%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT334_21 : TPTP v9.3.1. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 09:47:48 AM UTC 2026
% Result : Theorem 5.12s 1.69s
% Output : Refutation 5.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 6 unt; 0 typ; 2 def)
% Number of atoms : 94 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 59 ( 22 ~; 16 |; 16 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 30 ( 30 fml; 0 var)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 11 usr; 9 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 15 ( 0 sgn 10 !; 5 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'$ki_world': $tType ).
tff(func_def_0,type,
'$ki_local_world': '$ki_world' ).
tff(func_def_7,type,
sK0: '$ki_world' > '$ki_world' ).
tff(func_def_8,type,
sK1: '$ki_world' > $i ).
tff(func_def_9,type,
sK2: '$ki_world' > $i ).
tff(func_def_10,type,
sK3: '$ki_world' ).
tff(pred_def_1,type,
'$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).
tff(pred_def_2,type,
teach: ( '$ki_world' * $i * $i ) > $o ).
tff(pred_def_3,type,
'$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).
tff(f4,axiom,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ( teach(X0,john,math)
& ? [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
& teach(X0,X1,cs) )
& teach(X0,mary,psych)
& teach(X0,sue,psych) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',db) ).
tff(f5,conjecture,
! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
& teach(X0,X1,cs) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).
tff(f6,negated_conjecture,
~ ! [X0: '$ki_world'] :
( '$ki_accessible'('$ki_local_world',X0)
=> ? [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
& teach(X0,X1,cs) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
tff(f9,plain,
! [X0: '$ki_world'] :
( ( teach(X0,john,math)
& ? [X1: $i] :
( '$ki_exists_in_world_$i'(X0,X1)
& teach(X0,X1,cs) )
& teach(X0,mary,psych)
& teach(X0,sue,psych) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f4]) ).
tff(f10,plain,
? [X0: '$ki_world'] :
( ! [X1: $i] :
( ~ '$ki_exists_in_world_$i'(X0,X1)
| ~ teach(X0,X1,cs) )
& '$ki_accessible'('$ki_local_world',X0) ),
inference(ennf_transformation,[],[f6]) ).
tff(f13,plain,
! [X0: '$ki_world'] :
( ( teach(X0,john,math)
& '$ki_exists_in_world_$i'(X0,sK2(X0))
& teach(X0,sK2(X0),cs)
& teach(X0,mary,psych)
& teach(X0,sue,psych) )
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f9]) ).
tff(f14,plain,
( ! [X1: $i] :
( ~ '$ki_exists_in_world_$i'(sK3,X1)
| ~ teach(sK3,X1,cs) )
& '$ki_accessible'('$ki_local_world',sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f10]) ).
tff(f20,plain,
! [X0: '$ki_world'] :
( teach(X0,sK2(X0),cs)
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f13]) ).
tff(f21,plain,
! [X0: '$ki_world'] :
( '$ki_exists_in_world_$i'(X0,sK2(X0))
| ~ '$ki_accessible'('$ki_local_world',X0) ),
inference(cnf_transformation,[],[f13]) ).
tff(f23,plain,
'$ki_accessible'('$ki_local_world',sK3),
inference(cnf_transformation,[],[f14]) ).
tff(f24,plain,
! [X1: $i] :
( ~ '$ki_exists_in_world_$i'(sK3,X1)
| ~ teach(sK3,X1,cs) ),
inference(cnf_transformation,[],[f14]) ).
tff(f26,plain,
( ~ '$ki_accessible'('$ki_local_world',sK3)
| ~ teach(sK3,sK2(sK3),cs) ),
inference(resolution,[],[f21,f24]) ).
tff(f28,definition,
( spl4_1
<=> teach(sK3,sK2(sK3),cs) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
tff(f29,plain,
( ~ teach(sK3,sK2(sK3),cs)
| spl4_1 ),
inference(avatar_component_clause,[],[f28]) ).
tff(f31,definition,
( spl4_2
<=> '$ki_accessible'('$ki_local_world',sK3) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
tff(f32,plain,
( ~ '$ki_accessible'('$ki_local_world',sK3)
| spl4_2 ),
inference(avatar_component_clause,[],[f31]) ).
tff(f33,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f26,f31,f28]) ).
tff(f34,plain,
( ~ '$ki_accessible'('$ki_local_world',sK3)
| spl4_1 ),
inference(resolution,[],[f20,f29]) ).
tff(f35,plain,
( ~ spl4_2
| spl4_1 ),
inference(avatar_split_clause,[],[f34,f28,f31]) ).
tff(f36,plain,
( $false
| spl4_2 ),
inference(resolution,[],[f32,f23]) ).
tff(f37,plain,
spl4_2,
inference(avatar_contradiction_clause,[],[f36]) ).
cnf(s1,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f33]) ).
cnf(s2,plain,
( spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f35]) ).
cnf(s3,plain,
spl4_2,
inference(sat_conversion,[],[f37]) ).
cnf(s4,plain,
spl4_1,
inference(rat,[],[s2,s3]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s3,s4]) ).
tff(f38,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : DAT334_21 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.22 % Computer : n010.cluster.edu
% 0.12/0.22 % Model : x86_64 x86_64
% 0.12/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.22 % Memory : 8046.5625MB
% 0.12/0.22 % OS : Linux 6.8.0-71-generic
% 0.12/0.22 % CPULimit : 300
% 0.12/0.22 % WCLimit : 300
% 0.12/0.22 % DateTime : Tue Sep 29 00:20:18 UTC 2026
% 0.12/0.23 % CPUTime :
% 0.12/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.26 Running first-order theorem proving
% 0.12/0.26 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
% 5.12/1.69 % (2503526)Detected formulas, will run a generic FOF schedule.
% 5.12/1.69 % (2503638)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3315874924:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.12/1.69 % (2503638)Refutation not found, incomplete strategy
% 5.12/1.69 % (2503638)------------------------------
% 5.12/1.69 % (2503638)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.12/1.69 % (2503638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.12/1.69 % (2503638)CaDiCaL version: 2.1.3
% 5.12/1.69 % (2503638)Termination reason: Refutation not found, incomplete strategy
% 5.12/1.69 % (2503638)Time elapsed: 0.001 s
% 5.12/1.69 % (2503638)Peak memory usage: 88 MB
% 5.12/1.69 % (2503636)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=2217544473:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.12/1.69 % (2503641)dis-21_1_sil=8000:lcm=predicate:random_seed=1151083003: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)
% 5.12/1.69 % (2503641)First to succeed.
% 5.12/1.69 % (2503641)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2503526"
% 5.12/1.69 % (2503635)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=3692013532:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.12/1.69 % (2503637)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3978683878:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.12/1.69 % (2503634)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=3453211614:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.12/1.69 % (2503640)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2706234936:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.12/1.69 % (2503637)Refutation not found, incomplete strategy
% 5.12/1.69 % (2503637)------------------------------
% 5.12/1.69 % (2503637)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.12/1.69 % (2503637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.12/1.69 % (2503637)CaDiCaL version: 2.1.3
% 5.12/1.69 % (2503637)Termination reason: Refutation not found, incomplete strategy
% 5.12/1.69 % (2503637)Time elapsed: 0.001 s
% 5.12/1.69 % (2503637)Peak memory usage: 87 MB
% 5.12/1.69 % (2503640)Also succeeded, but the first one will report.
% 5.12/1.69 % (2503638)------------------------------
% 5.12/1.69 % (2503638)------------------------------
% 5.12/1.69 % (2503678)lrs+10_1_sil=8000:sp=occurrence:random_seed=1692675091:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 5.12/1.69 % (2503678)Also succeeded, but the first one will report.
% 5.12/1.69 % (2503641)Refutation found. Thanks to Tanya!
% 5.12/1.69 % SZS status Theorem for theBenchmark
% 5.12/1.69 % SZS output start Proof for theBenchmark
% See solution above
% 5.12/1.69 % (2503641)------------------------------
% 5.12/1.69 % (2503641)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.12/1.69 % (2503641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.12/1.69 % (2503641)CaDiCaL version: 2.1.3
% 5.12/1.69 % (2503641)Termination reason: Refutation
% 5.12/1.69 % (2503641)Time elapsed: 0.004 s
% 5.12/1.69 % (2503641)Peak memory usage: 89 MB
% 5.12/1.69 % (2503641)Instructions burned: 1 (million)
% 5.12/1.69 % (2503641)------------------------------
% 5.12/1.69 % (2503641)------------------------------
% 5.12/1.69 % (2503526)Success in time 0.605 s
% 5.12/1.69 % Vampire exiting
%------------------------------------------------------------------------------