%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC382+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 02:44:10 PM UTC 2026
% Result : Theorem 1.33s 0.63s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 16
% Syntax : Number of formulae : 106 ( 12 unt; 0 def)
% Number of atoms : 428 ( 140 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 531 ( 209 ~; 221 |; 47 &)
% ( 4 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-2 aty)
% Number of variables : 140 ( 0 sgn 72 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( neq(X4,nil)
| ~ neq(X2,nil) )
& ( ( segmentP(X2,X1)
& singletonP(X1) )
| ? [X5] :
( ? [X6] :
( neq(nil,X4)
& hd(X4) = X6
& cons(X6,nil) = X5
& ssItem(X6) )
& X3 != X5
& ssList(X5) )
| ~ neq(X2,nil) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax18) ).
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(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
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(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(ax19,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssItem(X4)
=> ( cons(X3,X1) = cons(X4,X2)
=> ( X2 = X1
& X3 = X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax19) ).
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(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(ax4,axiom,
! [X1] :
( ssList(X1)
=> ( singletonP(X1)
<=> ? [X2] :
( cons(X2,nil) = X1
& ssItem(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax4) ).
fof(ax20,axiom,
! [X1] :
( ssList(X1)
=> ( ? [X2] :
( ? [X3] :
( cons(X3,X2) = X1
& ssItem(X3) )
& ssList(X2) )
| nil = 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(ax7,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ? [X4] :
( app(app(X3,X2),X4) = X1
& ssList(X4) )
& ssList(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(c_0_16,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( neq(X4,nil)
| ~ neq(X2,nil) )
& ( ( segmentP(X2,X1)
& singletonP(X1) )
| ? [X5] :
( ? [X6] :
( neq(nil,X4)
& hd(X4) = X6
& cons(X6,nil) = X5
& ssItem(X6) )
& X3 != X5
& ssList(X5) )
| ~ neq(X2,nil) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_17,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( neq(X4,nil)
| ~ neq(X2,nil) )
& ( ( segmentP(X2,X1)
& singletonP(X1) )
| ? [X5] :
( ? [X6] :
( neq(nil,X4)
& hd(X4) = X6
& cons(X6,nil) = X5
& ssItem(X6) )
& X3 != X5
& ssList(X5) )
| ~ neq(X2,nil) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_18,negated_conjecture,
! [X255,X256] :
( ( ~ segmentP(esk49_0,esk48_0)
| ~ singletonP(esk48_0)
| ~ neq(esk51_0,nil) )
& ( ~ segmentP(esk49_0,esk48_0)
| ~ singletonP(esk48_0)
| neq(esk49_0,nil) )
& ( ~ neq(nil,esk51_0)
| hd(esk51_0) != X256
| cons(X256,nil) != X255
| ~ ssItem(X256)
| esk50_0 = X255
| ~ ssList(X255)
| ~ neq(esk51_0,nil) )
& ( ~ neq(nil,esk51_0)
| hd(esk51_0) != X256
| cons(X256,nil) != X255
| ~ ssItem(X256)
| esk50_0 = X255
| ~ ssList(X255)
| neq(esk49_0,nil) )
& ( neq(esk49_0,nil)
| ~ neq(esk51_0,nil) )
& ( neq(esk49_0,nil)
| neq(esk49_0,nil) )
& esk48_0 = esk50_0
& esk49_0 = esk51_0
& ssList(esk51_0)
& ssList(esk50_0)
& ssList(esk49_0)
& ssList(esk48_0) ),
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)],[c_0_17])])])])])]) ).
cnf(c_0_19,negated_conjecture,
( neq(esk49_0,nil)
| neq(esk49_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_20,negated_conjecture,
neq(esk49_0,nil),
inference(cn,[status(thm)],[c_0_19]) ).
cnf(c_0_21,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,negated_conjecture,
( ~ neq(nil,esk51_0)
| hd(esk51_0) != X2
| cons(X2,nil) != X1
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ neq(esk51_0,nil)
| esk50_0 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,negated_conjecture,
neq(esk51_0,nil),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_25,plain,
! [X111,X112] :
( ssList(cons(X112,X111))
| ~ ssItem(X112)
| ~ ssList(X111) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
fof(c_0_26,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
inference(fof_simplification,[status(thm)],[ax18]) ).
fof(c_0_27,plain,
! [X125,X126] :
( hd(cons(X126,X125)) = X126
| ~ ssItem(X126)
| ~ ssList(X125) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])])]) ).
cnf(c_0_28,negated_conjecture,
( ~ ssItem(hd(esk51_0))
| ~ neq(nil,esk51_0)
| ~ ssList(cons(hd(esk51_0),nil))
| cons(hd(esk51_0),nil) = esk48_0 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_24])])])]) ).
cnf(c_0_29,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_31,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
fof(c_0_32,plain,
! [X113,X114] :
( cons(X114,X113) != X113
| ~ ssItem(X114)
| ~ ssList(X113) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])]) ).
cnf(c_0_33,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| hd(cons(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,negated_conjecture,
( ~ ssItem(hd(esk51_0))
| ~ neq(nil,esk51_0)
| cons(hd(esk51_0),nil) = esk48_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
fof(c_0_35,plain,
! [X109,X110] :
( ( ~ ssList(X109)
| ~ ssList(X110)
| neq(X109,X110)
| X109 = X110 )
& ( ~ ssList(X109)
| ~ ssList(X110)
| X109 != X110
| ~ neq(X109,X110) ) ),
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_31])])])])]) ).
cnf(c_0_36,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_37,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax22]) ).
cnf(c_0_38,plain,
( cons(X2,X1) != X1
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_39,negated_conjecture,
( ~ ssItem(hd(esk51_0))
| ~ neq(nil,esk51_0)
| hd(esk48_0) = hd(esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_30])]) ).
cnf(c_0_40,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_41,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_36,c_0_21]) ).
fof(c_0_42,plain,
! [X124] :
( ssItem(hd(X124))
| nil = X124
| ~ ssList(X124) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])]) ).
cnf(c_0_43,negated_conjecture,
( ~ ssItem(hd(esk51_0))
| ~ neq(nil,esk51_0)
| esk48_0 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_34]),c_0_30])]) ).
fof(c_0_44,plain,
! [X115,X116,X117,X118] :
( ( ~ ssList(X115)
| ~ ssList(X116)
| ~ ssItem(X117)
| ~ ssItem(X118)
| cons(X117,X115) != cons(X118,X116)
| X116 = X115 )
& ( ~ ssList(X115)
| ~ ssList(X116)
| ~ ssItem(X117)
| ~ ssItem(X118)
| cons(X117,X115) != cons(X118,X116)
| X117 = X118 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax19])])])])]) ).
cnf(c_0_45,negated_conjecture,
( ~ ssItem(hd(esk51_0))
| esk51_0 = nil
| hd(esk48_0) = hd(esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),c_0_30])]) ).
cnf(c_0_46,plain,
( ~ ssList(X1)
| ssItem(hd(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_47,negated_conjecture,
( ~ ssItem(hd(esk51_0))
| esk48_0 != nil
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_40]),c_0_41]),c_0_30])]) ).
fof(c_0_48,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
inference(fof_simplification,[status(thm)],[ax78]) ).
cnf(c_0_49,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X3)
| ~ ssItem(X4)
| cons(X3,X2) != cons(X4,X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_50,negated_conjecture,
( esk51_0 = nil
| hd(esk48_0) = hd(esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_41])]) ).
cnf(c_0_51,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_52,negated_conjecture,
( esk48_0 != nil
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_46]),c_0_41])]) ).
fof(c_0_53,plain,
! [X213] :
( cons(hd(X213),tl(X213)) = X213
| nil = X213
| ~ ssList(X213) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])])]) ).
cnf(c_0_54,negated_conjecture,
( ~ ssItem(X2)
| ~ ssItem(hd(esk51_0))
| ~ neq(nil,esk51_0)
| ~ ssList(X1)
| cons(X2,X1) != esk48_0
| nil = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_34]),c_0_30])]) ).
cnf(c_0_55,negated_conjecture,
( ssItem(hd(esk51_0))
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_50]),c_0_51])]),c_0_52]) ).
cnf(c_0_56,plain,
( ~ ssList(X1)
| cons(hd(X1),tl(X1)) = X1
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
fof(c_0_57,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax24]) ).
cnf(c_0_58,negated_conjecture,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) != esk48_0
| nil = X1
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_40]),c_0_41]),c_0_30])]),c_0_55]) ).
cnf(c_0_59,negated_conjecture,
( esk51_0 = nil
| cons(hd(esk51_0),tl(esk48_0)) = esk48_0 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_50]),c_0_51])]),c_0_52]) ).
fof(c_0_60,plain,
! [X127] :
( ssList(tl(X127))
| nil = X127
| ~ ssList(X127) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])]) ).
cnf(c_0_61,negated_conjecture,
( ~ ssList(tl(esk48_0))
| esk51_0 = nil
| tl(esk48_0) = nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_55]) ).
cnf(c_0_62,plain,
( ~ ssList(X1)
| ssList(tl(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
fof(c_0_63,plain,
! [X17,X19] :
( ( ~ ssList(X17)
| singletonP(X17)
| cons(X19,nil) != X17
| ~ ssItem(X19) )
& ( ~ ssList(X17)
| ~ singletonP(X17)
| cons(esk5_1(X17),nil) = X17 )
& ( ~ ssList(X17)
| ~ singletonP(X17)
| ssItem(esk5_1(X17)) ) ),
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])])])])])]) ).
cnf(c_0_64,negated_conjecture,
( esk51_0 = nil
| tl(esk48_0) = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_51])]),c_0_52]) ).
cnf(c_0_65,plain,
( ~ ssList(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| singletonP(X2) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_66,plain,
( ~ ssList(X3)
| ~ ssList(X4)
| ~ ssItem(X1)
| ~ ssItem(X2)
| cons(X1,X3) != cons(X2,X4)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_67,negated_conjecture,
( esk51_0 = nil
| cons(hd(esk51_0),nil) = esk48_0 ),
inference(spm,[status(thm)],[c_0_59,c_0_64]) ).
cnf(c_0_68,plain,
( ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| singletonP(cons(X1,nil)) ),
inference(er,[status(thm)],[c_0_65]) ).
fof(c_0_69,plain,
! [X119] :
( ( ~ ssList(X119)
| nil = X119
| cons(esk45_1(X119),esk44_1(X119)) = X119 )
& ( ~ ssList(X119)
| nil = X119
| ssItem(esk45_1(X119)) )
& ( ~ ssList(X119)
| nil = X119
| ssList(esk44_1(X119)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])])]) ).
fof(c_0_70,plain,
! [X220,X221] :
( cons(X221,X220) = app(cons(X221,nil),X220)
| ~ ssItem(X221)
| ~ ssList(X220) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
cnf(c_0_71,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| cons(X1,X2) != esk48_0
| esk51_0 = nil
| X1 = hd(esk51_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_30])]),c_0_55]) ).
cnf(c_0_72,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(esk5_1(X1),nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_73,negated_conjecture,
( singletonP(esk48_0)
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_67]),c_0_51])]),c_0_55]) ).
cnf(c_0_74,negated_conjecture,
( ~ segmentP(esk49_0,esk48_0)
| ~ singletonP(esk48_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_75,plain,
! [X28,X29,X32,X33] :
( ( ~ ssList(X28)
| ~ ssList(X29)
| segmentP(X28,X29)
| app(app(X32,X29),X33) != X28
| ~ ssList(X33)
| ~ ssList(X32) )
& ( ~ ssList(X28)
| ~ ssList(X29)
| ~ segmentP(X28,X29)
| app(app(esk8_2(X28,X29),X29),esk9_2(X28,X29)) = X28 )
& ( ~ ssList(X28)
| ~ ssList(X29)
| ~ segmentP(X28,X29)
| ssList(esk9_2(X28,X29)) )
& ( ~ ssList(X28)
| ~ ssList(X29)
| ~ segmentP(X28,X29)
| ssList(esk8_2(X28,X29)) ) ),
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)],[ax7])])])])])]) ).
cnf(c_0_76,plain,
( ~ ssList(X1)
| nil = X1
| cons(esk45_1(X1),esk44_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_77,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(esk45_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_78,plain,
( ~ ssList(X1)
| nil = X1
| ssList(esk44_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_79,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_80,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| ssItem(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_81,negated_conjecture,
( ~ ssItem(esk5_1(esk48_0))
| esk51_0 = nil
| esk5_1(esk48_0) = hd(esk51_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_30])])]),c_0_51])]),c_0_73]) ).
cnf(c_0_82,negated_conjecture,
( ~ singletonP(esk48_0)
| ~ segmentP(esk51_0,esk48_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_24]),c_0_21])]) ).
cnf(c_0_83,negated_conjecture,
( ~ ssItem(hd(esk51_0))
| ~ neq(nil,esk51_0)
| singletonP(esk48_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_34]),c_0_51])]) ).
cnf(c_0_84,plain,
( ~ ssList(X4)
| ~ ssList(X3)
| app(app(X1,X3),X2) != X4
| ~ ssList(X2)
| ~ ssList(X1)
| segmentP(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
fof(c_0_85,plain,
! [X135] :
( app(nil,X135) = X135
| ~ ssList(X135) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
fof(c_0_86,plain,
! [X130,X131] :
( ssList(app(X130,X131))
| ~ ssList(X131)
| ~ ssList(X130) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
cnf(c_0_87,plain,
( ~ ssList(X1)
| nil = X1
| esk45_1(X1) = hd(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_76]),c_0_77]),c_0_78]) ).
cnf(c_0_88,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ singletonP(X1)
| cons(esk5_1(X1),X2) = app(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_72]),c_0_80]) ).
cnf(c_0_89,negated_conjecture,
( esk51_0 = nil
| esk5_1(esk48_0) = hd(esk51_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_80]),c_0_51])]),c_0_73]) ).
cnf(c_0_90,negated_conjecture,
( ~ ssItem(hd(esk51_0))
| ~ neq(nil,esk51_0)
| ~ segmentP(esk51_0,esk48_0) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_91,plain,
( ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(app(app(X1,X2),X3))
| segmentP(app(app(X1,X2),X3),X2) ),
inference(er,[status(thm)],[c_0_84]) ).
cnf(c_0_92,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_93,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_94,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),esk44_1(X1)) = X1 ),
inference(spm,[status(thm)],[c_0_76,c_0_87]) ).
cnf(c_0_95,negated_conjecture,
( ~ ssList(X1)
| esk51_0 = nil
| cons(hd(esk51_0),X1) = app(esk48_0,X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_51])]),c_0_73]) ).
cnf(c_0_96,negated_conjecture,
( ~ ssItem(hd(esk51_0))
| ~ segmentP(esk51_0,esk48_0)
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_40]),c_0_41]),c_0_30])]) ).
cnf(c_0_97,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| segmentP(app(X1,X2),X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_30])]),c_0_93]) ).
cnf(c_0_98,negated_conjecture,
( ~ ssList(esk44_1(esk51_0))
| esk51_0 = nil
| app(esk48_0,esk44_1(esk51_0)) = esk51_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_41])]) ).
cnf(c_0_99,negated_conjecture,
( ~ segmentP(esk51_0,esk48_0)
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_46]),c_0_41])]) ).
cnf(c_0_100,negated_conjecture,
( ~ ssList(esk44_1(esk51_0))
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_51])]),c_0_99]) ).
cnf(c_0_101,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_102,negated_conjecture,
esk51_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_78]),c_0_41])]) ).
cnf(c_0_103,plain,
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(er,[status(thm)],[c_0_101]) ).
cnf(c_0_104,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[c_0_24,c_0_102]) ).
cnf(c_0_105,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC382+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 08:22:15 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 1.33/0.63 % Version: 3.5.1
% 1.33/0.63 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.33/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.33/0.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.33/0.63 % Starting new_bool_3 with 300s (1) cores
% 1.33/0.63 % Starting new_bool_1 with 300s (1) cores
% 1.33/0.63 % Starting sh5l with 300s (1) cores
% 1.33/0.63 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1435219 completed with status 0
% 1.33/0.63 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.33/0.63 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.33/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.33/0.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.33/0.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.33/0.63 % No SInE strategy applied
% 1.33/0.63 % Search class: FGHSF-FSLM21-MFFFFFNN
% 1.33/0.63 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 1.33/0.63 % Starting SubtermCWHack with 136s (1) cores
% 1.33/0.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.33/0.63 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 1.33/0.63 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 1.33/0.63 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 1.33/0.63 % G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with pid 1435229 completed with status 0
% 1.33/0.63 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y
% 1.33/0.63 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.33/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.33/0.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.33/0.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.33/0.63 % No SInE strategy applied
% 1.33/0.63 % Search class: FGHSF-FSLM21-MFFFFFNN
% 1.33/0.63 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 1.33/0.63 % Starting SubtermCWHack with 136s (1) cores
% 1.33/0.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.33/0.63 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 1.33/0.63 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 1.33/0.63 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 1.33/0.63 % Preprocessing time : 0.003 s
% 1.33/0.63 % Presaturation interreduction done
% 1.33/0.63
% 1.33/0.63 % Proof found!
% 1.33/0.63 % SZS status Theorem
% 1.33/0.63 % SZS output start CNFRefutation
% See solution above
% 1.33/0.63 % Parsed axioms : 96
% 1.33/0.63 % Removed by relevancy pruning/SinE : 0
% 1.33/0.63 % Initial clauses : 202
% 1.33/0.63 % Removed in clause preprocessing : 2
% 1.33/0.63 % Initial clauses in saturation : 200
% 1.33/0.63 % Processed clauses : 2614
% 1.33/0.63 % ...of these trivial : 11
% 1.33/0.63 % ...subsumed : 1627
% 1.33/0.63 % ...remaining for further processing : 976
% 1.33/0.63 % Other redundant clauses eliminated : 191
% 1.33/0.63 % Clauses deleted for lack of memory : 0
% 1.33/0.63 % Backward-subsumed : 70
% 1.33/0.63 % Backward-rewritten : 272
% 1.33/0.63 % Generated clauses : 9559
% 1.33/0.63 % ...of the previous two non-redundant : 8930
% 1.33/0.63 % ...aggressively subsumed : 0
% 1.33/0.63 % Contextual simplify-reflections : 403
% 1.33/0.63 % Paramodulations : 9364
% 1.33/0.63 % Factorizations : 0
% 1.33/0.63 % NegExts : 0
% 1.33/0.63 % Equation resolutions : 198
% 1.33/0.63 % Disequality decompositions : 0
% 1.33/0.63 % Total rewrite steps : 4772
% 1.33/0.63 % ...of those cached : 4751
% 1.33/0.63 % Propositional unsat checks : 0
% 1.33/0.63 % Propositional check models : 0
% 1.33/0.63 % Propositional check unsatisfiable : 0
% 1.33/0.63 % Propositional clauses : 0
% 1.33/0.63 % Propositional clauses after purity: 0
% 1.33/0.63 % Propositional unsat core size : 0
% 1.33/0.63 % Propositional preprocessing time : 0.000
% 1.33/0.63 % Propositional encoding time : 0.000
% 1.33/0.63 % Propositional solver time : 0.000
% 1.33/0.63 % Success case prop preproc time : 0.000
% 1.33/0.63 % Success case prop encoding time : 0.000
% 1.33/0.63 % Success case prop solver time : 0.000
% 1.33/0.63 % Current number of processed clauses : 419
% 1.33/0.63 % Positive orientable unit clauses : 21
% 1.33/0.63 % Positive unorientable unit clauses: 0
% 1.33/0.63 % Negative unit clauses : 2
% 1.33/0.63 % Non-unit-clauses : 396
% 1.33/0.63 % Current number of unprocessed clauses: 6616
% 1.33/0.63 % ...number of literals in the above : 44358
% 1.33/0.63 % Current number of archived formulas : 0
% 1.33/0.63 % Current number of archived clauses : 533
% 1.33/0.63 % Clause-clause subsumption calls (NU) : 109428
% 1.33/0.63 % Rec. Clause-clause subsumption calls : 29772
% 1.33/0.63 % Non-unit clause-clause subsumptions : 2026
% 1.33/0.63 % Unit Clause-clause subsumption calls : 202
% 1.33/0.63 % Rewrite failures with RHS unbound : 0
% 1.33/0.63 % BW rewrite match attempts : 4
% 1.33/0.63 % BW rewrite match successes : 4
% 1.33/0.63 % Condensation attempts : 0
% 1.33/0.63 % Condensation successes : 0
% 1.33/0.63 % Termbank termtop insertions : 210553
% 1.33/0.63 % Search garbage collected termcells : 4322
% 1.33/0.63
% 1.33/0.63 % -------------------------------------------------
% 1.33/0.63 % User time : 0.194 s
% 1.33/0.63 % System time : 0.003 s
% 1.33/0.63 % Total time : 0.197 s
% 1.33/0.63 % Maximum resident set size: 4272 pages
% 1.33/0.63
% 1.33/0.63 % -------------------------------------------------
% 1.33/0.63 % User time : 0.924 s
% 1.33/0.63 % System time : 0.041 s
% 1.33/0.63 % Total time : 0.965 s
% 1.33/0.63 % Maximum resident set size: 4608 pages
% 1.33/0.63 % E exiting
%------------------------------------------------------------------------------