%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO894_8 : TPTP v9.3.1. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 02:32:50 PM UTC 2026
% Result : Theorem 0.08s 0.20s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 47 ( 7 unt; 0 typ; 5 def)
% Number of atoms : 141 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 166 ( 72 ~; 63 |; 15 &)
% ( 8 <=>; 6 =>; 0 <=; 2 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 26 ( 0 sgn 19 !; 7 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'$ki_world': $tType ).
tff(func_def_0,type,
'$ki_local_world': '$ki_world' ).
tff(func_def_1,type,
sK0: '$ki_world' ).
tff(func_def_2,type,
sK1: '$ki_world' ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
p: '$ki_world' > $o ).
tff(f2,conjecture,
( ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( p(X0)
=> ~ p(X0) ) )
<=> ~ ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& p(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
tff(f3,negated_conjecture,
~ ( ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( p(X0)
=> ~ p(X0) ) )
<=> ~ ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& p(X0) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f4,plain,
~ ( ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( p(X0)
=> ~ p(X0) ) )
<=> ~ ? [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
& p(X1) ) ),
inference(rectify,[],[f3]) ).
tff(f5,plain,
( ! [X0: '$ki_world'] :
( ~ p(X0)
| ~ p(X0)
| ~ '$ki_accessible'('$ki_local_world',X0) )
<~> ! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ p(X1) ) ),
inference(ennf_transformation,[],[f4]) ).
tff(f6,plain,
( ! [X0: '$ki_world'] :
( ~ p(X0)
| ~ p(X0)
| ~ '$ki_accessible'('$ki_local_world',X0) )
<~> ! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ p(X1) ) ),
inference(flattening,[],[f5]) ).
tff(f7,plain,
( ( ? [X1: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X1)
& p(X1) )
| ? [X0: '$ki_world'] :
( p(X0)
& p(X0)
& '$ki_accessible'('$ki_local_world',X0) ) )
& ( ! [X1: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X1)
| ~ p(X1) )
| ! [X0: '$ki_world'] :
( ~ p(X0)
| ~ p(X0)
| ~ '$ki_accessible'('$ki_local_world',X0) ) ) ),
inference(nnf_transformation,[],[f6]) ).
tff(f8,plain,
( ( ? [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
& p(X0) )
| ? [X1: '$ki_world'] :
( p(X1)
& p(X1)
& '$ki_accessible'('$ki_local_world',X1) ) )
& ( ! [X2: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X2)
| ~ p(X2) )
| ! [X3: '$ki_world'] :
( ~ p(X3)
| ~ p(X3)
| ~ '$ki_accessible'('$ki_local_world',X3) ) ) ),
inference(rectify,[],[f7]) ).
tff(f9,plain,
( ( ( '$ki_accessible'('$ki_local_world',sK0)
& p(sK0) )
| ( p(sK1)
& p(sK1)
& '$ki_accessible'('$ki_local_world',sK1) ) )
& ( ! [X2: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X2)
| ~ p(X2) )
| ! [X3: '$ki_world'] :
( ~ p(X3)
| ~ p(X3)
| ~ '$ki_accessible'('$ki_local_world',X3) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f8]) ).
tff(f11,plain,
! [X2: '$ki_world',X3: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X2)
| ~ p(X2)
| ~ p(X3)
| ~ p(X3)
| ~ '$ki_accessible'('$ki_local_world',X3) ),
inference(cnf_transformation,[],[f9]) ).
tff(f12,plain,
( p(sK0)
| '$ki_accessible'('$ki_local_world',sK1) ),
inference(cnf_transformation,[],[f9]) ).
tff(f14,plain,
( p(sK0)
| p(sK1) ),
inference(cnf_transformation,[],[f9]) ).
tff(f15,plain,
( '$ki_accessible'('$ki_local_world',sK0)
| '$ki_accessible'('$ki_local_world',sK1) ),
inference(cnf_transformation,[],[f9]) ).
tff(f17,plain,
( '$ki_accessible'('$ki_local_world',sK0)
| p(sK1) ),
inference(cnf_transformation,[],[f9]) ).
tff(f18,plain,
! [X2: '$ki_world',X3: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X2)
| ~ p(X2)
| ~ p(X3)
| ~ '$ki_accessible'('$ki_local_world',X3) ),
inference(duplicate_literal_removal,[],[f11]) ).
tff(f20,definition,
( spl2_1
<=> ! [X3: '$ki_world'] :
( ~ p(X3)
| ~ '$ki_accessible'('$ki_local_world',X3) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
tff(f21,plain,
( ! [X3: '$ki_world'] :
( ~ '$ki_accessible'('$ki_local_world',X3)
| ~ p(X3) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f20]) ).
tff(f22,plain,
( spl2_1
| spl2_1 ),
inference(avatar_split_clause,[],[f18,f20,f20]) ).
tff(f24,definition,
( spl2_2
<=> '$ki_accessible'('$ki_local_world',sK1) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
tff(f26,plain,
( '$ki_accessible'('$ki_local_world',sK1)
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f24]) ).
tff(f28,definition,
( spl2_3
<=> p(sK0) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
tff(f31,plain,
( spl2_2
| spl2_3 ),
inference(avatar_split_clause,[],[f12,f28,f24]) ).
tff(f33,definition,
( spl2_4
<=> p(sK1) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
tff(f35,plain,
( p(sK1)
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f33]) ).
tff(f37,plain,
( spl2_4
| spl2_3 ),
inference(avatar_split_clause,[],[f14,f28,f33]) ).
tff(f39,definition,
( spl2_5
<=> '$ki_accessible'('$ki_local_world',sK0) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
tff(f41,plain,
( '$ki_accessible'('$ki_local_world',sK0)
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f39]) ).
tff(f42,plain,
( spl2_2
| spl2_5 ),
inference(avatar_split_clause,[],[f15,f39,f24]) ).
tff(f44,plain,
( spl2_4
| spl2_5 ),
inference(avatar_split_clause,[],[f17,f39,f33]) ).
tff(f45,plain,
( ~ p(sK0)
| ~ spl2_1
| ~ spl2_5 ),
inference(resolution,[],[f21,f41]) ).
tff(f48,plain,
( ~ spl2_3
| ~ spl2_1
| ~ spl2_5 ),
inference(avatar_split_clause,[],[f45,f39,f20,f28]) ).
tff(f49,plain,
( ~ p(sK1)
| ~ spl2_1
| ~ spl2_2 ),
inference(resolution,[],[f26,f21]) ).
tff(f50,plain,
( $false
| ~ spl2_1
| ~ spl2_2
| ~ spl2_4 ),
inference(forward_subsumption_resolution,[],[f49,f35]) ).
tff(f51,plain,
( ~ spl2_1
| ~ spl2_2
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f50]) ).
cnf(s1,plain,
( spl2_1
| spl2_1 ),
inference(sat_conversion,[],[f22]) ).
cnf(s2,plain,
spl2_1,
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f31]) ).
cnf(s5,plain,
( spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f37]) ).
cnf(s6,plain,
( spl2_2
| spl2_5 ),
inference(sat_conversion,[],[f42]) ).
cnf(s8,plain,
( spl2_4
| spl2_5 ),
inference(sat_conversion,[],[f44]) ).
cnf(s10,plain,
( ~ spl2_1
| ~ spl2_3
| ~ spl2_5 ),
inference(sat_conversion,[],[f48]) ).
cnf(s11,plain,
( ~ spl2_1
| ~ spl2_2
| ~ spl2_4 ),
inference(sat_conversion,[],[f51]) ).
cnf(s12,plain,
spl2_2,
inference(rat,[],[s10,s3,s6,s2]) ).
cnf(s13,plain,
~ spl2_4,
inference(rat,[],[s11,s2,s12]) ).
cnf(s14,plain,
spl2_5,
inference(rat,[],[s8,s13]) ).
cnf(s15,plain,
spl2_3,
inference(rat,[],[s5,s13]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s10,s2,s14,s15]) ).
tff(f52,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYO894_8 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.14 % Computer : n012.cluster.edu
% 0.08/0.14 % Model : x86_64 x86_64
% 0.08/0.14 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.14 % Memory : 8046.5625MB
% 0.08/0.14 % OS : Linux 6.8.0-71-generic
% 0.08/0.14 % CPULimit : 300
% 0.08/0.14 % WCLimit : 300
% 0.08/0.14 % DateTime : Mon Sep 28 18:39:49 UTC 2026
% 0.08/0.15 % CPUTime :
% 0.08/0.15 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 Running first-order model finding
% 0.08/0.17 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.20 % (3618267)Will run a generic schedule for satisfiability detection.
% 0.08/0.20 % (3618273)% WARNING: option uhcvi not known.
% 0.08/0.20 % (3618276)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=768799996:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.08/0.20 % (3618274)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3120745252:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.08/0.20 % (3618277)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2736749996:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.08/0.20 % (3618278)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1374195958:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.08/0.20 % (3618273)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3343113437:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.08/0.20 % (3618275)dis+10_1_sil=32000:sp=arity:random_seed=2409427995:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.08/0.20 % (3618272)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1156010953_3000 on theBenchmark for (3000ds/0Mi)
% 0.08/0.20 % Detected minimum model sizes of [1]
% 0.08/0.20 % Detected maximum model sizes of [3]
% 0.08/0.20 % TRYING [1]
% 0.08/0.20 % TRYING [2]
% 0.08/0.20 % (3618277) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3618267-3618277"...
% 0.08/0.20 % (3618278) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3618267-3618278"...
% 0.08/0.20 % (3618275) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3618267-3618275"...
% 0.08/0.20 % (3618276) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3618267-3618276"...
% 0.08/0.20 % (3618273) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3618267-3618273"...
% 0.08/0.20 % TRYING [3]
% 0.08/0.20 % (3618274) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3618267-3618274"...
% 0.08/0.20 % (3618272) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3618267-3618272"...
% 0.08/0.20 % (3618276)...printing done.
% 0.08/0.20 % (3618273)...printing done.
% 0.08/0.20 % (3618275)...printing done.
% 0.08/0.20 % (3618277)...printing done.
% 0.08/0.20 % (3618278)...printing done.
% 0.08/0.20 % (3618272)...printing done.
% 0.08/0.20 % (3618274)...printing done.
% 0.08/0.20 % (3618275)Refutation found. Thanks to Tanya!
% 0.08/0.20 % SZS status Theorem for theBenchmark
% 0.08/0.20 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.20 % (3618275)------------------------------
% 0.08/0.20 % (3618275)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.20 % (3618275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.20 % (3618275)CaDiCaL version: 2.1.3
% 0.08/0.20 % (3618275)Termination reason: Refutation
% 0.08/0.20 % (3618275)Time elapsed: 0.002 s
% 0.08/0.20 % (3618275)Peak memory usage: 12 MB
% 0.08/0.20 % (3618275)Instructions burned: 1 (million)
% 0.08/0.20 % (3618267)Success in time 0.022 s
% 0.08/0.20 % Vampire exiting
%------------------------------------------------------------------------------