%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC381-1 : 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 : n007.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 01:03:43 PM UTC 2026
% Result : Unsatisfiable 2.83s 1.17s
% Output : Refutation 2.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 42 ( 11 unt; 5 def)
% Number of atoms : 95 ( 11 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 109 ( 56 ~; 48 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 4 ( 0 sgn 4 !; 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,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f213,negated_conjecture,
! [X0] :
( ~ ssItem(X0)
| cons(X0,nil) != sk1
| ~ memberP(sk2,X0)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
fof(f214,negated_conjecture,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
fof(f215,negated_conjecture,
( cons(sk5,nil) = sk3
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
fof(f216,plain,
( sk3 = cons(sk5,nil)
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f215]) ).
fof(f217,negated_conjecture,
( memberP(sk4,sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
fof(f220,plain,
( neq(sk4,nil)
| neq(sk4,nil) ),
inference(definition_unfolding,[],[f206,f204,f204]) ).
fof(f226,plain,
! [X0] :
( ~ ssItem(X0)
| cons(X0,nil) != sk3
| ~ memberP(sk4,X0)
| ~ neq(sk4,nil) ),
inference(definition_unfolding,[],[f213,f205,f204]) ).
fof(f237,plain,
neq(sk4,nil),
inference(duplicate_literal_removal,[],[f220]) ).
fof(f246,definition,
( spl0_3
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f249,definition,
( spl0_4
<=> memberP(sk4,sk5) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f250,plain,
( memberP(sk4,sk5)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f251,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f217,f249,f246]) ).
fof(f253,definition,
( spl0_5
<=> sk3 = cons(sk5,nil) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f254,plain,
( sk3 = cons(sk5,nil)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f255,plain,
( ~ spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f216,f253,f246]) ).
fof(f257,definition,
( spl0_6
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f258,plain,
( ssItem(sk5)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f259,plain,
( ~ spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f214,f257,f246]) ).
fof(f261,definition,
( spl0_7
<=> ! [X0] :
( ~ ssItem(X0)
| ~ memberP(sk4,X0)
| cons(X0,nil) != sk3 ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f262,plain,
( ! [X0] :
( cons(X0,nil) != sk3
| ~ memberP(sk4,X0)
| ~ ssItem(X0) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f263,plain,
( ~ spl0_3
| spl0_7 ),
inference(avatar_split_clause,[],[f226,f261,f246]) ).
fof(f269,plain,
spl0_3,
inference(avatar_split_clause,[],[f237,f246]) ).
fof(f270,plain,
( sk3 != sk3
| ~ memberP(sk4,sk5)
| ~ ssItem(sk5)
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f262,f254]) ).
fof(f271,plain,
( ~ memberP(sk4,sk5)
| ~ ssItem(sk5)
| ~ spl0_5
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f270]) ).
fof(f272,plain,
( ~ ssItem(sk5)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f271,f250]) ).
fof(f273,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f272,f258]) ).
fof(f274,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f273]) ).
cnf(s2,plain,
( ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f251]) ).
cnf(s3,plain,
( ~ spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f255]) ).
cnf(s4,plain,
( ~ spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f259]) ).
cnf(s5,plain,
( ~ spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f263]) ).
cnf(s10,plain,
spl0_3,
inference(sat_conversion,[],[f269]) ).
cnf(s11,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f274]) ).
cnf(s12,plain,
spl0_7,
inference(rat,[],[s5,s10]) ).
cnf(s13,plain,
spl0_6,
inference(rat,[],[s4,s10]) ).
cnf(s14,plain,
spl0_5,
inference(rat,[],[s3,s10]) ).
cnf(s15,plain,
~ spl0_4,
inference(rat,[],[s11,s12,s13,s14]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s2,s15,s10]) ).
fof(f275,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC381-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n007.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 09:20:40 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 2.83/1.17 % (2262720)Input is clausal, will run a generic CNF schedule.
% 2.83/1.17 % (2262729)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1868476049:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.83/1.17 % (2262729)First to succeed.
% 2.83/1.17 % (2262729)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2262720"
% 2.83/1.17 % (2262726)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2958331971:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.83/1.17 % (2262728)lrs+10_1_sil=8000:sp=occurrence:random_seed=1219415511:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.83/1.17 % (2262727)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2854874943:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.83/1.17 % (2262725)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=4025098757:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.83/1.17 % (2262728)Also succeeded, but the first one will report.
% 2.83/1.17 % (2262730)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1359119910:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.83/1.17 % (2262731)dis-21_1_sil=8000:lcm=predicate:random_seed=45962038: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)
% 2.83/1.17 % (2262731)Also succeeded, but the first one will report.
% 2.83/1.17 % (2262730)Also succeeded, but the first one will report.
% 2.83/1.17 % (2262729)Refutation found. Thanks to Tanya!
% 2.83/1.17 % SZS status Unsatisfiable for theBenchmark
% 2.83/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 2.83/1.17 % (2262729)------------------------------
% 2.83/1.17 % (2262729)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.83/1.17 % (2262729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/1.17 % (2262729)CaDiCaL version: 2.1.3
% 2.83/1.17 % (2262729)Termination reason: Refutation
% 2.83/1.17 % (2262729)Time elapsed: 0.002 s
% 2.83/1.17 % (2262729)Peak memory usage: 89 MB
% 2.83/1.17 % (2262729)Instructions burned: 3 (million)
% 2.83/1.17 % (2262729)------------------------------
% 2.83/1.17 % (2262729)------------------------------
% 2.83/1.17 % (2262720)Success in time 0.313 s
% 2.83/1.17 % Vampire exiting
%------------------------------------------------------------------------------