%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC031+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 : n010.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 05:17:58 PM UTC 2026
% Result : Theorem 2.07s 1.93s
% Output : CNFRefutation 2.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 28
% Syntax : Number of formulae : 151 ( 39 unt; 0 def)
% Number of atoms : 540 ( 150 equ)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 662 ( 273 ~; 274 |; 47 &)
% ( 7 <=>; 61 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 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 : 198 ( 0 sgn 107 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ frontsegP(X4,X3)
| ~ totalorderedP(X3)
| ? [X5] :
( ssList(X5)
& neq(X3,X5)
& frontsegP(X4,X5)
& segmentP(X5,X3)
& totalorderedP(X5) )
| ( ( nil != X2
| nil = X1 )
& ( nil != X1
| nil = X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax46,axiom,
! [X1] :
( ssList(X1)
=> ( frontsegP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax46) ).
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(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
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(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
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(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(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(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(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(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(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(ax45,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax45) ).
fof(ax57,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax57) ).
fof(ax65,axiom,
! [X1] :
( ssItem(X1)
=> totalorderedP(cons(X1,nil)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax65) ).
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(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_28,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ frontsegP(X4,X3)
| ~ totalorderedP(X3)
| ? [X5] :
( ssList(X5)
& neq(X3,X5)
& frontsegP(X4,X5)
& segmentP(X5,X3)
& totalorderedP(X5) )
| ( ( nil != X2
| nil = X1 )
& ( nil != X1
| nil = X2 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_29,negated_conjecture,
! [X463] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& frontsegP(esk51_0,esk50_0)
& totalorderedP(esk50_0)
& ( ~ ssList(X463)
| ~ neq(esk50_0,X463)
| ~ frontsegP(esk51_0,X463)
| ~ segmentP(X463,esk50_0)
| ~ totalorderedP(X463) )
& ( nil = esk48_0
| nil = esk49_0 )
& ( nil != esk49_0
| nil = esk49_0 )
& ( nil = esk48_0
| nil != esk48_0 )
& ( nil != esk49_0
| nil != esk48_0 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])])]) ).
cnf(c_0_30,negated_conjecture,
( nil = esk48_0
| nil = esk49_0 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_31,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_32,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_33,plain,
! [X380] :
( ( ~ frontsegP(nil,X380)
| nil = X380
| ~ ssList(X380) )
& ( nil != X380
| frontsegP(nil,X380)
| ~ ssList(X380) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax46])])]) ).
cnf(c_0_34,negated_conjecture,
frontsegP(esk51_0,esk50_0),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,negated_conjecture,
( esk51_0 = nil
| esk50_0 = nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_36,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_37,plain,
( nil = X1
| ~ frontsegP(nil,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,negated_conjecture,
( esk50_0 = nil
| frontsegP(nil,esk50_0) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_36,c_0_31]) ).
fof(c_0_40,plain,
! [X228,X229,X231] :
( ( ssList(esk6_2(X228,X229))
| ~ frontsegP(X228,X229)
| ~ ssList(X229)
| ~ ssList(X228) )
& ( app(X229,esk6_2(X228,X229)) = X228
| ~ frontsegP(X228,X229)
| ~ ssList(X229)
| ~ ssList(X228) )
& ( ~ ssList(X231)
| app(X229,X231) != X228
| frontsegP(X228,X229)
| ~ ssList(X229)
| ~ ssList(X228) ) ),
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_41,negated_conjecture,
esk50_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]) ).
cnf(c_0_42,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_43,plain,
! [X343] :
( ~ ssList(X343)
| app(nil,X343) = X343 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
cnf(c_0_44,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_45,negated_conjecture,
frontsegP(esk51_0,nil),
inference(rw,[status(thm)],[c_0_34,c_0_41]) ).
cnf(c_0_46,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_42,c_0_32]) ).
cnf(c_0_47,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_48,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_49,plain,
! [X236,X237,X240,X241] :
( ( ssList(esk8_2(X236,X237))
| ~ segmentP(X236,X237)
| ~ ssList(X237)
| ~ ssList(X236) )
& ( ssList(esk9_2(X236,X237))
| ~ segmentP(X236,X237)
| ~ ssList(X237)
| ~ ssList(X236) )
& ( app(app(esk8_2(X236,X237),X237),esk9_2(X236,X237)) = X236
| ~ segmentP(X236,X237)
| ~ ssList(X237)
| ~ ssList(X236) )
& ( ~ ssList(X240)
| ~ ssList(X241)
| app(app(X240,X237),X241) != X236
| segmentP(X236,X237)
| ~ ssList(X237)
| ~ ssList(X236) ) ),
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_50,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_51,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_44,c_0_45]),c_0_46]),c_0_47])]) ).
cnf(c_0_52,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_48,c_0_45]),c_0_47]),c_0_46])]) ).
cnf(c_0_53,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_49]) ).
cnf(c_0_54,negated_conjecture,
esk6_2(esk51_0,nil) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52])]) ).
cnf(c_0_55,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_53]) ).
cnf(c_0_56,negated_conjecture,
app(nil,esk51_0) = esk51_0,
inference(rw,[status(thm)],[c_0_51,c_0_54]) ).
fof(c_0_57,plain,
! [X435] :
( ~ ssList(X435)
| app(X435,nil) = X435 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
cnf(c_0_58,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_55,c_0_56]),c_0_46]),c_0_47])]) ).
cnf(c_0_59,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
fof(c_0_60,plain,
! [X338,X339] :
( ~ ssList(X338)
| ~ ssList(X339)
| ssList(app(X338,X339)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
fof(c_0_61,plain,
! [X430,X431,X432] :
( ~ ssList(X430)
| ~ ssList(X431)
| ~ ssList(X432)
| app(app(X430,X431),X432) = app(X430,app(X431,X432)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).
cnf(c_0_62,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_49]) ).
cnf(c_0_63,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_58,c_0_59]),c_0_46]),c_0_47])]) ).
cnf(c_0_64,plain,
( ssList(esk9_2(X1,X2))
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_65,plain,
( ssList(esk8_2(X1,X2))
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_66,plain,
( frontsegP(X3,X2)
| ~ ssList(X1)
| app(X2,X1) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_67,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_68,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_69,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_62,c_0_63]),c_0_46])]) ).
cnf(c_0_70,negated_conjecture,
ssList(esk9_2(esk51_0,esk51_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_63]),c_0_46])]) ).
cnf(c_0_71,negated_conjecture,
ssList(esk8_2(esk51_0,esk51_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_63]),c_0_46])]) ).
cnf(c_0_72,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_66]),c_0_67]) ).
cnf(c_0_73,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_68,c_0_69]),c_0_70]),c_0_46]),c_0_71])]) ).
fof(c_0_74,plain,
! [X387,X388,X389] :
( ~ ssList(X387)
| ~ ssList(X388)
| ~ ssList(X389)
| ~ rearsegP(X387,X388)
| rearsegP(app(X389,X387),X388) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax50])])]) ).
fof(c_0_75,plain,
! [X390] :
( ~ ssList(X390)
| rearsegP(X390,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax51])]) ).
cnf(c_0_76,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_72,c_0_73]),c_0_71])]) ).
cnf(c_0_77,plain,
( rearsegP(app(X3,X1),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ rearsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_78,plain,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_79,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_76,c_0_67]),c_0_70]),c_0_46])]) ).
fof(c_0_80,plain,
! [X232,X233,X235] :
( ( ssList(esk7_2(X232,X233))
| ~ rearsegP(X232,X233)
| ~ ssList(X233)
| ~ ssList(X232) )
& ( app(esk7_2(X232,X233),X233) = X232
| ~ rearsegP(X232,X233)
| ~ ssList(X233)
| ~ ssList(X232) )
& ( ~ ssList(X235)
| app(X235,X233) != X232
| rearsegP(X232,X233)
| ~ ssList(X233)
| ~ ssList(X232) ) ),
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_81,plain,
( rearsegP(app(X1,X2),nil)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_47])]) ).
cnf(c_0_82,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_44,c_0_79]),c_0_46]),c_0_71])]) ).
cnf(c_0_83,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_48,c_0_79]),c_0_71]),c_0_46])]) ).
cnf(c_0_84,plain,
( app(esk7_2(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_85,negated_conjecture,
rearsegP(esk51_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_71]),c_0_83])]) ).
cnf(c_0_86,plain,
( ssList(esk7_2(X1,X2))
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
fof(c_0_87,plain,
! [X421] :
( ~ ssList(X421)
| nil = X421
| cons(hd(X421),tl(X421)) = X421 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).
fof(c_0_88,plain,
! [X436,X437] :
( ~ ssList(X436)
| ~ ssList(X437)
| nil = X436
| hd(app(X436,X437)) = hd(X436) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax85])])]) ).
fof(c_0_89,plain,
! [X433,X434] :
( ( nil = X434
| nil != app(X433,X434)
| ~ ssList(X434)
| ~ ssList(X433) )
& ( nil = X433
| nil != app(X433,X434)
| ~ ssList(X434)
| ~ ssList(X433) )
& ( nil != X434
| nil != X433
| nil = app(X433,X434)
| ~ ssList(X434)
| ~ ssList(X433) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
cnf(c_0_90,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_84,c_0_85]),c_0_47]),c_0_46])]) ).
cnf(c_0_91,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_86,c_0_85]),c_0_47]),c_0_46])]) ).
cnf(c_0_92,negated_conjecture,
( nil != esk49_0
| nil != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_93,plain,
! [X323,X324,X325,X326] :
( ( X325 = X326
| cons(X325,X323) != cons(X326,X324)
| ~ ssItem(X326)
| ~ ssItem(X325)
| ~ ssList(X324)
| ~ ssList(X323) )
& ( X324 = X323
| cons(X325,X323) != cons(X326,X324)
| ~ ssItem(X326)
| ~ ssItem(X325)
| ~ ssList(X324)
| ~ ssList(X323) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax19])])])]) ).
fof(c_0_94,plain,
! [X327] :
( ( ssList(esk44_1(X327))
| nil = X327
| ~ ssList(X327) )
& ( ssItem(esk45_1(X327))
| nil = X327
| ~ ssList(X327) )
& ( cons(esk45_1(X327),esk44_1(X327)) = X327
| nil = X327
| ~ ssList(X327) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])]) ).
fof(c_0_95,plain,
! [X319,X320] :
( ~ ssList(X319)
| ~ ssItem(X320)
| ssList(cons(X320,X319)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
fof(c_0_96,plain,
! [X330,X331] :
( ~ ssList(X330)
| ~ ssItem(X331)
| nil != cons(X331,X330) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])]) ).
cnf(c_0_97,plain,
( nil = X1
| cons(hd(X1),tl(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_98,plain,
( nil = X1
| hd(app(X1,X2)) = hd(X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_99,plain,
( nil = X1
| nil != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_100,negated_conjecture,
esk7_2(esk51_0,nil) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_90]),c_0_91])]) ).
cnf(c_0_101,negated_conjecture,
( esk50_0 != nil
| esk51_0 != nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_31]),c_0_32]) ).
cnf(c_0_102,plain,
( X1 = X2
| cons(X3,X2) != cons(X4,X1)
| ~ ssItem(X4)
| ~ ssItem(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_103,plain,
( cons(esk45_1(X1),esk44_1(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_104,plain,
( ssItem(esk45_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_105,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_106,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| nil != cons(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_107,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_97,c_0_98]),c_0_67]),c_0_99]) ).
cnf(c_0_108,negated_conjecture,
app(esk51_0,nil) = esk51_0,
inference(rw,[status(thm)],[c_0_90,c_0_100]) ).
cnf(c_0_109,negated_conjecture,
esk51_0 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_41])]) ).
cnf(c_0_110,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_102,c_0_103])]),c_0_104]),c_0_105]),c_0_106]) ).
cnf(c_0_111,negated_conjecture,
cons(hd(esk51_0),tl(esk51_0)) = esk51_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_47]),c_0_46])]),c_0_109]) ).
cnf(c_0_112,negated_conjecture,
( esk44_1(esk51_0) = tl(esk51_0)
| ~ ssList(esk44_1(esk51_0))
| ~ ssList(tl(esk51_0))
| ~ ssItem(hd(esk51_0)) ),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_113,plain,
( ssList(esk44_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
fof(c_0_114,plain,
! [X335] :
( ~ ssList(X335)
| nil = X335
| ssList(tl(X335)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).
cnf(c_0_115,negated_conjecture,
( esk44_1(esk51_0) = tl(esk51_0)
| ~ ssList(tl(esk51_0))
| ~ ssItem(hd(esk51_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_46])]),c_0_109]) ).
cnf(c_0_116,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
fof(c_0_117,plain,
! [X332] :
( ~ ssList(X332)
| nil = X332
| ssItem(hd(X332)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).
cnf(c_0_118,negated_conjecture,
( esk44_1(esk51_0) = tl(esk51_0)
| ~ ssItem(hd(esk51_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_46])]),c_0_109]) ).
cnf(c_0_119,plain,
( nil = X1
| ssItem(hd(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
fof(c_0_120,plain,
! [X333,X334] :
( ~ ssList(X333)
| ~ ssItem(X334)
| hd(cons(X334,X333)) = X334 ),
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),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_46])]),c_0_109]) ).
fof(c_0_122,plain,
! [X375,X376,X377,X378] :
( ( X375 = X376
| ~ frontsegP(cons(X375,X377),cons(X376,X378))
| ~ ssList(X378)
| ~ ssList(X377)
| ~ ssItem(X376)
| ~ ssItem(X375) )
& ( frontsegP(X377,X378)
| ~ frontsegP(cons(X375,X377),cons(X376,X378))
| ~ ssList(X378)
| ~ ssList(X377)
| ~ ssItem(X376)
| ~ ssItem(X375) )
& ( X375 != X376
| ~ frontsegP(X377,X378)
| frontsegP(cons(X375,X377),cons(X376,X378))
| ~ ssList(X378)
| ~ ssList(X377)
| ~ ssItem(X376)
| ~ ssItem(X375) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax44])])])]) ).
cnf(c_0_123,plain,
( hd(cons(X2,X1)) = X2
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_124,negated_conjecture,
cons(esk45_1(esk51_0),tl(esk51_0)) = esk51_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_121]),c_0_46])]),c_0_109]) ).
cnf(c_0_125,negated_conjecture,
ssList(tl(esk51_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_121]),c_0_46])]),c_0_109]) ).
cnf(c_0_126,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_122]) ).
fof(c_0_127,plain,
! [X379] :
( ~ ssList(X379)
| frontsegP(X379,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])]) ).
cnf(c_0_128,negated_conjecture,
( esk45_1(esk51_0) = hd(esk51_0)
| ~ ssItem(esk45_1(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_125])]) ).
fof(c_0_129,plain,
! [X402] :
( ~ ssList(X402)
| segmentP(X402,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax57])]) ).
cnf(c_0_130,plain,
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(er,[status(thm)],[c_0_126]) ).
cnf(c_0_131,plain,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_132,negated_conjecture,
esk45_1(esk51_0) = hd(esk51_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_104]),c_0_46])]),c_0_109]) ).
cnf(c_0_133,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_29]) ).
cnf(c_0_134,plain,
( segmentP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_135,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_130,c_0_131]),c_0_47])]) ).
cnf(c_0_136,negated_conjecture,
ssItem(hd(esk51_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_132]),c_0_46])]),c_0_109]) ).
cnf(c_0_137,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_133,c_0_41]),c_0_41]),c_0_134]) ).
cnf(c_0_138,negated_conjecture,
frontsegP(esk51_0,cons(hd(esk51_0),nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_111]),c_0_125]),c_0_136])]) ).
cnf(c_0_139,negated_conjecture,
( ~ totalorderedP(cons(hd(esk51_0),nil))
| ~ ssList(cons(hd(esk51_0),nil))
| ~ neq(nil,cons(hd(esk51_0),nil)) ),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
fof(c_0_140,plain,
! [X407] :
( ~ ssItem(X407)
| totalorderedP(cons(X407,nil)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax65])]) ).
cnf(c_0_141,negated_conjecture,
( ~ totalorderedP(cons(hd(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_139,c_0_105]),c_0_47]),c_0_136])]) ).
cnf(c_0_142,plain,
( totalorderedP(cons(X1,nil))
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_140]) ).
fof(c_0_143,plain,
! [X317,X318] :
( ( ~ neq(X317,X318)
| X317 != X318
| ~ ssList(X318)
| ~ ssList(X317) )
& ( X317 = X318
| neq(X317,X318)
| ~ ssList(X318)
| ~ ssList(X317) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
cnf(c_0_144,negated_conjecture,
~ neq(nil,cons(hd(esk51_0),nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_136])]) ).
cnf(c_0_145,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_143]) ).
fof(c_0_146,plain,
! [X321,X322] :
( ~ ssList(X321)
| ~ ssItem(X322)
| cons(X322,X321) != X321 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])]) ).
cnf(c_0_147,negated_conjecture,
( cons(hd(esk51_0),nil) = nil
| ~ ssList(cons(hd(esk51_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_47])]) ).
cnf(c_0_148,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,X1) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_146]) ).
cnf(c_0_149,negated_conjecture,
cons(hd(esk51_0),nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_105]),c_0_47]),c_0_136])]) ).
cnf(c_0_150,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_47]),c_0_136])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC031+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 : n010.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 04:18:06 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 2.07/1.93 % Version : CSE_E---1.7
% 2.07/1.93 % Problem : theBenchmark.p
% 2.07/1.93 % SZS status Theorem for theBenchmark.p
% 2.07/1.93 % SZS output start CNFRefutation
% See solution above
% 2.07/1.94 % Total time : 1.372s
%------------------------------------------------------------------------------