%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC022+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 : n004.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 02:42:39 PM UTC 2026
% Result : Theorem 0.18s 0.49s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 88 ( 13 unt; 0 def)
% Number of atoms : 367 ( 102 equ)
% Maximal formula atoms : 34 ( 4 avg)
% Number of connectives : 456 ( 177 ~; 181 |; 50 &)
% ( 5 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 124 ( 0 sgn 69 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( neq(X4,nil)
| ~ neq(X2,nil) )
& ( ? [X6] :
( ? [X7] :
( neq(nil,X4)
& hd(X4) = X7
& cons(X7,nil) = X6
& ssItem(X7) )
& X3 != X6
& ssList(X6) )
| ? [X5] :
( frontsegP(X1,X5)
& frontsegP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| ~ neq(X2,nil) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax27,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax27) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(ax5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( app(X2,X3) = X1
& ssList(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(ax23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax23) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
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(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(ax42,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax42) ).
fof(ax46,axiom,
! [X1] :
( ssList(X1)
=> ( frontsegP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax46) ).
fof(ax45,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax45) ).
fof(c_0_16,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( neq(X4,nil)
| ~ neq(X2,nil) )
& ( ? [X6] :
( ? [X7] :
( neq(nil,X4)
& hd(X4) = X7
& cons(X7,nil) = X6
& ssItem(X7) )
& X3 != X6
& ssList(X6) )
| ? [X5] :
( frontsegP(X1,X5)
& frontsegP(X2,X5)
& neq(X5,nil)
& 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) )
& ( ? [X6] :
( ? [X7] :
( neq(nil,X4)
& hd(X4) = X7
& cons(X7,nil) = X6
& ssItem(X7) )
& X3 != X6
& ssList(X6) )
| ? [X5] :
( frontsegP(X1,X5)
& frontsegP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| ~ neq(X2,nil) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_18,negated_conjecture,
! [X12,X13,X14] :
( ( ~ neq(nil,esk4_0)
| hd(esk4_0) != X14
| cons(X14,nil) != X13
| ~ ssItem(X14)
| esk3_0 = X13
| ~ ssList(X13)
| ~ neq(esk4_0,nil) )
& ( ~ neq(nil,esk4_0)
| hd(esk4_0) != X14
| cons(X14,nil) != X13
| ~ ssItem(X14)
| esk3_0 = X13
| ~ ssList(X13)
| neq(esk2_0,nil) )
& ( ~ frontsegP(esk1_0,X12)
| ~ frontsegP(esk2_0,X12)
| ~ neq(X12,nil)
| ~ ssList(X12)
| ~ neq(esk4_0,nil) )
& ( ~ frontsegP(esk1_0,X12)
| ~ frontsegP(esk2_0,X12)
| ~ neq(X12,nil)
| ~ ssList(X12)
| 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,
! [X69,X70] :
( ssList(app(X69,X70))
| ~ ssList(X70)
| ~ ssList(X69) ),
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,
! [X54,X55,X56] :
( cons(X56,app(X55,X54)) = app(cons(X56,X55),X54)
| ~ ssItem(X56)
| ~ ssList(X55)
| ~ ssList(X54) ),
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,
! [X46,X47] :
( ssList(cons(X47,X46))
| ~ ssItem(X47)
| ~ ssList(X46) ),
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,
! [X32,X33] :
( ( ~ ssList(X32)
| ~ ssList(X33)
| nil = app(X32,X33)
| nil != X32
| nil != X33 )
& ( ~ ssList(X32)
| ~ ssList(X33)
| nil != app(X32,X33)
| nil = X32 )
& ( ~ ssList(X32)
| ~ ssList(X33)
| nil != app(X32,X33)
| nil = X33 ) ),
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]) ).
fof(c_0_29,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[ax21]) ).
cnf(c_0_30,negated_conjecture,
neq(esk2_0,nil),
inference(cn,[status(thm)],[c_0_23]) ).
cnf(c_0_31,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_32,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_33,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_34,plain,
! [X22,X23] :
( nil != cons(X23,X22)
| ~ ssItem(X23)
| ~ ssList(X22) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])])]) ).
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_30,c_0_31]) ).
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_32,c_0_33]),c_0_28])]) ).
fof(c_0_39,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax22]) ).
fof(c_0_40,plain,
! [X80,X81,X83] :
( ( ~ ssList(X80)
| ~ ssList(X81)
| frontsegP(X80,X81)
| app(X81,X83) != X80
| ~ ssList(X83) )
& ( ~ ssList(X80)
| ~ ssList(X81)
| ~ frontsegP(X80,X81)
| app(X81,esk10_2(X80,X81)) = X80 )
& ( ~ ssList(X80)
| ~ ssList(X81)
| ~ frontsegP(X80,X81)
| ssList(esk10_2(X80,X81)) ) ),
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])])])])])]) ).
fof(c_0_41,plain,
! [X37,X38] :
( hd(cons(X38,X37)) = X38
| ~ ssItem(X38)
| ~ ssList(X37) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])])]) ).
cnf(c_0_42,plain,
( nil != cons(X2,X1)
| ~ ssItem(X2)
| ~ ssList(X1) ),
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,
! [X24] :
( ssItem(hd(X24))
| nil = X24
| ~ ssList(X24) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])]) ).
fof(c_0_45,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
cnf(c_0_46,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| app(X2,X1) != X3
| ~ ssList(X1)
| frontsegP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_47,plain,
! [X30,X31] :
( cons(X31,X30) = app(cons(X31,nil),X30)
| ~ ssItem(X31)
| ~ ssList(X30) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
fof(c_0_48,plain,
! [X19] :
( ( ~ ssList(X19)
| nil = X19
| cons(esk6_1(X19),esk5_1(X19)) = X19 )
& ( ~ ssList(X19)
| nil = X19
| ssItem(esk6_1(X19)) )
& ( ~ ssList(X19)
| nil = X19
| ssList(esk5_1(X19)) ) ),
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_49,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| hd(cons(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_50,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_42,c_0_43]),c_0_28])]) ).
cnf(c_0_51,plain,
( ~ ssList(X1)
| ssItem(hd(X1))
| nil = X1 ),
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,
! [X17,X18] :
( ( ~ ssList(X17)
| ~ ssList(X18)
| neq(X17,X18)
| X17 = X18 )
& ( ~ ssList(X17)
| ~ ssList(X18)
| X17 != X18
| ~ neq(X17,X18) ) ),
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_45])])])])]) ).
cnf(c_0_54,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| frontsegP(app(X1,X2),X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_46]),c_0_24]) ).
cnf(c_0_55,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_56,plain,
( ~ ssList(X1)
| nil = X1
| cons(esk6_1(X1),esk5_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_57,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(esk6_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_58,plain,
( ~ ssList(X1)
| nil = X1
| ssList(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_59,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_49,c_0_43]),c_0_28])]) ).
cnf(c_0_60,negated_conjecture,
( ~ neq(nil,esk4_0)
| esk1_0 != nil
| esk4_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52])]) ).
cnf(c_0_61,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_62,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(cons(X1,nil))
| frontsegP(cons(X1,X2),cons(X1,nil)) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_63,negated_conjecture,
ssList(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_64,plain,
( ~ ssList(X1)
| nil = X1
| esk6_1(X1) = hd(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_56]),c_0_57]),c_0_58]) ).
cnf(c_0_65,negated_conjecture,
( ~ neq(nil,esk4_0)
| esk4_0 = nil
| hd(esk1_0) = hd(esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_51]),c_0_52])]) ).
cnf(c_0_66,negated_conjecture,
( esk1_0 != nil
| esk4_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_52]),c_0_28])]) ).
cnf(c_0_67,negated_conjecture,
( ~ frontsegP(esk1_0,X1)
| ~ frontsegP(esk2_0,X1)
| ~ neq(X1,nil)
| ~ ssList(X1)
| ~ neq(esk4_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_68,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_62,c_0_43]),c_0_63])]) ).
cnf(c_0_69,plain,
( ~ ssList(X1)
| nil = X1
| cons(hd(X1),esk5_1(X1)) = X1 ),
inference(spm,[status(thm)],[c_0_56,c_0_64]) ).
cnf(c_0_70,negated_conjecture,
( ~ neq(nil,esk4_0)
| 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_51,c_0_65]),c_0_63])]),c_0_66]) ).
cnf(c_0_71,negated_conjecture,
( ~ neq(X1,nil)
| ~ ssList(X1)
| ~ frontsegP(esk4_0,X1)
| ~ frontsegP(esk1_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_31]),c_0_37])]) ).
fof(c_0_72,plain,
! [X89] :
( frontsegP(X89,X89)
| ~ ssList(X89) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax42])])]) ).
cnf(c_0_73,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_68,c_0_69]),c_0_52])]),c_0_70]) ).
cnf(c_0_74,negated_conjecture,
( ~ ssList(X1)
| ~ frontsegP(esk4_0,X1)
| ~ frontsegP(esk1_0,X1)
| X1 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_61]),c_0_28])]) ).
cnf(c_0_75,plain,
( ~ ssList(X1)
| frontsegP(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_76,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_73,c_0_58]),c_0_52])]) ).
fof(c_0_77,plain,
! [X27] :
( ( ~ ssList(X27)
| frontsegP(nil,X27)
| nil != X27 )
& ( ~ ssList(X27)
| nil = X27
| ~ frontsegP(nil,X27) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax46])])])]) ).
cnf(c_0_78,negated_conjecture,
( ~ frontsegP(esk4_0,esk1_0)
| esk1_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_63])]) ).
cnf(c_0_79,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_76,c_0_61]),c_0_52]),c_0_28])]) ).
cnf(c_0_80,plain,
( ~ ssList(X1)
| nil != X1
| frontsegP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_81,negated_conjecture,
( ~ frontsegP(esk4_0,esk4_0)
| ~ frontsegP(esk1_0,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_37]),c_0_52])]) ).
cnf(c_0_82,negated_conjecture,
esk4_0 = nil,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_66]) ).
cnf(c_0_83,plain,
frontsegP(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_80]),c_0_28])]) ).
fof(c_0_84,plain,
! [X26] :
( frontsegP(X26,nil)
| ~ ssList(X26) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])])]) ).
cnf(c_0_85,negated_conjecture,
~ frontsegP(esk1_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_82]),c_0_82]),c_0_82]),c_0_83])]) ).
cnf(c_0_86,plain,
( ~ ssList(X1)
| frontsegP(X1,nil) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_87,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_63])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC022+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n004.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 21 07:49:51 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 0.18/0.49 % Version: 3.5.1
% 0.18/0.49 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.18/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.18/0.49 % Starting new_bool_3 with 300s (1) cores
% 0.18/0.49 % Starting new_bool_1 with 300s (1) cores
% 0.18/0.49 % Starting sh5l with 300s (1) cores
% 0.18/0.49 % sh5l with pid 2638294 completed with status 0
% 0.18/0.49 % Result found by sh5l
% 0.18/0.49 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.18/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.18/0.49 % Starting new_bool_3 with 300s (1) cores
% 0.18/0.49 % Starting new_bool_1 with 300s (1) cores
% 0.18/0.49 % Starting sh5l with 300s (1) cores
% 0.18/0.49 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.18/0.49 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.18/0.49 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.18/0.49 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.49 % Starting SubtermCWHack with 28s (1) cores
% 0.18/0.49 % SubtermCWHack with pid 2638297 completed with status 0
% 0.18/0.49 % Result found by SubtermCWHack
% 0.18/0.49 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.18/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.49 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.18/0.49 % Starting new_bool_3 with 300s (1) cores
% 0.18/0.49 % Starting new_bool_1 with 300s (1) cores
% 0.18/0.49 % Starting sh5l with 300s (1) cores
% 0.18/0.49 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.18/0.49 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.18/0.49 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.18/0.49 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.49 % Starting SubtermCWHack with 28s (1) cores
% 0.18/0.49 % Preprocessing time : 0.002 s
% 0.18/0.49
% 0.18/0.49 % Proof found!
% 0.18/0.49 % SZS status Theorem
% 0.18/0.49 % SZS output start CNFRefutation
% See solution above
% 0.18/0.49 % Parsed axioms : 96
% 0.18/0.49 % Removed by relevancy pruning/SinE : 12
% 0.18/0.49 % Initial clauses : 168
% 0.18/0.49 % Removed in clause preprocessing : 2
% 0.18/0.49 % Initial clauses in saturation : 166
% 0.18/0.49 % Processed clauses : 757
% 0.18/0.49 % ...of these trivial : 3
% 0.18/0.49 % ...subsumed : 406
% 0.18/0.49 % ...remaining for further processing : 348
% 0.18/0.49 % Other redundant clauses eliminated : 79
% 0.18/0.49 % Clauses deleted for lack of memory : 0
% 0.18/0.49 % Backward-subsumed : 23
% 0.18/0.49 % Backward-rewritten : 52
% 0.18/0.49 % Generated clauses : 2135
% 0.18/0.49 % ...of the previous two non-redundant : 1875
% 0.18/0.49 % ...aggressively subsumed : 0
% 0.18/0.49 % Contextual simplify-reflections : 88
% 0.18/0.49 % Paramodulations : 2053
% 0.18/0.49 % Factorizations : 0
% 0.18/0.49 % NegExts : 0
% 0.18/0.49 % Equation resolutions : 84
% 0.18/0.49 % Disequality decompositions : 0
% 0.18/0.49 % Total rewrite steps : 1047
% 0.18/0.49 % ...of those cached : 1030
% 0.18/0.49 % Propositional unsat checks : 0
% 0.18/0.49 % Propositional check models : 0
% 0.18/0.49 % Propositional check unsatisfiable : 0
% 0.18/0.49 % Propositional clauses : 0
% 0.18/0.49 % Propositional clauses after purity: 0
% 0.18/0.49 % Propositional unsat core size : 0
% 0.18/0.49 % Propositional preprocessing time : 0.000
% 0.18/0.49 % Propositional encoding time : 0.000
% 0.18/0.49 % Propositional solver time : 0.000
% 0.18/0.49 % Success case prop preproc time : 0.000
% 0.18/0.49 % Success case prop encoding time : 0.000
% 0.18/0.49 % Success case prop solver time : 0.000
% 0.18/0.49 % Current number of processed clauses : 254
% 0.18/0.49 % Positive orientable unit clauses : 17
% 0.18/0.49 % Positive unorientable unit clauses: 0
% 0.18/0.49 % Negative unit clauses : 2
% 0.18/0.49 % Non-unit-clauses : 235
% 0.18/0.49 % Current number of unprocessed clauses: 1229
% 0.18/0.49 % ...number of literals in the above : 7308
% 0.18/0.49 % Current number of archived formulas : 0
% 0.18/0.49 % Current number of archived clauses : 75
% 0.18/0.49 % Clause-clause subsumption calls (NU) : 19272
% 0.18/0.49 % Rec. Clause-clause subsumption calls : 6186
% 0.18/0.49 % Non-unit clause-clause subsumptions : 517
% 0.18/0.49 % Unit Clause-clause subsumption calls : 117
% 0.18/0.49 % Rewrite failures with RHS unbound : 0
% 0.18/0.49 % BW rewrite match attempts : 5
% 0.18/0.49 % BW rewrite match successes : 5
% 0.18/0.49 % Condensation attempts : 0
% 0.18/0.49 % Condensation successes : 0
% 0.18/0.49 % Termbank termtop insertions : 51579
% 0.18/0.49 % Search garbage collected termcells : 3692
% 0.18/0.49
% 0.18/0.49 % -------------------------------------------------
% 0.18/0.49 % User time : 0.046 s
% 0.18/0.49 % System time : 0.004 s
% 0.18/0.49 % Total time : 0.050 s
% 0.18/0.49 % Maximum resident set size: 4272 pages
% 0.18/0.49
% 0.18/0.49 % -------------------------------------------------
% 0.18/0.49 % User time : 0.048 s
% 0.18/0.49 % System time : 0.006 s
% 0.18/0.49 % Total time : 0.054 s
% 0.18/0.49 % Maximum resident set size: 4608 pages
% 0.18/0.49 % E exiting
%------------------------------------------------------------------------------