%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC279-1 : 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 : n020.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 01:03:15 PM UTC 2026
% Result : Unsatisfiable 2.54s 1.13s
% Output : Refutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 23
% Syntax : Number of formulae : 79 ( 25 unt; 11 def)
% Number of atoms : 200 ( 9 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 228 ( 107 ~; 110 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 11 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X1,cons(X0,nil)),X2) != sk3
| ~ ssItem(X3)
| leq(X0,X3)
| ~ memberP(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,plain,
! [X2,X3,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| sk3 != app(app(X1,cons(X0,nil)),X2)
| ~ ssItem(X3)
| leq(X0,X3)
| ~ memberP(X2,X3) ),
inference(reorient_equations,[],[f206]) ).
fof(f208,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X1,cons(X0,nil)),X2) != sk3
| ~ ssItem(X3)
| leq(X3,X0)
| ~ memberP(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f209,plain,
! [X2,X3,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| sk3 != app(app(X1,cons(X0,nil)),X2)
| ~ ssItem(X3)
| leq(X3,X0)
| ~ memberP(X1,X3) ),
inference(reorient_equations,[],[f208]) ).
fof(f210,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f211,negated_conjecture,
ssList(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f212,negated_conjecture,
ssList(sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f213,negated_conjecture,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f214,plain,
sk1 = app(app(sk6,cons(sk5,nil)),sk7),
inference(reorient_equations,[],[f213]) ).
fof(f215,negated_conjecture,
ssItem(sk8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
fof(f216,negated_conjecture,
( memberP(sk6,sk8)
| memberP(sk7,sk8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
fof(f217,negated_conjecture,
( memberP(sk6,sk8)
| ~ leq(sk5,sk8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f218,negated_conjecture,
( ~ leq(sk8,sk5)
| memberP(sk7,sk8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
fof(f219,negated_conjecture,
( ~ leq(sk8,sk5)
| ~ leq(sk5,sk8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
fof(f222,plain,
sk3 = app(app(sk6,cons(sk5,nil)),sk7),
inference(definition_unfolding,[],[f214,f205]) ).
fof(f242,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f243,plain,
! [X2,X3,X0,X1] :
( ~ sQ0_eqProxy(sk3,app(app(X1,cons(X0,nil)),X2))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X0)
| ~ ssItem(X3)
| leq(X0,X3)
| ~ memberP(X2,X3) ),
inference(equality_proxy_replacement,[],[f207,f242]) ).
fof(f244,plain,
! [X2,X3,X0,X1] :
( ~ sQ0_eqProxy(sk3,app(app(X1,cons(X0,nil)),X2))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X0)
| ~ ssItem(X3)
| leq(X3,X0)
| ~ memberP(X1,X3) ),
inference(equality_proxy_replacement,[],[f209,f242]) ).
fof(f245,plain,
sQ0_eqProxy(sk3,app(app(sk6,cons(sk5,nil)),sk7)),
inference(equality_proxy_replacement,[],[f222,f242]) ).
fof(f329,definition,
( spl1_8
<=> leq(sk5,sk8) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f332,definition,
( spl1_9
<=> leq(sk8,sk5) ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
fof(f334,plain,
( ~ spl1_8
| ~ spl1_9 ),
inference(avatar_split_clause,[],[f219,f332,f329]) ).
fof(f336,definition,
( spl1_10
<=> memberP(sk7,sk8) ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
fof(f337,plain,
( memberP(sk7,sk8)
| ~ spl1_10 ),
inference(avatar_component_clause,[],[f336]) ).
fof(f338,plain,
( spl1_10
| ~ spl1_9 ),
inference(avatar_split_clause,[],[f218,f332,f336]) ).
fof(f340,definition,
( spl1_11
<=> memberP(sk6,sk8) ),
introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition]) ).
fof(f341,plain,
( memberP(sk6,sk8)
| ~ spl1_11 ),
inference(avatar_component_clause,[],[f340]) ).
fof(f342,plain,
( ~ spl1_8
| spl1_11 ),
inference(avatar_split_clause,[],[f217,f340,f329]) ).
fof(f343,plain,
( spl1_10
| spl1_11 ),
inference(avatar_split_clause,[],[f216,f340,f336]) ).
fof(f346,plain,
! [X0] :
( ~ ssList(sk6)
| ~ ssList(sk7)
| ~ ssItem(sk5)
| ~ ssItem(X0)
| leq(sk5,X0)
| ~ memberP(sk7,X0) ),
inference(resolution,[],[f243,f245]) ).
fof(f348,definition,
( spl1_12
<=> ! [X0] :
( ~ ssItem(X0)
| ~ memberP(sk7,X0)
| leq(sk5,X0) ) ),
introduced(definition,[new_symbols(definition,[spl1_12])],[avatar_definition]) ).
fof(f349,plain,
( ! [X0] :
( ~ memberP(sk7,X0)
| ~ ssItem(X0)
| leq(sk5,X0) )
| ~ spl1_12 ),
inference(avatar_component_clause,[],[f348]) ).
fof(f351,definition,
( spl1_13
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[spl1_13])],[avatar_definition]) ).
fof(f352,plain,
( ~ ssItem(sk5)
| spl1_13 ),
inference(avatar_component_clause,[],[f351]) ).
fof(f354,definition,
( spl1_14
<=> ssList(sk7) ),
introduced(definition,[new_symbols(definition,[spl1_14])],[avatar_definition]) ).
fof(f355,plain,
( ~ ssList(sk7)
| spl1_14 ),
inference(avatar_component_clause,[],[f354]) ).
fof(f357,definition,
( spl1_15
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[spl1_15])],[avatar_definition]) ).
fof(f358,plain,
( ~ ssList(sk6)
| spl1_15 ),
inference(avatar_component_clause,[],[f357]) ).
fof(f359,plain,
( spl1_12
| ~ spl1_13
| ~ spl1_14
| ~ spl1_15 ),
inference(avatar_split_clause,[],[f346,f357,f354,f351,f348]) ).
fof(f360,plain,
( $false
| spl1_13 ),
inference(resolution,[],[f352,f210]) ).
fof(f361,plain,
spl1_13,
inference(avatar_contradiction_clause,[],[f360]) ).
fof(f362,plain,
( $false
| spl1_14 ),
inference(resolution,[],[f355,f212]) ).
fof(f363,plain,
spl1_14,
inference(avatar_contradiction_clause,[],[f362]) ).
fof(f364,plain,
( $false
| spl1_15 ),
inference(resolution,[],[f358,f211]) ).
fof(f365,plain,
spl1_15,
inference(avatar_contradiction_clause,[],[f364]) ).
fof(f366,plain,
( ~ ssItem(sk8)
| leq(sk5,sk8)
| ~ spl1_10
| ~ spl1_12 ),
inference(resolution,[],[f349,f337]) ).
fof(f369,definition,
( spl1_16
<=> ssItem(sk8) ),
introduced(definition,[new_symbols(definition,[spl1_16])],[avatar_definition]) ).
fof(f370,plain,
( ~ ssItem(sk8)
| spl1_16 ),
inference(avatar_component_clause,[],[f369]) ).
fof(f371,plain,
( spl1_8
| ~ spl1_16
| ~ spl1_10
| ~ spl1_12 ),
inference(avatar_split_clause,[],[f366,f348,f336,f369,f329]) ).
fof(f372,plain,
( $false
| spl1_16 ),
inference(resolution,[],[f370,f215]) ).
fof(f373,plain,
spl1_16,
inference(avatar_contradiction_clause,[],[f372]) ).
fof(f374,plain,
! [X0] :
( ~ ssList(sk6)
| ~ ssList(sk7)
| ~ ssItem(sk5)
| ~ ssItem(X0)
| leq(X0,sk5)
| ~ memberP(sk6,X0) ),
inference(resolution,[],[f244,f245]) ).
fof(f376,definition,
( spl1_17
<=> ! [X0] :
( ~ ssItem(X0)
| ~ memberP(sk6,X0)
| leq(X0,sk5) ) ),
introduced(definition,[new_symbols(definition,[spl1_17])],[avatar_definition]) ).
fof(f377,plain,
( ! [X0] :
( ~ memberP(sk6,X0)
| ~ ssItem(X0)
| leq(X0,sk5) )
| ~ spl1_17 ),
inference(avatar_component_clause,[],[f376]) ).
fof(f378,plain,
( spl1_17
| ~ spl1_13
| ~ spl1_14
| ~ spl1_15 ),
inference(avatar_split_clause,[],[f374,f357,f354,f351,f376]) ).
fof(f379,plain,
( ~ ssItem(sk8)
| leq(sk8,sk5)
| ~ spl1_11
| ~ spl1_17 ),
inference(resolution,[],[f377,f341]) ).
fof(f381,plain,
( spl1_9
| ~ spl1_16
| ~ spl1_11
| ~ spl1_17 ),
inference(avatar_split_clause,[],[f379,f376,f340,f369,f332]) ).
cnf(s7,plain,
( ~ spl1_8
| ~ spl1_9 ),
inference(sat_conversion,[],[f334]) ).
cnf(s8,plain,
( ~ spl1_9
| spl1_10 ),
inference(sat_conversion,[],[f338]) ).
cnf(s9,plain,
( ~ spl1_8
| spl1_11 ),
inference(sat_conversion,[],[f342]) ).
cnf(s10,plain,
( spl1_10
| spl1_11 ),
inference(sat_conversion,[],[f343]) ).
cnf(s12,plain,
( spl1_12
| ~ spl1_13
| ~ spl1_14
| ~ spl1_15 ),
inference(sat_conversion,[],[f359]) ).
cnf(s13,plain,
spl1_13,
inference(sat_conversion,[],[f361]) ).
cnf(s14,plain,
spl1_14,
inference(sat_conversion,[],[f363]) ).
cnf(s15,plain,
spl1_15,
inference(sat_conversion,[],[f365]) ).
cnf(s16,plain,
( spl1_8
| ~ spl1_10
| ~ spl1_12
| ~ spl1_16 ),
inference(sat_conversion,[],[f371]) ).
cnf(s17,plain,
spl1_16,
inference(sat_conversion,[],[f373]) ).
cnf(s18,plain,
( ~ spl1_13
| ~ spl1_14
| ~ spl1_15
| spl1_17 ),
inference(sat_conversion,[],[f378]) ).
cnf(s19,plain,
( spl1_9
| ~ spl1_11
| ~ spl1_16
| ~ spl1_17 ),
inference(sat_conversion,[],[f381]) ).
cnf(s20,plain,
( spl1_8
| ~ spl1_10
| ~ spl1_12 ),
inference(rat,[],[s16,s17]) ).
cnf(s21,plain,
spl1_17,
inference(rat,[],[s18,s14,s15,s13]) ).
cnf(s22,plain,
spl1_12,
inference(rat,[],[s12,s15,s14,s13]) ).
cnf(s29,plain,
spl1_10,
inference(rat,[],[s19,s8,s10,s17,s21]) ).
cnf(s30,plain,
spl1_8,
inference(rat,[],[s20,s22,s29]) ).
cnf(s31,plain,
spl1_11,
inference(rat,[],[s9,s30]) ).
cnf(s32,plain,
~ spl1_9,
inference(rat,[],[s7,s30]) ).
cnf(s33,plain,
$false,
inference(rat,[],[s19,s21,s17,s31,s32]) ).
fof(f382,plain,
$false,
inference(avatar_sat_refutation,[],[s33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC279-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n020.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 08:51:50 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 2.54/1.13 % (39806)Input is clausal, will run a generic CNF schedule.
% 2.54/1.13 % (39817)dis-21_1_sil=8000:lcm=predicate:random_seed=2815770580: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)
% 2.54/1.13 % (39817)First to succeed.
% 2.54/1.13 % (39817)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-39806"
% 2.54/1.13 % (39815)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2996802035:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.54/1.13 % (39815)Also succeeded, but the first one will report.
% 2.54/1.13 % (39814)lrs+10_1_sil=8000:sp=occurrence:random_seed=2425372905:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.54/1.13 % (39811)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=669198052:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.54/1.13 % (39813)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1606242177:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.54/1.13 % (39812)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3912829765:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.54/1.13 % (39814)Also succeeded, but the first one will report.
% 2.54/1.13 % (39816)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2705256998:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.54/1.13 % (39816)Also succeeded, but the first one will report.
% 2.54/1.13 % (39817)Refutation found. Thanks to Tanya!
% 2.54/1.13 % SZS status Unsatisfiable for theBenchmark
% 2.54/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 2.66/1.13 % (39817)------------------------------
% 2.66/1.13 % (39817)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.13 % (39817)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.13 % (39817)CaDiCaL version: 2.1.3
% 2.66/1.13 % (39817)Termination reason: Refutation
% 2.66/1.13 % (39817)Time elapsed: 0.003 s
% 2.66/1.13 % (39817)Peak memory usage: 89 MB
% 2.66/1.13 % (39817)Instructions burned: 7 (million)
% 2.66/1.13 % (39817)------------------------------
% 2.66/1.13 % (39817)------------------------------
% 2.66/1.13 % (39806)Success in time 0.279 s
% 2.66/1.13 % Vampire exiting
%------------------------------------------------------------------------------