%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC354+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 : n008.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 02:44:03 PM UTC 2026
% Result : Theorem 2.02s 0.73s
% Output : CNFRefutation 2.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 16
% Syntax : Number of formulae : 92 ( 13 unt; 0 def)
% Number of atoms : 373 ( 104 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 465 ( 184 ~; 190 |; 40 &)
% ( 4 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 140 ( 0 sgn 74 !; 9 ?)
% 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)
| ? [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/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(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(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
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(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
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(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
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(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).
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(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(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(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax55) ).
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)
| ? [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)
| ? [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,
! [X11,X12] :
( ( ~ segmentP(esk2_0,esk1_0)
| ~ neq(esk4_0,nil) )
& ( ~ segmentP(esk2_0,esk1_0)
| neq(esk2_0,nil) )
& ( ~ neq(nil,esk4_0)
| hd(esk4_0) != X12
| cons(X12,nil) != X11
| ~ ssItem(X12)
| esk3_0 = X11
| ~ ssList(X11)
| ~ neq(esk4_0,nil) )
& ( ~ neq(nil,esk4_0)
| hd(esk4_0) != X12
| cons(X12,nil) != X11
| ~ ssItem(X12)
| esk3_0 = X11
| ~ ssList(X11)
| neq(esk2_0,nil) )
& ( neq(esk2_0,nil)
| ~ neq(esk4_0,nil) )
& ( neq(esk2_0,nil)
| neq(esk2_0,nil) )
& esk1_0 = esk3_0
& esk2_0 = esk4_0
& ssList(esk4_0)
& ssList(esk3_0)
& ssList(esk2_0)
& ssList(esk1_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])])])])])]) ).
fof(c_0_19,plain,
! [X83,X84] :
( ssList(app(X83,X84))
| ~ ssList(X84)
| ~ ssList(X83) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
fof(c_0_20,plain,
! [X68,X69,X70] :
( cons(X70,app(X69,X68)) = app(cons(X70,X69),X68)
| ~ ssItem(X70)
| ~ ssList(X69)
| ~ ssList(X68) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])])]) ).
fof(c_0_21,plain,
! [X60,X61] :
( ssList(cons(X61,X60))
| ~ ssItem(X61)
| ~ ssList(X60) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
fof(c_0_22,plain,
! [X28,X29] :
( ( ~ ssList(X28)
| ~ ssList(X29)
| nil = app(X28,X29)
| nil != X28
| nil != X29 )
& ( ~ ssList(X28)
| ~ ssList(X29)
| nil != app(X28,X29)
| nil = X28 )
& ( ~ ssList(X28)
| ~ ssList(X29)
| nil != app(X28,X29)
| nil = X29 ) ),
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_23,negated_conjecture,
( neq(esk2_0,nil)
| neq(esk2_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
( ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != X2
| nil != X1
| nil = app(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_29,negated_conjecture,
neq(esk2_0,nil),
inference(cn,[status(thm)],[c_0_23]) ).
cnf(c_0_30,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_31,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ssList(cons(X1,app(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_32,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_27])]),c_0_28])]) ).
fof(c_0_33,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[ax21]) ).
fof(c_0_34,plain,
! [X51,X52] :
( hd(cons(X52,X51)) = X52
| ~ ssItem(X52)
| ~ ssList(X51) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])])]) ).
cnf(c_0_35,negated_conjecture,
( ~ neq(nil,esk4_0)
| hd(esk4_0) != X2
| cons(X2,nil) != X1
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ neq(esk4_0,nil)
| esk3_0 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_36,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_37,negated_conjecture,
neq(esk4_0,nil),
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_38,plain,
( ~ ssItem(X1)
| ssList(cons(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_28])]) ).
fof(c_0_39,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
fof(c_0_40,plain,
! [X20,X21] :
( nil != cons(X21,X20)
| ~ ssItem(X21)
| ~ ssList(X20) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])])]) ).
fof(c_0_41,plain,
! [X94,X95,X97] :
( ( ~ ssList(X94)
| ~ ssList(X95)
| frontsegP(X94,X95)
| app(X95,X97) != X94
| ~ ssList(X97) )
& ( ~ ssList(X94)
| ~ ssList(X95)
| ~ frontsegP(X94,X95)
| app(X95,esk12_2(X94,X95)) = X94 )
& ( ~ ssList(X94)
| ~ ssList(X95)
| ~ frontsegP(X94,X95)
| ssList(esk12_2(X94,X95)) ) ),
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_42,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| hd(cons(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_43,negated_conjecture,
( ~ ssItem(hd(esk4_0))
| ~ neq(nil,esk4_0)
| cons(hd(esk4_0),nil) = esk1_0 ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36]),c_0_37])])])]),c_0_38]) ).
fof(c_0_44,plain,
! [X15,X16] :
( ( ~ ssList(X15)
| ~ ssList(X16)
| neq(X15,X16)
| X15 = X16 )
& ( ~ ssList(X15)
| ~ ssList(X16)
| X15 != X16
| ~ neq(X15,X16) ) ),
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_39])])])])]) ).
fof(c_0_45,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax22]) ).
cnf(c_0_46,plain,
( nil != cons(X2,X1)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_47,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| app(X2,X1) != X3
| ~ ssList(X1)
| frontsegP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_48,plain,
! [X26,X27] :
( cons(X27,X26) = app(cons(X27,nil),X26)
| ~ ssItem(X27)
| ~ ssList(X26) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
fof(c_0_49,plain,
! [X17] :
( ( ~ ssList(X17)
| nil = X17
| cons(esk6_1(X17),esk5_1(X17)) = X17 )
& ( ~ ssList(X17)
| nil = X17
| ssItem(esk6_1(X17)) )
& ( ~ ssList(X17)
| nil = X17
| ssList(esk5_1(X17)) ) ),
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_50,negated_conjecture,
( ~ ssItem(hd(esk4_0))
| ~ neq(nil,esk4_0)
| hd(esk1_0) = hd(esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_28])]) ).
cnf(c_0_51,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_52,negated_conjecture,
ssList(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_53,plain,
! [X22] :
( ssItem(hd(X22))
| nil = X22
| ~ ssList(X22) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])]) ).
cnf(c_0_54,negated_conjecture,
( ~ ssItem(hd(esk4_0))
| ~ neq(nil,esk4_0)
| esk1_0 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_43]),c_0_28])]) ).
cnf(c_0_55,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| frontsegP(app(X1,X2),X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_47]),c_0_24]) ).
cnf(c_0_56,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_57,plain,
( ~ ssList(X1)
| nil = X1
| cons(esk6_1(X1),esk5_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_58,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(esk6_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_59,plain,
( ~ ssList(X1)
| nil = X1
| ssList(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_60,negated_conjecture,
( ~ ssItem(hd(esk4_0))
| esk4_0 = nil
| hd(esk1_0) = hd(esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_28])]) ).
cnf(c_0_61,plain,
( ~ ssList(X1)
| ssItem(hd(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_62,negated_conjecture,
( ~ ssItem(hd(esk4_0))
| esk1_0 != nil
| esk4_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_51]),c_0_52]),c_0_28])]) ).
cnf(c_0_63,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(cons(X1,nil))
| frontsegP(cons(X1,X2),cons(X1,nil)) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_64,negated_conjecture,
ssList(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_65,plain,
( ~ ssList(X1)
| nil = X1
| esk6_1(X1) = hd(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_57]),c_0_58]),c_0_59]) ).
cnf(c_0_66,negated_conjecture,
( esk4_0 = nil
| hd(esk1_0) = hd(esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_52])]) ).
cnf(c_0_67,negated_conjecture,
( esk1_0 != nil
| esk4_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_61]),c_0_52])]) ).
fof(c_0_68,plain,
! [X45,X46,X47,X48] :
( segmentP(app(app(X47,X45),X48),X46)
| ~ segmentP(X45,X46)
| ~ ssList(X48)
| ~ ssList(X47)
| ~ ssList(X46)
| ~ ssList(X45) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax56])])])]) ).
fof(c_0_69,plain,
! [X23] :
( app(nil,X23) = X23
| ~ ssList(X23) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
cnf(c_0_70,negated_conjecture,
( ~ ssItem(hd(esk4_0))
| ~ neq(nil,esk4_0)
| ~ ssList(X1)
| frontsegP(cons(hd(esk4_0),X1),esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_43]),c_0_64])]) ).
cnf(c_0_71,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),esk5_1(X1)) = X1 ),
inference(spm,[status(thm)],[c_0_57,c_0_65]) ).
cnf(c_0_72,negated_conjecture,
( ssItem(hd(esk4_0))
| esk4_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_66]),c_0_64])]),c_0_67]) ).
cnf(c_0_73,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_68]) ).
cnf(c_0_74,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_75,negated_conjecture,
( ~ neq(nil,esk4_0)
| ~ ssList(esk5_1(esk4_0))
| frontsegP(esk4_0,esk1_0)
| esk4_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_52])]),c_0_72]) ).
cnf(c_0_76,plain,
( ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ segmentP(X1,X3)
| segmentP(app(X1,X2),X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_28])]) ).
cnf(c_0_77,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X2,X1)
| app(X1,esk12_2(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_78,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ssList(esk12_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_79,negated_conjecture,
( ~ neq(nil,esk4_0)
| frontsegP(esk4_0,esk1_0)
| esk4_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_59]),c_0_52])]) ).
cnf(c_0_80,plain,
( ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ frontsegP(X1,X3)
| ~ segmentP(X3,X2)
| segmentP(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]) ).
cnf(c_0_81,negated_conjecture,
( frontsegP(esk4_0,esk1_0)
| esk4_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_51]),c_0_52]),c_0_28])]) ).
fof(c_0_82,plain,
! [X44] :
( segmentP(X44,X44)
| ~ ssList(X44) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])])]) ).
cnf(c_0_83,negated_conjecture,
( ~ segmentP(esk2_0,esk1_0)
| ~ neq(esk4_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_84,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(esk1_0,X1)
| segmentP(esk4_0,X1)
| esk4_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_64]),c_0_52])]) ).
cnf(c_0_85,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_86,negated_conjecture,
~ segmentP(esk4_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_37]),c_0_30])]) ).
cnf(c_0_87,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_88,negated_conjecture,
esk4_0 = nil,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_64])]),c_0_86]) ).
cnf(c_0_89,plain,
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(er,[status(thm)],[c_0_87]) ).
cnf(c_0_90,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[c_0_37,c_0_88]) ).
cnf(c_0_91,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC354+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n008.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 08:19:08 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.02/0.73 % Version: 3.5.1
% 2.02/0.73 % Preprocessing class: FSLSSMSSSSSNFFN.
% 2.02/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.02/0.73 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.02/0.73 % Starting new_bool_3 with 300s (1) cores
% 2.02/0.73 % Starting new_bool_1 with 300s (1) cores
% 2.02/0.73 % Starting sh5l with 300s (1) cores
% 2.02/0.73 % sh5l with pid 563543 completed with status 0
% 2.02/0.73 % Result found by sh5l
% 2.02/0.73 % Preprocessing class: FSLSSMSSSSSNFFN.
% 2.02/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.02/0.73 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.02/0.73 % Starting new_bool_3 with 300s (1) cores
% 2.02/0.73 % Starting new_bool_1 with 300s (1) cores
% 2.02/0.73 % Starting sh5l with 300s (1) cores
% 2.02/0.73 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 2.02/0.73 % SinE strategy is gf500_gu_R04_F100_L20000
% 2.02/0.73 % Search class: FGHSF-FSLM21-MFFFFFNN
% 2.02/0.73 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 2.02/0.73 % Starting SubtermCWHack with 28s (1) cores
% 2.02/0.73 % SubtermCWHack with pid 563546 completed with status 0
% 2.02/0.73 % Result found by SubtermCWHack
% 2.02/0.73 % Preprocessing class: FSLSSMSSSSSNFFN.
% 2.02/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.02/0.73 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.02/0.73 % Starting new_bool_3 with 300s (1) cores
% 2.02/0.73 % Starting new_bool_1 with 300s (1) cores
% 2.02/0.73 % Starting sh5l with 300s (1) cores
% 2.02/0.73 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 2.02/0.73 % SinE strategy is gf500_gu_R04_F100_L20000
% 2.02/0.73 % Search class: FGHSF-FSLM21-MFFFFFNN
% 2.02/0.73 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 2.02/0.73 % Starting SubtermCWHack with 28s (1) cores
% 2.02/0.73 % Preprocessing time : 0.002 s
% 2.02/0.73
% 2.02/0.73 % Proof found!
% 2.02/0.73 % SZS status Theorem
% 2.02/0.73 % SZS output start CNFRefutation
% See solution above
% 2.02/0.73 % Parsed axioms : 96
% 2.02/0.73 % Removed by relevancy pruning/SinE : 12
% 2.02/0.73 % Initial clauses : 168
% 2.02/0.73 % Removed in clause preprocessing : 2
% 2.02/0.73 % Initial clauses in saturation : 166
% 2.02/0.73 % Processed clauses : 3805
% 2.02/0.73 % ...of these trivial : 3
% 2.02/0.73 % ...subsumed : 2860
% 2.02/0.73 % ...remaining for further processing : 942
% 2.02/0.73 % Other redundant clauses eliminated : 238
% 2.02/0.73 % Clauses deleted for lack of memory : 0
% 2.02/0.73 % Backward-subsumed : 67
% 2.02/0.73 % Backward-rewritten : 304
% 2.02/0.73 % Generated clauses : 23104
% 2.02/0.73 % ...of the previous two non-redundant : 21504
% 2.02/0.73 % ...aggressively subsumed : 0
% 2.02/0.73 % Contextual simplify-reflections : 461
% 2.02/0.73 % Paramodulations : 22857
% 2.02/0.73 % Factorizations : 0
% 2.02/0.73 % NegExts : 0
% 2.02/0.73 % Equation resolutions : 249
% 2.02/0.73 % Disequality decompositions : 0
% 2.02/0.73 % Total rewrite steps : 12714
% 2.02/0.73 % ...of those cached : 12696
% 2.02/0.73 % Propositional unsat checks : 0
% 2.02/0.73 % Propositional check models : 0
% 2.02/0.73 % Propositional check unsatisfiable : 0
% 2.02/0.73 % Propositional clauses : 0
% 2.02/0.73 % Propositional clauses after purity: 0
% 2.02/0.73 % Propositional unsat core size : 0
% 2.02/0.73 % Propositional preprocessing time : 0.000
% 2.02/0.73 % Propositional encoding time : 0.000
% 2.02/0.73 % Propositional solver time : 0.000
% 2.02/0.73 % Success case prop preproc time : 0.000
% 2.02/0.73 % Success case prop encoding time : 0.000
% 2.02/0.73 % Success case prop solver time : 0.000
% 2.02/0.73 % Current number of processed clauses : 552
% 2.02/0.73 % Positive orientable unit clauses : 18
% 2.02/0.73 % Positive unorientable unit clauses: 0
% 2.02/0.73 % Negative unit clauses : 2
% 2.02/0.73 % Non-unit-clauses : 532
% 2.02/0.73 % Current number of unprocessed clauses: 17683
% 2.02/0.73 % ...number of literals in the above : 107182
% 2.02/0.73 % Current number of archived formulas : 0
% 2.02/0.73 % Current number of archived clauses : 371
% 2.02/0.73 % Clause-clause subsumption calls (NU) : 146623
% 2.02/0.73 % Rec. Clause-clause subsumption calls : 59913
% 2.02/0.73 % Non-unit clause-clause subsumptions : 3388
% 2.02/0.73 % Unit Clause-clause subsumption calls : 350
% 2.02/0.73 % Rewrite failures with RHS unbound : 0
% 2.02/0.73 % BW rewrite match attempts : 5
% 2.02/0.73 % BW rewrite match successes : 5
% 2.02/0.73 % Condensation attempts : 0
% 2.02/0.73 % Condensation successes : 0
% 2.02/0.73 % Termbank termtop insertions : 432046
% 2.02/0.73 % Search garbage collected termcells : 3666
% 2.02/0.73
% 2.02/0.73 % -------------------------------------------------
% 2.02/0.73 % User time : 0.274 s
% 2.02/0.73 % System time : 0.017 s
% 2.02/0.73 % Total time : 0.290 s
% 2.02/0.73 % Maximum resident set size: 4272 pages
% 2.02/0.73
% 2.02/0.73 % -------------------------------------------------
% 2.02/0.73 % User time : 0.275 s
% 2.02/0.73 % System time : 0.020 s
% 2.02/0.73 % Total time : 0.295 s
% 2.02/0.73 % Maximum resident set size: 4864 pages
% 2.02/0.73 % E exiting
%------------------------------------------------------------------------------