%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC393+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 : n006.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 05:19:28 PM UTC 2026
% Result : Theorem 13.13s 8.44s
% Output : CNFRefutation 13.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 18
% Syntax : Number of formulae : 119 ( 35 unt; 0 def)
% Number of atoms : 426 ( 81 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 528 ( 221 ~; 219 |; 38 &)
% ( 8 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 157 ( 0 sgn 77 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X1,X5)
| memberP(X2,X5) ) )
| ( nil != X3
& nil = X4 )
| ( neq(X4,nil)
& ( ~ neq(X3,nil)
| ~ segmentP(X4,X3) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
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(ax3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ( memberP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(X3,cons(X2,X4)) = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax3) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
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(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
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(ax36,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(app(X2,X3),X1)
<=> ( memberP(X2,X1)
| memberP(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax36) ).
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(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
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(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(ax52,axiom,
! [X1] :
( ssList(X1)
=> ( rearsegP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax52) ).
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(c_0_18,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X1,X5)
| memberP(X2,X5) ) )
| ( nil != X3
& nil = X4 )
| ( neq(X4,nil)
& ( ~ neq(X3,nil)
| ~ segmentP(X4,X3) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_19,negated_conjecture,
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ssItem(esk52_0)
& memberP(esk48_0,esk52_0)
& ~ memberP(esk49_0,esk52_0)
& ( nil = esk50_0
| nil != esk51_0 )
& ( neq(esk50_0,nil)
| ~ neq(esk51_0,nil) )
& ( segmentP(esk51_0,esk50_0)
| ~ neq(esk51_0,nil) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])]) ).
fof(c_0_20,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])])])])]) ).
fof(c_0_21,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_22,plain,
! [X219,X220,X223,X224] :
( ( ssList(esk3_2(X219,X220))
| ~ memberP(X219,X220)
| ~ ssItem(X220)
| ~ ssList(X219) )
& ( ssList(esk4_2(X219,X220))
| ~ memberP(X219,X220)
| ~ ssItem(X220)
| ~ ssList(X219) )
& ( app(esk3_2(X219,X220),cons(X220,esk4_2(X219,X220))) = X219
| ~ memberP(X219,X220)
| ~ ssItem(X220)
| ~ ssList(X219) )
& ( ~ ssList(X223)
| ~ ssList(X224)
| app(X223,cons(X220,X224)) != X219
| memberP(X219,X220)
| ~ ssItem(X220)
| ~ ssList(X219) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])])])]) ).
cnf(c_0_23,negated_conjecture,
memberP(esk48_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( frontsegP(X3,X2)
| ~ ssList(X1)
| app(X2,X1) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
( app(esk3_2(X1,X2),cons(X2,esk4_2(X1,X2))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,negated_conjecture,
memberP(esk50_0,esk52_0),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_31,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_32,plain,
( ssList(esk3_2(X1,X2))
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_33,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_26]),c_0_27]) ).
cnf(c_0_34,negated_conjecture,
app(esk3_2(esk50_0,esk52_0),cons(esk52_0,esk4_2(esk50_0,esk52_0))) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31])]) ).
cnf(c_0_35,negated_conjecture,
ssList(esk3_2(esk50_0,esk52_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_29]),c_0_30]),c_0_31])]) ).
fof(c_0_36,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])])]) ).
cnf(c_0_37,plain,
( ssList(esk4_2(X1,X2))
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_38,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_39,plain,
! [X390] :
( ~ ssList(X390)
| rearsegP(X390,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax51])]) ).
cnf(c_0_40,negated_conjecture,
( frontsegP(esk50_0,esk3_2(esk50_0,esk52_0))
| ~ ssList(cons(esk52_0,esk4_2(esk50_0,esk52_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).
cnf(c_0_41,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_42,negated_conjecture,
ssList(esk4_2(esk50_0,esk52_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_29]),c_0_30]),c_0_31])]) ).
cnf(c_0_43,plain,
( rearsegP(app(X3,X1),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ rearsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_44,plain,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_45,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_46,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_47,negated_conjecture,
frontsegP(esk50_0,esk3_2(esk50_0,esk52_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_31])]) ).
cnf(c_0_48,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_49,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_50,plain,
( rearsegP(app(X1,X2),nil)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).
cnf(c_0_51,negated_conjecture,
app(esk3_2(esk50_0,esk52_0),esk6_2(esk50_0,esk3_2(esk50_0,esk52_0))) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_30]),c_0_35])]) ).
cnf(c_0_52,negated_conjecture,
ssList(esk6_2(esk50_0,esk3_2(esk50_0,esk52_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_47]),c_0_35]),c_0_30])]) ).
fof(c_0_53,plain,
! [X435] :
( ~ ssList(X435)
| app(X435,nil) = X435 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
cnf(c_0_54,plain,
( app(esk7_2(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_55,negated_conjecture,
rearsegP(esk50_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_35]),c_0_52])]) ).
cnf(c_0_56,plain,
( ssList(esk7_2(X1,X2))
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
fof(c_0_57,plain,
! [X359,X360,X361] :
( ( ~ memberP(app(X360,X361),X359)
| memberP(X360,X359)
| memberP(X361,X359)
| ~ ssList(X361)
| ~ ssList(X360)
| ~ ssItem(X359) )
& ( ~ memberP(X360,X359)
| memberP(app(X360,X361),X359)
| ~ ssList(X361)
| ~ ssList(X360)
| ~ ssItem(X359) )
& ( ~ memberP(X361,X359)
| memberP(app(X360,X361),X359)
| ~ ssList(X361)
| ~ ssList(X360)
| ~ ssItem(X359) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax36])])])]) ).
fof(c_0_58,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_59,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_60,negated_conjecture,
app(esk7_2(esk50_0,nil),nil) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_45]),c_0_30])]) ).
cnf(c_0_61,negated_conjecture,
ssList(esk7_2(esk50_0,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_55]),c_0_45]),c_0_30])]) ).
cnf(c_0_62,plain,
( memberP(app(X1,X3),X2)
| ~ memberP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_63,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_64,negated_conjecture,
esk7_2(esk50_0,nil) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61])]) ).
cnf(c_0_65,plain,
( memberP(app(X3,X1),X2)
| ~ memberP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_66,negated_conjecture,
( memberP(app(esk50_0,X1),esk52_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_29]),c_0_30]),c_0_31])]) ).
cnf(c_0_67,plain,
( ssList(app(X1,app(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_63]),c_0_27]) ).
cnf(c_0_68,negated_conjecture,
app(esk50_0,nil) = esk50_0,
inference(rw,[status(thm)],[c_0_60,c_0_64]) ).
fof(c_0_69,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
cnf(c_0_70,negated_conjecture,
( memberP(app(X1,app(esk50_0,X2)),esk52_0)
| ~ ssList(app(esk50_0,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_31])]) ).
cnf(c_0_71,negated_conjecture,
( ssList(app(X1,esk50_0))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_45]),c_0_30])]) ).
fof(c_0_72,plain,
! [X343] :
( ~ ssList(X343)
| app(nil,X343) = X343 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
fof(c_0_73,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_74,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_75,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_76,plain,
! [X365] :
( ~ ssItem(X365)
| ~ memberP(nil,X365) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_69])]) ).
cnf(c_0_77,negated_conjecture,
( memberP(app(X1,app(esk50_0,esk50_0)),esk52_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_30])]) ).
cnf(c_0_78,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_79,negated_conjecture,
( memberP(app(X1,esk50_0),esk52_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_29]),c_0_30]),c_0_31])]) ).
fof(c_0_80,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_81,negated_conjecture,
( segmentP(esk51_0,esk50_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_82,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_83,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_74,c_0_75]) ).
fof(c_0_84,plain,
! [X391] :
( ( ~ rearsegP(nil,X391)
| nil = X391
| ~ ssList(X391) )
& ( nil != X391
| rearsegP(nil,X391)
| ~ ssList(X391) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax52])])]) ).
cnf(c_0_85,plain,
( memberP(X1,X3)
| memberP(X2,X3)
| ~ memberP(app(X1,X2),X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_86,plain,
( app(esk7_2(X1,nil),nil) = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_44]),c_0_45])]) ).
cnf(c_0_87,plain,
( ssList(esk7_2(X1,nil))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_44]),c_0_45])]) ).
cnf(c_0_88,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_89,negated_conjecture,
( memberP(app(esk50_0,esk50_0),esk52_0)
| ~ ssList(app(esk50_0,esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_45])]) ).
cnf(c_0_90,negated_conjecture,
( memberP(app(app(X1,esk50_0),X2),esk52_0)
| ~ ssList(app(X1,esk50_0))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_79]),c_0_31])]) ).
cnf(c_0_91,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_80]) ).
cnf(c_0_92,negated_conjecture,
( esk51_0 = nil
| segmentP(esk51_0,esk50_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_45]),c_0_83])]) ).
cnf(c_0_93,negated_conjecture,
~ memberP(esk49_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_94,plain,
( ssList(esk8_2(X1,X2))
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_95,plain,
( ssList(esk9_2(X1,X2))
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_96,plain,
( rearsegP(nil,X1)
| nil != X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_97,plain,
( memberP(esk7_2(X1,nil),X2)
| ~ memberP(X1,X2)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_45])]),c_0_87]),c_0_88]) ).
cnf(c_0_98,negated_conjecture,
memberP(app(esk50_0,esk50_0),esk52_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_27]),c_0_30])]) ).
cnf(c_0_99,negated_conjecture,
( memberP(app(app(X1,esk50_0),X2),esk52_0)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_27]),c_0_30])]) ).
cnf(c_0_100,negated_conjecture,
( app(app(esk8_2(esk51_0,esk50_0),esk50_0),esk9_2(esk51_0,esk50_0)) = esk51_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_30]),c_0_83])]) ).
cnf(c_0_101,negated_conjecture,
~ memberP(esk51_0,esk52_0),
inference(rw,[status(thm)],[c_0_93,c_0_75]) ).
cnf(c_0_102,negated_conjecture,
( esk51_0 = nil
| ssList(esk8_2(esk51_0,esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_92]),c_0_30]),c_0_83])]) ).
cnf(c_0_103,negated_conjecture,
( esk51_0 = nil
| ssList(esk9_2(esk51_0,esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_92]),c_0_30]),c_0_83])]) ).
fof(c_0_104,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_105,plain,
rearsegP(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_96]),c_0_45])]) ).
cnf(c_0_106,negated_conjecture,
( memberP(esk7_2(app(esk50_0,esk50_0),nil),esk52_0)
| ~ ssList(app(esk50_0,esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_31])]) ).
cnf(c_0_107,negated_conjecture,
( nil = esk50_0
| nil != esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_108,negated_conjecture,
esk51_0 = nil,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_101]),c_0_102]),c_0_103]) ).
cnf(c_0_109,plain,
( nil = app(X2,X1)
| nil != X1
| nil != X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_110,plain,
( nil = X1
| nil != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_111,plain,
app(esk7_2(nil,nil),nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_105]),c_0_45])]) ).
cnf(c_0_112,plain,
ssList(esk7_2(nil,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_105]),c_0_45])]) ).
cnf(c_0_113,negated_conjecture,
memberP(esk7_2(app(esk50_0,esk50_0),nil),esk52_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_27]),c_0_30])]) ).
cnf(c_0_114,negated_conjecture,
esk50_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_108])]) ).
cnf(c_0_115,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_109])]),c_0_45])]) ).
cnf(c_0_116,plain,
esk7_2(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_45]),c_0_112])]) ).
cnf(c_0_117,negated_conjecture,
~ memberP(nil,esk52_0),
inference(rw,[status(thm)],[c_0_101,c_0_108]) ).
cnf(c_0_118,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_114]),c_0_114]),c_0_115]),c_0_116]),c_0_117]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC393+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 : n006.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 04:48:16 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 13.13/8.44 % Version : CSE_E---1.7
% 13.13/8.44 % Problem : theBenchmark.p
% 13.13/8.44 % SZS status Theorem for theBenchmark.p
% 13.13/8.44 % SZS output start CNFRefutation
% See solution above
% 13.13/8.49 % Total time : 6.382s
%------------------------------------------------------------------------------