88/6.19 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 5.88/6.19 % Starting SubtermCWHack with 136s (1) cores
% 5.88/6.19 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 5.88/6.19 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 5.88/6.19 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 5.88/6.19 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 5.88/6.19 % G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with pid 2812047 completed with status 0
% 5.88/6.19 % Result found by G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S
% 5.88/6.19 % Preprocessing class: FSLSSMSSSSSNFFN.
% 5.88/6.19 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.88/6.19 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 5.88/6.19 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.88/6.19 % No SInE strategy applied
% 5.88/6.19 % Search class: FGHSF-FSLM21-MFFFFFNN
% 5.88/6.19 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 5.88/6.19 % Starting SubtermCWHack with 136s (1) cores
% 5.88/6.19 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 5.88/6.19 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 5.88/6.19 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 5.88/6.19 % Preprocessing time : 0.005 s
% 5.88/6.19 % Presaturation interreduction done
% 5.88/6.19
% 5.88/6.19 % Proof found!
% 5.88/6.19 % SZS status Theorem
% 5.88/6.19 % SZS output start CNFRefutation
% See solution above
% 5.88/6.19 % Parsed axioms : 96
% 5.88/6.19 % Removed by relevancy pruning/SinE : 0
% 5.88/6.19 % Initial clauses : 200
% 5.88/6.19 % Removed in clause preprocessing : 2
% 5.88/6.19 % Initial clauses in saturation : 198
% 5.88/6.19 % Processed clauses : 4079
% 5.88/6.19 % ...of these trivial : 139
% 5.88/6.19 % ...subsumed : 2470
% 5.88/6.19 % ...remaining for further processing : 1470
% 5.88/6.19 % Other redundant clauses eliminated : 221
% 5.88/6.19 % Clauses deleted for lack of memory : 0
% 5.88/6.19 % Backward-subsumed : 79
% 5.88/6.19 % Backward-rewritten : 288
% 5.88/6.19 % Generated clauses : 23939
% 5.88/6.19 % ...of the previous two non-redundant : 22111
% 5.88/6.19 % ...aggressively subsumed : 0
% 5.88/6.19 % Contextual simplify-reflections : 641
% 5.88/6.19 % Paramodulations : 23710
% 5.88/6.19 % Factorizations : 0
% 5.88/6.19 % NegExts : 0
% 5.88/6.19 % Equation resolutions : 229
% 5.88/6.19 % Disequality decompositions : 0
% 5.88/6.19 % Total rewrite steps : 19142
% 5.88/6.19 % ...of those cached : 18993
% 5.88/6.19 % Propositional unsat checks : 0
% 5.88/6.19 % Propositional check models : 0
% 5.88/6.19 % Propositional check unsatisfiable : 0
% 5.88/6.19 % Propositional clauses : 0
% 5.88/6.19 % Propositional clauses after purity: 0
% 5.88/6.19 % Propositional unsat core size : 0
% 5.88/6.19 % Propositional preprocessing time : 0.000
% 5.88/6.19 % Propositional encoding time : 0.000
% 5.88/6.19 % Propositional solver time : 0.000
% 5.88/6.19 % Success case prop preproc time : 0.000
% 5.88/6.19 % Success case prop encoding time : 0.000
% 5.88/6.19 % Success case prop solver time : 0.000
% 5.88/6.19 % Current number of processed clauses : 883
% 5.88/6.19 % Positive orientable unit clauses : 82
% 5.88/6.19 % Positive unorientable unit clauses: 0
% 5.88/6.19 % Negative unit clauses : 17
% 5.88/6.19 % Non-unit-clauses : 784
% 5.88/6.19 % Current number of unprocessed clauses: 17892
% 5.88/6.19 % ...number of literals in the above : 119293
% 5.88/6.19 % Current number of archived formulas : 0
% 5.88/6.19 % Current number of archived clauses : 563
% 5.88/6.19 % Clause-clause subsumption calls (NU) : 209614
% 5.88/6.19 % Rec. Clause-clause subsumption calls : 26910
% 5.88/6.19 % Non-unit clause-clause subsumptions : 2588
% 5.88/6.19 % Unit Clause-clause subsumption calls : 11513
% 5.88/6.19 % Rewrite failures with RHS unbound : 0
% 5.88/6.19 % BW rewrite match attempts : 59
% 5.88/6.19 % BW rewrite match successes : 59
% 5.88/6.19 % Condensation attempts : 0
% 5.88/6.19 % Condensation successes : 0
% 5.88/6.19 % Termbank termtop insertions : 551832
% 5.88/6.19 % Search garbage collected termcells : 4395
% 5.88/6.19
% 5.88/6.19 % -------------------------------------------------
% 5.88/6.19 % User time : 0.715 s
% 5.88/6.19 % System time : 0.032 s
% 5.88/6.19 % Total time : 0.747 s
% 5.88/6.19 % Maximum resident set size: 4276 pages
% 5.88/6.19
% 5.88/6.19 % -------------------------------------------------
% 5.88/6.19 % User time : 3.524 s
% 5.88/6.19 % System time : 0.148 s
% 5.88/6.19 % Total time : 3.672 s
% 5.88/6.19 % Maximum resident set size: 4864 pages
% 5.88/6.19 % E exiting
%------------------------------------------------------------------------------