%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC058+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 : n015.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 05:18:05 PM UTC 2026
% Result : Theorem 1.49s 1.77s
% Output : CNFRefutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 95 ( 12 unt; 0 def)
% Number of atoms : 351 ( 95 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 427 ( 171 ~; 185 |; 37 &)
% ( 4 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 112 ( 0 sgn 57 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X2,X5)
& segmentP(X1,X5) ) ) )
| ( ( nil != X4
| nil != X3 )
& ( ~ neq(X3,nil)
| ~ rearsegP(X4,X3) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
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(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
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(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(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(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax55) ).
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(ax57,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax57) ).
fof(c_0_15,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X2,X5)
& segmentP(X1,X5) ) ) )
| ( ( nil != X4
| nil != X3 )
& ( ~ neq(X3,nil)
| ~ rearsegP(X4,X3) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_16,negated_conjecture,
! [X463] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ( neq(esk49_0,nil)
| nil = esk49_0 )
& ( ~ ssList(X463)
| ~ neq(X463,nil)
| ~ segmentP(esk49_0,X463)
| ~ segmentP(esk48_0,X463)
| nil = esk49_0 )
& ( neq(esk49_0,nil)
| nil != esk48_0 )
& ( ~ ssList(X463)
| ~ neq(X463,nil)
| ~ segmentP(esk49_0,X463)
| ~ segmentP(esk48_0,X463)
| nil != esk48_0 )
& ( neq(esk50_0,nil)
| nil = esk51_0 )
& ( rearsegP(esk51_0,esk50_0)
| nil = esk51_0 )
& ( neq(esk50_0,nil)
| nil = esk50_0 )
& ( rearsegP(esk51_0,esk50_0)
| nil = esk50_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_15])])])])]) ).
fof(c_0_17,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_18,plain,
! [X390] :
( ~ ssList(X390)
| rearsegP(X390,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax51])]) ).
fof(c_0_19,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_20,negated_conjecture,
( rearsegP(esk51_0,esk50_0)
| nil = esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
( rearsegP(app(X3,X1),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ rearsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_27,plain,
( app(esk7_2(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,negated_conjecture,
( esk49_0 = nil
| rearsegP(esk49_0,esk50_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_21]) ).
cnf(c_0_29,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_31,plain,
( ssList(esk7_2(X1,X2))
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_32,plain,
( rearsegP(app(X1,X2),nil)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_33,negated_conjecture,
( app(esk7_2(esk49_0,esk50_0),esk50_0) = esk49_0
| esk49_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30])]) ).
cnf(c_0_34,negated_conjecture,
( esk49_0 = nil
| ssList(esk7_2(esk49_0,esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_28]),c_0_29]),c_0_30])]) ).
fof(c_0_35,plain,
! [X435] :
( ~ ssList(X435)
| app(X435,nil) = X435 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
fof(c_0_36,plain,
! [X372,X373,X374] :
( ~ ssList(X372)
| ~ ssList(X373)
| ~ ssList(X374)
| ~ frontsegP(X372,X373)
| frontsegP(app(X372,X374),X373) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax43])])]) ).
fof(c_0_37,plain,
! [X379] :
( ~ ssList(X379)
| frontsegP(X379,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])]) ).
cnf(c_0_38,negated_conjecture,
( esk49_0 = nil
| rearsegP(esk49_0,nil) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_29])]),c_0_34]) ).
cnf(c_0_39,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_40,plain,
( app(esk7_2(X1,nil),nil) = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_25]),c_0_26])]) ).
cnf(c_0_41,plain,
( ssList(esk7_2(X1,nil))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_25]),c_0_26])]) ).
fof(c_0_42,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_43,plain,
( frontsegP(app(X1,X3),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_44,plain,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_45,negated_conjecture,
( app(esk7_2(esk49_0,nil),nil) = esk49_0
| esk49_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_38]),c_0_26]),c_0_30])]) ).
cnf(c_0_46,plain,
( esk7_2(X1,nil) = X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
fof(c_0_47,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_48,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_42]) ).
fof(c_0_49,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])])]) ).
cnf(c_0_50,negated_conjecture,
( rearsegP(esk51_0,esk50_0)
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_51,plain,
( frontsegP(app(X1,X2),nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_26])]) ).
cnf(c_0_52,negated_conjecture,
( app(esk49_0,nil) = esk49_0
| esk49_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_30])]) ).
fof(c_0_53,plain,
! [X343] :
( ~ ssList(X343)
| app(nil,X343) = X343 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
cnf(c_0_54,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_55,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_56,negated_conjecture,
( nil = esk49_0
| ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk49_0,X1)
| ~ segmentP(esk48_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_57,plain,
! [X397] :
( ~ ssList(X397)
| segmentP(X397,X397) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])]) ).
cnf(c_0_58,negated_conjecture,
( neq(esk50_0,nil)
| nil = esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_59,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_48]) ).
cnf(c_0_60,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_61,negated_conjecture,
( esk50_0 = nil
| rearsegP(esk49_0,esk50_0) ),
inference(rw,[status(thm)],[c_0_50,c_0_21]) ).
fof(c_0_62,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_63,negated_conjecture,
( esk49_0 = nil
| frontsegP(esk49_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_26]),c_0_30])]) ).
cnf(c_0_64,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_65,plain,
( app(nil,esk6_2(X1,nil)) = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_44]),c_0_26])]) ).
cnf(c_0_66,plain,
( ssList(esk6_2(X1,nil))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_44]),c_0_26])]) ).
cnf(c_0_67,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk49_0,X1)
| ~ segmentP(esk48_0,X1)
| nil != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_68,plain,
! [X402] :
( ~ ssList(X402)
| segmentP(X402,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax57])]) ).
cnf(c_0_69,negated_conjecture,
( esk49_0 = nil
| ~ segmentP(esk50_0,X1)
| ~ segmentP(esk49_0,X1)
| ~ ssList(X1)
| ~ neq(X1,nil) ),
inference(rw,[status(thm)],[c_0_56,c_0_23]) ).
cnf(c_0_70,plain,
( segmentP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_71,negated_conjecture,
( esk49_0 = nil
| neq(esk50_0,nil) ),
inference(rw,[status(thm)],[c_0_58,c_0_21]) ).
cnf(c_0_72,plain,
( segmentP(app(X1,X2),X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_39]),c_0_26])]),c_0_60]) ).
cnf(c_0_73,negated_conjecture,
( app(esk7_2(esk49_0,esk50_0),esk50_0) = esk49_0
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_61]),c_0_29]),c_0_30])]) ).
cnf(c_0_74,negated_conjecture,
( esk50_0 = nil
| ssList(esk7_2(esk49_0,esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_61]),c_0_29]),c_0_30])]) ).
cnf(c_0_75,plain,
( nil = X1
| nil != app(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_76,negated_conjecture,
( app(nil,esk6_2(esk49_0,nil)) = esk49_0
| esk49_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_63]),c_0_30]),c_0_26])]) ).
cnf(c_0_77,plain,
( esk6_2(X1,nil) = X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]) ).
cnf(c_0_78,negated_conjecture,
( esk50_0 != nil
| ~ segmentP(esk50_0,X1)
| ~ segmentP(esk49_0,X1)
| ~ ssList(X1)
| ~ neq(X1,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_23]),c_0_23]) ).
cnf(c_0_79,plain,
( segmentP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_80,negated_conjecture,
( neq(esk49_0,nil)
| nil != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_81,negated_conjecture,
( esk49_0 = nil
| ~ segmentP(esk49_0,esk50_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_29])]),c_0_71]) ).
cnf(c_0_82,negated_conjecture,
( esk50_0 = nil
| segmentP(esk49_0,esk50_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_29])]),c_0_74]) ).
cnf(c_0_83,negated_conjecture,
( esk50_0 = nil
| esk49_0 != nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_73]),c_0_29])]),c_0_74]) ).
cnf(c_0_84,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_59,c_0_64]),c_0_26])]),c_0_60]) ).
cnf(c_0_85,negated_conjecture,
( app(nil,esk49_0) = esk49_0
| esk49_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_30])]) ).
cnf(c_0_86,negated_conjecture,
( esk50_0 != nil
| ~ segmentP(esk49_0,nil)
| ~ neq(nil,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_26]),c_0_29])]) ).
cnf(c_0_87,negated_conjecture,
( neq(esk49_0,nil)
| esk50_0 != nil ),
inference(rw,[status(thm)],[c_0_80,c_0_23]) ).
cnf(c_0_88,negated_conjecture,
esk50_0 = nil,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83]) ).
cnf(c_0_89,negated_conjecture,
( esk49_0 = nil
| segmentP(esk49_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_26]),c_0_30])]) ).
cnf(c_0_90,negated_conjecture,
( esk50_0 != nil
| ~ neq(nil,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_79]),c_0_30])]) ).
cnf(c_0_91,negated_conjecture,
neq(esk49_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_88])]) ).
cnf(c_0_92,negated_conjecture,
esk49_0 = nil,
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_88]),c_0_89]) ).
cnf(c_0_93,negated_conjecture,
~ neq(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_88])]) ).
cnf(c_0_94,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_92]),c_0_93]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC058+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n015.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 04:20:17 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.49/1.77 % Version : CSE_E---1.7
% 1.49/1.77 % Problem : theBenchmark.p
% 1.49/1.77 % SZS status Theorem for theBenchmark.p
% 1.49/1.77 % SZS output start CNFRefutation
% See solution above
% 1.49/1.78 % Total time : 1.372s
%------------------------------------------------------------------------------