%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC005+1 : TPTP v9.2.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n023.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 05:17:51 PM UTC 2026
% Result : Theorem 3.69s 3.16s
% Output : CNFRefutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 25
% Syntax : Number of formulae : 144 ( 13 unt; 0 def)
% Number of atoms : 568 ( 190 equ)
% Maximal formula atoms : 34 ( 3 avg)
% Number of connectives : 715 ( 291 ~; 311 |; 48 &)
% ( 5 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 222 ( 0 sgn 106 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X5,X6),X7) = X2
& app(X5,X7) = X1
& neq(X6,nil) ) ) )
| ? [X8] :
( ssList(X8)
& X3 != X8
& tl(X4) = X8
& neq(nil,X4) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(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/sandbox/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/sandbox/benchmark/Axioms/SWC001+0.ax',ax20) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
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/sandbox/benchmark/Axioms/SWC001+0.ax',ax44) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(ax42,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax42) ).
fof(ax80,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X2,X3) = app(X2,X1)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax80) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(ax6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X3,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax6) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax81,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax81) ).
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/sandbox/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax23) ).
fof(ax27,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax27) ).
fof(ax86,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax86) ).
fof(ax18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(c_0_25,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X5,X6),X7) = X2
& app(X5,X7) = X1
& neq(X6,nil) ) ) )
| ? [X8] :
( ssList(X8)
& X3 != X8
& tl(X4) = X8
& neq(nil,X4) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_26,negated_conjecture,
! [X468,X469,X470,X471] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ( neq(esk49_0,nil)
| neq(esk49_0,nil) )
& ( ~ neq(esk51_0,nil)
| neq(esk49_0,nil) )
& ( neq(esk49_0,nil)
| ~ ssList(X468)
| ~ ssList(X469)
| ~ ssList(X470)
| app(app(X468,X469),X470) != esk49_0
| app(X468,X470) != esk48_0
| ~ neq(X469,nil) )
& ( ~ neq(esk51_0,nil)
| ~ ssList(X468)
| ~ ssList(X469)
| ~ ssList(X470)
| app(app(X468,X469),X470) != esk49_0
| app(X468,X470) != esk48_0
| ~ neq(X469,nil) )
& ( neq(esk49_0,nil)
| ~ ssList(X471)
| esk50_0 = X471
| tl(esk51_0) != X471
| ~ neq(nil,esk51_0) )
& ( ~ neq(esk51_0,nil)
| ~ ssList(X471)
| esk50_0 = X471
| tl(esk51_0) != X471
| ~ neq(nil,esk51_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_25])])])])]) ).
cnf(c_0_27,negated_conjecture,
( neq(esk49_0,nil)
| neq(esk49_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_28,negated_conjecture,
neq(esk49_0,nil),
inference(cn,[status(thm)],[c_0_27]) ).
cnf(c_0_29,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_30,negated_conjecture,
( esk50_0 = X1
| ~ neq(esk51_0,nil)
| ~ ssList(X1)
| tl(esk51_0) != X1
| ~ neq(nil,esk51_0) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,negated_conjecture,
neq(esk51_0,nil),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_33,plain,
! [X340] :
( ~ ssList(X340)
| nil = X340
| ssList(tl(X340)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).
cnf(c_0_34,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,negated_conjecture,
( tl(esk51_0) = esk48_0
| ~ ssList(tl(esk51_0))
| ~ neq(nil,esk51_0) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_32])])]) ).
cnf(c_0_36,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_37,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_34,c_0_29]) ).
fof(c_0_38,plain,
! [X322,X323] :
( ( ~ neq(X322,X323)
| X322 != X323
| ~ ssList(X323)
| ~ ssList(X322) )
& ( X322 = X323
| neq(X322,X323)
| ~ ssList(X323)
| ~ ssList(X322) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
fof(c_0_39,plain,
! [X328,X329,X330,X331] :
( ( X330 = X331
| cons(X330,X328) != cons(X331,X329)
| ~ ssItem(X331)
| ~ ssItem(X330)
| ~ ssList(X329)
| ~ ssList(X328) )
& ( X329 = X328
| cons(X330,X328) != cons(X331,X329)
| ~ ssItem(X331)
| ~ ssItem(X330)
| ~ ssList(X329)
| ~ ssList(X328) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax19])])])]) ).
fof(c_0_40,plain,
! [X332] :
( ( ssList(esk44_1(X332))
| nil = X332
| ~ ssList(X332) )
& ( ssItem(esk45_1(X332))
| nil = X332
| ~ ssList(X332) )
& ( cons(esk45_1(X332),esk44_1(X332)) = X332
| nil = X332
| ~ ssList(X332) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])]) ).
fof(c_0_41,plain,
! [X324,X325] :
( ~ ssList(X324)
| ~ ssItem(X325)
| ssList(cons(X325,X324)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
fof(c_0_42,plain,
! [X335,X336] :
( ~ ssList(X335)
| ~ ssItem(X336)
| nil != cons(X336,X335) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])]) ).
fof(c_0_43,plain,
! [X426] :
( ~ ssList(X426)
| nil = X426
| cons(hd(X426),tl(X426)) = X426 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).
cnf(c_0_44,negated_conjecture,
( tl(esk51_0) = esk48_0
| esk51_0 = nil
| ~ neq(nil,esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).
cnf(c_0_45,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_47,plain,
( X1 = X2
| cons(X3,X2) != cons(X4,X1)
| ~ ssItem(X4)
| ~ ssItem(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_48,plain,
( cons(esk45_1(X1),esk44_1(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_49,plain,
( ssItem(esk45_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_50,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_51,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| nil != cons(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_52,plain,
( nil = X1
| cons(hd(X1),tl(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_53,negated_conjecture,
( tl(esk51_0) = esk48_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_37]),c_0_46])]) ).
cnf(c_0_54,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_47,c_0_48])]),c_0_49]),c_0_50]),c_0_51]) ).
cnf(c_0_55,negated_conjecture,
( cons(hd(esk51_0),esk48_0) = esk51_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_37])]) ).
cnf(c_0_56,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_57,plain,
! [X380,X381,X382,X383] :
( ( X380 = X381
| ~ frontsegP(cons(X380,X382),cons(X381,X383))
| ~ ssList(X383)
| ~ ssList(X382)
| ~ ssItem(X381)
| ~ ssItem(X380) )
& ( frontsegP(X382,X383)
| ~ frontsegP(cons(X380,X382),cons(X381,X383))
| ~ ssList(X383)
| ~ ssList(X382)
| ~ ssItem(X381)
| ~ ssItem(X380) )
& ( X380 != X381
| ~ frontsegP(X382,X383)
| frontsegP(cons(X380,X382),cons(X381,X383))
| ~ ssList(X383)
| ~ ssList(X382)
| ~ ssItem(X381)
| ~ ssItem(X380) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax44])])])]) ).
cnf(c_0_58,negated_conjecture,
( esk44_1(esk51_0) = esk48_0
| esk51_0 = nil
| ~ ssList(esk44_1(esk51_0))
| ~ ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56])]) ).
cnf(c_0_59,plain,
( ssList(esk44_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_60,plain,
! [X337] :
( ~ ssList(X337)
| nil = X337
| ssItem(hd(X337)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).
cnf(c_0_61,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_57]) ).
fof(c_0_62,plain,
! [X376] :
( ~ ssList(X376)
| frontsegP(X376,X376) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax42])]) ).
cnf(c_0_63,negated_conjecture,
( esk44_1(esk51_0) = esk48_0
| esk51_0 = nil
| ~ ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_37])]) ).
cnf(c_0_64,plain,
( nil = X1
| ssItem(hd(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_65,plain,
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(er,[status(thm)],[c_0_61]) ).
cnf(c_0_66,plain,
( frontsegP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_67,negated_conjecture,
( esk44_1(esk51_0) = esk48_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_37])]) ).
cnf(c_0_68,plain,
( frontsegP(cons(X1,X2),cons(X1,X2))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_69,negated_conjecture,
( cons(esk45_1(esk51_0),esk48_0) = esk51_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_67]),c_0_37])]) ).
fof(c_0_70,plain,
! [X430,X431,X432] :
( ~ ssList(X430)
| ~ ssList(X431)
| ~ ssList(X432)
| app(X431,X432) != app(X431,X430)
| X432 = X430 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])]) ).
fof(c_0_71,plain,
! [X440] :
( ~ ssList(X440)
| app(X440,nil) = X440 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
fof(c_0_72,plain,
! [X233,X234,X236] :
( ( ssList(esk6_2(X233,X234))
| ~ frontsegP(X233,X234)
| ~ ssList(X234)
| ~ ssList(X233) )
& ( app(X234,esk6_2(X233,X234)) = X233
| ~ frontsegP(X233,X234)
| ~ ssList(X234)
| ~ ssList(X233) )
& ( ~ ssList(X236)
| app(X234,X236) != X233
| frontsegP(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)],[ax5])])])])]) ).
fof(c_0_73,plain,
! [X237,X238,X240] :
( ( ssList(esk7_2(X237,X238))
| ~ rearsegP(X237,X238)
| ~ ssList(X238)
| ~ ssList(X237) )
& ( app(esk7_2(X237,X238),X238) = X237
| ~ rearsegP(X237,X238)
| ~ ssList(X238)
| ~ ssList(X237) )
& ( ~ ssList(X240)
| app(X240,X238) != X237
| rearsegP(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)],[ax6])])])])]) ).
fof(c_0_74,plain,
! [X343,X344] :
( ~ ssList(X343)
| ~ ssList(X344)
| ssList(app(X343,X344)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
cnf(c_0_75,negated_conjecture,
( esk51_0 = nil
| frontsegP(esk51_0,esk51_0)
| ~ ssItem(esk45_1(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_56])]) ).
cnf(c_0_76,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X2,X3) != app(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_77,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_78,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_79,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_80,plain,
( rearsegP(X3,X2)
| ~ ssList(X1)
| app(X1,X2) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_81,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
fof(c_0_82,plain,
! [X433,X434] :
( ~ ssList(X433)
| ~ ssItem(X434)
| cons(X434,X433) = app(cons(X434,nil),X433) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
fof(c_0_83,plain,
! [X435,X436,X437] :
( ~ ssList(X435)
| ~ ssList(X436)
| ~ ssList(X437)
| app(app(X435,X436),X437) = app(X435,app(X436,X437)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).
fof(c_0_84,plain,
! [X438,X439] :
( ( nil = X439
| nil != app(X438,X439)
| ~ ssList(X439)
| ~ ssList(X438) )
& ( nil = X438
| nil != app(X438,X439)
| ~ ssList(X439)
| ~ ssList(X438) )
& ( nil != X439
| nil != X438
| nil = app(X438,X439)
| ~ ssList(X439)
| ~ ssList(X438) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
fof(c_0_85,plain,
! [X338,X339] :
( ~ ssList(X338)
| ~ ssItem(X339)
| hd(cons(X339,X338)) = X339 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])]) ).
cnf(c_0_86,negated_conjecture,
( esk51_0 = nil
| frontsegP(esk51_0,esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_49]),c_0_37])]) ).
cnf(c_0_87,plain,
( X1 = nil
| app(X2,X1) != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_46])]) ).
cnf(c_0_88,plain,
( app(X1,esk6_2(X1,X1)) = X1
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_66]) ).
cnf(c_0_89,plain,
( ssList(esk6_2(X1,X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_79,c_0_66]) ).
cnf(c_0_90,plain,
( rearsegP(app(X1,X2),X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_80]),c_0_81]) ).
cnf(c_0_91,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
fof(c_0_92,plain,
! [X345,X346,X347] :
( ~ ssList(X345)
| ~ ssList(X346)
| ~ ssItem(X347)
| cons(X347,app(X346,X345)) = app(cons(X347,X346),X345) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])]) ).
cnf(c_0_93,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_94,plain,
( nil = app(X2,X1)
| nil != X1
| nil != X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_95,plain,
( hd(cons(X2,X1)) = X2
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
fof(c_0_96,plain,
! [X443,X444] :
( ~ ssList(X443)
| ~ ssList(X444)
| nil = X443
| tl(app(X443,X444)) = app(tl(X443),X444) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax86])])]) ).
cnf(c_0_97,negated_conjecture,
( app(esk51_0,esk6_2(esk51_0,esk51_0)) = esk51_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_86]),c_0_37])]) ).
cnf(c_0_98,plain,
( esk6_2(X1,X1) = nil
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89]) ).
cnf(c_0_99,plain,
( rearsegP(cons(X1,X2),X2)
| ~ ssList(cons(X1,nil))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
fof(c_0_100,plain,
! [X326,X327] :
( ~ ssList(X326)
| ~ ssItem(X327)
| cons(X327,X326) != X326 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])]) ).
cnf(c_0_101,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_102,plain,
( ssList(app(X1,app(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_93]),c_0_81]) ).
cnf(c_0_103,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_94])]),c_0_46])]) ).
cnf(c_0_104,plain,
( cons(X1,tl(cons(X1,X2))) = cons(X1,X2)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_95]),c_0_50]),c_0_51]) ).
cnf(c_0_105,plain,
( nil = X1
| tl(app(X1,X2)) = app(tl(X1),X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_106,plain,
( nil = X1
| nil != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_107,negated_conjecture,
( app(esk51_0,nil) = esk51_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_37])]) ).
cnf(c_0_108,negated_conjecture,
( ~ neq(esk51_0,nil)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X1,X2),X3) != esk49_0
| app(X1,X3) != esk48_0
| ~ neq(X2,nil) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_109,plain,
! [X348] :
( ~ ssList(X348)
| app(nil,X348) = X348 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
cnf(c_0_110,plain,
( rearsegP(cons(X1,X2),X2)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_50]),c_0_46])]) ).
cnf(c_0_111,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,X1) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_112,plain,
( cons(X1,app(X2,nil)) = cons(X1,X2)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_101]),c_0_46])]),c_0_50]) ).
cnf(c_0_113,plain,
( ssList(app(X1,nil))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_46])]) ).
cnf(c_0_114,negated_conjecture,
( cons(esk45_1(esk51_0),tl(esk51_0)) = esk51_0
| esk51_0 = nil
| ~ ssItem(esk45_1(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_69]),c_0_56])]) ).
cnf(c_0_115,plain,
( nil = X1
| ssList(app(tl(X1),X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_105]),c_0_81]),c_0_106]) ).
cnf(c_0_116,negated_conjecture,
( app(tl(esk51_0),nil) = tl(esk51_0)
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_107]),c_0_46]),c_0_37])]) ).
cnf(c_0_117,negated_conjecture,
( app(app(X1,X2),X3) != esk51_0
| app(X1,X3) != esk48_0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(X2,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_108,c_0_29]),c_0_32])]) ).
cnf(c_0_118,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_119,negated_conjecture,
( esk51_0 = nil
| rearsegP(esk51_0,esk48_0)
| ~ ssItem(esk45_1(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_69]),c_0_56])]) ).
cnf(c_0_120,plain,
( cons(X1,X2) != app(X2,nil)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_113]) ).
cnf(c_0_121,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_114,c_0_49]),c_0_37])]) ).
cnf(c_0_122,negated_conjecture,
( esk51_0 = nil
| ssList(tl(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_46]),c_0_37])]) ).
cnf(c_0_123,negated_conjecture,
( app(app(nil,X1),esk48_0) != esk51_0
| ~ ssList(X1)
| ~ neq(X1,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_46])])]),c_0_56])]) ).
cnf(c_0_124,plain,
( app(esk7_2(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_125,negated_conjecture,
( esk51_0 = nil
| rearsegP(esk51_0,esk48_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_49]),c_0_37])]) ).
cnf(c_0_126,plain,
( ssList(esk7_2(X1,X2))
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_127,negated_conjecture,
( esk51_0 = nil
| app(tl(esk51_0),nil) != esk51_0
| ~ ssItem(esk45_1(esk51_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_122]) ).
cnf(c_0_128,negated_conjecture,
( app(X1,esk48_0) != esk51_0
| ~ ssList(X1)
| ~ neq(X1,nil) ),
inference(spm,[status(thm)],[c_0_123,c_0_118]) ).
cnf(c_0_129,negated_conjecture,
( app(esk7_2(esk51_0,esk48_0),esk48_0) = esk51_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_56]),c_0_37])]) ).
cnf(c_0_130,negated_conjecture,
( esk51_0 = nil
| ssList(esk7_2(esk51_0,esk48_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_125]),c_0_56]),c_0_37])]) ).
cnf(c_0_131,negated_conjecture,
( esk51_0 = nil
| app(tl(esk51_0),nil) != esk51_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_49]),c_0_37])]) ).
cnf(c_0_132,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_93]),c_0_46])]),c_0_81]) ).
cnf(c_0_133,plain,
( app(nil,app(X1,X2)) = app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_118]),c_0_46])]) ).
cnf(c_0_134,negated_conjecture,
( esk51_0 = nil
| ~ neq(esk7_2(esk51_0,esk48_0),nil) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_130]) ).
cnf(c_0_135,negated_conjecture,
( esk51_0 = nil
| app(esk48_0,nil) != esk51_0 ),
inference(spm,[status(thm)],[c_0_131,c_0_53]) ).
cnf(c_0_136,plain,
( app(X1,nil) = app(nil,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_46])]) ).
cnf(c_0_137,negated_conjecture,
( esk7_2(esk51_0,esk48_0) = nil
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_45]),c_0_46])]),c_0_130]) ).
cnf(c_0_138,negated_conjecture,
( esk51_0 = nil
| app(nil,esk48_0) != esk51_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_56])]) ).
cnf(c_0_139,plain,
( ~ neq(X1,X2)
| X1 != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_140,negated_conjecture,
esk51_0 = nil,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_137]),c_0_138]) ).
cnf(c_0_141,plain,
( ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(er,[status(thm)],[c_0_139]) ).
cnf(c_0_142,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[c_0_32,c_0_140]) ).
cnf(c_0_143,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_46])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC005+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n023.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 04:14:53 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 3.69/3.16 % Version : CSE_E---1.7
% 3.69/3.16 % Problem : theBenchmark.p
% 3.69/3.16 % SZS status Theorem for theBenchmark.p
% 3.69/3.16 % SZS output start CNFRefutation
% See solution above
% 3.69/3.17 % Total time : 2.373s
%------------------------------------------------------------------------------