%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC088+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 02:42:57 PM UTC 2026
% Result : Theorem 221.85s 32.54s
% Output : CNFRefutation 221.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 17
% Syntax : Number of formulae : 114 ( 23 unt; 0 def)
% Number of atoms : 425 ( 136 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 524 ( 213 ~; 216 |; 44 &)
% ( 4 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 4 ( 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 : 179 ( 0 sgn 79 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( nil = X4
& nil != X3 )
| ? [X6] :
( ? [X7] :
( app(cons(X6,nil),X7) = X4
& app(X7,cons(X6,nil)) != X3
& ssList(X7) )
& ssItem(X6) )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| ~ neq(X2,nil)
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax79,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X3,X2) = app(X1,X2)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax79) ).
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(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
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(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(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(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
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(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(ax54,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( segmentP(X2,X1)
& segmentP(X1,X2) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax54) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
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(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(c_0_17,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( nil = X4
& nil != X3 )
| ? [X6] :
( ? [X7] :
( app(cons(X6,nil),X7) = X4
& app(X7,cons(X6,nil)) != X3
& ssList(X7) )
& ssItem(X6) )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| ~ neq(X2,nil)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_18,plain,
! [X26,X27,X28] :
( X28 = X26
| app(X28,X27) != app(X26,X27)
| ~ ssList(X28)
| ~ ssList(X27)
| ~ ssList(X26) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])])]) ).
fof(c_0_19,plain,
! [X34,X35,X36] :
( app(app(X34,X35),X36) = app(X34,app(X35,X36))
| ~ ssList(X36)
| ~ ssList(X35)
| ~ ssList(X34) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).
fof(c_0_20,plain,
! [X20,X21] :
( ssList(app(X20,X21))
| ~ ssList(X21)
| ~ ssList(X20) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
fof(c_0_21,plain,
! [X25] :
( app(nil,X25) = X25
| ~ ssList(X25) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
fof(c_0_22,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( nil = X4
& nil != X3 )
| ? [X6] :
( ? [X7] :
( app(cons(X6,nil),X7) = X4
& app(X7,cons(X6,nil)) != X3
& ssList(X7) )
& ssItem(X6) )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| ~ neq(X2,nil)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( app(X3,X2) != app(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X1,X2),X3) = app(X1,app(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_28,negated_conjecture,
! [X12,X13,X14] :
( ( nil != esk4_0
| nil = esk3_0 )
& ( app(cons(X13,nil),X14) != esk4_0
| app(X14,cons(X13,nil)) = esk3_0
| ~ ssList(X14)
| ~ ssItem(X13) )
& ( ~ segmentP(esk1_0,X12)
| ~ segmentP(esk2_0,X12)
| ~ neq(X12,nil)
| ~ ssList(X12) )
& 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(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_22])])])])]) ).
fof(c_0_29,plain,
! [X37,X38] :
( ( ~ ssList(X37)
| ~ ssList(X38)
| nil = app(X37,X38)
| nil != X37
| nil != X38 )
& ( ~ ssList(X37)
| ~ ssList(X38)
| nil != app(X37,X38)
| nil = X37 )
& ( ~ ssList(X37)
| ~ ssList(X38)
| nil != app(X37,X38)
| nil = X38 ) ),
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_30,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X4)
| app(X1,X4) != app(X2,app(X3,X4))
| X1 = app(X2,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_31,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_24,c_0_26]),c_0_27])]) ).
cnf(c_0_32,negated_conjecture,
ssList(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_34,plain,
! [X50,X51,X54,X55] :
( ( ~ ssList(X50)
| ~ ssList(X51)
| segmentP(X50,X51)
| app(app(X54,X51),X55) != X50
| ~ ssList(X55)
| ~ ssList(X54) )
& ( ~ ssList(X50)
| ~ ssList(X51)
| ~ segmentP(X50,X51)
| app(app(esk9_2(X50,X51),X51),esk10_2(X50,X51)) = X50 )
& ( ~ ssList(X50)
| ~ ssList(X51)
| ~ segmentP(X50,X51)
| ssList(esk10_2(X50,X51)) )
& ( ~ ssList(X50)
| ~ ssList(X51)
| ~ segmentP(X50,X51)
| ssList(esk9_2(X50,X51)) ) ),
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_35,negated_conjecture,
( ~ segmentP(esk1_0,X1)
| ~ segmentP(esk2_0,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_37,negated_conjecture,
neq(esk2_0,nil),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_38,plain,
! [X29,X30,X31] :
( X31 = X29
| app(X30,X31) != app(X30,X29)
| ~ ssList(X31)
| ~ ssList(X30)
| ~ ssList(X29) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])])]) ).
cnf(c_0_39,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != X2
| nil != X1
| nil = app(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_40,plain,
! [X39] :
( app(X39,nil) = X39
| ~ ssList(X39) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).
cnf(c_0_41,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(X1,X3) != app(X2,X3)
| X1 = app(nil,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_27])]) ).
cnf(c_0_42,negated_conjecture,
ssList(esk4_0),
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_43,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_34]) ).
fof(c_0_44,plain,
! [X22,X23,X24] :
( cons(X24,app(X23,X22)) = app(cons(X24,X23),X22)
| ~ ssItem(X24)
| ~ ssList(X23)
| ~ ssList(X22) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])])]) ).
fof(c_0_45,plain,
! [X15] :
( ( ~ ssList(X15)
| nil = X15
| cons(esk6_1(X15),esk5_1(X15)) = X15 )
& ( ~ ssList(X15)
| nil = X15
| ssItem(esk6_1(X15)) )
& ( ~ ssList(X15)
| nil = X15
| ssList(esk5_1(X15)) ) ),
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_46,negated_conjecture,
( ~ neq(X1,nil)
| ~ ssList(X1)
| ~ segmentP(esk4_0,X1)
| ~ segmentP(esk3_0,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36]),c_0_33]) ).
cnf(c_0_47,negated_conjecture,
neq(esk4_0,nil),
inference(rw,[status(thm)],[c_0_37,c_0_33]) ).
cnf(c_0_48,plain,
( app(X2,X3) != app(X2,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_49,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_39])]),c_0_27])]) ).
cnf(c_0_50,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_51,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ssList(app(X1,app(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_24]),c_0_25]) ).
cnf(c_0_52,negated_conjecture,
( ~ ssList(X2)
| ~ ssList(X1)
| app(X1,esk4_0) != app(X2,esk4_0)
| X1 = app(nil,X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
fof(c_0_53,plain,
! [X59,X60] :
( X59 = X60
| ~ segmentP(X60,X59)
| ~ segmentP(X59,X60)
| ~ ssList(X60)
| ~ ssList(X59) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax54])])])]) ).
cnf(c_0_54,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_43]) ).
cnf(c_0_55,plain,
( ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_56,plain,
( ~ ssList(X1)
| nil = X1
| cons(esk6_1(X1),esk5_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_57,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(esk6_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_58,plain,
( ~ ssList(X1)
| nil = X1
| ssList(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_59,negated_conjecture,
( ~ segmentP(esk4_0,esk4_0)
| ~ segmentP(esk3_0,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_42])]) ).
cnf(c_0_60,negated_conjecture,
( nil != esk4_0
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_61,plain,
! [X61] :
( segmentP(X61,X61)
| ~ ssList(X61) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])])]) ).
fof(c_0_62,plain,
! [X40,X41] :
( ssList(cons(X41,X40))
| ~ ssItem(X41)
| ~ ssList(X40) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
fof(c_0_63,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
fof(c_0_64,plain,
! [X32,X33] :
( cons(X33,X32) = app(cons(X33,nil),X32)
| ~ ssItem(X33)
| ~ ssList(X32) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
cnf(c_0_65,plain,
( ~ ssList(X1)
| app(nil,X1) != nil
| X1 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_27])]) ).
cnf(c_0_66,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_50,c_0_24]),c_0_27])]),c_0_25]) ).
cnf(c_0_67,plain,
( ~ ssList(X1)
| ssList(app(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_49]),c_0_27])]) ).
cnf(c_0_68,negated_conjecture,
( ~ ssList(X1)
| app(esk4_0,esk4_0) != app(X1,esk4_0)
| app(nil,X1) = esk4_0 ),
inference(spm,[status(thm)],[c_0_52,c_0_42]) ).
cnf(c_0_69,plain,
( ~ segmentP(X2,X1)
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_70,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| segmentP(app(X1,X2),X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_50]),c_0_27])]),c_0_25]) ).
cnf(c_0_71,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| app(cons(X1,X2),nil) = cons(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_50]),c_0_27])]) ).
cnf(c_0_72,negated_conjecture,
( esk4_0 = nil
| cons(esk6_1(esk4_0),esk5_1(esk4_0)) = esk4_0 ),
inference(spm,[status(thm)],[c_0_56,c_0_42]) ).
cnf(c_0_73,negated_conjecture,
( ssItem(esk6_1(esk4_0))
| esk4_0 = nil ),
inference(spm,[status(thm)],[c_0_57,c_0_42]) ).
cnf(c_0_74,negated_conjecture,
( ssList(esk5_1(esk4_0))
| esk4_0 = nil ),
inference(spm,[status(thm)],[c_0_58,c_0_42]) ).
cnf(c_0_75,negated_conjecture,
( ~ segmentP(esk4_0,esk4_0)
| ~ segmentP(nil,esk4_0)
| esk4_0 != nil ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_76,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_77,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
fof(c_0_78,plain,
! [X70,X71] :
( ( ~ ssList(X70)
| ~ ssList(X71)
| neq(X70,X71)
| X70 = X71 )
& ( ~ ssList(X70)
| ~ ssList(X71)
| X70 != X71
| ~ neq(X70,X71) ) ),
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_63])])])])]) ).
cnf(c_0_79,negated_conjecture,
( app(cons(X1,nil),X2) != esk4_0
| ~ ssList(X2)
| ~ ssItem(X1)
| app(X2,cons(X1,nil)) = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_80,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_81,plain,
( ~ ssList(X1)
| app(nil,X1) != nil
| app(X1,nil) = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_27])]),c_0_67]) ).
cnf(c_0_82,negated_conjecture,
app(nil,esk4_0) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_68]),c_0_42])]) ).
cnf(c_0_83,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X2,app(X1,X2))
| app(X1,X2) = X2 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_25]) ).
cnf(c_0_84,negated_conjecture,
( esk4_0 = nil
| app(esk4_0,nil) = esk4_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]),c_0_74]) ).
cnf(c_0_85,negated_conjecture,
( ~ segmentP(nil,esk4_0)
| esk4_0 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_42])]) ).
cnf(c_0_86,plain,
( ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ssList(app(cons(X1,X2),X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_55]),c_0_25]) ).
cnf(c_0_87,plain,
( ~ ssItem(X1)
| app(cons(X1,nil),nil) = cons(X1,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_49]),c_0_27])]) ).
cnf(c_0_88,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_89,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_54,c_0_26]),c_0_27])]),c_0_25]) ).
cnf(c_0_90,negated_conjecture,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) != esk4_0
| app(X1,cons(X2,nil)) = esk3_0 ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_91,negated_conjecture,
( esk4_0 != nil
| app(esk4_0,nil) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_42])]) ).
cnf(c_0_92,negated_conjecture,
~ segmentP(nil,esk4_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_27]),c_0_42])]),c_0_85]) ).
cnf(c_0_93,plain,
( ~ ssItem(X1)
| ssList(cons(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_27])]) ).
cnf(c_0_94,plain,
( ~ ssList(X1)
| neq(X1,nil)
| X1 = nil ),
inference(spm,[status(thm)],[c_0_88,c_0_27]) ).
cnf(c_0_95,negated_conjecture,
( ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(cons(X2,nil))
| cons(X2,X1) != esk4_0
| segmentP(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_96,negated_conjecture,
esk4_0 != nil,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_91]),c_0_42]),c_0_27])]),c_0_92]) ).
cnf(c_0_97,plain,
( ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(app(cons(X1,X2),X3),X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_80]),c_0_93]),c_0_86]) ).
cnf(c_0_98,negated_conjecture,
( neq(esk5_1(esk4_0),nil)
| esk4_0 = nil
| esk5_1(esk4_0) = nil ),
inference(spm,[status(thm)],[c_0_94,c_0_74]) ).
cnf(c_0_99,negated_conjecture,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) != esk4_0
| segmentP(esk3_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_77]),c_0_27])]) ).
cnf(c_0_100,negated_conjecture,
cons(esk6_1(esk4_0),esk5_1(esk4_0)) = esk4_0,
inference(sr,[status(thm)],[c_0_72,c_0_96]) ).
cnf(c_0_101,negated_conjecture,
ssList(esk5_1(esk4_0)),
inference(sr,[status(thm)],[c_0_74,c_0_96]) ).
cnf(c_0_102,negated_conjecture,
ssItem(esk6_1(esk4_0)),
inference(sr,[status(thm)],[c_0_73,c_0_96]) ).
cnf(c_0_103,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| segmentP(cons(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_71]),c_0_27])]) ).
cnf(c_0_104,negated_conjecture,
( neq(esk5_1(esk4_0),nil)
| esk5_1(esk4_0) = nil ),
inference(sr,[status(thm)],[c_0_98,c_0_96]) ).
cnf(c_0_105,negated_conjecture,
segmentP(esk3_0,esk5_1(esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_101]),c_0_102])]) ).
cnf(c_0_106,negated_conjecture,
segmentP(esk4_0,esk5_1(esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_100]),c_0_101]),c_0_102])]) ).
cnf(c_0_107,negated_conjecture,
esk5_1(esk4_0) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_104]),c_0_105]),c_0_106]),c_0_101])]) ).
cnf(c_0_108,negated_conjecture,
segmentP(esk4_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_82]),c_0_42]),c_0_27])]) ).
cnf(c_0_109,negated_conjecture,
( ~ ssItem(X1)
| cons(X1,nil) != esk4_0
| app(nil,cons(X1,nil)) = esk3_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_87]),c_0_27])]) ).
cnf(c_0_110,negated_conjecture,
cons(esk6_1(esk4_0),nil) = esk4_0,
inference(rw,[status(thm)],[c_0_100,c_0_107]) ).
cnf(c_0_111,negated_conjecture,
~ segmentP(esk3_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_108])]) ).
cnf(c_0_112,negated_conjecture,
esk3_0 = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_82]),c_0_102])]) ).
cnf(c_0_113,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_112]),c_0_108])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC088+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.42 % Computer : n008.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Mon Sep 21 07:55:38 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.42 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.49 Running first-order theorem proving
% 0.17/0.49 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
% 221.85/32.54 % Version: 3.5.1
% 221.85/32.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 221.85/32.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 221.85/32.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 221.85/32.54 % Starting new_bool_3 with 300s (1) cores
% 221.85/32.54 % Starting new_bool_1 with 300s (1) cores
% 221.85/32.54 % Starting sh5l with 300s (1) cores
% 221.85/32.54 % new_bool_3 with pid 527136 completed with status 0
% 221.85/32.54 % Result found by new_bool_3
% 221.85/32.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 221.85/32.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 221.85/32.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 221.85/32.54 % Starting new_bool_3 with 300s (1) cores
% 221.85/32.54 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 221.85/32.54 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 221.85/32.54 % Search class: FGHSF-FFMM21-MFFFFFNN
% 221.85/32.54 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 221.85/32.54 % Starting SubtermCWHack with 31s (1) cores
% 221.85/32.54 % SubtermCWHack with pid 527139 completed with status 8
% 221.85/32.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 221.85/32.54 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 528138 completed with status 0
% 221.85/32.54 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 221.85/32.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 221.85/32.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 221.85/32.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 221.85/32.54 % Starting new_bool_3 with 300s (1) cores
% 221.85/32.54 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 221.85/32.54 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 221.85/32.54 % Search class: FGHSF-FFMM21-MFFFFFNN
% 221.85/32.54 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 221.85/32.54 % Starting SubtermCWHack with 31s (1) cores
% 221.85/32.54 % SubtermCWHack with pid 527139 completed with status 8
% 221.85/32.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 221.85/32.54 % Preprocessing time : 0.002 s
% 221.85/32.54 % Presaturation interreduction done
% 221.85/32.54
% 221.85/32.54 % Proof found!
% 221.85/32.54 % SZS status Theorem
% 221.85/32.54 % SZS output start CNFRefutation
% See solution above
% 221.85/32.54 % Parsed axioms : 96
% 221.85/32.54 % Removed by relevancy pruning/SinE : 70
% 221.85/32.54 % Initial clauses : 48
% 221.85/32.54 % Removed in clause preprocessing : 0
% 221.85/32.54 % Initial clauses in saturation : 48
% 221.85/32.54 % Processed clauses : 1481
% 221.85/32.54 % ...of these trivial : 32
% 221.85/32.54 % ...subsumed : 634
% 221.85/32.54 % ...remaining for further processing : 815
% 221.85/32.54 % Other redundant clauses eliminated : 35
% 221.85/32.54 % Clauses deleted for lack of memory : 0
% 221.85/32.54 % Backward-subsumed : 69
% 221.85/32.54 % Backward-rewritten : 321
% 221.85/32.54 % Generated clauses : 17563
% 221.85/32.54 % ...of the previous two non-redundant : 17056
% 221.85/32.54 % ...aggressively subsumed : 0
% 221.85/32.54 % Contextual simplify-reflections : 139
% 221.85/32.54 % Paramodulations : 17431
% 221.85/32.54 % Factorizations : 0
% 221.85/32.54 % NegExts : 0
% 221.85/32.54 % Equation resolutions : 49
% 221.85/32.54 % Disequality decompositions : 0
% 221.85/32.54 % Total rewrite steps : 4016
% 221.85/32.54 % ...of those cached : 3980
% 221.85/32.54 % Propositional unsat checks : 0
% 221.85/32.54 % Propositional check models : 0
% 221.85/32.54 % Propositional check unsatisfiable : 0
% 221.85/32.54 % Propositional clauses : 0
% 221.85/32.54 % Propositional clauses after purity: 0
% 221.85/32.54 % Propositional unsat core size : 0
% 221.85/32.54 % Propositional preprocessing time : 0.000
% 221.85/32.54 % Propositional encoding time : 0.000
% 221.85/32.54 % Propositional solver time : 0.000
% 221.85/32.54 % Success case prop preproc time : 0.000
% 221.85/32.54 % Success case prop encoding time : 0.000
% 221.85/32.54 % Success case prop solver time : 0.000
% 221.85/32.54 % Current number of processed clauses : 290
% 221.85/32.54 % Positive orientable unit clauses : 38
% 221.85/32.54 % Positive unorientable unit clauses: 0
% 221.85/32.54 % Negative unit clauses : 3
% 221.85/32.54 % Non-unit-clauses : 249
% 221.85/32.54 % Current number of unprocessed clauses: 15642
% 221.85/32.54 % ...number of literals in the above : 59365
% 221.85/32.54 % Current number of archived formulas : 0
% 221.85/32.54 % Current number of archived clauses : 520
% 221.85/32.54 % Clause-clause subsumption calls (NU) : 21389
% 221.85/32.54 % Rec. Clause-clause subsumption calls : 10979
% 221.85/32.54 % Non-unit clause-clause subsumptions : 791
% 221.85/32.54 % Unit Clause-clause subsumption calls : 1798
% 221.85/32.54 % Rewrite failures with RHS unbound : 0
% 221.85/32.54 % BW rewrite match attempts : 52
% 221.85/32.54 % BW rewrite match successes : 13
% 221.85/32.54 % Condensation attempts : 0
% 221.85/32.54 % Condensation successes : 0
% 221.85/32.54 % Termbank termtop insertions : 359720
% 221.85/32.54 % Search garbage collected termcells : 1578
% 221.85/32.54
% 221.85/32.54 % -------------------------------------------------
% 221.85/32.54 % User time : 30.243 s
% 221.85/32.54 % System time : 1.257 s
% 221.85/32.54 % Total time : 31.500 s
% 221.85/32.54 % Maximum resident set size: 3760 pages
% 221.85/32.54
% 221.85/32.54 % -------------------------------------------------
% 221.85/32.54 % User time : 30.252 s
% 221.85/32.54 % System time : 1.263 s
% 221.85/32.54 % Total time : 31.515 s
% 221.85/32.54 % Maximum resident set size: 4864 pages
% 221.85/32.54 % E exiting
%------------------------------------------------------------------------------