%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : AGT016+2 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 09:06:35 AM UTC 2026
% Result : Theorem 0.16s 1.30s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 18 unt; 5 def)
% Number of atoms : 99 ( 0 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 101 ( 42 ~; 39 |; 14 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 6 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 11 con; 0-0 aty)
% Number of variables : 12 ( 0 sgn 8 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [X0] :
( ( accept_population(X0,atheist,n75)
& accept_population(X0,christian,n24)
& accept_population(X0,muslim,n1)
& accept_population(X0,native,n0)
& accept_population(X0,other,n0) )
<=> accept_city(X0,towna) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2_9) ).
fof(f635,axiom,
~ accept_city(muslimcountrybhumanitarianorganization,towna),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',deduced_366) ).
fof(f923,conjecture,
? [X0,X1] : ~ accept_population(muslimcountrybhumanitarianorganization,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',query_16) ).
fof(f924,negated_conjecture,
~ ? [X0,X1] : ~ accept_population(muslimcountrybhumanitarianorganization,X0,X1),
inference(negated_conjecture,[status(cth)],[f923]) ).
fof(f943,plain,
! [X0,X1] : accept_population(muslimcountrybhumanitarianorganization,X0,X1),
inference(ennf_transformation,[],[f924]) ).
fof(f950,plain,
! [X0] :
( ( ( accept_population(X0,atheist,n75)
& accept_population(X0,christian,n24)
& accept_population(X0,muslim,n1)
& accept_population(X0,native,n0)
& accept_population(X0,other,n0) )
| ~ accept_city(X0,towna) )
& ( accept_city(X0,towna)
| ~ accept_population(X0,atheist,n75)
| ~ accept_population(X0,christian,n24)
| ~ accept_population(X0,muslim,n1)
| ~ accept_population(X0,native,n0)
| ~ accept_population(X0,other,n0) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f951,plain,
! [X0] :
( ( ( accept_population(X0,atheist,n75)
& accept_population(X0,christian,n24)
& accept_population(X0,muslim,n1)
& accept_population(X0,native,n0)
& accept_population(X0,other,n0) )
| ~ accept_city(X0,towna) )
& ( accept_city(X0,towna)
| ~ accept_population(X0,atheist,n75)
| ~ accept_population(X0,christian,n24)
| ~ accept_population(X0,muslim,n1)
| ~ accept_population(X0,native,n0)
| ~ accept_population(X0,other,n0) ) ),
inference(flattening,[],[f950]) ).
fof(f956,plain,
! [X0,X1] : accept_population(muslimcountrybhumanitarianorganization,X0,X1),
inference(cnf_transformation,[],[f943]) ).
fof(f1033,plain,
~ accept_city(muslimcountrybhumanitarianorganization,towna),
inference(cnf_transformation,[],[f635]) ).
fof(f1116,plain,
! [X0] :
( accept_city(X0,towna)
| ~ accept_population(X0,atheist,n75)
| ~ accept_population(X0,christian,n24)
| ~ accept_population(X0,muslim,n1)
| ~ accept_population(X0,native,n0)
| ~ accept_population(X0,other,n0) ),
inference(cnf_transformation,[],[f951]) ).
fof(f1999,plain,
( ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75)
| ~ accept_population(muslimcountrybhumanitarianorganization,christian,n24)
| ~ accept_population(muslimcountrybhumanitarianorganization,muslim,n1)
| ~ accept_population(muslimcountrybhumanitarianorganization,native,n0)
| ~ accept_population(muslimcountrybhumanitarianorganization,other,n0) ),
inference(resolution,[],[f1116,f1033]) ).
fof(f2007,definition,
( spl0_1
<=> accept_population(muslimcountrybhumanitarianorganization,other,n0) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f2008,plain,
( ~ accept_population(muslimcountrybhumanitarianorganization,other,n0)
| spl0_1 ),
inference(avatar_component_clause,[],[f2007]) ).
fof(f2010,definition,
( spl0_2
<=> accept_population(muslimcountrybhumanitarianorganization,native,n0) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f2011,plain,
( ~ accept_population(muslimcountrybhumanitarianorganization,native,n0)
| spl0_2 ),
inference(avatar_component_clause,[],[f2010]) ).
fof(f2013,definition,
( spl0_3
<=> accept_population(muslimcountrybhumanitarianorganization,muslim,n1) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f2014,plain,
( ~ accept_population(muslimcountrybhumanitarianorganization,muslim,n1)
| spl0_3 ),
inference(avatar_component_clause,[],[f2013]) ).
fof(f2016,definition,
( spl0_4
<=> accept_population(muslimcountrybhumanitarianorganization,christian,n24) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f2017,plain,
( ~ accept_population(muslimcountrybhumanitarianorganization,christian,n24)
| spl0_4 ),
inference(avatar_component_clause,[],[f2016]) ).
fof(f2019,definition,
( spl0_5
<=> accept_population(muslimcountrybhumanitarianorganization,atheist,n75) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f2020,plain,
( ~ accept_population(muslimcountrybhumanitarianorganization,atheist,n75)
| spl0_5 ),
inference(avatar_component_clause,[],[f2019]) ).
fof(f2021,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f1999,f2019,f2016,f2013,f2010,f2007]) ).
fof(f2022,plain,
( $false
| spl0_1 ),
inference(resolution,[],[f2008,f956]) ).
fof(f2023,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f2022]) ).
fof(f2024,plain,
( $false
| spl0_2 ),
inference(resolution,[],[f2011,f956]) ).
fof(f2025,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f2024]) ).
fof(f2026,plain,
( $false
| spl0_3 ),
inference(resolution,[],[f2014,f956]) ).
fof(f2027,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f2026]) ).
fof(f2028,plain,
( $false
| spl0_4 ),
inference(resolution,[],[f2017,f956]) ).
fof(f2029,plain,
spl0_4,
inference(avatar_contradiction_clause,[],[f2028]) ).
fof(f2030,plain,
( $false
| spl0_5 ),
inference(resolution,[],[f2020,f956]) ).
fof(f2031,plain,
spl0_5,
inference(avatar_contradiction_clause,[],[f2030]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f2021]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f2023]) ).
cnf(s3,plain,
spl0_2,
inference(sat_conversion,[],[f2025]) ).
cnf(s4,plain,
spl0_3,
inference(sat_conversion,[],[f2027]) ).
cnf(s5,plain,
spl0_4,
inference(sat_conversion,[],[f2029]) ).
cnf(s6,plain,
spl0_5,
inference(sat_conversion,[],[f2031]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s6,s5,s4,s3,s2]) ).
fof(f2032,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : AGT016+2 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n004.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 19:11:22 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 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
% 3.00/1.12 % (667463)Detected formulas, will run a generic FOF schedule.
% 3.00/1.12 % (667469)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3278443625:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.00/1.12 % (667472)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3642534285:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.00/1.12 % (667468)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=403902683:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.00/1.12 % (667472)Refutation not found, incomplete strategy
% 3.00/1.12 % (667472)------------------------------
% 3.00/1.12 % (667472)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.12 % (667472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.12 % (667472)CaDiCaL version: 2.1.3
% 3.00/1.12 % (667472)Termination reason: Refutation not found, incomplete strategy
% 3.00/1.12 % (667472)Time elapsed: 0.003 s
% 3.00/1.12 % (667472)Peak memory usage: 88 MB
% 3.00/1.12 % (667472)Instructions burned: 4 (million)
% 3.00/1.12 % (667471)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1997805811:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.00/1.12 % (667470)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=4092710740:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.00/1.12 % (667471)Refutation not found, incomplete strategy
% 3.00/1.12 % (667471)------------------------------
% 3.00/1.12 % (667471)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.12 % (667471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.12 % (667471)CaDiCaL version: 2.1.3
% 3.00/1.12 % (667471)Termination reason: Refutation not found, incomplete strategy
% 3.00/1.12 % (667471)Time elapsed: 0.002 s
% 3.00/1.12 % (667471)Peak memory usage: 87 MB
% 3.00/1.12 % (667471)Instructions burned: 2 (million)
% 3.00/1.12 % (667473)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2858599769:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.00/1.12 % (667474)dis-21_1_sil=8000:lcm=predicate:random_seed=538418740:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.00/1.12 % (667474)First to succeed.
% 3.00/1.12 % (667474)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-667463"
% 3.00/1.12 % (667473)Also succeeded, but the first one will report.
% 3.00/1.12 [W928 19:11:23.861875081 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 3.00/1.12 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 3.00/1.12 [W928 19:11:23.861946139 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 3.00/1.12 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 3.00/1.12 [W928 19:11:23.861972993 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 3.00/1.12 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 3.00/1.12 [W928 19:11:23.861979497 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 3.00/1.12 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 3.00/1.12 [W928 19:11:23.861993176 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 3.00/1.12 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.16/1.30 [W928 19:11:23.861998702 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 0.16/1.30 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.16/1.30 [W928 19:11:23.862020439 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 0.16/1.30 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.16/1.30 [W928 19:11:23.862026205 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 0.16/1.30 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.16/1.30 [W928 19:11:23.862038985 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 0.16/1.30 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.16/1.30 [W928 19:11:23.862044356 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 0.16/1.30 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.16/1.30 [W928 19:11:23.862057635 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 0.16/1.30 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.16/1.30 [W928 19:11:23.862062889 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 0.16/1.30 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.16/1.30 % (667471)------------------------------
% 0.16/1.30 % (667471)------------------------------
% 0.16/1.30 % (667472)------------------------------
% 0.16/1.30 % (667472)------------------------------
% 0.16/1.30 % (667474)Refutation found. Thanks to Tanya!
% 0.16/1.30 % SZS status Theorem for theBenchmark
% 0.16/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.30 % (667474)------------------------------
% 0.16/1.30 % (667474)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.30 % (667474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.30 % (667474)CaDiCaL version: 2.1.3
% 0.16/1.30 % (667474)Termination reason: Refutation
% 0.16/1.30 % (667474)Time elapsed: 0.013 s
% 0.16/1.30 % (667474)Peak memory usage: 90 MB
% 0.16/1.30 % (667474)Instructions burned: 23 (million)
% 0.16/1.30 % (667474)------------------------------
% 0.16/1.30 % (667474)------------------------------
% 0.16/1.30 % (667463)Success in time 0.472 s
% 0.16/1.30 % Vampire exiting
%------------------------------------------------------------------------------