%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HWV021-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 10:20:15 AM UTC 2026
% Result : Unsatisfiable 0.21s 1.50s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 27 ( 11 unt; 1 def)
% Number of atoms : 55 ( 8 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 60 ( 32 ~; 27 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,axiom,
! [X0] :
( X0 = n0
| gt(X0,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_15) ).
fof(f19,plain,
! [X0] :
( gt(X0,n0)
| n0 = X0 ),
inference(reorient_equations,[],[f18]) ).
fof(f29,axiom,
! [X0] :
( int_level(X0) != n0
| p_Empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_24) ).
fof(f30,plain,
! [X0] :
( n0 != int_level(X0)
| p_Empty(X0) ),
inference(reorient_equations,[],[f29]) ).
fof(f40,axiom,
! [X0] :
( ~ p_Rd_error(plus(X0,n1))
| ~ p_Reset(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_30) ).
fof(f66,axiom,
! [X0] :
( p_Reset(X0)
| ~ p_Wr(X0)
| ~ p_Rd(X0)
| ~ gt(int_level(X0),n0)
| ~ p_Rd_error(plus(X0,n1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_52) ).
fof(f89,axiom,
! [X0] :
( p_Reset(X0)
| p_Wr(X0)
| ~ p_Rd(X0)
| ~ gt(int_level(X0),n0)
| ~ p_Rd_error(plus(X0,n1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_70) ).
fof(f113,negated_conjecture,
p_Rd_error(plus(t_139,n1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_1) ).
fof(f114,negated_conjecture,
p_Rd(t_139),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_2) ).
fof(f116,negated_conjecture,
~ p_Empty(t_139),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_4) ).
fof(f119,plain,
! [X0] :
( ~ p_Wr(X0)
| ~ p_Rd(X0)
| ~ gt(int_level(X0),n0)
| ~ p_Rd_error(plus(X0,n1)) ),
inference(forward_subsumption_resolution,[],[f66,f40]) ).
fof(f120,plain,
! [X0] :
( p_Wr(X0)
| ~ p_Rd(X0)
| ~ gt(int_level(X0),n0)
| ~ p_Rd_error(plus(X0,n1)) ),
inference(forward_subsumption_resolution,[],[f89,f40]) ).
fof(f124,plain,
! [X0] :
( ~ p_Rd_error(plus(X0,n1))
| ~ gt(int_level(X0),n0)
| ~ p_Rd(X0) ),
inference(forward_subsumption_resolution,[],[f120,f119]) ).
fof(f194,plain,
( ~ gt(int_level(t_139),n0)
| ~ p_Rd(t_139) ),
inference(resolution,[],[f124,f113]) ).
fof(f197,plain,
~ gt(int_level(t_139),n0),
inference(forward_subsumption_resolution,[],[f194,f114]) ).
fof(f198,plain,
n0 = int_level(t_139),
inference(resolution,[],[f197,f19]) ).
fof(f202,definition,
( spl0_5
<=> n0 = int_level(t_139) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f204,plain,
( n0 = int_level(t_139)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f211,plain,
spl0_5,
inference(avatar_split_clause,[],[f198,f202]) ).
fof(f220,plain,
( n0 != n0
| p_Empty(t_139)
| ~ spl0_5 ),
inference(superposition,[],[f30,f204]) ).
fof(f221,plain,
( p_Empty(t_139)
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f220]) ).
fof(f222,plain,
( $false
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f221,f116]) ).
fof(f223,plain,
~ spl0_5,
inference(avatar_contradiction_clause,[],[f222]) ).
cnf(s6,plain,
spl0_5,
inference(sat_conversion,[],[f211]) ).
cnf(s7,plain,
~ spl0_5,
inference(sat_conversion,[],[f223]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s6,s7]) ).
fof(f224,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HWV021-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n007.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 10:55:55 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.16/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.45 Running first-order theorem proving
% 0.16/0.45 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
% 0.21/1.50 % (1239273)Input is clausal, will run a generic CNF schedule.
% 0.21/1.50 % (1239283)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=683423946:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.21/1.50 % (1239288)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4106947719:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.21/1.50 % (1239284)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1150598095:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.21/1.50 % (1239289)dis-21_1_sil=8000:lcm=predicate:random_seed=3646834401: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)
% 0.21/1.50 % (1239286)lrs+10_1_sil=8000:sp=occurrence:random_seed=1977619433:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.21/1.50 % (1239287)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4119927540:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.21/1.50 % (1239285)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=863186755:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.21/1.50 % (1239286)First to succeed.
% 0.21/1.50 % (1239286)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1239273"
% 0.21/1.50 % (1239287)Also succeeded, but the first one will report.
% 0.21/1.50 % (1239288)Also succeeded, but the first one will report.
% 0.21/1.50 % (1239289)Also succeeded, but the first one will report.
% 0.21/1.50 % (1239286)Refutation found. Thanks to Tanya!
% 0.21/1.50 % SZS status Unsatisfiable for theBenchmark
% 0.21/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/1.50 % (1239286)------------------------------
% 0.21/1.50 % (1239286)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.50 % (1239286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.50 % (1239286)CaDiCaL version: 2.1.3
% 0.21/1.50 % (1239286)Termination reason: Refutation
% 0.21/1.50 % (1239286)Time elapsed: 0.005 s
% 0.21/1.50 % (1239286)Peak memory usage: 89 MB
% 0.21/1.50 % (1239286)Instructions burned: 4 (million)
% 0.21/1.50 % (1239286)------------------------------
% 0.21/1.50 % (1239286)------------------------------
% 0.21/1.50 % (1239273)Success in time 0.398 s
% 0.21/1.50 % Vampire exiting
%------------------------------------------------------------------------------