%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM003-2 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 09:38:59 AM UTC 2026
% Result : Unsatisfiable 2.74s 1.18s
% Output : Refutation 2.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 43 ( 9 unt; 5 def)
% Number of atoms : 79 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 74 ( 38 ~; 31 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 6 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 41 ( 0 sgn 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [X0,X1] :
( ~ program_halts2(X0,X1)
| halts2(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_halts3a) ).
fof(f17,axiom,
! [X0,X1] :
( ~ program_not_halts2(X0,X1)
| ~ halts2(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_not_halts3a) ).
fof(f22,axiom,
! [X2,X3,X0,X1] :
( ~ program_halts2_halts3_outputs(X0,X1,X2,X3)
| program_halts2(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_halts2_halts3_outputs1) ).
fof(f25,axiom,
! [X2,X3,X0,X1] :
( ~ program_not_halts2_halts3_outputs(X0,X1,X2,X3)
| program_not_halts2(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_not_halts2_halts3_outputs1) ).
fof(f34,axiom,
! [X0] :
( ~ algorithm_program_decides(X0)
| program_program_decides(c1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom1_1) ).
fof(f35,axiom,
! [X2,X0,X1] :
( program_halts2_halts3_outputs(X0,X1,X2,good)
| ~ program_program_decides(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom2_1) ).
fof(f36,axiom,
! [X2,X0,X1] :
( program_not_halts2_halts3_outputs(X0,X1,X2,bad)
| ~ program_program_decides(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom2_2) ).
fof(f43,negated_conjecture,
algorithm_program_decides(c4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_algorithm_does_not_exist) ).
fof(f77,definition,
( spl0_9
<=> program_program_decides(c1) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f79,plain,
( program_program_decides(c1)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f81,definition,
( spl0_10
<=> ! [X0] : ~ algorithm_program_decides(X0) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f82,plain,
( ! [X0] : ~ algorithm_program_decides(X0)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f83,plain,
( spl0_9
| spl0_10 ),
inference(avatar_split_clause,[],[f34,f81,f77]) ).
fof(f94,plain,
! [X2,X0,X1] :
( program_halts2(X0,X1)
| ~ program_program_decides(X2) ),
inference(resolution,[],[f22,f35]) ).
fof(f96,definition,
( spl0_11
<=> ! [X2] : ~ program_program_decides(X2) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f97,plain,
( ! [X2] : ~ program_program_decides(X2)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f99,definition,
( spl0_12
<=> ! [X0,X1] : program_halts2(X0,X1) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f100,plain,
( ! [X0,X1] : program_halts2(X0,X1)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f101,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f94,f99,f96]) ).
fof(f102,plain,
! [X2,X0,X1] :
( program_not_halts2(X0,X1)
| ~ program_program_decides(X2) ),
inference(resolution,[],[f25,f36]) ).
fof(f103,plain,
( $false
| ~ spl0_9
| ~ spl0_11 ),
inference(resolution,[],[f97,f79]) ).
fof(f104,plain,
( ~ spl0_9
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f103]) ).
fof(f105,plain,
( $false
| ~ spl0_10 ),
inference(resolution,[],[f82,f43]) ).
fof(f106,plain,
~ spl0_10,
inference(avatar_contradiction_clause,[],[f105]) ).
fof(f108,definition,
( spl0_13
<=> ! [X0,X1] : program_not_halts2(X0,X1) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f109,plain,
( ! [X0,X1] : program_not_halts2(X0,X1)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f110,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f102,f108,f96]) ).
fof(f114,plain,
( ! [X0,X1] : halts2(X0,X1)
| ~ spl0_12 ),
inference(resolution,[],[f100,f11]) ).
fof(f120,plain,
( ! [X0,X1] : ~ halts2(X0,X1)
| ~ spl0_13 ),
inference(resolution,[],[f109,f17]) ).
fof(f122,plain,
( $false
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f120,f114]) ).
fof(f123,plain,
( ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f122]) ).
cnf(s7,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f83]) ).
cnf(s8,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f101]) ).
cnf(s9,plain,
( ~ spl0_9
| ~ spl0_11 ),
inference(sat_conversion,[],[f104]) ).
cnf(s10,plain,
~ spl0_10,
inference(sat_conversion,[],[f106]) ).
cnf(s11,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f110]) ).
cnf(s12,plain,
( ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f123]) ).
cnf(s13,plain,
spl0_9,
inference(rat,[],[s7,s10]) ).
cnf(s14,plain,
~ spl0_11,
inference(rat,[],[s9,s13]) ).
cnf(s15,plain,
spl0_13,
inference(rat,[],[s11,s14]) ).
cnf(s16,plain,
spl0_12,
inference(rat,[],[s8,s14]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s12,s15,s16]) ).
fof(f124,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM003-2 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n006.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Mon Sep 28 21:43:31 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running first-order theorem proving
% 0.10/0.24 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
% 2.74/1.18 % (237208)Input is clausal, will run a generic CNF schedule.
% 2.74/1.18 % (237216)lrs+10_1_sil=8000:sp=occurrence:random_seed=1830187924:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.74/1.18 % (237216)First to succeed.
% 2.74/1.18 % (237216)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-237208"
% 2.74/1.18 % (237218)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2909301915:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.74/1.18 % (237213)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=974122641:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.74/1.18 % (237217)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3935134654:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.74/1.18 % (237214)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=326642441:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.74/1.18 % (237215)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1990226165:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.74/1.18 % (237219)dis-21_1_sil=8000:lcm=predicate:random_seed=3523324159: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)
% 2.74/1.18 % (237217)Also succeeded, but the first one will report.
% 2.74/1.18 % (237219)Also succeeded, but the first one will report.
% 2.74/1.18 % (237218)Also succeeded, but the first one will report.
% 2.74/1.18 % (237216)Refutation found. Thanks to Tanya!
% 2.74/1.18 % SZS status Unsatisfiable for theBenchmark
% 2.74/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 2.74/1.18 % (237216)------------------------------
% 2.74/1.18 % (237216)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.18 % (237216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.18 % (237216)CaDiCaL version: 2.1.3
% 2.74/1.18 % (237216)Termination reason: Refutation
% 2.74/1.18 % (237216)Time elapsed: 0.002 s
% 2.74/1.18 % (237216)Peak memory usage: 89 MB
% 2.74/1.18 % (237216)Instructions burned: 2 (million)
% 2.74/1.18 % (237216)------------------------------
% 2.74/1.18 % (237216)------------------------------
% 2.74/1.18 % (237208)Success in time 0.296 s
% 2.74/1.18 % Vampire exiting
%------------------------------------------------------------------------------