%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC006-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 01:02:00 PM UTC 2026
% Result : Unsatisfiable 2.69s 1.35s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 43 ( 21 unt; 5 def)
% Number of atoms : 83 ( 11 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 78 ( 38 ~; 35 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X0,X1),X2) != sk2
| app(X0,X2) != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
ssList(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
ssList(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
ssList(sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f210,negated_conjecture,
app(app(sk5,sk6),sk7) = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f211,plain,
sk4 = app(app(sk5,sk6),sk7),
inference(reorient_equations,[],[f210]) ).
fof(f212,negated_conjecture,
app(sk5,sk7) = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f213,plain,
sk3 = app(sk5,sk7),
inference(reorient_equations,[],[f212]) ).
fof(f216,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X0,X1),X2) != sk4
| app(X0,X2) != sk3 ),
inference(definition_unfolding,[],[f206,f204,f205]) ).
fof(f236,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f237,plain,
! [X2,X0,X1] :
( ~ sQ0_eqProxy(app(app(X0,X1),X2),sk4)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ sQ0_eqProxy(app(X0,X2),sk3) ),
inference(equality_proxy_replacement,[],[f216,f236,f236]) ).
fof(f238,plain,
sQ0_eqProxy(sk4,app(app(sk5,sk6),sk7)),
inference(equality_proxy_replacement,[],[f211,f236]) ).
fof(f239,plain,
sQ0_eqProxy(sk3,app(sk5,sk7)),
inference(equality_proxy_replacement,[],[f213,f236]) ).
fof(f291,plain,
! [X0,X1] :
( sQ0_eqProxy(X1,X0)
| ~ sQ0_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f236]) ).
fof(f325,plain,
! [X2,X0,X1] :
( ~ sQ0_eqProxy(sk4,app(app(X0,X1),X2))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ sQ0_eqProxy(app(X0,X2),sk3) ),
inference(resolution,[],[f291,f237]) ).
fof(f326,plain,
( ~ ssList(sk6)
| ~ ssList(sk7)
| ~ ssList(sk5)
| ~ sQ0_eqProxy(app(sk5,sk7),sk3) ),
inference(resolution,[],[f325,f238]) ).
fof(f329,definition,
( spl1_8
<=> sQ0_eqProxy(app(sk5,sk7),sk3) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f330,plain,
( ~ sQ0_eqProxy(app(sk5,sk7),sk3)
| spl1_8 ),
inference(avatar_component_clause,[],[f329]) ).
fof(f332,definition,
( spl1_9
<=> ssList(sk5) ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
fof(f333,plain,
( ~ ssList(sk5)
| spl1_9 ),
inference(avatar_component_clause,[],[f332]) ).
fof(f335,definition,
( spl1_10
<=> ssList(sk7) ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
fof(f336,plain,
( ~ ssList(sk7)
| spl1_10 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f338,definition,
( spl1_11
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition]) ).
fof(f339,plain,
( ~ ssList(sk6)
| spl1_11 ),
inference(avatar_component_clause,[],[f338]) ).
fof(f340,plain,
( ~ spl1_8
| ~ spl1_9
| ~ spl1_10
| ~ spl1_11 ),
inference(avatar_split_clause,[],[f326,f338,f335,f332,f329]) ).
fof(f341,plain,
( ~ sQ0_eqProxy(sk3,app(sk5,sk7))
| spl1_8 ),
inference(resolution,[],[f330,f291]) ).
fof(f342,plain,
( $false
| spl1_8 ),
inference(resolution,[],[f341,f239]) ).
fof(f344,plain,
spl1_8,
inference(avatar_contradiction_clause,[],[f342]) ).
fof(f345,plain,
( $false
| spl1_9 ),
inference(resolution,[],[f333,f207]) ).
fof(f346,plain,
spl1_9,
inference(avatar_contradiction_clause,[],[f345]) ).
fof(f347,plain,
( $false
| spl1_10 ),
inference(resolution,[],[f336,f209]) ).
fof(f348,plain,
spl1_10,
inference(avatar_contradiction_clause,[],[f347]) ).
fof(f349,plain,
( $false
| spl1_11 ),
inference(resolution,[],[f339,f208]) ).
fof(f350,plain,
spl1_11,
inference(avatar_contradiction_clause,[],[f349]) ).
cnf(s8,plain,
( ~ spl1_8
| ~ spl1_9
| ~ spl1_10
| ~ spl1_11 ),
inference(sat_conversion,[],[f340]) ).
cnf(s9,plain,
spl1_8,
inference(sat_conversion,[],[f344]) ).
cnf(s10,plain,
spl1_9,
inference(sat_conversion,[],[f346]) ).
cnf(s11,plain,
spl1_10,
inference(sat_conversion,[],[f348]) ).
cnf(s12,plain,
spl1_11,
inference(sat_conversion,[],[f350]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s8,s12,s11,s10,s9]) ).
fof(f351,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC006-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 07:27:59 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.69/1.35 % (3675731)Input is clausal, will run a generic CNF schedule.
% 2.69/1.35 % (3675743)dis-21_1_sil=8000:lcm=predicate:random_seed=3206631508: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)
% 2.69/1.35 % (3675743)First to succeed.
% 2.69/1.35 % (3675743)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3675731"
% 2.69/1.35 % (3675742)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1104523785:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.69/1.35 % (3675738)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3977884392:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.69/1.35 % (3675740)lrs+10_1_sil=8000:sp=occurrence:random_seed=361421871:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.69/1.35 % (3675737)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=581299340:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.69/1.35 % (3675741)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2368789709:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.69/1.35 % (3675739)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=387797076:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.69/1.35 % (3675740)Also succeeded, but the first one will report.
% 2.69/1.35 % (3675741)Also succeeded, but the first one will report.
% 2.69/1.35 % (3675742)Also succeeded, but the first one will report.
% 2.69/1.35 % (3675743)Refutation found. Thanks to Tanya!
% 2.69/1.35 % SZS status Unsatisfiable for theBenchmark
% 2.69/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.69/1.35 % (3675743)------------------------------
% 2.69/1.35 % (3675743)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.35 % (3675743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.35 % (3675743)CaDiCaL version: 2.1.3
% 2.69/1.35 % (3675743)Termination reason: Refutation
% 2.69/1.35 % (3675743)Time elapsed: 0.003 s
% 2.69/1.35 % (3675743)Peak memory usage: 89 MB
% 2.69/1.35 % (3675743)Instructions burned: 7 (million)
% 2.69/1.35 % (3675743)------------------------------
% 2.69/1.35 % (3675743)------------------------------
% 2.69/1.35 % (3675731)Success in time 0.299 s
% 2.69/1.35 % Vampire exiting
%------------------------------------------------------------------------------