%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC409+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:44:18 PM UTC 2026
% Result : Theorem 3.89s 1.21s
% Output : CNFRefutation 3.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 22
% Syntax : Number of formulae : 154 ( 37 unt; 0 def)
% Number of atoms : 533 ( 170 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 625 ( 246 ~; 261 |; 38 &)
% ( 6 <=>; 74 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 203 ( 0 sgn 107 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( nil = X4
& nil != X3 )
| ! [X7] :
( ssItem(X7)
=> ( memberP(X1,X7)
| ~ memberP(X2,X7) ) )
| ? [X5] :
( ? [X6] :
( app(cons(X5,nil),X6) = X4
& app(X6,cons(X5,nil)) != X3
& ssList(X6) )
& ssItem(X5) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax36,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(app(X2,X3),X1)
<=> ( memberP(X3,X1)
| memberP(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax36) ).
fof(ax46,axiom,
! [X1] :
( ssList(X1)
=> ( frontsegP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax46) ).
fof(ax5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( app(X2,X3) = X1
& ssList(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ( memberP(X1,X2)
<=> ? [X3] :
( ? [X4] :
( app(X3,cons(X2,X4)) = X1
& ssList(X4) )
& ssList(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax3) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X1
& nil = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
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(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax85,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax85) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
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(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(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax24) ).
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(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
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(ax37,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(cons(X2,X3),X1)
<=> ( memberP(X3,X1)
| X1 = X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(c_0_22,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( nil = X4
& nil != X3 )
| ! [X7] :
( ssItem(X7)
=> ( memberP(X1,X7)
| ~ memberP(X2,X7) ) )
| ? [X5] :
( ? [X6] :
( app(cons(X5,nil),X6) = X4
& app(X6,cons(X5,nil)) != X3
& ssList(X6) )
& ssItem(X5) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_23,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( nil = X4
& nil != X3 )
| ! [X7] :
( ssItem(X7)
=> ( memberP(X1,X7)
| ~ memberP(X2,X7) ) )
| ? [X5] :
( ? [X6] :
( app(cons(X5,nil),X6) = X4
& app(X6,cons(X5,nil)) != X3
& ssList(X6) )
& ssItem(X5) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_24,negated_conjecture,
! [X256,X257] :
( ( nil != esk51_0
| nil = esk50_0 )
& ~ memberP(esk48_0,esk52_0)
& memberP(esk49_0,esk52_0)
& ssItem(esk52_0)
& ( app(cons(X256,nil),X257) != esk51_0
| app(X257,cons(X256,nil)) = esk50_0
| ~ ssList(X257)
| ~ ssItem(X256) )
& esk48_0 = esk50_0
& esk49_0 = esk51_0
& ssList(esk51_0)
& ssList(esk50_0)
& ssList(esk49_0)
& ssList(esk48_0) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])])]) ).
fof(c_0_25,plain,
! [X152,X153,X154] :
( ( ~ ssItem(X152)
| ~ ssList(X153)
| ~ ssList(X154)
| memberP(app(X153,X154),X152)
| ~ memberP(X154,X152) )
& ( ~ ssItem(X152)
| ~ ssList(X153)
| ~ ssList(X154)
| memberP(app(X153,X154),X152)
| ~ memberP(X153,X152) )
& ( ~ ssItem(X152)
| ~ ssList(X153)
| ~ ssList(X154)
| memberP(X154,X152)
| memberP(X153,X152)
| ~ memberP(app(X153,X154),X152) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax36])])])])]) ).
cnf(c_0_26,negated_conjecture,
memberP(esk49_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_27,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_29,plain,
! [X173] :
( ( ~ ssList(X173)
| frontsegP(nil,X173)
| nil != X173 )
& ( ~ ssList(X173)
| nil = X173
| ~ frontsegP(nil,X173) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax46])])])]) ).
cnf(c_0_30,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ memberP(X1,X2)
| memberP(app(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,negated_conjecture,
memberP(esk51_0,esk52_0),
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_28,c_0_27]) ).
cnf(c_0_33,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_34,plain,
! [X21,X22,X24] :
( ( ~ ssList(X21)
| ~ ssList(X22)
| frontsegP(X21,X22)
| app(X22,X24) != X21
| ~ ssList(X24) )
& ( ~ ssList(X21)
| ~ ssList(X22)
| ~ frontsegP(X21,X22)
| app(X22,esk6_2(X21,X22)) = X21 )
& ( ~ ssList(X21)
| ~ ssList(X22)
| ~ frontsegP(X21,X22)
| ssList(esk6_2(X21,X22)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax5])])])])])]) ).
cnf(c_0_35,plain,
( ~ ssList(X1)
| nil != X1
| frontsegP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_37,plain,
! [X131,X132] :
( ssList(app(X131,X132))
| ~ ssList(X132)
| ~ ssList(X131) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
fof(c_0_38,plain,
! [X12,X13,X16,X17] :
( ( ~ ssList(X12)
| ~ ssItem(X13)
| memberP(X12,X13)
| app(X16,cons(X13,X17)) != X12
| ~ ssList(X17)
| ~ ssList(X16) )
& ( ~ ssList(X12)
| ~ ssItem(X13)
| ~ memberP(X12,X13)
| app(esk3_2(X12,X13),cons(X13,esk4_2(X12,X13))) = X12 )
& ( ~ ssList(X12)
| ~ ssItem(X13)
| ~ memberP(X12,X13)
| ssList(esk4_2(X12,X13)) )
& ( ~ ssList(X12)
| ~ ssItem(X13)
| ~ memberP(X12,X13)
| ssList(esk3_2(X12,X13)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_39,negated_conjecture,
( ~ ssList(X1)
| memberP(app(esk51_0,X1),esk52_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_33])]) ).
fof(c_0_40,plain,
! [X226,X227] :
( ( ~ ssList(X226)
| ~ ssList(X227)
| nil = app(X226,X227)
| nil != X226
| nil != X227 )
& ( ~ ssList(X226)
| ~ ssList(X227)
| nil != app(X226,X227)
| nil = X226 )
& ( ~ ssList(X226)
| ~ ssList(X227)
| nil != app(X226,X227)
| nil = X227 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])])]) ).
cnf(c_0_41,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X2,X1)
| app(X1,esk6_2(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,plain,
frontsegP(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_35]),c_0_36])]) ).
cnf(c_0_43,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ssList(esk6_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_44,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| app(X2,X1) != X3
| ~ ssList(X1)
| frontsegP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_45,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_46,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| app(esk3_2(X1,X2),cons(X2,esk4_2(X1,X2))) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_47,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| ssList(esk3_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_48,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(app(esk51_0,X1))
| memberP(app(app(esk51_0,X1),X2),esk52_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_39]),c_0_33])]) ).
fof(c_0_49,plain,
! [X223,X224,X225] :
( app(app(X223,X224),X225) = app(X223,app(X224,X225))
| ~ ssList(X225)
| ~ ssList(X224)
| ~ ssList(X223) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).
cnf(c_0_50,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != app(X2,X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_51,plain,
app(nil,esk6_2(nil,nil)) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_36])]) ).
cnf(c_0_52,plain,
ssList(esk6_2(nil,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_42]),c_0_36])]) ).
cnf(c_0_53,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| frontsegP(app(X1,X2),X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_44]),c_0_45]) ).
cnf(c_0_54,negated_conjecture,
app(esk3_2(esk51_0,esk52_0),cons(esk52_0,esk4_2(esk51_0,esk52_0))) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_31]),c_0_32]),c_0_33])]) ).
cnf(c_0_55,negated_conjecture,
ssList(esk3_2(esk51_0,esk52_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_31]),c_0_32]),c_0_33])]) ).
fof(c_0_56,plain,
! [X112,X113] :
( ssList(cons(X113,X112))
| ~ ssItem(X113)
| ~ ssList(X112) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
cnf(c_0_57,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| ssList(esk4_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_58,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(X2)
| memberP(app(app(esk51_0,X1),X2),esk52_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_45]),c_0_32])]) ).
cnf(c_0_59,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X1,X2),X3) = app(X1,app(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_60,plain,
esk6_2(nil,nil) = 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_36]),c_0_52])]) ).
fof(c_0_61,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
inference(fof_simplification,[status(thm)],[ax85]) ).
cnf(c_0_62,negated_conjecture,
( ~ ssList(cons(esk52_0,esk4_2(esk51_0,esk52_0)))
| frontsegP(esk51_0,esk3_2(esk51_0,esk52_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55])]) ).
cnf(c_0_63,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_64,negated_conjecture,
ssList(esk4_2(esk51_0,esk52_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_31]),c_0_32]),c_0_33])]) ).
cnf(c_0_65,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(X2)
| memberP(app(esk51_0,app(X1,X2)),esk52_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_32])]) ).
cnf(c_0_66,plain,
app(nil,nil) = nil,
inference(rw,[status(thm)],[c_0_51,c_0_60]) ).
fof(c_0_67,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax22]) ).
fof(c_0_68,plain,
! [X229,X230] :
( hd(app(X229,X230)) = hd(X229)
| nil = X229
| ~ ssList(X230)
| ~ ssList(X229) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_61])])])]) ).
cnf(c_0_69,negated_conjecture,
frontsegP(esk51_0,esk3_2(esk51_0,esk52_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]),c_0_33])]) ).
fof(c_0_70,plain,
! [X136] :
( app(nil,X136) = X136
| ~ ssList(X136) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
cnf(c_0_71,negated_conjecture,
memberP(app(esk51_0,nil),esk52_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_36])]) ).
fof(c_0_72,plain,
! [X125] :
( ssItem(hd(X125))
| nil = X125
| ~ ssList(X125) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_67])])]) ).
cnf(c_0_73,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| hd(app(X1,X2)) = hd(X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_74,negated_conjecture,
app(esk3_2(esk51_0,esk52_0),esk6_2(esk51_0,esk3_2(esk51_0,esk52_0))) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_69]),c_0_32]),c_0_55])]) ).
cnf(c_0_75,negated_conjecture,
ssList(esk6_2(esk51_0,esk3_2(esk51_0,esk52_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_69]),c_0_55]),c_0_32])]) ).
cnf(c_0_76,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_77,negated_conjecture,
( ~ ssList(app(esk51_0,nil))
| app(esk3_2(app(esk51_0,nil),esk52_0),cons(esk52_0,esk4_2(app(esk51_0,nil),esk52_0))) = app(esk51_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_71]),c_0_33])]) ).
cnf(c_0_78,negated_conjecture,
( ~ ssList(app(esk51_0,nil))
| ssList(esk3_2(app(esk51_0,nil),esk52_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_71]),c_0_33])]) ).
cnf(c_0_79,plain,
( ~ ssList(X1)
| ssItem(hd(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_80,negated_conjecture,
( esk3_2(esk51_0,esk52_0) = nil
| hd(esk3_2(esk51_0,esk52_0)) = hd(esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]),c_0_55])]) ).
fof(c_0_81,plain,
! [X218,X219,X220] :
( X220 = X218
| app(X219,X220) != app(X219,X218)
| ~ ssList(X220)
| ~ ssList(X219)
| ~ ssList(X218) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])])]) ).
fof(c_0_82,plain,
! [X228] :
( app(X228,nil) = X228
| ~ ssList(X228) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).
fof(c_0_83,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
inference(fof_simplification,[status(thm)],[ax86]) ).
fof(c_0_84,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax24]) ).
cnf(c_0_85,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(nil,app(X1,X2)) = app(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_76]),c_0_36])]) ).
cnf(c_0_86,negated_conjecture,
app(esk3_2(app(esk51_0,nil),esk52_0),cons(esk52_0,esk4_2(app(esk51_0,nil),esk52_0))) = app(esk51_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_45]),c_0_36]),c_0_32])]) ).
cnf(c_0_87,negated_conjecture,
ssList(esk3_2(app(esk51_0,nil),esk52_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_45]),c_0_36]),c_0_32])]) ).
cnf(c_0_88,negated_conjecture,
( ~ ssList(app(esk51_0,nil))
| ssList(esk4_2(app(esk51_0,nil),esk52_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_71]),c_0_33])]) ).
cnf(c_0_89,negated_conjecture,
( ssItem(hd(esk51_0))
| esk3_2(esk51_0,esk52_0) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_55])]) ).
cnf(c_0_90,plain,
( app(X2,X3) != app(X2,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_91,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
fof(c_0_92,plain,
! [X231,X232] :
( tl(app(X231,X232)) = app(tl(X231),X232)
| nil = X231
| ~ ssList(X232)
| ~ ssList(X231) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_83])])])]) ).
fof(c_0_93,plain,
! [X128] :
( ssList(tl(X128))
| nil = X128
| ~ ssList(X128) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_84])])]) ).
cnf(c_0_94,negated_conjecture,
( ~ ssList(cons(esk52_0,esk4_2(app(esk51_0,nil),esk52_0)))
| app(nil,app(esk51_0,nil)) = app(esk51_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87])]) ).
cnf(c_0_95,negated_conjecture,
ssList(esk4_2(app(esk51_0,nil),esk52_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_45]),c_0_36]),c_0_32])]) ).
fof(c_0_96,plain,
! [X221,X222] :
( cons(X222,X221) = app(cons(X222,nil),X221)
| ~ ssItem(X222)
| ~ ssList(X221) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
cnf(c_0_97,negated_conjecture,
( ssItem(hd(esk51_0))
| app(nil,cons(esk52_0,esk4_2(esk51_0,esk52_0))) = esk51_0 ),
inference(spm,[status(thm)],[c_0_54,c_0_89]) ).
fof(c_0_98,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
inference(fof_simplification,[status(thm)],[ax78]) ).
cnf(c_0_99,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X2,X1) != X2
| X1 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_36])]) ).
cnf(c_0_100,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X1,X2)) = app(tl(X1),X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_101,plain,
( ~ ssList(X1)
| ssList(tl(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_102,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,app(X2,nil)) = app(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_59]),c_0_36])]),c_0_45]) ).
cnf(c_0_103,negated_conjecture,
app(nil,app(esk51_0,nil)) = app(esk51_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_63]),c_0_95]),c_0_33])]) ).
cnf(c_0_104,negated_conjecture,
app(nil,esk51_0) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_74]),c_0_75]),c_0_55])]) ).
cnf(c_0_105,negated_conjecture,
( app(cons(X1,nil),X2) != esk51_0
| ~ ssList(X2)
| ~ ssItem(X1)
| app(X2,cons(X1,nil)) = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_106,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_107,negated_conjecture,
( ~ ssList(cons(esk52_0,esk4_2(esk51_0,esk52_0)))
| ssItem(hd(esk51_0))
| cons(esk52_0,esk4_2(esk51_0,esk52_0)) = esk51_0 ),
inference(spm,[status(thm)],[c_0_76,c_0_97]) ).
fof(c_0_108,plain,
! [X214] :
( cons(hd(X214),tl(X214)) = X214
| nil = X214
| ~ ssList(X214) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_98])])]) ).
fof(c_0_109,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[ax21]) ).
cnf(c_0_110,negated_conjecture,
( ~ ssList(cons(esk52_0,esk4_2(esk51_0,esk52_0)))
| esk3_2(esk51_0,esk52_0) != esk51_0
| cons(esk52_0,esk4_2(esk51_0,esk52_0)) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_54]),c_0_55])]) ).
cnf(c_0_111,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ssList(tl(app(X1,X2)))
| nil = X1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_100]),c_0_101]) ).
cnf(c_0_112,negated_conjecture,
app(esk51_0,nil) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_104]),c_0_32]),c_0_36])]) ).
cnf(c_0_113,negated_conjecture,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) != esk51_0
| app(X1,cons(X2,nil)) = esk50_0 ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_114,negated_conjecture,
( ssItem(hd(esk51_0))
| cons(esk52_0,esk4_2(esk51_0,esk52_0)) = esk51_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_63]),c_0_64]),c_0_33])]) ).
cnf(c_0_115,plain,
( ~ ssList(X1)
| cons(hd(X1),tl(X1)) = X1
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_116,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != app(X1,X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_117,plain,
! [X123,X124] :
( nil != cons(X124,X123)
| ~ ssItem(X124)
| ~ ssList(X123) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_109])])])]) ).
cnf(c_0_118,negated_conjecture,
( esk3_2(esk51_0,esk52_0) != esk51_0
| cons(esk52_0,esk4_2(esk51_0,esk52_0)) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_63]),c_0_64]),c_0_33])]) ).
cnf(c_0_119,negated_conjecture,
( ssList(tl(esk51_0))
| esk3_2(esk51_0,esk52_0) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_74]),c_0_75]),c_0_55])]) ).
cnf(c_0_120,negated_conjecture,
( ssList(tl(esk51_0))
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_36]),c_0_32])]) ).
cnf(c_0_121,plain,
( ~ ssList(X4)
| ~ ssItem(X3)
| app(X1,cons(X3,X2)) != X4
| ~ ssList(X2)
| ~ ssList(X1)
| memberP(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_122,negated_conjecture,
( ssItem(hd(esk51_0))
| app(esk4_2(esk51_0,esk52_0),cons(esk52_0,nil)) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_64]),c_0_33])]) ).
cnf(c_0_123,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_124,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_125,negated_conjecture,
~ memberP(esk48_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_126,plain,
! [X133,X134,X135] :
( cons(X135,app(X134,X133)) = app(cons(X135,X134),X133)
| ~ ssItem(X135)
| ~ ssList(X134)
| ~ ssList(X133) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])])]) ).
cnf(c_0_127,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil = X1
| cons(hd(X1),tl(app(X1,X2))) = app(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_73]),c_0_45]),c_0_116]) ).
cnf(c_0_128,plain,
( nil != cons(X2,X1)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_129,negated_conjecture,
( ssList(tl(esk51_0))
| cons(esk52_0,esk4_2(esk51_0,esk52_0)) = nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_120]) ).
cnf(c_0_130,negated_conjecture,
( ~ ssList(X1)
| esk50_0 != X1
| ssItem(hd(esk51_0))
| memberP(X1,esk52_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_36]),c_0_64]),c_0_33])]) ).
cnf(c_0_131,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_132,negated_conjecture,
~ memberP(esk50_0,esk52_0),
inference(rw,[status(thm)],[c_0_125,c_0_124]) ).
cnf(c_0_133,plain,
( ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_134,negated_conjecture,
( esk51_0 = nil
| cons(hd(esk51_0),tl(esk51_0)) = esk51_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_112]),c_0_36]),c_0_32])]) ).
cnf(c_0_135,negated_conjecture,
ssList(tl(esk51_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_64]),c_0_33])]) ).
cnf(c_0_136,negated_conjecture,
ssItem(hd(esk51_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_130]),c_0_131])]),c_0_132]) ).
cnf(c_0_137,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil = X1
| cons(hd(X1),app(tl(X1),X2)) = app(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_115]),c_0_79]),c_0_101]) ).
cnf(c_0_138,negated_conjecture,
( esk51_0 = nil
| app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_134]),c_0_135]),c_0_136])]) ).
cnf(c_0_139,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(cons(X1,nil))
| memberP(app(esk51_0,cons(X1,X2)),esk52_0) ),
inference(spm,[status(thm)],[c_0_65,c_0_106]) ).
cnf(c_0_140,negated_conjecture,
( ~ ssList(cons(hd(esk51_0),nil))
| esk51_0 = nil
| app(esk51_0,cons(hd(esk51_0),nil)) = cons(hd(esk51_0),esk50_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_32])]) ).
fof(c_0_141,plain,
! [X155,X156,X157] :
( ( ~ ssItem(X155)
| ~ ssItem(X156)
| ~ ssList(X157)
| memberP(cons(X156,X157),X155)
| ~ memberP(X157,X155) )
& ( ~ ssItem(X155)
| ~ ssItem(X156)
| ~ ssList(X157)
| memberP(cons(X156,X157),X155)
| X155 != X156 )
& ( ~ ssItem(X155)
| ~ ssItem(X156)
| ~ ssList(X157)
| memberP(X157,X155)
| X155 = X156
| ~ memberP(cons(X156,X157),X155) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])])]) ).
cnf(c_0_142,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| memberP(app(esk51_0,cons(X1,X2)),esk52_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_63]),c_0_36])]) ).
cnf(c_0_143,negated_conjecture,
( esk51_0 = nil
| app(esk51_0,cons(hd(esk51_0),nil)) = cons(hd(esk51_0),esk50_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_63]),c_0_36]),c_0_136])]) ).
cnf(c_0_144,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(app(X1,cons(X2,X3)))
| memberP(app(X1,cons(X2,X3)),X2) ),
inference(er,[status(thm)],[c_0_121]) ).
cnf(c_0_145,plain,
( ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X3)
| memberP(X2,X3)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_141]) ).
cnf(c_0_146,negated_conjecture,
( memberP(cons(hd(esk51_0),esk50_0),esk52_0)
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_36]),c_0_136])]) ).
cnf(c_0_147,negated_conjecture,
( memberP(esk50_0,hd(esk51_0))
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_138]),c_0_131]),c_0_36]),c_0_135]),c_0_136])]) ).
cnf(c_0_148,negated_conjecture,
( esk51_0 = nil
| hd(esk51_0) = esk52_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_131]),c_0_33]),c_0_136])]),c_0_132]) ).
cnf(c_0_149,negated_conjecture,
( nil != esk51_0
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_150,negated_conjecture,
esk51_0 = nil,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_132]) ).
cnf(c_0_151,negated_conjecture,
esk50_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_149,c_0_150])]) ).
cnf(c_0_152,negated_conjecture,
~ memberP(nil,esk52_0),
inference(rw,[status(thm)],[c_0_132,c_0_151]) ).
cnf(c_0_153,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_150]),c_0_152]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC409+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.47 % Computer : n003.cluster.edu
% 0.18/0.47 % Model : x86_64 x86_64
% 0.18/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.47 % Memory : 8046.5625MB
% 0.18/0.47 % OS : Linux 6.8.0-71-generic
% 0.18/0.47 % CPULimit : 300
% 0.18/0.47 % WCLimit : 300
% 0.18/0.47 % DateTime : Mon Sep 21 08:24:01 UTC 2026
% 0.18/0.48 % CPUTime :
% 0.18/0.48 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.55 Running first-order theorem proving
% 0.22/0.55 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.89/1.21 % Version: 3.5.1
% 3.89/1.21 % Preprocessing class: FSLSSMSSSSSNFFN.
% 3.89/1.21 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.89/1.21 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 3.89/1.21 % Starting new_bool_3 with 300s (1) cores
% 3.89/1.21 % Starting new_bool_1 with 300s (1) cores
% 3.89/1.21 % Starting sh5l with 300s (1) cores
% 3.89/1.21 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 3845318 completed with status 0
% 3.89/1.21 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 3.89/1.21 % Preprocessing class: FSLSSMSSSSSNFFN.
% 3.89/1.21 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.89/1.21 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 3.89/1.21 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.89/1.21 % No SInE strategy applied
% 3.89/1.21 % Search class: FGHSF-FSLM21-MFFFFFNN
% 3.89/1.21 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 3.89/1.21 % Starting SubtermCWHack with 136s (1) cores
% 3.89/1.21 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 3.89/1.21 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 3.89/1.21 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 3.89/1.21 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 3.89/1.21 % G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with pid 3845324 completed with status 0
% 3.89/1.21 % Result found by G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d
% 3.89/1.21 % Preprocessing class: FSLSSMSSSSSNFFN.
% 3.89/1.21 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.89/1.21 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 3.89/1.21 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.89/1.21 % No SInE strategy applied
% 3.89/1.21 % Search class: FGHSF-FSLM21-MFFFFFNN
% 3.89/1.21 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 3.89/1.21 % Starting SubtermCWHack with 136s (1) cores
% 3.89/1.21 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 3.89/1.21 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 3.89/1.21 % Preprocessing time : 0.006 s
% 3.89/1.21
% 3.89/1.21 % Proof found!
% 3.89/1.21 % SZS status Theorem
% 3.89/1.21 % SZS output start CNFRefutation
% See solution above
% 3.89/1.22 % Parsed axioms : 96
% 3.89/1.22 % Removed by relevancy pruning/SinE : 0
% 3.89/1.22 % Initial clauses : 201
% 3.89/1.22 % Removed in clause preprocessing : 2
% 3.89/1.22 % Initial clauses in saturation : 199
% 3.89/1.22 % Processed clauses : 2205
% 3.89/1.22 % ...of these trivial : 16
% 3.89/1.22 % ...subsumed : 968
% 3.89/1.22 % ...remaining for further processing : 1220
% 3.89/1.22 % Other redundant clauses eliminated : 188
% 3.89/1.22 % Clauses deleted for lack of memory : 0
% 3.89/1.22 % Backward-subsumed : 210
% 3.89/1.22 % Backward-rewritten : 409
% 3.89/1.22 % Generated clauses : 11065
% 3.89/1.22 % ...of the previous two non-redundant : 9710
% 3.89/1.22 % ...aggressively subsumed : 0
% 3.89/1.22 % Contextual simplify-reflections : 232
% 3.89/1.22 % Paramodulations : 10806
% 3.89/1.22 % Factorizations : 0
% 3.89/1.22 % NegExts : 0
% 3.89/1.22 % Equation resolutions : 259
% 3.89/1.22 % Disequality decompositions : 0
% 3.89/1.22 % Total rewrite steps : 11689
% 3.89/1.22 % ...of those cached : 11573
% 3.89/1.22 % Propositional unsat checks : 0
% 3.89/1.22 % Propositional check models : 0
% 3.89/1.22 % Propositional check unsatisfiable : 0
% 3.89/1.22 % Propositional clauses : 0
% 3.89/1.22 % Propositional clauses after purity: 0
% 3.89/1.22 % Propositional unsat core size : 0
% 3.89/1.22 % Propositional preprocessing time : 0.000
% 3.89/1.22 % Propositional encoding time : 0.000
% 3.89/1.22 % Propositional solver time : 0.000
% 3.89/1.22 % Success case prop preproc time : 0.000
% 3.89/1.22 % Success case prop encoding time : 0.000
% 3.89/1.22 % Success case prop solver time : 0.000
% 3.89/1.22 % Current number of processed clauses : 595
% 3.89/1.22 % Positive orientable unit clauses : 85
% 3.89/1.22 % Positive unorientable unit clauses: 0
% 3.89/1.22 % Negative unit clauses : 3
% 3.89/1.22 % Non-unit-clauses : 507
% 3.89/1.22 % Current number of unprocessed clauses: 7483
% 3.89/1.22 % ...number of literals in the above : 42949
% 3.89/1.22 % Current number of archived formulas : 0
% 3.89/1.22 % Current number of archived clauses : 619
% 3.89/1.22 % Clause-clause subsumption calls (NU) : 125979
% 3.89/1.22 % Rec. Clause-clause subsumption calls : 66643
% 3.89/1.22 % Non-unit clause-clause subsumptions : 1394
% 3.89/1.22 % Unit Clause-clause subsumption calls : 7372
% 3.89/1.22 % Rewrite failures with RHS unbound : 0
% 3.89/1.22 % BW rewrite match attempts : 613
% 3.89/1.22 % BW rewrite match successes : 68
% 3.89/1.22 % Condensation attempts : 0
% 3.89/1.22 % Condensation successes : 0
% 3.89/1.22 % Termbank termtop insertions : 242334
% 3.89/1.22 % Search garbage collected termcells : 4298
% 3.89/1.22
% 3.89/1.22 % -------------------------------------------------
% 3.89/1.22 % User time : 0.594 s
% 3.89/1.22 % System time : 0.025 s
% 3.89/1.22 % Total time : 0.619 s
% 3.89/1.22 % Maximum resident set size: 4016 pages
% 3.89/1.22
% 3.89/1.22 % -------------------------------------------------
% 3.89/1.22 % User time : 2.335 s
% 3.89/1.22 % System time : 0.106 s
% 3.89/1.22 % Total time : 2.441 s
% 3.89/1.22 % Maximum resident set size: 4608 pages
% 3.89/1.22 % E exiting
%------------------------------------------------------------------------------