%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SWC113+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 : n017.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 02:44:59 PM UTC 2026
% Result : Theorem 200.19s 29.56s
% Output : CNFRefutation 200.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 16
% Syntax : Number of formulae : 117 ( 15 unt; 0 def)
% Number of atoms : 462 ( 134 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 603 ( 258 ~; 256 |; 38 &)
% ( 5 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 190 ( 0 sgn 85 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ( ( ( segmentP(X2,X1)
& neq(X1,nil) )
| ~ neq(X2,nil) )
& ( nil = X1
| nil != X2 ) )
| ( ( nil != X3
| nil != X4 )
& ! [X5] :
( ~ memberP(X4,X5)
| cons(X5,nil) != X3
| ~ ssItem(X5) ) )
| X1 != X3
| X2 != X4
| ~ ssList(X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(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(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
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(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(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(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/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
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(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(ax3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ( memberP(X1,X2)
<=> ? [X3] :
( ? [X4] :
( app(X3,cons(X2,X4)) = X1
& ssList(X4) )
& ssList(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax3) ).
fof(c_0_16,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ( ( ( segmentP(X2,X1)
& neq(X1,nil) )
| ~ neq(X2,nil) )
& ( nil = X1
| nil != X2 ) )
| ( ( nil != X3
| nil != X4 )
& ! [X5] :
( ~ memberP(X4,X5)
| cons(X5,nil) != X3
| ~ ssItem(X5) ) )
| X1 != X3
| X2 != X4
| ~ ssList(X4) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_17,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ( ( ( segmentP(X2,X1)
& neq(X1,nil) )
| ~ neq(X2,nil) )
& ( nil = X1
| nil != X2 ) )
| ( ( nil != X3
| nil != X4 )
& ! [X5] :
( ~ memberP(X4,X5)
| cons(X5,nil) != X3
| ~ ssItem(X5) ) )
| X1 != X3
| X2 != X4
| ~ ssList(X4) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_18,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[ax21]) ).
fof(c_0_19,negated_conjecture,
( ( nil != esk1_0
| ~ segmentP(esk2_0,esk1_0)
| ~ neq(esk1_0,nil) )
& ( nil != esk1_0
| neq(esk2_0,nil) )
& ( nil = esk2_0
| ~ segmentP(esk2_0,esk1_0)
| ~ neq(esk1_0,nil) )
& ( nil = esk2_0
| neq(esk2_0,nil) )
& ( memberP(esk4_0,esk5_0)
| nil = esk3_0 )
& ( memberP(esk4_0,esk5_0)
| nil = esk4_0 )
& ( cons(esk5_0,nil) = esk3_0
| nil = esk3_0 )
& ( cons(esk5_0,nil) = esk3_0
| nil = esk4_0 )
& ( ssItem(esk5_0)
| nil = esk3_0 )
& ( ssItem(esk5_0)
| nil = esk4_0 )
& 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(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])])]) ).
fof(c_0_20,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
fof(c_0_21,plain,
! [X37,X38] :
( nil != cons(X38,X37)
| ~ ssItem(X38)
| ~ ssList(X37) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])]) ).
cnf(c_0_22,negated_conjecture,
( cons(esk5_0,nil) = esk3_0
| nil = esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,negated_conjecture,
( ssItem(esk5_0)
| nil = esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_26,plain,
! [X32,X33] :
( ( ~ ssList(X32)
| ~ ssList(X33)
| neq(X32,X33)
| X32 = X33 )
& ( ~ ssList(X32)
| ~ ssList(X33)
| X32 != X33
| ~ neq(X32,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)],[c_0_20])])])])]) ).
cnf(c_0_27,plain,
( nil != cons(X2,X1)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,negated_conjecture,
( esk2_0 = nil
| cons(esk5_0,nil) = esk1_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_29,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_30,negated_conjecture,
( ssItem(esk5_0)
| esk2_0 = nil ),
inference(rw,[status(thm)],[c_0_25,c_0_23]) ).
fof(c_0_31,plain,
! [X76,X77,X78] :
( app(app(X76,X77),X78) = app(X76,app(X77,X78))
| ~ ssList(X78)
| ~ ssList(X77)
| ~ ssList(X76) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).
fof(c_0_32,plain,
! [X69] :
( app(nil,X69) = X69
| ~ ssList(X69) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
fof(c_0_33,plain,
! [X81] :
( app(X81,nil) = X81
| ~ ssList(X81) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).
fof(c_0_34,plain,
! [X67,X68] :
( ssList(app(X67,X68))
| ~ ssList(X68)
| ~ ssList(X67) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
cnf(c_0_35,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,negated_conjecture,
( nil != esk1_0
| neq(esk2_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_37,negated_conjecture,
( esk1_0 != nil
| esk2_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_38,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X1,X2),X3) = app(X1,app(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_39,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,negated_conjecture,
( cons(esk5_0,nil) = esk3_0
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_43,plain,
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(er,[status(thm)],[c_0_35]) ).
cnf(c_0_44,negated_conjecture,
( esk1_0 != nil
| neq(nil,nil) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_45,negated_conjecture,
( ssItem(esk5_0)
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_46,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_38,c_0_39]),c_0_29])]) ).
cnf(c_0_47,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,app(X2,nil)) = app(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_38]),c_0_29])]),c_0_41]) ).
fof(c_0_48,plain,
! [X63,X64] :
( cons(X64,X63) = app(cons(X64,nil),X63)
| ~ ssItem(X64)
| ~ ssList(X63) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
cnf(c_0_49,negated_conjecture,
( esk1_0 = nil
| cons(esk5_0,nil) = esk1_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_24]),c_0_24]) ).
cnf(c_0_50,negated_conjecture,
esk1_0 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_29])]) ).
cnf(c_0_51,negated_conjecture,
( ssItem(esk5_0)
| esk1_0 = nil ),
inference(rw,[status(thm)],[c_0_45,c_0_24]) ).
fof(c_0_52,plain,
! [X73,X74,X75] :
( X75 = X73
| app(X74,X75) != app(X74,X73)
| ~ ssList(X75)
| ~ ssList(X74)
| ~ ssList(X73) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])])]) ).
cnf(c_0_53,plain,
( ~ ssList(X1)
| app(nil,X1) = app(X1,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_29])]) ).
cnf(c_0_54,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_55,negated_conjecture,
cons(esk5_0,nil) = esk1_0,
inference(sr,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_56,negated_conjecture,
ssItem(esk5_0),
inference(sr,[status(thm)],[c_0_51,c_0_50]) ).
fof(c_0_57,plain,
! [X24,X25,X26,X27] :
( segmentP(app(app(X26,X24),X27),X25)
| ~ segmentP(X24,X25)
| ~ ssList(X27)
| ~ ssList(X26)
| ~ ssList(X25)
| ~ ssList(X24) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax56])])])]) ).
cnf(c_0_58,plain,
( app(X2,X3) != app(X2,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_59,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,app(nil,X2)) = app(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_40]),c_0_29])]) ).
cnf(c_0_60,plain,
( ~ ssList(X1)
| ssList(app(nil,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_53]),c_0_29])]) ).
fof(c_0_61,plain,
! [X12,X13,X16,X17] :
( ( ~ ssList(X12)
| ~ ssList(X13)
| segmentP(X12,X13)
| app(app(X16,X13),X17) != X12
| ~ ssList(X17)
| ~ ssList(X16) )
& ( ~ ssList(X12)
| ~ ssList(X13)
| ~ segmentP(X12,X13)
| app(app(esk6_2(X12,X13),X13),esk7_2(X12,X13)) = X12 )
& ( ~ ssList(X12)
| ~ ssList(X13)
| ~ segmentP(X12,X13)
| ssList(esk7_2(X12,X13)) )
& ( ~ ssList(X12)
| ~ ssList(X13)
| ~ segmentP(X12,X13)
| ssList(esk6_2(X12,X13)) ) ),
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_62,negated_conjecture,
( ~ ssList(X1)
| cons(esk5_0,X1) = app(esk1_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56])]) ).
fof(c_0_63,plain,
! [X52,X53] :
( ssList(cons(X53,X52))
| ~ ssItem(X53)
| ~ ssList(X52) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
fof(c_0_64,plain,
! [X60,X61,X62] :
( cons(X62,app(X61,X60)) = app(cons(X62,X61),X60)
| ~ ssItem(X62)
| ~ ssList(X61)
| ~ ssList(X60) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])])]) ).
cnf(c_0_65,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_57]) ).
cnf(c_0_66,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(X3,X1) != app(X3,X2)
| X1 = app(nil,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]) ).
cnf(c_0_67,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_61]) ).
cnf(c_0_68,negated_conjecture,
app(esk1_0,nil) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_62]),c_0_29])]) ).
cnf(c_0_69,negated_conjecture,
ssList(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_70,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_71,plain,
( ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
fof(c_0_72,plain,
! [X79,X80] :
( ( ~ ssList(X79)
| ~ ssList(X80)
| nil = app(X79,X80)
| nil != X79
| nil != X80 )
& ( ~ ssList(X79)
| ~ ssList(X80)
| nil != app(X79,X80)
| nil = X79 )
& ( ~ ssList(X79)
| ~ ssList(X80)
| nil != app(X79,X80)
| nil = X80 ) ),
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_73,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_65,c_0_39]),c_0_29])]) ).
cnf(c_0_74,plain,
( ~ ssList(X1)
| app(nil,app(nil,X1)) = X1 ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_39]),c_0_29])])]),c_0_60]) ).
fof(c_0_75,plain,
! [X39,X40,X43,X44] :
( ( ~ ssList(X39)
| ~ ssItem(X40)
| memberP(X39,X40)
| app(X43,cons(X40,X44)) != X39
| ~ ssList(X44)
| ~ ssList(X43) )
& ( ~ ssList(X39)
| ~ ssItem(X40)
| ~ memberP(X39,X40)
| app(esk10_2(X39,X40),cons(X40,esk11_2(X39,X40))) = X39 )
& ( ~ ssList(X39)
| ~ ssItem(X40)
| ~ memberP(X39,X40)
| ssList(esk11_2(X39,X40)) )
& ( ~ ssList(X39)
| ~ ssItem(X40)
| ~ memberP(X39,X40)
| ssList(esk10_2(X39,X40)) ) ),
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)],[ax3])])])])])]) ).
cnf(c_0_76,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_67]) ).
cnf(c_0_77,negated_conjecture,
app(nil,esk1_0) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_68]),c_0_29]),c_0_69])]) ).
cnf(c_0_78,negated_conjecture,
( ~ ssList(X1)
| ssList(app(esk1_0,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_62]),c_0_56])]) ).
cnf(c_0_79,negated_conjecture,
( ~ ssList(X2)
| ~ ssList(X1)
| app(cons(esk5_0,X1),X2) = app(esk1_0,app(X1,X2)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_71]),c_0_56])]),c_0_41]) ).
cnf(c_0_80,plain,
( ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ssList(app(cons(X1,X2),X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_41]) ).
cnf(c_0_81,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != app(X2,X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_82,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ segmentP(app(X1,X2),X4)
| segmentP(app(X1,app(X2,X3)),X4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_38]),c_0_41]) ).
cnf(c_0_83,plain,
( ~ ssList(X1)
| app(nil,app(X1,nil)) = X1 ),
inference(spm,[status(thm)],[c_0_74,c_0_53]) ).
cnf(c_0_84,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| app(esk10_2(X1,X2),cons(X2,esk11_2(X1,X2))) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_85,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| ssList(esk10_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_86,negated_conjecture,
( ~ ssList(X1)
| segmentP(app(esk1_0,X1),esk1_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_69]),c_0_29])]),c_0_78]) ).
cnf(c_0_87,negated_conjecture,
( ~ ssList(X1)
| app(esk1_0,app(nil,X1)) = cons(esk5_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_79]),c_0_56]),c_0_29])]) ).
cnf(c_0_88,negated_conjecture,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(esk1_0,app(X1,X2))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_79]),c_0_56])]) ).
cnf(c_0_89,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != app(X1,X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_90,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| app(X2,app(X3,X1)) != nil
| nil = X1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_38]),c_0_41]) ).
cnf(c_0_91,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(app(nil,X1),X2)
| segmentP(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_29])]) ).
cnf(c_0_92,plain,
( ~ ssItem(X4)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(cons(X4,esk11_2(X1,X4)))
| ~ memberP(X1,X4)
| ~ segmentP(cons(X4,esk11_2(X1,X4)),X3)
| segmentP(app(X1,X2),X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_84]),c_0_85]) ).
cnf(c_0_93,negated_conjecture,
( ~ ssList(X1)
| segmentP(cons(esk5_0,X1),esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_60]) ).
cnf(c_0_94,negated_conjecture,
( ~ ssList(X1)
| ssList(cons(esk5_0,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_87]),c_0_29])]) ).
cnf(c_0_95,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X1,app(X2,X3)) != nil
| app(X1,X2) = nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_38]),c_0_41]) ).
cnf(c_0_96,negated_conjecture,
( ~ ssList(X1)
| app(esk1_0,app(nil,X1)) = app(esk1_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_68]),c_0_29]),c_0_69])]) ).
cnf(c_0_97,negated_conjecture,
( ~ ssList(X1)
| app(X1,esk1_0) != nil ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_77]),c_0_69]),c_0_29])]),c_0_50]) ).
cnf(c_0_98,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(app(X1,nil),X2)
| segmentP(X1,X2) ),
inference(spm,[status(thm)],[c_0_91,c_0_53]) ).
cnf(c_0_99,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(esk11_2(X1,esk5_0))
| ~ memberP(X1,esk5_0)
| segmentP(app(X1,X2),esk1_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_69]),c_0_56])]),c_0_94]) ).
cnf(c_0_100,negated_conjecture,
( memberP(esk4_0,esk5_0)
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_101,negated_conjecture,
( ~ ssList(X2)
| ~ ssList(X1)
| app(X1,app(esk1_0,X2)) != nil ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_69])]),c_0_60]),c_0_97]) ).
cnf(c_0_102,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(esk11_2(X1,esk5_0))
| ~ memberP(X1,esk5_0)
| app(esk10_2(X1,esk5_0),app(esk1_0,esk11_2(X1,esk5_0))) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_62]),c_0_56])]) ).
cnf(c_0_103,negated_conjecture,
( ~ segmentP(esk2_0,esk1_0)
| ~ neq(esk1_0,nil)
| nil = esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_104,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_105,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(esk11_2(X1,esk5_0))
| ~ memberP(X1,esk5_0)
| segmentP(X1,esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_69]),c_0_29])]) ).
cnf(c_0_106,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| ssList(esk11_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_107,negated_conjecture,
( memberP(esk2_0,esk5_0)
| esk1_0 = nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_24]),c_0_23]) ).
cnf(c_0_108,negated_conjecture,
( ~ ssList(esk11_2(nil,esk5_0))
| ~ ssList(esk10_2(nil,esk5_0))
| ~ memberP(nil,esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102])]),c_0_29])]) ).
cnf(c_0_109,negated_conjecture,
( ~ segmentP(esk2_0,esk1_0)
| esk2_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_29]),c_0_69])]),c_0_37]) ).
cnf(c_0_110,negated_conjecture,
( ~ ssList(X1)
| ~ memberP(X1,esk5_0)
| segmentP(X1,esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_56])]) ).
cnf(c_0_111,negated_conjecture,
memberP(esk2_0,esk5_0),
inference(sr,[status(thm)],[c_0_107,c_0_50]) ).
cnf(c_0_112,negated_conjecture,
ssList(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_113,negated_conjecture,
( ~ ssList(esk10_2(nil,esk5_0))
| ~ memberP(nil,esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_106]),c_0_29]),c_0_56])]) ).
cnf(c_0_114,negated_conjecture,
esk2_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_111]),c_0_112])]) ).
cnf(c_0_115,negated_conjecture,
~ memberP(nil,esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_85]),c_0_29]),c_0_56])]) ).
cnf(c_0_116,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_114]),c_0_115]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC113+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 07:51:43 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.43 Running first-order theorem proving
% 0.15/0.43 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
% 200.19/29.56 % Version: 3.5.1
% 200.19/29.56 % Preprocessing class: FSLSSMSSSSSNFFN.
% 200.19/29.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 200.19/29.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 200.19/29.56 % Starting new_bool_3 with 300s (1) cores
% 200.19/29.56 % Starting new_bool_1 with 300s (1) cores
% 200.19/29.56 % Starting sh5l with 300s (1) cores
% 200.19/29.56 % new_bool_3 with pid 1828344 completed with status 0
% 200.19/29.56 % Result found by new_bool_3
% 200.19/29.56 % Preprocessing class: FSLSSMSSSSSNFFN.
% 200.19/29.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 200.19/29.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 200.19/29.56 % Starting new_bool_3 with 300s (1) cores
% 200.19/29.56 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 200.19/29.56 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 200.19/29.56 % Search class: FGHSF-FFMM21-MFFFFFNN
% 200.19/29.56 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 200.19/29.56 % Starting SubtermCWHack with 31s (1) cores
% 200.19/29.56 % SubtermCWHack with pid 1828347 completed with status 0
% 200.19/29.56 % Result found by SubtermCWHack
% 200.19/29.56 % Preprocessing class: FSLSSMSSSSSNFFN.
% 200.19/29.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 200.19/29.56 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 200.19/29.56 % Starting new_bool_3 with 300s (1) cores
% 200.19/29.56 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 200.19/29.56 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 200.19/29.56 % Search class: FGHSF-FFMM21-MFFFFFNN
% 200.19/29.56 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 200.19/29.56 % Starting SubtermCWHack with 31s (1) cores
% 200.19/29.56 % Preprocessing time : 0.001 s
% 200.19/29.56
% 200.19/29.56 % Proof found!
% 200.19/29.56 % SZS status Theorem
% 200.19/29.56 % SZS output start CNFRefutation
% See solution above
% 200.19/29.56 % Parsed axioms : 96
% 200.19/29.56 % Removed by relevancy pruning/SinE : 66
% 200.19/29.56 % Initial clauses : 65
% 200.19/29.56 % Removed in clause preprocessing : 0
% 200.19/29.56 % Initial clauses in saturation : 65
% 200.19/29.56 % Processed clauses : 77531
% 200.19/29.56 % ...of these trivial : 433
% 200.19/29.56 % ...subsumed : 70784
% 200.19/29.56 % ...remaining for further processing : 6314
% 200.19/29.56 % Other redundant clauses eliminated : 2103
% 200.19/29.56 % Clauses deleted for lack of memory : 4689
% 200.19/29.56 % Backward-subsumed : 83
% 200.19/29.56 % Backward-rewritten : 37
% 200.19/29.56 % Generated clauses : 2461281
% 200.19/29.56 % ...of the previous two non-redundant : 2366683
% 200.19/29.56 % ...aggressively subsumed : 0
% 200.19/29.56 % Contextual simplify-reflections : 3944
% 200.19/29.56 % Paramodulations : 2458971
% 200.19/29.56 % Factorizations : 0
% 200.19/29.56 % NegExts : 0
% 200.19/29.56 % Equation resolutions : 2308
% 200.19/29.56 % Disequality decompositions : 0
% 200.19/29.56 % Total rewrite steps : 1950916
% 200.19/29.56 % ...of those cached : 1950673
% 200.19/29.56 % Propositional unsat checks : 0
% 200.19/29.56 % Propositional check models : 0
% 200.19/29.56 % Propositional check unsatisfiable : 0
% 200.19/29.56 % Propositional clauses : 0
% 200.19/29.56 % Propositional clauses after purity: 0
% 200.19/29.56 % Propositional unsat core size : 0
% 200.19/29.56 % Propositional preprocessing time : 0.000
% 200.19/29.56 % Propositional encoding time : 0.000
% 200.19/29.56 % Propositional solver time : 0.000
% 200.19/29.56 % Success case prop preproc time : 0.000
% 200.19/29.56 % Success case prop encoding time : 0.000
% 200.19/29.56 % Success case prop solver time : 0.000
% 200.19/29.56 % Current number of processed clauses : 6184
% 200.19/29.56 % Positive orientable unit clauses : 243
% 200.19/29.56 % Positive unorientable unit clauses: 0
% 200.19/29.56 % Negative unit clauses : 187
% 200.19/29.56 % Non-unit-clauses : 5754
% 200.19/29.56 % Current number of unprocessed clauses: 1209193
% 200.19/29.56 % ...number of literals in the above : 7299445
% 200.19/29.56 % Current number of archived formulas : 0
% 200.19/29.56 % Current number of archived clauses : 123
% 200.19/29.56 % Clause-clause subsumption calls (NU) : 7213780
% 200.19/29.56 % Rec. Clause-clause subsumption calls : 2742077
% 200.19/29.56 % Non-unit clause-clause subsumptions : 50572
% 200.19/29.56 % Unit Clause-clause subsumption calls : 5340
% 200.19/29.56 % Rewrite failures with RHS unbound : 0
% 200.19/29.56 % BW rewrite match attempts : 3473
% 200.19/29.56 % BW rewrite match successes : 13
% 200.19/29.56 % Condensation attempts : 0
% 200.19/29.56 % Condensation successes : 0
% 200.19/29.56 % Termbank termtop insertions : 64846715
% 200.19/29.56 % Search garbage collected termcells : 528956
% 200.19/29.56
% 200.19/29.56 % -------------------------------------------------
% 200.19/29.56 % User time : 27.441 s
% 200.19/29.56 % System time : 1.069 s
% 200.19/29.56 % Total time : 28.510 s
% 200.19/29.56 % Maximum resident set size: 3760 pages
% 200.19/29.56
% 200.19/29.56 % -------------------------------------------------
% 200.19/29.56 % User time : 27.447 s
% 200.19/29.56 % System time : 1.073 s
% 200.19/29.56 % Total time : 28.521 s
% 200.19/29.56 % Maximum resident set size: 4864 pages
% 200.19/29.56 % E exiting
%------------------------------------------------------------------------------