%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PHI023+1 : TPTP v9.3.1. Released v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 12:27:21 PM UTC 2026
% Result : Theorem 3.35s 1.25s
% Output : Refutation 3.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 57 ( 10 unt; 2 def)
% Number of atoms : 154 ( 0 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 154 ( 57 ~; 52 |; 29 &)
% ( 7 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 18 ( 17 usr; 3 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 40 ( 0 sgn 39 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( selfCaused(X0)
<=> ( essenceInvExistence(X0)
& natureConcOnlyByExistence(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',self_caused) ).
fof(f3,axiom,
! [X0] :
( substance(X0)
<=> ( inItself(X0)
& conceivedThruItself(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substance) ).
fof(f6,axiom,
! [X0] :
( god(X0)
<=> ( being(X0)
& absolutelyInfinite(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',god) ).
fof(f7,axiom,
! [X0,X1] :
( absolutelyInfinite(X0)
<=> ( substance(X0)
& constInInfAttributes(X0)
& ( attributeOf(X1,X0)
=> ( expressesEternalEssentiality(X1)
& expressesInfiniteEssentiality(X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absolutely_infinite) ).
fof(f18,axiom,
! [X0] :
( inItself(X0)
=> selfCaused(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',is_in_itself_is_self_caused) ).
fof(f19,axiom,
! [X0] :
( being(X0)
=> hasEssence(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',being_has_essense) ).
fof(f20,axiom,
! [X0] :
( ( essenceInvExistence(X0)
& hasEssence(X0) )
=> exists(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',essence_involves_existence_exists) ).
fof(f21,conjecture,
! [X0] :
( god(X0)
=> exists(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',if_god_then_exists) ).
fof(f22,negated_conjecture,
~ ! [X0] :
( god(X0)
=> exists(X0) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
! [X0] :
( god(X0)
=> ( being(X0)
& absolutelyInfinite(X0) ) ),
inference(unused_predicate_definition_removal,[],[f6]) ).
fof(f24,plain,
! [X0] :
( selfCaused(X0)
=> ( essenceInvExistence(X0)
& natureConcOnlyByExistence(X0) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f25,plain,
! [X0] :
( selfCaused(X0)
=> essenceInvExistence(X0) ),
inference(pure_predicate_removal,[],[f24]) ).
fof(f27,plain,
! [X0] :
( selfCaused(X0)
| ~ inItself(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f28,plain,
! [X0] :
( hasEssence(X0)
| ~ being(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f29,plain,
! [X0] :
( exists(X0)
| ~ essenceInvExistence(X0)
| ~ hasEssence(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f30,plain,
! [X0] :
( exists(X0)
| ~ essenceInvExistence(X0)
| ~ hasEssence(X0) ),
inference(flattening,[],[f29]) ).
fof(f31,plain,
? [X0] :
( ~ exists(X0)
& god(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f32,plain,
! [X0] :
( essenceInvExistence(X0)
| ~ selfCaused(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f33,plain,
! [X0] :
( ( being(X0)
& absolutelyInfinite(X0) )
| ~ god(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f34,plain,
! [X0,X1] :
( absolutelyInfinite(X0)
<=> ( substance(X0)
& constInInfAttributes(X0)
& ( ( expressesEternalEssentiality(X1)
& expressesInfiniteEssentiality(X1) )
| ~ attributeOf(X1,X0) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f36,plain,
( ~ exists(sK0)
& god(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f31]) ).
fof(f37,plain,
! [X0] :
( ( substance(X0)
| ~ inItself(X0)
| ~ conceivedThruItself(X0) )
& ( ( inItself(X0)
& conceivedThruItself(X0) )
| ~ substance(X0) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f38,plain,
! [X0] :
( ( substance(X0)
| ~ inItself(X0)
| ~ conceivedThruItself(X0) )
& ( ( inItself(X0)
& conceivedThruItself(X0) )
| ~ substance(X0) ) ),
inference(flattening,[],[f37]) ).
fof(f41,plain,
! [X0,X1] :
( ( absolutelyInfinite(X0)
| ~ substance(X0)
| ~ constInInfAttributes(X0)
| ( ( ~ expressesEternalEssentiality(X1)
| ~ expressesInfiniteEssentiality(X1) )
& attributeOf(X1,X0) ) )
& ( ( substance(X0)
& constInInfAttributes(X0)
& ( ( expressesEternalEssentiality(X1)
& expressesInfiniteEssentiality(X1) )
| ~ attributeOf(X1,X0) ) )
| ~ absolutelyInfinite(X0) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f42,plain,
! [X0,X1] :
( ( absolutelyInfinite(X0)
| ~ substance(X0)
| ~ constInInfAttributes(X0)
| ( ( ~ expressesEternalEssentiality(X1)
| ~ expressesInfiniteEssentiality(X1) )
& attributeOf(X1,X0) ) )
& ( ( substance(X0)
& constInInfAttributes(X0)
& ( ( expressesEternalEssentiality(X1)
& expressesInfiniteEssentiality(X1) )
| ~ attributeOf(X1,X0) ) )
| ~ absolutelyInfinite(X0) ) ),
inference(flattening,[],[f41]) ).
fof(f45,plain,
! [X0] :
( selfCaused(X0)
| ~ inItself(X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f46,plain,
! [X0] :
( hasEssence(X0)
| ~ being(X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f47,plain,
! [X0] :
( ~ hasEssence(X0)
| ~ essenceInvExistence(X0)
| exists(X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f48,plain,
god(sK0),
inference(cnf_transformation,[],[f36]) ).
fof(f49,plain,
~ exists(sK0),
inference(cnf_transformation,[],[f36]) ).
fof(f50,plain,
! [X0] :
( essenceInvExistence(X0)
| ~ selfCaused(X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f52,plain,
! [X0] :
( inItself(X0)
| ~ substance(X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f54,plain,
! [X0] :
( ~ god(X0)
| absolutelyInfinite(X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f55,plain,
! [X0] :
( being(X0)
| ~ god(X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f63,plain,
! [X0] :
( ~ absolutelyInfinite(X0)
| substance(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f98,plain,
absolutelyInfinite(sK0),
inference(resolution,[],[f54,f48]) ).
fof(f101,plain,
! [X0] :
( ~ being(X0)
| exists(X0)
| ~ essenceInvExistence(X0) ),
inference(resolution,[],[f47,f46]) ).
fof(f103,plain,
! [X0] :
( ~ essenceInvExistence(X0)
| exists(X0)
| ~ god(X0) ),
inference(resolution,[],[f101,f55]) ).
fof(f107,plain,
! [X0] :
( ~ selfCaused(X0)
| ~ god(X0)
| exists(X0) ),
inference(resolution,[],[f103,f50]) ).
fof(f108,plain,
! [X0] :
( ~ god(X0)
| exists(X0)
| ~ inItself(X0) ),
inference(resolution,[],[f107,f45]) ).
fof(f109,plain,
( exists(sK0)
| ~ inItself(sK0) ),
inference(resolution,[],[f108,f48]) ).
fof(f111,definition,
( spl2_6
<=> inItself(sK0) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f112,plain,
( ~ inItself(sK0)
| spl2_6 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f114,definition,
( spl2_7
<=> exists(sK0) ),
introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition]) ).
fof(f115,plain,
( exists(sK0)
| ~ spl2_7 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f116,plain,
( ~ spl2_6
| spl2_7 ),
inference(avatar_split_clause,[],[f109,f114,f111]) ).
fof(f118,plain,
( ~ substance(sK0)
| spl2_6 ),
inference(resolution,[],[f112,f52]) ).
fof(f121,plain,
( $false
| ~ spl2_7 ),
inference(resolution,[],[f115,f49]) ).
fof(f123,plain,
~ spl2_7,
inference(avatar_contradiction_clause,[],[f121]) ).
fof(f125,plain,
substance(sK0),
inference(resolution,[],[f63,f98]) ).
fof(f127,plain,
( $false
| spl2_6 ),
inference(resolution,[],[f125,f118]) ).
fof(f128,plain,
spl2_6,
inference(avatar_contradiction_clause,[],[f127]) ).
cnf(s4,plain,
( ~ spl2_6
| spl2_7 ),
inference(sat_conversion,[],[f116]) ).
cnf(s6,plain,
~ spl2_7,
inference(sat_conversion,[],[f123]) ).
cnf(s7,plain,
spl2_6,
inference(sat_conversion,[],[f128]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s4,s6,s7]) ).
fof(f129,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PHI023+1 : TPTP v9.3.1. Released v7.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n001.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 22:13:17 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 3.35/1.25 % (4011943)Detected formulas, will run a generic FOF schedule.
% 3.35/1.25 % (4011949)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=101833912:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.35/1.25 % (4011953)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=388688880:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.35/1.25 % (4011952)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3013224199:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.35/1.25 % (4011950)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=163836689:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.35/1.25 % (4011948)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=4258072788:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.35/1.25 % (4011954)dis-21_1_sil=8000:lcm=predicate:random_seed=3568917919: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)
% 3.35/1.25 % (4011951)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2523476973:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.35/1.25 % (4011952)Refutation not found, incomplete strategy
% 3.35/1.25 % (4011952)------------------------------
% 3.35/1.25 % (4011952)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.25 % (4011952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.25 % (4011952)CaDiCaL version: 2.1.3
% 3.35/1.25 % (4011952)Termination reason: Refutation not found, incomplete strategy
% 3.35/1.25 % (4011952)Time elapsed: 0.001 s
% 3.35/1.25 % (4011951)Refutation not found, incomplete strategy
% 3.35/1.25 % (4011951)------------------------------
% 3.35/1.25 % (4011951)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.25 % (4011952)Peak memory usage: 86 MB
% 3.35/1.25 % (4011951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.25 % (4011951)CaDiCaL version: 2.1.3
% 3.35/1.25 % (4011951)Termination reason: Refutation not found, incomplete strategy
% 3.35/1.25 % (4011951)Time elapsed: 0.001 s
% 3.35/1.25 % (4011951)Peak memory usage: 86 MB
% 3.35/1.25 % (4011954)First to succeed.
% 3.35/1.25 % (4011953)Also succeeded, but the first one will report.
% 3.35/1.25 % (4011954)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4011943"
% 3.35/1.25 % (4011951)------------------------------
% 3.35/1.25 % (4011951)------------------------------
% 3.35/1.25 % (4011952)------------------------------
% 3.35/1.25 % (4011952)------------------------------
% 3.35/1.25 % (4011954)Refutation found. Thanks to Tanya!
% 3.35/1.25 % SZS status Theorem for theBenchmark
% 3.35/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 3.35/1.25 % (4011954)------------------------------
% 3.35/1.25 % (4011954)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.25 % (4011954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.25 % (4011954)CaDiCaL version: 2.1.3
% 3.35/1.25 % (4011954)Termination reason: Refutation
% 3.35/1.25 % (4011954)Time elapsed: 0.003 s
% 3.35/1.25 % (4011954)Peak memory usage: 89 MB
% 3.35/1.25 % (4011954)Instructions burned: 3 (million)
% 3.35/1.25 % (4011954)------------------------------
% 3.35/1.25 % (4011954)------------------------------
% 3.35/1.25 % (4011943)Success in time 0.421 s
% 3.35/1.25 % Vampire exiting
%------------------------------------------------------------------------------