%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC396+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 02:44:14 PM UTC 2026
% Result : Theorem 0.14s 6.19s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 14
% Syntax : Number of formulae : 95 ( 17 unt; 0 def)
% Number of atoms : 442 ( 149 equ)
% Maximal formula atoms : 25 ( 4 avg)
% Number of connectives : 552 ( 205 ~; 224 |; 60 &)
% ( 6 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 132 ( 0 sgn 76 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( ? [X6] :
( ? [X7] :
( ? [X8] :
( neq(nil,X3)
& ? [X9] :
( neq(nil,X3)
& hd(X3) = X9
& cons(X9,nil) = X8
& ssItem(X9) )
& app(X7,X8) = X6
& tl(X3) = X7
& ssList(X8) )
& ssList(X7) )
& X4 != X6
& ssList(X6) )
| ~ neq(X3,nil) )
& neq(X4,nil) )
| ( nil = X4
& nil != X3 )
| ! [X5] :
( ssItem(X5)
=> ( memberP(X2,X5)
| ~ memberP(X1,X5) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
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(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(ax86,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax86) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X1
& nil = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax85,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax85) ).
fof(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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax36) ).
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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax3) ).
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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(c_0_14,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( ? [X6] :
( ? [X7] :
( ? [X8] :
( neq(nil,X3)
& ? [X9] :
( neq(nil,X3)
& hd(X3) = X9
& cons(X9,nil) = X8
& ssItem(X9) )
& app(X7,X8) = X6
& tl(X3) = X7
& ssList(X8) )
& ssList(X7) )
& X4 != X6
& ssList(X6) )
| ~ neq(X3,nil) )
& neq(X4,nil) )
| ( nil = X4
& nil != X3 )
| ! [X5] :
( ssItem(X5)
=> ( memberP(X2,X5)
| ~ memberP(X1,X5) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( ? [X6] :
( ? [X7] :
( ? [X8] :
( neq(nil,X3)
& ? [X9] :
( neq(nil,X3)
& hd(X3) = X9
& cons(X9,nil) = X8
& ssItem(X9) )
& app(X7,X8) = X6
& tl(X3) = X7
& ssList(X8) )
& ssList(X7) )
& X4 != X6
& ssList(X6) )
| ~ neq(X3,nil) )
& neq(X4,nil) )
| ( nil = X4
& nil != X3 )
| ! [X5] :
( ssItem(X5)
=> ( memberP(X2,X5)
| ~ memberP(X1,X5) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_16,negated_conjecture,
! [X259,X260,X261,X262] :
( ( ~ neq(esk51_0,nil)
| ~ neq(nil,esk50_0)
| ~ neq(nil,esk50_0)
| hd(esk50_0) != X262
| cons(X262,nil) != X261
| ~ ssItem(X262)
| app(X260,X261) != X259
| tl(esk50_0) != X260
| ~ ssList(X261)
| ~ ssList(X260)
| esk51_0 = X259
| ~ ssList(X259) )
& ( ~ neq(esk51_0,nil)
| neq(esk50_0,nil) )
& ( nil != esk51_0
| nil = esk50_0 )
& ~ memberP(esk49_0,esk52_0)
& memberP(esk48_0,esk52_0)
& ssItem(esk52_0)
& esk48_0 = esk50_0
& esk49_0 = esk51_0
& ssList(esk51_0)
& ssList(esk50_0)
& ssList(esk49_0)
& ssList(esk48_0) ),
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)],[c_0_15])])])])])]) ).
cnf(c_0_17,negated_conjecture,
( ~ neq(esk51_0,nil)
| ~ neq(nil,esk50_0)
| ~ neq(nil,esk50_0)
| hd(esk50_0) != X4
| cons(X4,nil) != X3
| ~ ssItem(X4)
| app(X2,X3) != X1
| tl(esk50_0) != X2
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| esk51_0 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_18,plain,
! [X133,X134] :
( ssList(app(X133,X134))
| ~ ssList(X134)
| ~ ssList(X133) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
fof(c_0_19,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax24]) ).
cnf(c_0_20,negated_conjecture,
( ~ neq(esk51_0,nil)
| ~ neq(nil,esk50_0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X4)
| cons(X4,nil) != X3
| app(X2,X3) != X1
| tl(esk50_0) != X2
| hd(esk50_0) != X4
| esk51_0 = X1 ),
inference(cn,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_22,plain,
! [X130] :
( ssList(tl(X130))
| nil = X130
| ~ ssList(X130) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
cnf(c_0_23,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_25,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
cnf(c_0_26,negated_conjecture,
( ~ ssItem(hd(esk50_0))
| ~ neq(esk51_0,nil)
| ~ neq(nil,esk50_0)
| ~ ssList(tl(esk50_0))
| ~ ssList(cons(hd(esk50_0),nil))
| app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0 ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_20])])])]),c_0_21]) ).
cnf(c_0_27,plain,
( ~ ssList(X1)
| ssList(tl(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
fof(c_0_29,plain,
! [X112,X113] :
( ( ~ ssList(X112)
| ~ ssList(X113)
| neq(X112,X113)
| X112 = X113 )
& ( ~ ssList(X112)
| ~ ssList(X113)
| X112 != X113
| ~ neq(X112,X113) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])])])]) ).
cnf(c_0_30,negated_conjecture,
( ~ ssItem(hd(esk50_0))
| ~ neq(esk51_0,nil)
| ~ neq(nil,esk50_0)
| ~ ssList(cons(hd(esk50_0),nil))
| esk50_0 = nil
| app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
cnf(c_0_31,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_32,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_33,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_34,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_35,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax22]) ).
cnf(c_0_36,negated_conjecture,
( ~ ssItem(hd(esk50_0))
| ~ neq(esk51_0,nil)
| ~ ssList(cons(hd(esk50_0),nil))
| esk50_0 = nil
| app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_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_28]),c_0_32])]) ).
cnf(c_0_37,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
( nil != esk51_0
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_39,plain,
! [X127] :
( ssItem(hd(X127))
| nil = X127
| ~ ssList(X127) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])]) ).
fof(c_0_40,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
inference(fof_simplification,[status(thm)],[ax78]) ).
fof(c_0_41,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
inference(fof_simplification,[status(thm)],[ax86]) ).
cnf(c_0_42,negated_conjecture,
( ~ ssItem(hd(esk50_0))
| ~ ssList(cons(hd(esk50_0),nil))
| esk50_0 = nil
| app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_31]),c_0_32]),c_0_37])]),c_0_38]) ).
cnf(c_0_43,plain,
( ~ ssList(X1)
| ssItem(hd(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_44,plain,
! [X114,X115] :
( ssList(cons(X115,X114))
| ~ ssItem(X115)
| ~ ssList(X114) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
fof(c_0_45,plain,
! [X216] :
( cons(hd(X216),tl(X216)) = X216
| nil = X216
| ~ ssList(X216) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])]) ).
fof(c_0_46,plain,
! [X233,X234] :
( tl(app(X233,X234)) = app(tl(X233),X234)
| nil = X233
| ~ ssList(X234)
| ~ ssList(X233) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])])]) ).
fof(c_0_47,plain,
! [X228,X229] :
( ( ~ ssList(X228)
| ~ ssList(X229)
| nil = app(X228,X229)
| nil != X228
| nil != X229 )
& ( ~ ssList(X228)
| ~ ssList(X229)
| nil != app(X228,X229)
| nil = X228 )
& ( ~ ssList(X228)
| ~ ssList(X229)
| nil != app(X228,X229)
| nil = X229 ) ),
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_48,negated_conjecture,
( ~ ssList(cons(hd(esk50_0),nil))
| esk50_0 = nil
| app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_28])]) ).
cnf(c_0_49,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_50,plain,
( ~ ssList(X1)
| cons(hd(X1),tl(X1)) = X1
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_51,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| tl(app(X1,X2)) = app(tl(X1),X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_52,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != app(X1,X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_53,negated_conjecture,
( ~ ssItem(hd(esk50_0))
| esk50_0 = nil
| app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_32])]) ).
cnf(c_0_54,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil = X1
| cons(hd(app(X1,X2)),app(tl(X1),X2)) = app(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_21]),c_0_52]) ).
cnf(c_0_55,negated_conjecture,
( esk50_0 = nil
| app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_43]),c_0_28])]) ).
cnf(c_0_56,negated_conjecture,
( ~ ssList(cons(hd(esk50_0),nil))
| esk50_0 = nil
| cons(hd(app(esk50_0,cons(hd(esk50_0),nil))),esk51_0) = app(esk50_0,cons(hd(esk50_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_28])]) ).
fof(c_0_57,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
inference(fof_simplification,[status(thm)],[ax85]) ).
cnf(c_0_58,negated_conjecture,
( ~ ssItem(hd(esk50_0))
| esk50_0 = nil
| cons(hd(app(esk50_0,cons(hd(esk50_0),nil))),esk51_0) = app(esk50_0,cons(hd(esk50_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_49]),c_0_32])]) ).
fof(c_0_59,plain,
! [X231,X232] :
( hd(app(X231,X232)) = hd(X231)
| 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_57])])])]) ).
cnf(c_0_60,negated_conjecture,
( esk50_0 = nil
| cons(hd(app(esk50_0,cons(hd(esk50_0),nil))),esk51_0) = app(esk50_0,cons(hd(esk50_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_43]),c_0_28])]) ).
cnf(c_0_61,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| hd(app(X1,X2)) = hd(X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
fof(c_0_62,plain,
! [X154,X155,X156] :
( ( ~ ssItem(X154)
| ~ ssList(X155)
| ~ ssList(X156)
| memberP(app(X155,X156),X154)
| ~ memberP(X156,X154) )
& ( ~ ssItem(X154)
| ~ ssList(X155)
| ~ ssList(X156)
| memberP(app(X155,X156),X154)
| ~ memberP(X155,X154) )
& ( ~ ssItem(X154)
| ~ ssList(X155)
| ~ ssList(X156)
| memberP(X156,X154)
| memberP(X155,X154)
| ~ memberP(app(X155,X156),X154) ) ),
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_63,negated_conjecture,
memberP(esk48_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_64,negated_conjecture,
( ~ ssList(cons(hd(esk50_0),nil))
| esk50_0 = nil
| app(esk50_0,cons(hd(esk50_0),nil)) = cons(hd(esk50_0),esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_28])]) ).
cnf(c_0_65,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ memberP(X1,X2)
| memberP(app(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_66,negated_conjecture,
memberP(esk50_0,esk52_0),
inference(rw,[status(thm)],[c_0_63,c_0_24]) ).
cnf(c_0_67,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_68,negated_conjecture,
( ~ ssItem(hd(esk50_0))
| esk50_0 = nil
| app(esk50_0,cons(hd(esk50_0),nil)) = cons(hd(esk50_0),esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_49]),c_0_32])]) ).
fof(c_0_69,plain,
! [X14,X15,X18,X19] :
( ( ~ ssList(X14)
| ~ ssItem(X15)
| memberP(X14,X15)
| app(X18,cons(X15,X19)) != X14
| ~ ssList(X19)
| ~ ssList(X18) )
& ( ~ ssList(X14)
| ~ ssItem(X15)
| ~ memberP(X14,X15)
| app(esk3_2(X14,X15),cons(X15,esk4_2(X14,X15))) = X14 )
& ( ~ ssList(X14)
| ~ ssItem(X15)
| ~ memberP(X14,X15)
| ssList(esk4_2(X14,X15)) )
& ( ~ ssList(X14)
| ~ ssItem(X15)
| ~ memberP(X14,X15)
| ssList(esk3_2(X14,X15)) ) ),
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_70,negated_conjecture,
( ~ ssList(X1)
| memberP(app(esk50_0,X1),esk52_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_28]),c_0_67])]) ).
cnf(c_0_71,negated_conjecture,
( esk50_0 = nil
| app(esk50_0,cons(hd(esk50_0),nil)) = cons(hd(esk50_0),esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_43]),c_0_28])]) ).
cnf(c_0_72,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_69]) ).
cnf(c_0_73,negated_conjecture,
( ~ ssList(cons(hd(esk50_0),nil))
| memberP(cons(hd(esk50_0),esk51_0),esk52_0)
| esk50_0 = nil ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_74,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_72]) ).
fof(c_0_75,plain,
! [X157,X158,X159] :
( ( ~ ssItem(X157)
| ~ ssItem(X158)
| ~ ssList(X159)
| memberP(cons(X158,X159),X157)
| ~ memberP(X159,X157) )
& ( ~ ssItem(X157)
| ~ ssItem(X158)
| ~ ssList(X159)
| memberP(cons(X158,X159),X157)
| X157 != X158 )
& ( ~ ssItem(X157)
| ~ ssItem(X158)
| ~ ssList(X159)
| memberP(X159,X157)
| X157 = X158
| ~ memberP(cons(X158,X159),X157) ) ),
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_76,negated_conjecture,
( ~ ssItem(hd(esk50_0))
| memberP(cons(hd(esk50_0),esk51_0),esk52_0)
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_49]),c_0_32])]) ).
cnf(c_0_77,negated_conjecture,
~ memberP(esk49_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_78,negated_conjecture,
( ~ ssItem(hd(esk50_0))
| ~ ssList(tl(esk50_0))
| memberP(esk51_0,hd(esk50_0))
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_55]),c_0_37]),c_0_32])]) ).
cnf(c_0_79,plain,
( ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X3)
| memberP(X2,X3)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_80,negated_conjecture,
( memberP(cons(hd(esk50_0),esk51_0),esk52_0)
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_43]),c_0_28])]) ).
cnf(c_0_81,negated_conjecture,
~ memberP(esk51_0,esk52_0),
inference(rw,[status(thm)],[c_0_77,c_0_34]) ).
cnf(c_0_82,negated_conjecture,
( ~ ssItem(hd(esk50_0))
| memberP(esk51_0,hd(esk50_0))
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_27]),c_0_28])]) ).
cnf(c_0_83,negated_conjecture,
( ~ ssItem(hd(esk50_0))
| esk50_0 = nil
| hd(esk50_0) = esk52_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_37]),c_0_67])]),c_0_81]) ).
cnf(c_0_84,negated_conjecture,
( ~ neq(esk51_0,nil)
| neq(esk50_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_85,negated_conjecture,
( memberP(esk51_0,hd(esk50_0))
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_43]),c_0_28])]) ).
cnf(c_0_86,negated_conjecture,
( esk50_0 = nil
| hd(esk50_0) = esk52_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_43]),c_0_28])]) ).
cnf(c_0_87,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_88,negated_conjecture,
( neq(esk50_0,nil)
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_31]),c_0_32]),c_0_37])]) ).
cnf(c_0_89,negated_conjecture,
esk50_0 = nil,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_81]) ).
cnf(c_0_90,plain,
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(er,[status(thm)],[c_0_87]) ).
cnf(c_0_91,negated_conjecture,
( neq(nil,nil)
| esk51_0 = nil ),
inference(rw,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_92,negated_conjecture,
esk51_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_32])]) ).
cnf(c_0_93,negated_conjecture,
~ memberP(nil,esk52_0),
inference(rw,[status(thm)],[c_0_81,c_0_92]) ).
cnf(c_0_94,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_89]),c_0_93]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC396+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/5.98 % Computer : n012.cluster.edu
% 0.08/5.98 % Model : x86_64 x86_64
% 0.08/5.98 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.98 % Memory : 8046.5625MB
% 0.08/5.98 % OS : Linux 6.8.0-71-generic
% 0.08/5.98 % CPULimit : 300
% 0.08/5.98 % WCLimit : 300
% 0.08/5.98 % DateTime : Mon Sep 21 08:21:16 UTC 2026
% 0.08/5.98 % CPUTime :
% 0.08/5.98 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/6.02 Running first-order theorem proving
% 0.08/6.02 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.14/6.19 % Version: 3.5.1
% 0.14/6.19 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/6.19 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/6.19 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/6.19 % Starting new_bool_3 with 300s (1) cores
% 0.14/6.19 % Starting new_bool_1 with 300s (1) cores
% 0.14/6.19 % Starting sh5l with 300s (1) cores
% 0.14/6.19 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1973258 completed with status 0
% 0.14/6.19 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.14/6.19 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/6.19 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/6.19 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/6.19 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/6.19 % No SInE strategy applied
% 0.14/6.19 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.14/6.19 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/6.19 % Starting SubtermCWHack with 136s (1) cores
% 0.14/6.19 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.14/6.19 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.14/6.19 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 0.14/6.19 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 0.14/6.19 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1973265 completed with status 0
% 0.14/6.19 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.14/6.19 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/6.19 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/6.19 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/6.19 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/6.19 % No SInE strategy applied
% 0.14/6.19 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.14/6.19 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/6.19 % Starting SubtermCWHack with 136s (1) cores
% 0.14/6.19 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.14/6.19 % Preprocessing time : 0.003 s
% 0.14/6.19 % Presaturation interreduction done
% 0.14/6.19
% 0.14/6.19 % Proof found!
% 0.14/6.19 % SZS status Theorem
% 0.14/6.19 % SZS output start CNFRefutation
% See solution above
% 0.14/6.19 % Parsed axioms : 96
% 0.14/6.19 % Removed by relevancy pruning/SinE : 0
% 0.14/6.19 % Initial clauses : 202
% 0.14/6.19 % Removed in clause preprocessing : 2
% 0.14/6.19 % Initial clauses in saturation : 200
% 0.14/6.19 % Processed clauses : 1034
% 0.14/6.19 % ...of these trivial : 2
% 0.14/6.19 % ...subsumed : 310
% 0.14/6.19 % ...remaining for further processing : 721
% 0.14/6.19 % Other redundant clauses eliminated : 90
% 0.14/6.19 % Clauses deleted for lack of memory : 0
% 0.14/6.19 % Backward-subsumed : 121
% 0.14/6.19 % Backward-rewritten : 80
% 0.14/6.19 % Generated clauses : 2632
% 0.14/6.19 % ...of the previous two non-redundant : 2336
% 0.14/6.19 % ...aggressively subsumed : 0
% 0.14/6.19 % Contextual simplify-reflections : 112
% 0.14/6.19 % Paramodulations : 2541
% 0.14/6.19 % Factorizations : 0
% 0.14/6.19 % NegExts : 0
% 0.14/6.19 % Equation resolutions : 96
% 0.14/6.19 % Disequality decompositions : 0
% 0.14/6.19 % Total rewrite steps : 1342
% 0.14/6.19 % ...of those cached : 1318
% 0.14/6.19 % Propositional unsat checks : 0
% 0.14/6.19 % Propositional check models : 0
% 0.14/6.19 % Propositional check unsatisfiable : 0
% 0.14/6.19 % Propositional clauses : 0
% 0.14/6.19 % Propositional clauses after purity: 0
% 0.14/6.19 % Propositional unsat core size : 0
% 0.14/6.19 % Propositional preprocessing time : 0.000
% 0.14/6.19 % Propositional encoding time : 0.000
% 0.14/6.19 % Propositional solver time : 0.000
% 0.14/6.19 % Success case prop preproc time : 0.000
% 0.14/6.19 % Success case prop encoding time : 0.000
% 0.14/6.19 % Success case prop solver time : 0.000
% 0.14/6.19 % Current number of processed clauses : 302
% 0.14/6.19 % Positive orientable unit clauses : 25
% 0.14/6.19 % Positive unorientable unit clauses: 0
% 0.14/6.19 % Negative unit clauses : 3
% 0.14/6.19 % Non-unit-clauses : 274
% 0.14/6.19 % Current number of unprocessed clauses: 1654
% 0.14/6.19 % ...number of literals in the above : 10998
% 0.14/6.19 % Current number of archived formulas : 0
% 0.14/6.19 % Current number of archived clauses : 395
% 0.14/6.19 % Clause-clause subsumption calls (NU) : 39625
% 0.14/6.19 % Rec. Clause-clause subsumption calls : 8224
% 0.14/6.19 % Non-unit clause-clause subsumptions : 501
% 0.14/6.19 % Unit Clause-clause subsumption calls : 166
% 0.14/6.19 % Rewrite failures with RHS unbound : 0
% 0.14/6.19 % BW rewrite match attempts : 4
% 0.14/6.19 % BW rewrite match successes : 4
% 0.14/6.19 % Condensation attempts : 0
% 0.14/6.19 % Condensation successes : 0
% 0.14/6.19 % Termbank termtop insertions : 71566
% 0.14/6.19 % Search garbage collected termcells : 4409
% 0.14/6.19
% 0.14/6.19 % -------------------------------------------------
% 0.14/6.19 % User time : 0.116 s
% 0.14/6.19 % System time : 0.012 s
% 0.14/6.19 % Total time : 0.128 s
% 0.14/6.19 % Maximum resident set size: 4276 pages
% 0.14/6.19
% 0.14/6.19 % -------------------------------------------------
% 0.14/6.19 % User time : 0.485 s
% 0.14/6.19 % System time : 0.045 s
% 0.14/6.19 % Total time : 0.529 s
% 0.14/6.19 % Maximum resident set size: 4608 pages
% 0.14/6.19 % E exiting
%------------------------------------------------------------------------------