%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC077+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 : n005.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 02:42:53 PM UTC 2026
% Result : Theorem 2.03s 0.78s
% Output : CNFRefutation 2.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 22
% Syntax : Number of formulae : 116 ( 15 unt; 0 def)
% Number of atoms : 499 ( 112 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 657 ( 274 ~; 260 |; 57 &)
% ( 8 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-2 aty)
% Number of variables : 187 ( 0 sgn 97 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( nil = X1
& nil = X2 )
| ? [X6] :
( strictorderedP(X6)
& segmentP(X6,X3)
& frontsegP(X4,X6)
& neq(X3,X6)
& ssList(X6) )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| ~ strictorderedP(X3)
| ~ frontsegP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
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(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
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(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
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(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
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(ax18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax18) ).
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(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax25,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> tl(cons(X2,X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax25) ).
fof(ax4,axiom,
! [X1] :
( ssList(X1)
=> ( singletonP(X1)
<=> ? [X2] :
( cons(X2,nil) = X1
& ssItem(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax4) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(ax58,axiom,
! [X1] :
( ssList(X1)
=> ( segmentP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax58) ).
fof(ax44,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( frontsegP(cons(X1,X3),cons(X2,X4))
<=> ( frontsegP(X3,X4)
& X1 = X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax44) ).
fof(ax68,axiom,
! [X1] :
( ssItem(X1)
=> strictorderedP(cons(X1,nil)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax68) ).
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(ax45,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax45) ).
fof(c_0_22,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( nil = X1
& nil = X2 )
| ? [X6] :
( strictorderedP(X6)
& segmentP(X6,X3)
& frontsegP(X4,X6)
& neq(X3,X6)
& ssList(X6) )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| ~ strictorderedP(X3)
| ~ frontsegP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_23,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( nil = X1
& nil = X2 )
| ? [X6] :
( strictorderedP(X6)
& segmentP(X6,X3)
& frontsegP(X4,X6)
& neq(X3,X6)
& ssList(X6) )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| ~ strictorderedP(X3)
| ~ frontsegP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_24,plain,
! [X28,X29,X32,X33] :
( ( ~ ssList(X28)
| ~ ssList(X29)
| segmentP(X28,X29)
| app(app(X32,X29),X33) != X28
| ~ ssList(X33)
| ~ ssList(X32) )
& ( ~ ssList(X28)
| ~ ssList(X29)
| ~ segmentP(X28,X29)
| app(app(esk8_2(X28,X29),X29),esk9_2(X28,X29)) = X28 )
& ( ~ ssList(X28)
| ~ ssList(X29)
| ~ segmentP(X28,X29)
| ssList(esk9_2(X28,X29)) )
& ( ~ ssList(X28)
| ~ ssList(X29)
| ~ segmentP(X28,X29)
| ssList(esk8_2(X28,X29)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax7])])])])])]) ).
fof(c_0_25,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
fof(c_0_26,negated_conjecture,
! [X255,X256] :
( ( nil != esk48_0
| nil != esk49_0 )
& ( ~ strictorderedP(X256)
| ~ segmentP(X256,esk50_0)
| ~ frontsegP(esk51_0,X256)
| ~ neq(esk50_0,X256)
| ~ ssList(X256) )
& ( ~ segmentP(esk48_0,X255)
| ~ segmentP(esk49_0,X255)
| ~ neq(X255,nil)
| ~ ssList(X255) )
& strictorderedP(esk50_0)
& frontsegP(esk51_0,esk50_0)
& esk48_0 = esk50_0
& esk49_0 = esk51_0
& ssList(esk51_0)
& ssList(esk50_0)
& ssList(esk49_0)
& ssList(esk48_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_23])])])])]) ).
fof(c_0_27,plain,
! [X225,X226] :
( ( ~ ssList(X225)
| ~ ssList(X226)
| nil = app(X225,X226)
| nil != X225
| nil != X226 )
& ( ~ ssList(X225)
| ~ ssList(X226)
| nil != app(X225,X226)
| nil = X225 )
& ( ~ ssList(X225)
| ~ ssList(X226)
| nil != app(X225,X226)
| nil = X226 ) ),
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_28,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_24]) ).
fof(c_0_29,plain,
! [X135] :
( app(nil,X135) = X135
| ~ ssList(X135) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
fof(c_0_30,plain,
! [X130,X131] :
( ssList(app(X130,X131))
| ~ ssList(X131)
| ~ ssList(X130) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
fof(c_0_31,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
inference(fof_simplification,[status(thm)],[ax78]) ).
fof(c_0_32,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[ax21]) ).
fof(c_0_33,plain,
! [X109,X110] :
( ( ~ ssList(X109)
| ~ ssList(X110)
| neq(X109,X110)
| X109 = X110 )
& ( ~ ssList(X109)
| ~ ssList(X110)
| X109 != X110
| ~ neq(X109,X110) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])])])]) ).
cnf(c_0_34,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_36,plain,
! [X190,X191,X192,X193] :
( segmentP(app(app(X192,X190),X193),X191)
| ~ segmentP(X190,X191)
| ~ ssList(X193)
| ~ ssList(X192)
| ~ ssList(X191)
| ~ ssList(X190) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax56])])])]) ).
cnf(c_0_37,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != X2
| nil != X1
| nil = app(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_38,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_39,negated_conjecture,
( ~ segmentP(esk48_0,X1)
| ~ segmentP(esk49_0,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_40,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_41,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_28]) ).
cnf(c_0_42,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_43,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_44,plain,
! [X20,X21,X23] :
( ( ~ ssList(X20)
| ~ ssList(X21)
| frontsegP(X20,X21)
| app(X21,X23) != X20
| ~ ssList(X23) )
& ( ~ ssList(X20)
| ~ ssList(X21)
| ~ frontsegP(X20,X21)
| app(X21,esk6_2(X20,X21)) = X20 )
& ( ~ ssList(X20)
| ~ ssList(X21)
| ~ frontsegP(X20,X21)
| ssList(esk6_2(X20,X21)) ) ),
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_45,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
inference(fof_simplification,[status(thm)],[ax18]) ).
fof(c_0_46,plain,
! [X213] :
( cons(hd(X213),tl(X213)) = X213
| nil = X213
| ~ ssList(X213) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])]) ).
fof(c_0_47,plain,
! [X125,X126] :
( hd(cons(X126,X125)) = X126
| ~ ssItem(X126)
| ~ ssList(X125) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])])]) ).
fof(c_0_48,plain,
! [X111,X112] :
( ssList(cons(X112,X111))
| ~ ssItem(X112)
| ~ ssList(X111) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
fof(c_0_49,plain,
! [X122,X123] :
( nil != cons(X123,X122)
| ~ ssItem(X123)
| ~ ssList(X122) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])])]) ).
fof(c_0_50,plain,
! [X128,X129] :
( tl(cons(X129,X128)) = X128
| ~ ssItem(X129)
| ~ ssList(X128) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])])]) ).
fof(c_0_51,plain,
! [X17,X19] :
( ( ~ ssList(X17)
| singletonP(X17)
| cons(X19,nil) != X17
| ~ ssItem(X19) )
& ( ~ ssList(X17)
| ~ singletonP(X17)
| cons(esk5_1(X17),nil) = X17 )
& ( ~ ssList(X17)
| ~ singletonP(X17)
| ssItem(esk5_1(X17)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])])])])]) ).
cnf(c_0_52,negated_conjecture,
( ~ strictorderedP(X1)
| ~ segmentP(X1,esk50_0)
| ~ frontsegP(esk51_0,X1)
| ~ neq(esk50_0,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_53,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_54,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_55,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_36]) ).
cnf(c_0_56,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_37])]),c_0_38])]) ).
cnf(c_0_57,negated_conjecture,
( ~ neq(X1,nil)
| ~ ssList(X1)
| ~ segmentP(esk51_0,X1)
| ~ segmentP(esk50_0,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_35]),c_0_40]) ).
cnf(c_0_58,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_41,c_0_42]),c_0_38])]),c_0_43]) ).
cnf(c_0_59,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X2,X1)
| app(X1,esk6_2(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_60,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ssList(esk6_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_61,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_62,plain,
! [X113,X114] :
( cons(X114,X113) != X113
| ~ ssItem(X114)
| ~ ssList(X113) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])]) ).
cnf(c_0_63,plain,
( ~ ssList(X1)
| cons(hd(X1),tl(X1)) = X1
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_64,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| hd(cons(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_65,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_66,plain,
( nil != cons(X2,X1)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_67,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| tl(cons(X2,X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_68,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(esk5_1(X1),nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_69,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| ssItem(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_70,plain,
( ~ ssList(X2)
| cons(X1,nil) != X2
| ~ ssItem(X1)
| singletonP(X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_71,negated_conjecture,
( ~ ssList(X1)
| ~ frontsegP(esk51_0,X1)
| ~ segmentP(X1,esk50_0)
| ~ strictorderedP(X1)
| esk50_0 = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54])]) ).
cnf(c_0_72,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(nil,X2)
| segmentP(app(nil,X1),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_38])]) ).
cnf(c_0_73,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(esk51_0,X1)
| ~ segmentP(esk50_0,X1)
| X1 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_53]),c_0_38])]) ).
cnf(c_0_74,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| segmentP(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]) ).
cnf(c_0_75,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_61,c_0_40]) ).
fof(c_0_76,plain,
! [X189] :
( segmentP(X189,X189)
| ~ ssList(X189) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])])]) ).
fof(c_0_77,plain,
! [X195] :
( ( ~ ssList(X195)
| segmentP(nil,X195)
| nil != X195 )
& ( ~ ssList(X195)
| nil = X195
| ~ segmentP(nil,X195) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax58])])])]) ).
cnf(c_0_78,plain,
( cons(X2,X1) != X1
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_79,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| cons(X1,tl(cons(X1,X2))) = cons(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]),c_0_66]) ).
cnf(c_0_80,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| tl(X1) = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_38])]),c_0_69]) ).
cnf(c_0_81,plain,
( ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| singletonP(cons(X1,nil)) ),
inference(er,[status(thm)],[c_0_70]) ).
cnf(c_0_82,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(app(nil,X1))
| ~ frontsegP(esk51_0,app(nil,X1))
| ~ segmentP(nil,esk50_0)
| ~ strictorderedP(app(nil,X1))
| app(nil,X1) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_54])]) ).
cnf(c_0_83,negated_conjecture,
( ~ ssList(X1)
| ~ frontsegP(esk51_0,X1)
| ~ segmentP(esk50_0,X1)
| X1 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75])]) ).
cnf(c_0_84,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_85,negated_conjecture,
frontsegP(esk51_0,esk50_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_86,plain,
( ~ ssList(X1)
| nil != X1
| segmentP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_87,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(tl(cons(X1,X2)))
| tl(cons(X1,X2)) != cons(X1,X2) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_88,plain,
( ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| tl(cons(X1,nil)) = nil ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
fof(c_0_89,plain,
! [X167,X168,X169,X170] :
( ( ~ ssItem(X167)
| ~ ssItem(X168)
| ~ ssList(X169)
| ~ ssList(X170)
| frontsegP(cons(X167,X169),cons(X168,X170))
| ~ frontsegP(X169,X170)
| X167 != X168 )
& ( ~ ssItem(X167)
| ~ ssItem(X168)
| ~ ssList(X169)
| ~ ssList(X170)
| ~ frontsegP(cons(X167,X169),cons(X168,X170))
| frontsegP(X169,X170) )
& ( ~ ssItem(X167)
| ~ ssItem(X168)
| ~ ssList(X169)
| ~ ssList(X170)
| ~ frontsegP(cons(X167,X169),cons(X168,X170))
| X167 = X168 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax44])])])])]) ).
cnf(c_0_90,negated_conjecture,
( ~ ssList(X1)
| ~ frontsegP(esk51_0,X1)
| ~ segmentP(nil,esk50_0)
| ~ strictorderedP(X1)
| X1 = esk50_0 ),
inference(spm,[status(thm)],[c_0_82,c_0_42]) ).
cnf(c_0_91,negated_conjecture,
esk50_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85]),c_0_54])]) ).
cnf(c_0_92,plain,
segmentP(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_86]),c_0_38])]) ).
fof(c_0_93,plain,
! [X202] :
( strictorderedP(cons(X202,nil))
| ~ ssItem(X202) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax68])])]) ).
cnf(c_0_94,plain,
( ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| cons(X1,nil) != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_38])]) ).
cnf(c_0_95,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ frontsegP(X3,X4)
| X1 != X2
| frontsegP(cons(X1,X3),cons(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
fof(c_0_96,plain,
! [X119] :
( ( ~ ssList(X119)
| nil = X119
| cons(esk45_1(X119),esk44_1(X119)) = X119 )
& ( ~ ssList(X119)
| nil = X119
| ssItem(esk45_1(X119)) )
& ( ~ ssList(X119)
| nil = X119
| ssList(esk44_1(X119)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])])]) ).
cnf(c_0_97,negated_conjecture,
( nil != esk48_0
| nil != esk49_0 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_98,negated_conjecture,
( ~ ssList(X1)
| ~ frontsegP(esk51_0,X1)
| ~ strictorderedP(X1)
| X1 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_91]),c_0_91]),c_0_92])]) ).
cnf(c_0_99,plain,
( ~ ssItem(X1)
| strictorderedP(cons(X1,nil)) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_100,plain,
( ~ ssItem(X1)
| cons(X1,nil) != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_65]),c_0_38])]) ).
cnf(c_0_101,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X2,X3)
| frontsegP(cons(X1,X2),cons(X1,X3)) ),
inference(er,[status(thm)],[c_0_95]) ).
cnf(c_0_102,plain,
( ~ ssList(X1)
| nil = X1
| cons(esk45_1(X1),esk44_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_103,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(esk45_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_104,plain,
( ~ ssList(X1)
| nil = X1
| ssList(esk44_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_105,negated_conjecture,
( esk51_0 != nil
| esk50_0 != nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_35]),c_0_40]) ).
cnf(c_0_106,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ frontsegP(esk51_0,cons(X1,nil)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_100]) ).
cnf(c_0_107,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(esk44_1(X1),X2)
| frontsegP(X1,cons(esk45_1(X1),X2))
| nil = X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_103]),c_0_104]) ).
cnf(c_0_108,negated_conjecture,
esk51_0 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_91])]) ).
fof(c_0_109,plain,
! [X171] :
( frontsegP(X171,nil)
| ~ ssList(X171) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])])]) ).
cnf(c_0_110,negated_conjecture,
( ~ ssItem(esk45_1(esk51_0))
| ~ ssList(cons(esk45_1(esk51_0),nil))
| ~ frontsegP(esk44_1(esk51_0),nil) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_38]),c_0_75])]),c_0_108]) ).
cnf(c_0_111,plain,
( ~ ssList(X1)
| frontsegP(X1,nil) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_112,negated_conjecture,
( ~ ssItem(esk45_1(esk51_0))
| ~ ssList(esk44_1(esk51_0))
| ~ ssList(cons(esk45_1(esk51_0),nil)) ),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_113,negated_conjecture,
( ~ ssItem(esk45_1(esk51_0))
| ~ ssList(esk44_1(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_65]),c_0_38])]) ).
cnf(c_0_114,negated_conjecture,
~ ssList(esk44_1(esk51_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_103]),c_0_75])]),c_0_108]) ).
cnf(c_0_115,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_104]),c_0_75])]),c_0_108]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC077+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 : n005.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 07:53:18 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.03/0.78 % Version: 3.5.1
% 2.03/0.78 % Preprocessing class: FSLSSMSSSSSNFFN.
% 2.03/0.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.03/0.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.03/0.78 % Starting new_bool_3 with 300s (1) cores
% 2.03/0.78 % Starting new_bool_1 with 300s (1) cores
% 2.03/0.78 % Starting sh5l with 300s (1) cores
% 2.03/0.78 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2949348 completed with status 0
% 2.03/0.78 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 2.03/0.78 % Preprocessing class: FSLSSMSSSSSNFFN.
% 2.03/0.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.03/0.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.03/0.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.03/0.78 % No SInE strategy applied
% 2.03/0.78 % Search class: FGHSF-FSLM21-MFFFFFNN
% 2.03/0.78 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 2.03/0.78 % Starting SubtermCWHack with 136s (1) cores
% 2.03/0.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 2.03/0.78 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 2.03/0.78 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 2.03/0.78 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 2.03/0.78 % G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with pid 2949359 completed with status 0
% 2.03/0.78 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y
% 2.03/0.78 % Preprocessing class: FSLSSMSSSSSNFFN.
% 2.03/0.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.03/0.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.03/0.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.03/0.78 % No SInE strategy applied
% 2.03/0.78 % Search class: FGHSF-FSLM21-MFFFFFNN
% 2.03/0.78 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 2.03/0.78 % Starting SubtermCWHack with 136s (1) cores
% 2.03/0.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 2.03/0.78 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 2.03/0.78 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 2.03/0.78 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 2.03/0.78 % Preprocessing time : 0.004 s
% 2.03/0.78 % Presaturation interreduction done
% 2.03/0.78
% 2.03/0.78 % Proof found!
% 2.03/0.78 % SZS status Theorem
% 2.03/0.78 % SZS output start CNFRefutation
% See solution above
% 2.03/0.79 % Parsed axioms : 96
% 2.03/0.79 % Removed by relevancy pruning/SinE : 0
% 2.03/0.79 % Initial clauses : 201
% 2.03/0.79 % Removed in clause preprocessing : 2
% 2.03/0.79 % Initial clauses in saturation : 199
% 2.03/0.79 % Processed clauses : 2027
% 2.03/0.79 % ...of these trivial : 13
% 2.03/0.79 % ...subsumed : 1177
% 2.03/0.79 % ...remaining for further processing : 837
% 2.03/0.79 % Other redundant clauses eliminated : 236
% 2.03/0.79 % Clauses deleted for lack of memory : 0
% 2.03/0.79 % Backward-subsumed : 50
% 2.03/0.79 % Backward-rewritten : 32
% 2.03/0.79 % Generated clauses : 6380
% 2.03/0.79 % ...of the previous two non-redundant : 5574
% 2.03/0.79 % ...aggressively subsumed : 0
% 2.03/0.79 % Contextual simplify-reflections : 262
% 2.03/0.79 % Paramodulations : 6138
% 2.03/0.79 % Factorizations : 0
% 2.03/0.79 % NegExts : 0
% 2.03/0.79 % Equation resolutions : 244
% 2.03/0.79 % Disequality decompositions : 0
% 2.03/0.79 % Total rewrite steps : 3102
% 2.03/0.79 % ...of those cached : 3080
% 2.03/0.79 % Propositional unsat checks : 0
% 2.03/0.79 % Propositional check models : 0
% 2.03/0.79 % Propositional check unsatisfiable : 0
% 2.03/0.79 % Propositional clauses : 0
% 2.03/0.79 % Propositional clauses after purity: 0
% 2.03/0.79 % Propositional unsat core size : 0
% 2.03/0.79 % Propositional preprocessing time : 0.000
% 2.03/0.79 % Propositional encoding time : 0.000
% 2.03/0.79 % Propositional solver time : 0.000
% 2.03/0.79 % Success case prop preproc time : 0.000
% 2.03/0.79 % Success case prop encoding time : 0.000
% 2.03/0.79 % Success case prop solver time : 0.000
% 2.03/0.79 % Current number of processed clauses : 539
% 2.03/0.79 % Positive orientable unit clauses : 24
% 2.03/0.79 % Positive unorientable unit clauses: 0
% 2.03/0.79 % Negative unit clauses : 8
% 2.03/0.79 % Non-unit-clauses : 507
% 2.03/0.79 % Current number of unprocessed clauses: 3827
% 2.03/0.79 % ...number of literals in the above : 27012
% 2.03/0.79 % Current number of archived formulas : 0
% 2.03/0.79 % Current number of archived clauses : 275
% 2.03/0.79 % Clause-clause subsumption calls (NU) : 103098
% 2.03/0.79 % Rec. Clause-clause subsumption calls : 16819
% 2.03/0.79 % Non-unit clause-clause subsumptions : 1282
% 2.03/0.79 % Unit Clause-clause subsumption calls : 1211
% 2.03/0.79 % Rewrite failures with RHS unbound : 0
% 2.03/0.79 % BW rewrite match attempts : 5
% 2.03/0.79 % BW rewrite match successes : 5
% 2.03/0.79 % Condensation attempts : 0
% 2.03/0.79 % Condensation successes : 0
% 2.03/0.79 % Termbank termtop insertions : 140821
% 2.03/0.79 % Search garbage collected termcells : 4319
% 2.03/0.79
% 2.03/0.79 % -------------------------------------------------
% 2.03/0.79 % User time : 0.242 s
% 2.03/0.79 % System time : 0.017 s
% 2.03/0.79 % Total time : 0.259 s
% 2.03/0.79 % Maximum resident set size: 4272 pages
% 2.03/0.79
% 2.03/0.79 % -------------------------------------------------
% 2.03/0.79 % User time : 1.509 s
% 2.03/0.79 % System time : 0.067 s
% 2.03/0.79 % Total time : 1.576 s
% 2.03/0.79 % Maximum resident set size: 4608 pages
% 2.03/0.79 % E exiting
%------------------------------------------------------------------------------