%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PHI011+1 : TPTP v9.3.1. Released v7.2.0.
% 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 12:27:19 PM UTC 2026
% Result : Theorem 0.21s 1.50s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 12 unt; 3 def)
% Number of atoms : 108 ( 4 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 112 ( 40 ~; 34 |; 25 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 31 ( 0 sgn 20 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( ( object(X0)
& property(X1)
& object(X2) )
=> ( ( is_the(X0,X1)
& X0 = X2 )
=> exemplifies_property(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_1) ).
fof(f5,conjecture,
! [X0] :
( property(X0)
=> ( ? [X1] :
( object(X1)
& is_the(X1,X0) )
=> ! [X2] :
( object(X2)
=> ( is_the(X2,X0)
=> exemplifies_property(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',description_theorem_2) ).
fof(f6,negated_conjecture,
~ ! [X0] :
( property(X0)
=> ( ? [X1] :
( object(X1)
& is_the(X1,X0) )
=> ! [X2] :
( object(X2)
=> ( is_the(X2,X0)
=> exemplifies_property(X0,X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f10,plain,
! [X0,X1,X2] :
( exemplifies_property(X1,X2)
| ~ is_the(X0,X1)
| X0 != X2
| ~ object(X0)
| ~ property(X1)
| ~ object(X2) ),
inference(ennf_transformation,[],[f4]) ).
fof(f11,plain,
! [X0,X1,X2] :
( exemplifies_property(X1,X2)
| ~ is_the(X0,X1)
| X0 != X2
| ~ object(X0)
| ~ property(X1)
| ~ object(X2) ),
inference(flattening,[],[f10]) ).
fof(f12,plain,
? [X0] :
( ? [X2] :
( ~ exemplifies_property(X0,X2)
& is_the(X2,X0)
& object(X2) )
& ? [X1] :
( object(X1)
& is_the(X1,X0) )
& property(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f13,plain,
? [X0] :
( ? [X2] :
( ~ exemplifies_property(X0,X2)
& is_the(X2,X0)
& object(X2) )
& ? [X1] :
( object(X1)
& is_the(X1,X0) )
& property(X0) ),
inference(flattening,[],[f12]) ).
fof(f14,plain,
? [X0] :
( ? [X1] :
( ~ exemplifies_property(X0,X1)
& is_the(X1,X0)
& object(X1) )
& ? [X2] :
( object(X2)
& is_the(X2,X0) )
& property(X0) ),
inference(rectify,[],[f13]) ).
fof(f15,plain,
( ~ exemplifies_property(sK0,sK1)
& is_the(sK1,sK0)
& object(sK1)
& object(sK2)
& is_the(sK2,sK0)
& property(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f14]) ).
fof(f21,plain,
! [X2,X0,X1] :
( exemplifies_property(X1,X2)
| ~ is_the(X0,X1)
| X0 != X2
| ~ object(X0)
| ~ property(X1)
| ~ object(X2) ),
inference(cnf_transformation,[],[f11]) ).
fof(f22,plain,
property(sK0),
inference(cnf_transformation,[],[f15]) ).
fof(f25,plain,
object(sK1),
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
is_the(sK1,sK0),
inference(cnf_transformation,[],[f15]) ).
fof(f27,plain,
~ exemplifies_property(sK0,sK1),
inference(cnf_transformation,[],[f15]) ).
fof(f28,plain,
! [X2,X1] :
( exemplifies_property(X1,X2)
| ~ is_the(X2,X1)
| ~ object(X2)
| ~ property(X1)
| ~ object(X2) ),
inference(equality_resolution,[],[f21]) ).
fof(f29,plain,
! [X2,X1] :
( exemplifies_property(X1,X2)
| ~ is_the(X2,X1)
| ~ object(X2)
| ~ property(X1) ),
inference(duplicate_literal_removal,[],[f28]) ).
fof(f35,plain,
( ~ is_the(sK1,sK0)
| ~ object(sK1)
| ~ property(sK0) ),
inference(resolution,[],[f29,f27]) ).
fof(f39,definition,
( spl3_1
<=> property(sK0) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f40,plain,
( ~ property(sK0)
| spl3_1 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f42,definition,
( spl3_2
<=> object(sK1) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f43,plain,
( ~ object(sK1)
| spl3_2 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f45,definition,
( spl3_3
<=> is_the(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f46,plain,
( ~ is_the(sK1,sK0)
| spl3_3 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f47,plain,
( ~ spl3_1
| ~ spl3_2
| ~ spl3_3 ),
inference(avatar_split_clause,[],[f35,f45,f42,f39]) ).
fof(f48,plain,
( $false
| spl3_1 ),
inference(resolution,[],[f40,f22]) ).
fof(f49,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f48]) ).
fof(f50,plain,
( $false
| spl3_2 ),
inference(resolution,[],[f43,f25]) ).
fof(f51,plain,
spl3_2,
inference(avatar_contradiction_clause,[],[f50]) ).
fof(f52,plain,
( $false
| spl3_3 ),
inference(resolution,[],[f46,f26]) ).
fof(f53,plain,
spl3_3,
inference(avatar_contradiction_clause,[],[f52]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2
| ~ spl3_3 ),
inference(sat_conversion,[],[f47]) ).
cnf(s2,plain,
spl3_1,
inference(sat_conversion,[],[f49]) ).
cnf(s3,plain,
spl3_2,
inference(sat_conversion,[],[f51]) ).
cnf(s4,plain,
spl3_3,
inference(sat_conversion,[],[f53]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4,s3,s2]) ).
fof(f54,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI011+1 : TPTP v9.3.1. Released v7.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.43 % Computer : n006.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sun Sep 27 22:06:55 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 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 % (3369528)Detected formulas, will run a generic FOF schedule.
% 0.21/1.50 % (3369543)dis-21_1_sil=8000:lcm=predicate:random_seed=3707080611: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)
% 0.21/1.50 % (3369542)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=600746764:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.21/1.50 % (3369543)First to succeed.
% 0.21/1.50 % (3369542)Also succeeded, but the first one will report.
% 0.21/1.50 % (3369543)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3369528"
% 0.21/1.50 % (3369537)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=3541149561:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.21/1.50 % (3369539)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=1233700104:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.21/1.50 % (3369538)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=4017655989:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.21/1.50 % (3369541)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=334451960:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.21/1.50 % (3369540)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1930992179:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.21/1.50 % (3369541)Refutation not found, incomplete strategy
% 0.21/1.50 % (3369541)------------------------------
% 0.21/1.50 % (3369541)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.50 % (3369540)Refutation not found, incomplete strategy
% 0.21/1.50 % (3369540)------------------------------
% 0.21/1.50 % (3369540)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.50 % (3369541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.50 % (3369540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.50 % (3369541)CaDiCaL version: 2.1.3
% 0.21/1.50 % (3369541)Termination reason: Refutation not found, incomplete strategy
% 0.21/1.50 % (3369541)Time elapsed: 0.002 s
% 0.21/1.50 % (3369540)CaDiCaL version: 2.1.3
% 0.21/1.50 % (3369541)Peak memory usage: 87 MB
% 0.21/1.50 % (3369540)Termination reason: Refutation not found, incomplete strategy
% 0.21/1.50 % (3369540)Time elapsed: 0.001 s
% 0.21/1.50 % (3369540)Peak memory usage: 88 MB
% 0.21/1.50 % (3369543)Refutation found. Thanks to Tanya!
% 0.21/1.50 % SZS status Theorem for theBenchmark
% 0.21/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/1.50 % (3369543)------------------------------
% 0.21/1.50 % (3369543)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.50 % (3369543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.50 % (3369543)CaDiCaL version: 2.1.3
% 0.21/1.50 % (3369543)Termination reason: Refutation
% 0.21/1.50 % (3369543)Time elapsed: 0.002 s
% 0.21/1.50 % (3369543)Peak memory usage: 89 MB
% 0.21/1.50 % (3369543)Instructions burned: 1 (million)
% 0.21/1.50 % (3369543)------------------------------
% 0.21/1.50 % (3369543)------------------------------
% 0.21/1.50 % (3369528)Success in time 0.351 s
% 0.21/1.50 % Vampire exiting
%------------------------------------------------------------------------------