%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC091+1 : TPTP v9.2.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:18:14 PM UTC 2026
% Result : Theorem 2.54s 2.05s
% Output : CNFRefutation 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 30
% Syntax : Number of formulae : 181 ( 39 unt; 0 def)
% Number of atoms : 633 ( 160 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 763 ( 311 ~; 329 |; 48 &)
% ( 6 <=>; 69 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 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 : 232 ( 0 sgn 120 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ~ frontsegP(X4,X3)
| ~ totalorderedP(X3)
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X2,X5)
& segmentP(X1,X5) )
| ? [X6] :
( ssList(X6)
& neq(X3,X6)
& frontsegP(X4,X6)
& segmentP(X6,X3)
& totalorderedP(X6) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax43,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( frontsegP(X1,X2)
=> frontsegP(app(X1,X3),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax43) ).
fof(ax45,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax45) ).
fof(ax5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax50,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( rearsegP(X1,X2)
=> rearsegP(app(X3,X1),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax50) ).
fof(ax51,axiom,
! [X1] :
( ssList(X1)
=> rearsegP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax51) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax7,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(ax6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X3,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax6) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(ax85,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax85) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax19,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssItem(X4)
=> ( cons(X3,X1) = cons(X4,X2)
=> ( X3 = X4
& X2 = X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax19) ).
fof(ax20,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax20) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax21) ).
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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(ax23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax23) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(ax44,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( frontsegP(cons(X1,X3),cons(X2,X4))
<=> ( X1 = X2
& frontsegP(X3,X4) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax44) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax57,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax57) ).
fof(ax79,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X3,X2) = app(X1,X2)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax79) ).
fof(ax65,axiom,
! [X1] :
( ssItem(X1)
=> totalorderedP(cons(X1,nil)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax65) ).
fof(ax18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(c_0_30,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ~ frontsegP(X4,X3)
| ~ totalorderedP(X3)
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X2,X5)
& segmentP(X1,X5) )
| ? [X6] :
( ssList(X6)
& neq(X3,X6)
& frontsegP(X4,X6)
& segmentP(X6,X3)
& totalorderedP(X6) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_31,negated_conjecture,
! [X464,X465] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& neq(esk49_0,nil)
& frontsegP(esk51_0,esk50_0)
& totalorderedP(esk50_0)
& ( ~ ssList(X464)
| ~ neq(X464,nil)
| ~ segmentP(esk49_0,X464)
| ~ segmentP(esk48_0,X464) )
& ( ~ ssList(X465)
| ~ neq(esk50_0,X465)
| ~ frontsegP(esk51_0,X465)
| ~ segmentP(X465,esk50_0)
| ~ totalorderedP(X465) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])])]) ).
fof(c_0_32,plain,
! [X373,X374,X375] :
( ~ ssList(X373)
| ~ ssList(X374)
| ~ ssList(X375)
| ~ frontsegP(X373,X374)
| frontsegP(app(X373,X375),X374) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax43])])]) ).
fof(c_0_33,plain,
! [X380] :
( ~ ssList(X380)
| frontsegP(X380,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])]) ).
fof(c_0_34,plain,
! [X229,X230,X232] :
( ( ssList(esk6_2(X229,X230))
| ~ frontsegP(X229,X230)
| ~ ssList(X230)
| ~ ssList(X229) )
& ( app(X230,esk6_2(X229,X230)) = X229
| ~ frontsegP(X229,X230)
| ~ ssList(X230)
| ~ ssList(X229) )
& ( ~ ssList(X232)
| app(X230,X232) != X229
| frontsegP(X229,X230)
| ~ ssList(X230)
| ~ ssList(X229) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax5])])])])]) ).
cnf(c_0_35,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_37,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_39,plain,
( frontsegP(app(X1,X3),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,plain,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_42,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_43,negated_conjecture,
frontsegP(esk51_0,esk50_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_44,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_45,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_46,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_47,plain,
( frontsegP(app(X1,X2),nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]) ).
cnf(c_0_48,negated_conjecture,
app(esk50_0,esk6_2(esk51_0,esk50_0)) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_45])]) ).
cnf(c_0_49,negated_conjecture,
ssList(esk6_2(esk51_0,esk50_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_43]),c_0_45]),c_0_44])]) ).
fof(c_0_50,plain,
! [X388,X389,X390] :
( ~ ssList(X388)
| ~ ssList(X389)
| ~ ssList(X390)
| ~ rearsegP(X388,X389)
| rearsegP(app(X390,X388),X389) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax50])])]) ).
fof(c_0_51,plain,
! [X391] :
( ~ ssList(X391)
| rearsegP(X391,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax51])]) ).
fof(c_0_52,plain,
! [X344] :
( ~ ssList(X344)
| app(nil,X344) = X344 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
cnf(c_0_53,negated_conjecture,
frontsegP(esk51_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_45])]) ).
cnf(c_0_54,plain,
( rearsegP(app(X3,X1),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ rearsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_55,plain,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
fof(c_0_56,plain,
! [X237,X238,X241,X242] :
( ( ssList(esk8_2(X237,X238))
| ~ segmentP(X237,X238)
| ~ ssList(X238)
| ~ ssList(X237) )
& ( ssList(esk9_2(X237,X238))
| ~ segmentP(X237,X238)
| ~ ssList(X238)
| ~ ssList(X237) )
& ( app(app(esk8_2(X237,X238),X238),esk9_2(X237,X238)) = X237
| ~ segmentP(X237,X238)
| ~ ssList(X238)
| ~ ssList(X237) )
& ( ~ ssList(X241)
| ~ ssList(X242)
| app(app(X241,X238),X242) != X237
| segmentP(X237,X238)
| ~ ssList(X238)
| ~ ssList(X237) ) ),
inference(distribute,[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_57,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_58,negated_conjecture,
app(nil,esk6_2(esk51_0,nil)) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_53]),c_0_44]),c_0_41])]) ).
cnf(c_0_59,negated_conjecture,
ssList(esk6_2(esk51_0,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_53]),c_0_41]),c_0_44])]) ).
fof(c_0_60,plain,
! [X233,X234,X236] :
( ( ssList(esk7_2(X233,X234))
| ~ rearsegP(X233,X234)
| ~ ssList(X234)
| ~ ssList(X233) )
& ( app(esk7_2(X233,X234),X234) = X233
| ~ rearsegP(X233,X234)
| ~ ssList(X234)
| ~ ssList(X233) )
& ( ~ ssList(X236)
| app(X236,X234) != X233
| rearsegP(X233,X234)
| ~ ssList(X234)
| ~ ssList(X233) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])])])])]) ).
cnf(c_0_61,plain,
( rearsegP(app(X1,X2),nil)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_41])]) ).
cnf(c_0_62,plain,
( segmentP(X4,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X1,X3),X2) != X4
| ~ ssList(X3)
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_63,negated_conjecture,
esk6_2(esk51_0,nil) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59])]) ).
fof(c_0_64,plain,
! [X436] :
( ~ ssList(X436)
| app(X436,nil) = X436 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
cnf(c_0_65,plain,
( app(esk7_2(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_66,negated_conjecture,
rearsegP(esk51_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_48]),c_0_45]),c_0_49])]) ).
cnf(c_0_67,plain,
( ssList(esk7_2(X1,X2))
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_68,plain,
( segmentP(app(app(X1,X2),X3),X2)
| ~ ssList(app(app(X1,X2),X3))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(er,[status(thm)],[c_0_62]) ).
cnf(c_0_69,negated_conjecture,
app(nil,esk51_0) = esk51_0,
inference(rw,[status(thm)],[c_0_58,c_0_63]) ).
fof(c_0_70,plain,
! [X422] :
( ~ ssList(X422)
| nil = X422
| cons(hd(X422),tl(X422)) = X422 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).
fof(c_0_71,plain,
! [X437,X438] :
( ~ ssList(X437)
| ~ ssList(X438)
| nil = X437
| hd(app(X437,X438)) = hd(X437) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax85])])]) ).
fof(c_0_72,plain,
! [X339,X340] :
( ~ ssList(X339)
| ~ ssList(X340)
| ssList(app(X339,X340)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
fof(c_0_73,plain,
! [X434,X435] :
( ( nil = X435
| nil != app(X434,X435)
| ~ ssList(X435)
| ~ ssList(X434) )
& ( nil = X434
| nil != app(X434,X435)
| ~ ssList(X435)
| ~ ssList(X434) )
& ( nil != X435
| nil != X434
| nil = app(X434,X435)
| ~ ssList(X435)
| ~ ssList(X434) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
cnf(c_0_74,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_75,negated_conjecture,
app(esk7_2(esk51_0,nil),nil) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_41]),c_0_44])]) ).
cnf(c_0_76,negated_conjecture,
ssList(esk7_2(esk51_0,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_66]),c_0_41]),c_0_44])]) ).
cnf(c_0_77,negated_conjecture,
( segmentP(app(esk51_0,X1),esk51_0)
| ~ ssList(app(esk51_0,X1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_44]),c_0_41])]) ).
fof(c_0_78,plain,
! [X324,X325,X326,X327] :
( ( X326 = X327
| cons(X326,X324) != cons(X327,X325)
| ~ ssItem(X327)
| ~ ssItem(X326)
| ~ ssList(X325)
| ~ ssList(X324) )
& ( X325 = X324
| cons(X326,X324) != cons(X327,X325)
| ~ ssItem(X327)
| ~ ssItem(X326)
| ~ ssList(X325)
| ~ ssList(X324) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax19])])])]) ).
fof(c_0_79,plain,
! [X328] :
( ( ssList(esk44_1(X328))
| nil = X328
| ~ ssList(X328) )
& ( ssItem(esk45_1(X328))
| nil = X328
| ~ ssList(X328) )
& ( cons(esk45_1(X328),esk44_1(X328)) = X328
| nil = X328
| ~ ssList(X328) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])]) ).
fof(c_0_80,plain,
! [X320,X321] :
( ~ ssList(X320)
| ~ ssItem(X321)
| ssList(cons(X321,X320)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
fof(c_0_81,plain,
! [X331,X332] :
( ~ ssList(X331)
| ~ ssItem(X332)
| nil != cons(X332,X331) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])]) ).
cnf(c_0_82,plain,
( nil = X1
| cons(hd(X1),tl(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_83,plain,
( nil = X1
| hd(app(X1,X2)) = hd(X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_84,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_85,plain,
( nil = X1
| nil != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_86,negated_conjecture,
esk7_2(esk51_0,nil) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76])]) ).
fof(c_0_87,plain,
! [X431,X432,X433] :
( ~ ssList(X431)
| ~ ssList(X432)
| ~ ssList(X433)
| app(app(X431,X432),X433) = app(X431,app(X432,X433)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).
cnf(c_0_88,plain,
( app(app(esk8_2(X1,X2),X2),esk9_2(X1,X2)) = X1
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_89,negated_conjecture,
segmentP(esk51_0,esk51_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_74]),c_0_44]),c_0_41])]) ).
cnf(c_0_90,plain,
( ssList(esk9_2(X1,X2))
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_91,plain,
( ssList(esk8_2(X1,X2))
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_92,plain,
( X1 = X2
| cons(X3,X2) != cons(X4,X1)
| ~ ssItem(X4)
| ~ ssItem(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_93,plain,
( cons(esk45_1(X1),esk44_1(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_94,plain,
( ssItem(esk45_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_95,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_96,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| nil != cons(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_97,plain,
( cons(hd(X1),tl(app(X1,X2))) = app(X1,X2)
| nil = X1
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84]),c_0_85]) ).
cnf(c_0_98,negated_conjecture,
app(esk51_0,nil) = esk51_0,
inference(rw,[status(thm)],[c_0_75,c_0_86]) ).
cnf(c_0_99,plain,
( frontsegP(X3,X2)
| ~ ssList(X1)
| app(X2,X1) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_100,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_101,negated_conjecture,
app(app(esk8_2(esk51_0,esk51_0),esk51_0),esk9_2(esk51_0,esk51_0)) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_44])]) ).
cnf(c_0_102,negated_conjecture,
ssList(esk9_2(esk51_0,esk51_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_89]),c_0_44])]) ).
cnf(c_0_103,negated_conjecture,
ssList(esk8_2(esk51_0,esk51_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_89]),c_0_44])]) ).
cnf(c_0_104,plain,
( esk44_1(cons(X1,X2)) = X2
| ~ ssList(esk44_1(cons(X1,X2)))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93])]),c_0_94]),c_0_95]),c_0_96]) ).
cnf(c_0_105,negated_conjecture,
( cons(hd(esk51_0),tl(esk51_0)) = esk51_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_41]),c_0_44])]) ).
cnf(c_0_106,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_99]),c_0_84]) ).
cnf(c_0_107,negated_conjecture,
app(esk8_2(esk51_0,esk51_0),app(esk51_0,esk9_2(esk51_0,esk51_0))) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_102]),c_0_44]),c_0_103])]) ).
cnf(c_0_108,negated_conjecture,
( esk44_1(esk51_0) = tl(esk51_0)
| esk51_0 = nil
| ~ ssList(esk44_1(esk51_0))
| ~ ssList(tl(esk51_0))
| ~ ssItem(hd(esk51_0)) ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_109,plain,
( ssList(esk44_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
fof(c_0_110,plain,
! [X336] :
( ~ ssList(X336)
| nil = X336
| ssList(tl(X336)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).
cnf(c_0_111,negated_conjecture,
( frontsegP(esk51_0,esk8_2(esk51_0,esk51_0))
| ~ ssList(app(esk51_0,esk9_2(esk51_0,esk51_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_103])]) ).
cnf(c_0_112,negated_conjecture,
( esk44_1(esk51_0) = tl(esk51_0)
| esk51_0 = nil
| ~ ssList(tl(esk51_0))
| ~ ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_44])]) ).
cnf(c_0_113,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
fof(c_0_114,plain,
! [X333] :
( ~ ssList(X333)
| nil = X333
| ssItem(hd(X333)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).
cnf(c_0_115,negated_conjecture,
frontsegP(esk51_0,esk8_2(esk51_0,esk51_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_84]),c_0_102]),c_0_44])]) ).
cnf(c_0_116,negated_conjecture,
( esk44_1(esk51_0) = tl(esk51_0)
| esk51_0 = nil
| ~ ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_44])]) ).
cnf(c_0_117,plain,
( nil = X1
| ssItem(hd(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_118,negated_conjecture,
app(esk8_2(esk51_0,esk51_0),esk6_2(esk51_0,esk8_2(esk51_0,esk51_0))) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_115]),c_0_44]),c_0_103])]) ).
cnf(c_0_119,negated_conjecture,
ssList(esk6_2(esk51_0,esk8_2(esk51_0,esk51_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_115]),c_0_103]),c_0_44])]) ).
fof(c_0_120,plain,
! [X334,X335] :
( ~ ssList(X334)
| ~ ssItem(X335)
| hd(cons(X335,X334)) = X335 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])]) ).
cnf(c_0_121,negated_conjecture,
( esk44_1(esk51_0) = tl(esk51_0)
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_44])]) ).
cnf(c_0_122,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk49_0,X1)
| ~ segmentP(esk48_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_123,plain,
! [X398] :
( ~ ssList(X398)
| segmentP(X398,X398) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])]) ).
fof(c_0_124,plain,
! [X376,X377,X378,X379] :
( ( X376 = X377
| ~ frontsegP(cons(X376,X378),cons(X377,X379))
| ~ ssList(X379)
| ~ ssList(X378)
| ~ ssItem(X377)
| ~ ssItem(X376) )
& ( frontsegP(X378,X379)
| ~ frontsegP(cons(X376,X378),cons(X377,X379))
| ~ ssList(X379)
| ~ ssList(X378)
| ~ ssItem(X377)
| ~ ssItem(X376) )
& ( X376 != X377
| ~ frontsegP(X378,X379)
| frontsegP(cons(X376,X378),cons(X377,X379))
| ~ ssList(X379)
| ~ ssList(X378)
| ~ ssItem(X377)
| ~ ssItem(X376) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax44])])])]) ).
cnf(c_0_125,negated_conjecture,
( hd(esk8_2(esk51_0,esk51_0)) = hd(esk51_0)
| esk8_2(esk51_0,esk51_0) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_118]),c_0_119]),c_0_103])]) ).
cnf(c_0_126,plain,
( hd(cons(X2,X1)) = X2
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_127,negated_conjecture,
( cons(esk45_1(esk51_0),tl(esk51_0)) = esk51_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_121]),c_0_44])]) ).
cnf(c_0_128,negated_conjecture,
( esk51_0 = nil
| ssList(tl(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_121]),c_0_44])]) ).
cnf(c_0_129,negated_conjecture,
( ~ segmentP(esk50_0,X1)
| ~ segmentP(esk51_0,X1)
| ~ ssList(X1)
| ~ neq(X1,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_38]),c_0_36]) ).
cnf(c_0_130,plain,
( segmentP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_131,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_57]),c_0_41])]),c_0_84]) ).
cnf(c_0_132,plain,
( frontsegP(cons(X1,X3),cons(X2,X4))
| X1 != X2
| ~ frontsegP(X3,X4)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_133,negated_conjecture,
( esk8_2(esk51_0,esk51_0) = nil
| ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_125]),c_0_103])]) ).
cnf(c_0_134,negated_conjecture,
( esk45_1(esk51_0) = hd(esk51_0)
| esk51_0 = nil
| ~ ssItem(esk45_1(esk51_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_128]) ).
cnf(c_0_135,negated_conjecture,
( ~ segmentP(esk51_0,esk50_0)
| ~ neq(esk50_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_45])]) ).
cnf(c_0_136,negated_conjecture,
segmentP(esk51_0,esk50_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_48]),c_0_45]),c_0_49])]) ).
fof(c_0_137,plain,
! [X318,X319] :
( ( ~ neq(X318,X319)
| X318 != X319
| ~ ssList(X319)
| ~ ssList(X318) )
& ( X318 = X319
| neq(X318,X319)
| ~ ssList(X319)
| ~ ssList(X318) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
cnf(c_0_138,plain,
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(er,[status(thm)],[c_0_132]) ).
cnf(c_0_139,plain,
( app(X1,X2) = nil
| app(X1,app(X2,X3)) != nil
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_100]),c_0_84]) ).
cnf(c_0_140,negated_conjecture,
( app(esk51_0,esk9_2(esk51_0,esk51_0)) = esk51_0
| ssItem(hd(esk51_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_133]),c_0_69]) ).
cnf(c_0_141,negated_conjecture,
( esk45_1(esk51_0) = hd(esk51_0)
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_94]),c_0_44])]) ).
cnf(c_0_142,negated_conjecture,
~ neq(esk50_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_135,c_0_136])]) ).
cnf(c_0_143,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_137]) ).
fof(c_0_144,plain,
! [X403] :
( ~ ssList(X403)
| segmentP(X403,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax57])]) ).
cnf(c_0_145,plain,
( frontsegP(cons(X1,X2),cons(X1,nil))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_40]),c_0_41])]) ).
cnf(c_0_146,negated_conjecture,
( app(X1,nil) = nil
| app(X1,esk51_0) != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_69]),c_0_44]),c_0_41])]) ).
cnf(c_0_147,negated_conjecture,
( app(esk8_2(esk51_0,esk51_0),esk51_0) = esk51_0
| ssItem(hd(esk51_0)) ),
inference(spm,[status(thm)],[c_0_107,c_0_140]) ).
cnf(c_0_148,negated_conjecture,
( esk51_0 = nil
| ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_141]),c_0_44])]) ).
fof(c_0_149,plain,
! [X423,X424,X425] :
( ~ ssList(X423)
| ~ ssList(X424)
| ~ ssList(X425)
| app(X425,X424) != app(X423,X424)
| X425 = X423 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])]) ).
cnf(c_0_150,negated_conjecture,
( ~ ssList(X1)
| ~ neq(esk50_0,X1)
| ~ frontsegP(esk51_0,X1)
| ~ segmentP(X1,esk50_0)
| ~ totalorderedP(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_151,negated_conjecture,
esk50_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_41]),c_0_45])]) ).
cnf(c_0_152,plain,
( segmentP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
cnf(c_0_153,negated_conjecture,
( esk51_0 = nil
| frontsegP(esk51_0,cons(esk45_1(esk51_0),nil))
| ~ ssItem(esk45_1(esk51_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_127]),c_0_128]) ).
cnf(c_0_154,negated_conjecture,
( app(esk8_2(esk51_0,esk51_0),nil) = nil
| ssItem(hd(esk51_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_103])]),c_0_148]) ).
cnf(c_0_155,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X3,X2) != app(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_149]) ).
cnf(c_0_156,negated_conjecture,
( ~ totalorderedP(X1)
| ~ frontsegP(esk51_0,X1)
| ~ ssList(X1)
| ~ neq(nil,X1) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_150,c_0_151]),c_0_151]),c_0_152]) ).
cnf(c_0_157,negated_conjecture,
( esk51_0 = nil
| frontsegP(esk51_0,cons(esk45_1(esk51_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_94]),c_0_44])]) ).
fof(c_0_158,plain,
! [X408] :
( ~ ssItem(X408)
| totalorderedP(cons(X408,nil)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax65])]) ).
cnf(c_0_159,negated_conjecture,
( ~ segmentP(nil,X1)
| ~ segmentP(esk51_0,X1)
| ~ ssList(X1)
| ~ neq(X1,nil) ),
inference(rw,[status(thm)],[c_0_129,c_0_151]) ).
cnf(c_0_160,negated_conjecture,
( segmentP(nil,esk8_2(esk51_0,esk51_0))
| ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_154]),c_0_103]),c_0_41])]) ).
cnf(c_0_161,negated_conjecture,
segmentP(esk51_0,esk8_2(esk51_0,esk51_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_118]),c_0_103]),c_0_119])]) ).
cnf(c_0_162,negated_conjecture,
( X1 = esk51_0
| app(X1,nil) != esk51_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_98]),c_0_44]),c_0_41])]) ).
cnf(c_0_163,negated_conjecture,
neq(esk49_0,nil),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_164,negated_conjecture,
( esk51_0 = nil
| ~ totalorderedP(cons(esk45_1(esk51_0),nil))
| ~ ssList(cons(esk45_1(esk51_0),nil))
| ~ neq(nil,cons(esk45_1(esk51_0),nil)) ),
inference(spm,[status(thm)],[c_0_156,c_0_157]) ).
cnf(c_0_165,plain,
( totalorderedP(cons(X1,nil))
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_158]) ).
cnf(c_0_166,negated_conjecture,
( ssItem(hd(esk51_0))
| ~ neq(esk8_2(esk51_0,esk51_0),nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_161]),c_0_103])]) ).
cnf(c_0_167,negated_conjecture,
( esk8_2(esk51_0,esk51_0) = esk51_0
| ssItem(hd(esk51_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_154]),c_0_103])]),c_0_148]) ).
cnf(c_0_168,negated_conjecture,
neq(esk51_0,nil),
inference(rw,[status(thm)],[c_0_163,c_0_36]) ).
cnf(c_0_169,negated_conjecture,
( esk51_0 = nil
| ~ neq(nil,cons(esk45_1(esk51_0),nil))
| ~ ssItem(esk45_1(esk51_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_95]),c_0_41])]),c_0_165]) ).
cnf(c_0_170,plain,
( esk45_1(X1) = hd(X1)
| nil = X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_93]),c_0_94]),c_0_109]) ).
cnf(c_0_171,negated_conjecture,
ssItem(hd(esk51_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_167]),c_0_168])]) ).
cnf(c_0_172,negated_conjecture,
( esk51_0 = nil
| ~ neq(nil,cons(hd(esk51_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_171]),c_0_44])]) ).
fof(c_0_173,plain,
! [X322,X323] :
( ~ ssList(X322)
| ~ ssItem(X323)
| cons(X323,X322) != X322 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])]) ).
cnf(c_0_174,negated_conjecture,
( cons(hd(esk51_0),nil) = nil
| esk51_0 = nil
| ~ ssList(cons(hd(esk51_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_143]),c_0_41])]) ).
cnf(c_0_175,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,X1) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_173]) ).
cnf(c_0_176,negated_conjecture,
( cons(hd(esk51_0),nil) = nil
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_95]),c_0_41]),c_0_171])]) ).
cnf(c_0_177,negated_conjecture,
( ~ segmentP(esk51_0,nil)
| ~ neq(nil,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_152]),c_0_41]),c_0_45])]) ).
cnf(c_0_178,negated_conjecture,
esk51_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_176]),c_0_41]),c_0_171])]) ).
cnf(c_0_179,negated_conjecture,
~ neq(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_152]),c_0_44])]) ).
cnf(c_0_180,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_168,c_0_178]),c_0_179]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC091+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n017.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 04:25:27 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 2.54/2.05 % Version : CSE_E---1.7
% 2.54/2.05 % Problem : theBenchmark.p
% 2.54/2.05 % SZS status Theorem for theBenchmark.p
% 2.54/2.05 % SZS output start CNFRefutation
% See solution above
% 2.54/2.06 % Total time : 1.374s
%------------------------------------------------------------------------------