%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC412-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 : Tue Sep 29 01:03:52 PM UTC 2026
% Result : Unsatisfiable 1.87s 1.41s
% Output : Refutation 4.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 44
% Syntax : Number of formulae : 183 ( 10 unt; 12 def)
% Number of atoms : 515 ( 87 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 560 ( 228 ~; 320 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 16 ( 14 usr; 12 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 122 ( 0 sgn 122 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ~ ssItem(X3)
| ~ ssItem(X4)
| ~ ssList(X5)
| app(app(cons(X4,nil),X5),cons(X3,nil)) = sk3
| app(app(cons(X3,nil),X5),cons(X4,nil)) != sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ~ ssItem(X3)
| ~ ssItem(X4)
| ~ ssList(X5)
| sk3 = app(app(cons(X4,nil),X5),cons(X3,nil))
| sk4 != app(app(cons(X3,nil),X5),cons(X4,nil)) ),
inference(reorient_equations,[],[f206]) ).
fof(f216,negated_conjecture,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ssItem(sk11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f217,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ssItem(sk11) ),
inference(reorient_equations,[],[f216]) ).
fof(f218,negated_conjecture,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ssItem(sk12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
fof(f219,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ssItem(sk12) ),
inference(reorient_equations,[],[f218]) ).
fof(f220,negated_conjecture,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ssList(sk13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
fof(f221,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| ssList(sk13) ),
inference(reorient_equations,[],[f220]) ).
fof(f222,negated_conjecture,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f223,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| sk2 = app(app(cons(sk11,nil),sk13),cons(sk12,nil)) ),
inference(reorient_equations,[],[f222]) ).
fof(f224,negated_conjecture,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
fof(f225,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| sk1 != app(app(cons(sk12,nil),sk13),cons(sk11,nil)) ),
inference(reorient_equations,[],[f224]) ).
fof(f226,negated_conjecture,
! [X2,X0,X1] :
( ssItem(sk5)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(cons(X1,nil),X2),cons(X0,nil)) = sk3
| app(app(cons(X0,nil),X2),cons(X1,nil)) != sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
fof(f227,plain,
! [X2,X0,X1] :
( ssItem(sk5)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk3 = app(app(cons(X1,nil),X2),cons(X0,nil))
| sk4 != app(app(cons(X0,nil),X2),cons(X1,nil)) ),
inference(reorient_equations,[],[f226]) ).
fof(f228,negated_conjecture,
! [X2,X0,X1] :
( ssItem(sk6)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(cons(X1,nil),X2),cons(X0,nil)) = sk3
| app(app(cons(X0,nil),X2),cons(X1,nil)) != sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
fof(f229,plain,
! [X2,X0,X1] :
( ssItem(sk6)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk3 = app(app(cons(X1,nil),X2),cons(X0,nil))
| sk4 != app(app(cons(X0,nil),X2),cons(X1,nil)) ),
inference(reorient_equations,[],[f228]) ).
fof(f230,negated_conjecture,
! [X2,X0,X1] :
( ssList(sk7)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(cons(X1,nil),X2),cons(X0,nil)) = sk3
| app(app(cons(X0,nil),X2),cons(X1,nil)) != sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_19) ).
fof(f231,plain,
! [X2,X0,X1] :
( ssList(sk7)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk3 = app(app(cons(X1,nil),X2),cons(X0,nil))
| sk4 != app(app(cons(X0,nil),X2),cons(X1,nil)) ),
inference(reorient_equations,[],[f230]) ).
fof(f232,negated_conjecture,
! [X2,X0,X1] :
( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| app(app(cons(X1,nil),X2),cons(X0,nil)) = sk3
| app(app(cons(X0,nil),X2),cons(X1,nil)) != sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_20) ).
fof(f233,plain,
! [X2,X0,X1] :
( sk2 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk3 = app(app(cons(X1,nil),X2),cons(X0,nil))
| sk4 != app(app(cons(X0,nil),X2),cons(X1,nil)) ),
inference(reorient_equations,[],[f232]) ).
fof(f239,negated_conjecture,
( ssItem(sk5)
| ssItem(sk11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_25) ).
fof(f240,negated_conjecture,
( ssItem(sk5)
| ssItem(sk12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_26) ).
fof(f241,negated_conjecture,
( ssItem(sk5)
| ssList(sk13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_27) ).
fof(f242,negated_conjecture,
( ssItem(sk5)
| app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_28) ).
fof(f243,plain,
( ssItem(sk5)
| sk2 = app(app(cons(sk11,nil),sk13),cons(sk12,nil)) ),
inference(reorient_equations,[],[f242]) ).
fof(f244,negated_conjecture,
( ssItem(sk5)
| app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_29) ).
fof(f245,plain,
( ssItem(sk5)
| sk1 != app(app(cons(sk12,nil),sk13),cons(sk11,nil)) ),
inference(reorient_equations,[],[f244]) ).
fof(f264,negated_conjecture,
( ssItem(sk6)
| ssItem(sk11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_42) ).
fof(f265,negated_conjecture,
( ssItem(sk6)
| ssItem(sk12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_43) ).
fof(f266,negated_conjecture,
( ssItem(sk6)
| ssList(sk13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_44) ).
fof(f267,negated_conjecture,
( ssItem(sk6)
| app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_45) ).
fof(f268,plain,
( ssItem(sk6)
| sk2 = app(app(cons(sk11,nil),sk13),cons(sk12,nil)) ),
inference(reorient_equations,[],[f267]) ).
fof(f269,negated_conjecture,
( ssItem(sk6)
| app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_46) ).
fof(f270,plain,
( ssItem(sk6)
| sk1 != app(app(cons(sk12,nil),sk13),cons(sk11,nil)) ),
inference(reorient_equations,[],[f269]) ).
fof(f271,negated_conjecture,
( ssList(sk7)
| ssItem(sk11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_47) ).
fof(f272,negated_conjecture,
( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2
| ssItem(sk11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_48) ).
fof(f273,plain,
( sk2 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7)
| ssItem(sk11) ),
inference(reorient_equations,[],[f272]) ).
fof(f274,negated_conjecture,
( ssList(sk7)
| ssItem(sk12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_49) ).
fof(f275,negated_conjecture,
( ssList(sk7)
| ssList(sk13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_50) ).
fof(f276,negated_conjecture,
( ssList(sk7)
| app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_51) ).
fof(f277,plain,
( ssList(sk7)
| sk2 = app(app(cons(sk11,nil),sk13),cons(sk12,nil)) ),
inference(reorient_equations,[],[f276]) ).
fof(f278,negated_conjecture,
( ssList(sk7)
| app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_52) ).
fof(f279,plain,
( ssList(sk7)
| sk1 != app(app(cons(sk12,nil),sk13),cons(sk11,nil)) ),
inference(reorient_equations,[],[f278]) ).
fof(f280,negated_conjecture,
( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2
| ssItem(sk12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_53) ).
fof(f281,plain,
( sk2 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7)
| ssItem(sk12) ),
inference(reorient_equations,[],[f280]) ).
fof(f282,negated_conjecture,
( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2
| ssList(sk13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_54) ).
fof(f283,plain,
( sk2 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7)
| ssList(sk13) ),
inference(reorient_equations,[],[f282]) ).
fof(f284,negated_conjecture,
( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2
| app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_55) ).
fof(f285,plain,
( sk2 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7)
| sk2 = app(app(cons(sk11,nil),sk13),cons(sk12,nil)) ),
inference(reorient_equations,[],[f284]) ).
fof(f286,negated_conjecture,
( app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2
| app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_56) ).
fof(f287,plain,
( sk2 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7)
| sk1 != app(app(cons(sk12,nil),sk13),cons(sk11,nil)) ),
inference(reorient_equations,[],[f286]) ).
fof(f291,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| sk4 = app(app(cons(sk11,nil),sk13),cons(sk12,nil)) ),
inference(definition_unfolding,[],[f223,f204]) ).
fof(f292,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk4 != app(app(cons(X0,nil),cons(X1,nil)),X2)
| sk3 != app(app(cons(sk12,nil),sk13),cons(sk11,nil)) ),
inference(definition_unfolding,[],[f225,f205]) ).
fof(f293,plain,
! [X2,X0,X1] :
( sk4 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sk3 = app(app(cons(X1,nil),X2),cons(X0,nil))
| sk4 != app(app(cons(X0,nil),X2),cons(X1,nil)) ),
inference(definition_unfolding,[],[f233,f204]) ).
fof(f295,plain,
( ssItem(sk5)
| sk4 = app(app(cons(sk11,nil),sk13),cons(sk12,nil)) ),
inference(definition_unfolding,[],[f243,f204]) ).
fof(f296,plain,
( ssItem(sk5)
| sk3 != app(app(cons(sk12,nil),sk13),cons(sk11,nil)) ),
inference(definition_unfolding,[],[f245,f205]) ).
fof(f303,plain,
( ssItem(sk6)
| sk4 = app(app(cons(sk11,nil),sk13),cons(sk12,nil)) ),
inference(definition_unfolding,[],[f268,f204]) ).
fof(f304,plain,
( ssItem(sk6)
| sk3 != app(app(cons(sk12,nil),sk13),cons(sk11,nil)) ),
inference(definition_unfolding,[],[f270,f205]) ).
fof(f305,plain,
( sk4 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7)
| ssItem(sk11) ),
inference(definition_unfolding,[],[f273,f204]) ).
fof(f306,plain,
( ssList(sk7)
| sk4 = app(app(cons(sk11,nil),sk13),cons(sk12,nil)) ),
inference(definition_unfolding,[],[f277,f204]) ).
fof(f307,plain,
( ssList(sk7)
| sk3 != app(app(cons(sk12,nil),sk13),cons(sk11,nil)) ),
inference(definition_unfolding,[],[f279,f205]) ).
fof(f308,plain,
( sk4 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7)
| ssItem(sk12) ),
inference(definition_unfolding,[],[f281,f204]) ).
fof(f309,plain,
( sk4 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7)
| ssList(sk13) ),
inference(definition_unfolding,[],[f283,f204]) ).
fof(f310,plain,
( sk4 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7)
| sk4 = app(app(cons(sk11,nil),sk13),cons(sk12,nil)) ),
inference(definition_unfolding,[],[f285,f204,f204]) ).
fof(f311,plain,
( sk4 = app(app(cons(sk5,nil),cons(sk6,nil)),sk7)
| sk3 != app(app(cons(sk12,nil),sk13),cons(sk11,nil)) ),
inference(definition_unfolding,[],[f287,f204,f205]) ).
fof(f314,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f315,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ sQ0_eqProxy(sk4,app(app(cons(X0,nil),cons(X1,nil)),X2))
| ~ ssItem(X3)
| ~ ssItem(X4)
| ~ ssList(X5)
| sQ0_eqProxy(sk3,app(app(cons(X4,nil),X5),cons(X3,nil)))
| ~ sQ0_eqProxy(sk4,app(app(cons(X3,nil),X5),cons(X4,nil))) ),
inference(equality_proxy_replacement,[],[f207,f314,f314,f314]) ).
fof(f320,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ sQ0_eqProxy(sk4,app(app(cons(X0,nil),cons(X1,nil)),X2))
| ssItem(sk11) ),
inference(equality_proxy_replacement,[],[f217,f314]) ).
fof(f321,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ sQ0_eqProxy(sk4,app(app(cons(X0,nil),cons(X1,nil)),X2))
| ssItem(sk12) ),
inference(equality_proxy_replacement,[],[f219,f314]) ).
fof(f322,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ sQ0_eqProxy(sk4,app(app(cons(X0,nil),cons(X1,nil)),X2))
| ssList(sk13) ),
inference(equality_proxy_replacement,[],[f221,f314]) ).
fof(f323,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ sQ0_eqProxy(sk4,app(app(cons(X0,nil),cons(X1,nil)),X2))
| sQ0_eqProxy(sk4,app(app(cons(sk11,nil),sk13),cons(sk12,nil))) ),
inference(equality_proxy_replacement,[],[f291,f314,f314]) ).
fof(f324,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ sQ0_eqProxy(sk4,app(app(cons(X0,nil),cons(X1,nil)),X2))
| ~ sQ0_eqProxy(sk3,app(app(cons(sk12,nil),sk13),cons(sk11,nil))) ),
inference(equality_proxy_replacement,[],[f292,f314,f314]) ).
fof(f325,plain,
! [X2,X0,X1] :
( ssItem(sk5)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sQ0_eqProxy(sk3,app(app(cons(X1,nil),X2),cons(X0,nil)))
| ~ sQ0_eqProxy(sk4,app(app(cons(X0,nil),X2),cons(X1,nil))) ),
inference(equality_proxy_replacement,[],[f227,f314,f314]) ).
fof(f326,plain,
! [X2,X0,X1] :
( ssItem(sk6)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sQ0_eqProxy(sk3,app(app(cons(X1,nil),X2),cons(X0,nil)))
| ~ sQ0_eqProxy(sk4,app(app(cons(X0,nil),X2),cons(X1,nil))) ),
inference(equality_proxy_replacement,[],[f229,f314,f314]) ).
fof(f327,plain,
! [X2,X0,X1] :
( ssList(sk7)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sQ0_eqProxy(sk3,app(app(cons(X1,nil),X2),cons(X0,nil)))
| ~ sQ0_eqProxy(sk4,app(app(cons(X0,nil),X2),cons(X1,nil))) ),
inference(equality_proxy_replacement,[],[f231,f314,f314]) ).
fof(f328,plain,
! [X2,X0,X1] :
( sQ0_eqProxy(sk4,app(app(cons(sk5,nil),cons(sk6,nil)),sk7))
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| sQ0_eqProxy(sk3,app(app(cons(X1,nil),X2),cons(X0,nil)))
| ~ sQ0_eqProxy(sk4,app(app(cons(X0,nil),X2),cons(X1,nil))) ),
inference(equality_proxy_replacement,[],[f293,f314,f314,f314]) ).
fof(f330,plain,
( ssItem(sk5)
| sQ0_eqProxy(sk4,app(app(cons(sk11,nil),sk13),cons(sk12,nil))) ),
inference(equality_proxy_replacement,[],[f295,f314]) ).
fof(f331,plain,
( ssItem(sk5)
| ~ sQ0_eqProxy(sk3,app(app(cons(sk12,nil),sk13),cons(sk11,nil))) ),
inference(equality_proxy_replacement,[],[f296,f314]) ).
fof(f338,plain,
( ssItem(sk6)
| sQ0_eqProxy(sk4,app(app(cons(sk11,nil),sk13),cons(sk12,nil))) ),
inference(equality_proxy_replacement,[],[f303,f314]) ).
fof(f339,plain,
( ssItem(sk6)
| ~ sQ0_eqProxy(sk3,app(app(cons(sk12,nil),sk13),cons(sk11,nil))) ),
inference(equality_proxy_replacement,[],[f304,f314]) ).
fof(f340,plain,
( sQ0_eqProxy(sk4,app(app(cons(sk5,nil),cons(sk6,nil)),sk7))
| ssItem(sk11) ),
inference(equality_proxy_replacement,[],[f305,f314]) ).
fof(f341,plain,
( ssList(sk7)
| sQ0_eqProxy(sk4,app(app(cons(sk11,nil),sk13),cons(sk12,nil))) ),
inference(equality_proxy_replacement,[],[f306,f314]) ).
fof(f342,plain,
( ssList(sk7)
| ~ sQ0_eqProxy(sk3,app(app(cons(sk12,nil),sk13),cons(sk11,nil))) ),
inference(equality_proxy_replacement,[],[f307,f314]) ).
fof(f343,plain,
( sQ0_eqProxy(sk4,app(app(cons(sk5,nil),cons(sk6,nil)),sk7))
| ssItem(sk12) ),
inference(equality_proxy_replacement,[],[f308,f314]) ).
fof(f344,plain,
( sQ0_eqProxy(sk4,app(app(cons(sk5,nil),cons(sk6,nil)),sk7))
| ssList(sk13) ),
inference(equality_proxy_replacement,[],[f309,f314]) ).
fof(f345,plain,
( sQ0_eqProxy(sk4,app(app(cons(sk5,nil),cons(sk6,nil)),sk7))
| sQ0_eqProxy(sk4,app(app(cons(sk11,nil),sk13),cons(sk12,nil))) ),
inference(equality_proxy_replacement,[],[f310,f314,f314]) ).
fof(f346,plain,
( sQ0_eqProxy(sk4,app(app(cons(sk5,nil),cons(sk6,nil)),sk7))
| ~ sQ0_eqProxy(sk3,app(app(cons(sk12,nil),sk13),cons(sk11,nil))) ),
inference(equality_proxy_replacement,[],[f311,f314,f314]) ).
fof(f372,definition,
( spl1_3
<=> sQ0_eqProxy(sk3,app(app(cons(sk12,nil),sk13),cons(sk11,nil))) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f373,plain,
( ~ sQ0_eqProxy(sk3,app(app(cons(sk12,nil),sk13),cons(sk11,nil)))
| spl1_3 ),
inference(avatar_component_clause,[],[f372]) ).
fof(f375,definition,
( spl1_4
<=> sQ0_eqProxy(sk4,app(app(cons(sk5,nil),cons(sk6,nil)),sk7)) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f376,plain,
( sQ0_eqProxy(sk4,app(app(cons(sk5,nil),cons(sk6,nil)),sk7))
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f375]) ).
fof(f377,plain,
( ~ spl1_3
| spl1_4 ),
inference(avatar_split_clause,[],[f346,f375,f372]) ).
fof(f379,definition,
( spl1_5
<=> sQ0_eqProxy(sk4,app(app(cons(sk11,nil),sk13),cons(sk12,nil))) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f381,plain,
( spl1_5
| spl1_4 ),
inference(avatar_split_clause,[],[f345,f375,f379]) ).
fof(f383,definition,
( spl1_6
<=> ssList(sk13) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f385,plain,
( spl1_6
| spl1_4 ),
inference(avatar_split_clause,[],[f344,f375,f383]) ).
fof(f387,definition,
( spl1_7
<=> ssItem(sk12) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
fof(f389,plain,
( spl1_7
| spl1_4 ),
inference(avatar_split_clause,[],[f343,f375,f387]) ).
fof(f391,definition,
( spl1_8
<=> ssList(sk7) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f393,plain,
( ~ spl1_3
| spl1_8 ),
inference(avatar_split_clause,[],[f342,f391,f372]) ).
fof(f394,plain,
( spl1_5
| spl1_8 ),
inference(avatar_split_clause,[],[f341,f391,f379]) ).
fof(f395,plain,
( spl1_6
| spl1_8 ),
inference(avatar_split_clause,[],[f275,f391,f383]) ).
fof(f396,plain,
( spl1_7
| spl1_8 ),
inference(avatar_split_clause,[],[f274,f391,f387]) ).
fof(f398,definition,
( spl1_9
<=> ssItem(sk11) ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
fof(f400,plain,
( spl1_9
| spl1_4 ),
inference(avatar_split_clause,[],[f340,f375,f398]) ).
fof(f401,plain,
( spl1_9
| spl1_8 ),
inference(avatar_split_clause,[],[f271,f391,f398]) ).
fof(f403,definition,
( spl1_10
<=> ssItem(sk6) ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
fof(f405,plain,
( ~ spl1_3
| spl1_10 ),
inference(avatar_split_clause,[],[f339,f403,f372]) ).
fof(f406,plain,
( spl1_5
| spl1_10 ),
inference(avatar_split_clause,[],[f338,f403,f379]) ).
fof(f407,plain,
( spl1_6
| spl1_10 ),
inference(avatar_split_clause,[],[f266,f403,f383]) ).
fof(f408,plain,
( spl1_7
| spl1_10 ),
inference(avatar_split_clause,[],[f265,f403,f387]) ).
fof(f409,plain,
( spl1_9
| spl1_10 ),
inference(avatar_split_clause,[],[f264,f403,f398]) ).
fof(f435,definition,
( spl1_15
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[spl1_15])],[avatar_definition]) ).
fof(f437,plain,
( ~ spl1_3
| spl1_15 ),
inference(avatar_split_clause,[],[f331,f435,f372]) ).
fof(f438,plain,
( spl1_5
| spl1_15 ),
inference(avatar_split_clause,[],[f330,f435,f379]) ).
fof(f439,plain,
( spl1_6
| spl1_15 ),
inference(avatar_split_clause,[],[f241,f435,f383]) ).
fof(f440,plain,
( spl1_7
| spl1_15 ),
inference(avatar_split_clause,[],[f240,f435,f387]) ).
fof(f441,plain,
( spl1_9
| spl1_15 ),
inference(avatar_split_clause,[],[f239,f435,f398]) ).
fof(f447,definition,
( spl1_16
<=> ! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ sQ0_eqProxy(sk4,app(app(cons(X0,nil),X2),cons(X1,nil)))
| ~ ssList(X2)
| ~ ssItem(X1)
| sQ0_eqProxy(sk3,app(app(cons(X1,nil),X2),cons(X0,nil))) ) ),
introduced(definition,[new_symbols(definition,[spl1_16])],[avatar_definition]) ).
fof(f448,plain,
( ! [X2,X0,X1] :
( sQ0_eqProxy(sk3,app(app(cons(X1,nil),X2),cons(X0,nil)))
| ~ sQ0_eqProxy(sk4,app(app(cons(X0,nil),X2),cons(X1,nil)))
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) )
| ~ spl1_16 ),
inference(avatar_component_clause,[],[f447]) ).
fof(f449,plain,
( spl1_16
| spl1_4 ),
inference(avatar_split_clause,[],[f328,f375,f447]) ).
fof(f450,plain,
( spl1_16
| spl1_8 ),
inference(avatar_split_clause,[],[f327,f391,f447]) ).
fof(f451,plain,
( spl1_16
| spl1_10 ),
inference(avatar_split_clause,[],[f326,f403,f447]) ).
fof(f452,plain,
( spl1_16
| spl1_15 ),
inference(avatar_split_clause,[],[f325,f435,f447]) ).
fof(f454,definition,
( spl1_17
<=> ! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ sQ0_eqProxy(sk4,app(app(cons(X0,nil),cons(X1,nil)),X2))
| ~ ssList(X2)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[spl1_17])],[avatar_definition]) ).
fof(f455,plain,
( ! [X2,X0,X1] :
( ~ sQ0_eqProxy(sk4,app(app(cons(X0,nil),cons(X1,nil)),X2))
| ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssItem(X1) )
| ~ spl1_17 ),
inference(avatar_component_clause,[],[f454]) ).
fof(f456,plain,
( ~ spl1_3
| spl1_17 ),
inference(avatar_split_clause,[],[f324,f454,f372]) ).
fof(f457,plain,
( spl1_5
| spl1_17 ),
inference(avatar_split_clause,[],[f323,f454,f379]) ).
fof(f458,plain,
( spl1_6
| spl1_17 ),
inference(avatar_split_clause,[],[f322,f454,f383]) ).
fof(f459,plain,
( spl1_7
| spl1_17 ),
inference(avatar_split_clause,[],[f321,f454,f387]) ).
fof(f460,plain,
( spl1_9
| spl1_17 ),
inference(avatar_split_clause,[],[f320,f454,f398]) ).
fof(f465,plain,
( spl1_16
| spl1_17 ),
inference(avatar_split_clause,[],[f315,f454,f447]) ).
fof(f466,plain,
( ~ sQ0_eqProxy(sk4,app(app(cons(sk11,nil),sk13),cons(sk12,nil)))
| ~ ssList(sk13)
| ~ ssItem(sk12)
| ~ ssItem(sk11)
| spl1_3
| ~ spl1_16 ),
inference(resolution,[],[f448,f373]) ).
fof(f471,plain,
( ~ spl1_9
| ~ spl1_7
| ~ spl1_6
| ~ spl1_5
| spl1_3
| ~ spl1_16 ),
inference(avatar_split_clause,[],[f466,f447,f372,f379,f383,f387,f398]) ).
fof(f473,plain,
( ~ ssItem(sk5)
| ~ ssList(sk7)
| ~ ssItem(sk6)
| ~ spl1_4
| ~ spl1_17 ),
inference(resolution,[],[f455,f376]) ).
fof(f477,plain,
( ~ spl1_10
| ~ spl1_8
| ~ spl1_15
| ~ spl1_4
| ~ spl1_17 ),
inference(avatar_split_clause,[],[f473,f454,f375,f435,f391,f403]) ).
cnf(s2,plain,
( ~ spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f377]) ).
cnf(s3,plain,
( spl1_4
| spl1_5 ),
inference(sat_conversion,[],[f381]) ).
cnf(s4,plain,
( spl1_4
| spl1_6 ),
inference(sat_conversion,[],[f385]) ).
cnf(s5,plain,
( spl1_4
| spl1_7 ),
inference(sat_conversion,[],[f389]) ).
cnf(s6,plain,
( ~ spl1_3
| spl1_8 ),
inference(sat_conversion,[],[f393]) ).
cnf(s7,plain,
( spl1_5
| spl1_8 ),
inference(sat_conversion,[],[f394]) ).
cnf(s8,plain,
( spl1_6
| spl1_8 ),
inference(sat_conversion,[],[f395]) ).
cnf(s9,plain,
( spl1_7
| spl1_8 ),
inference(sat_conversion,[],[f396]) ).
cnf(s10,plain,
( spl1_4
| spl1_9 ),
inference(sat_conversion,[],[f400]) ).
cnf(s11,plain,
( spl1_8
| spl1_9 ),
inference(sat_conversion,[],[f401]) ).
cnf(s12,plain,
( ~ spl1_3
| spl1_10 ),
inference(sat_conversion,[],[f405]) ).
cnf(s13,plain,
( spl1_5
| spl1_10 ),
inference(sat_conversion,[],[f406]) ).
cnf(s14,plain,
( spl1_6
| spl1_10 ),
inference(sat_conversion,[],[f407]) ).
cnf(s15,plain,
( spl1_7
| spl1_10 ),
inference(sat_conversion,[],[f408]) ).
cnf(s16,plain,
( spl1_9
| spl1_10 ),
inference(sat_conversion,[],[f409]) ).
cnf(s29,plain,
( ~ spl1_3
| spl1_15 ),
inference(sat_conversion,[],[f437]) ).
cnf(s30,plain,
( spl1_5
| spl1_15 ),
inference(sat_conversion,[],[f438]) ).
cnf(s31,plain,
( spl1_6
| spl1_15 ),
inference(sat_conversion,[],[f439]) ).
cnf(s32,plain,
( spl1_7
| spl1_15 ),
inference(sat_conversion,[],[f440]) ).
cnf(s33,plain,
( spl1_9
| spl1_15 ),
inference(sat_conversion,[],[f441]) ).
cnf(s38,plain,
( spl1_4
| spl1_16 ),
inference(sat_conversion,[],[f449]) ).
cnf(s39,plain,
( spl1_8
| spl1_16 ),
inference(sat_conversion,[],[f450]) ).
cnf(s40,plain,
( spl1_10
| spl1_16 ),
inference(sat_conversion,[],[f451]) ).
cnf(s41,plain,
( spl1_15
| spl1_16 ),
inference(sat_conversion,[],[f452]) ).
cnf(s42,plain,
( ~ spl1_3
| spl1_17 ),
inference(sat_conversion,[],[f456]) ).
cnf(s43,plain,
( spl1_5
| spl1_17 ),
inference(sat_conversion,[],[f457]) ).
cnf(s44,plain,
( spl1_6
| spl1_17 ),
inference(sat_conversion,[],[f458]) ).
cnf(s45,plain,
( spl1_7
| spl1_17 ),
inference(sat_conversion,[],[f459]) ).
cnf(s46,plain,
( spl1_9
| spl1_17 ),
inference(sat_conversion,[],[f460]) ).
cnf(s51,plain,
( spl1_16
| spl1_17 ),
inference(sat_conversion,[],[f465]) ).
cnf(s52,plain,
( spl1_3
| ~ spl1_5
| ~ spl1_6
| ~ spl1_7
| ~ spl1_9
| ~ spl1_16 ),
inference(sat_conversion,[],[f471]) ).
cnf(s53,plain,
( ~ spl1_4
| ~ spl1_8
| ~ spl1_10
| ~ spl1_15
| ~ spl1_17 ),
inference(sat_conversion,[],[f477]) ).
cnf(s55,plain,
( spl1_4
| spl1_3 ),
inference(rat,[],[s52,s3,s4,s5,s10,s38]) ).
cnf(s56,plain,
( spl1_16
| ~ spl1_4 ),
inference(rat,[],[s53,s39,s40,s41,s51]) ).
cnf(s57,plain,
( spl1_9
| ~ spl1_4 ),
inference(rat,[],[s53,s11,s16,s33,s46]) ).
cnf(s58,plain,
( spl1_7
| ~ spl1_4 ),
inference(rat,[],[s53,s9,s15,s32,s45]) ).
cnf(s59,plain,
( spl1_6
| ~ spl1_4 ),
inference(rat,[],[s53,s8,s14,s31,s44]) ).
cnf(s60,plain,
spl1_3,
inference(rat,[],[s53,s7,s13,s30,s43,s52,s59,s58,s57,s56,s55]) ).
cnf(s61,plain,
spl1_17,
inference(rat,[],[s42,s60]) ).
cnf(s62,plain,
spl1_15,
inference(rat,[],[s29,s60]) ).
cnf(s63,plain,
spl1_10,
inference(rat,[],[s12,s60]) ).
cnf(s64,plain,
spl1_8,
inference(rat,[],[s6,s60]) ).
cnf(s65,plain,
spl1_4,
inference(rat,[],[s2,s60]) ).
cnf(s66,plain,
$false,
inference(rat,[],[s53,s61,s62,s65,s63,s64]) ).
fof(f482,plain,
$false,
inference(avatar_sat_refutation,[],[s66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC412-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 % Computer : n017.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.23 % DateTime : Mon Sep 28 09:27:35 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.29 Running first-order theorem proving
% 0.25/0.29 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.87/1.41 % (3427483)Input is clausal, will run a generic CNF schedule.
% 1.87/1.41 % (3427494)dis-21_1_sil=8000:lcm=predicate:random_seed=188813234:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 1.87/1.41 % (3427494)First to succeed.
% 1.87/1.41 % (3427494)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3427483"
% 1.87/1.41 % (3427493)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2679462254:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 1.87/1.41 % (3427491)lrs+10_1_sil=8000:sp=occurrence:random_seed=1174975798:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 1.87/1.41 % (3427488)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=383375808:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 1.87/1.41 % (3427490)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1898300232:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 1.87/1.41 % (3427489)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2100044433:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 1.87/1.41 % (3427492)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2001637878:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 1.87/1.41 % (3427493)Also succeeded, but the first one will report.
% 1.87/1.41 % (3427491)Also succeeded, but the first one will report.
% 1.87/1.41 % (3427492)Also succeeded, but the first one will report.
% 1.87/1.41 % (3427494)Refutation found. Thanks to Tanya!
% 1.87/1.41 % SZS status Unsatisfiable for theBenchmark
% 1.87/1.41 % SZS output start Proof for theBenchmark
% See solution above
% 4.73/1.56 % (3427494)------------------------------
% 4.73/1.56 % (3427494)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.73/1.56 % (3427494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.73/1.56 % (3427494)CaDiCaL version: 2.1.3
% 4.73/1.56 % (3427494)Termination reason: Refutation
% 4.73/1.56 % (3427494)Time elapsed: 0.009 s
% 4.73/1.56 % (3427494)Peak memory usage: 89 MB
% 4.73/1.56 % (3427494)Instructions burned: 10 (million)
% 4.73/1.56 % (3427494)------------------------------
% 4.73/1.56 % (3427494)------------------------------
% 4.73/1.56 % (3427483)Success in time 0.565 s
% 4.73/1.56 % Vampire exiting
%------------------------------------------------------------------------------