%------------------------------------------------------------------------------
% File : Vampire-SAT---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 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 12:27:29 PM UTC 2026
% Result : Theorem 0.07s 0.36s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of formulae : 69 ( 6 unt; 0 def)
% Number of atoms : 223 ( 11 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 242 ( 88 ~; 89 |; 48 &)
% ( 7 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 93 ( 92 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( selfCaused(X0)
<=> ( essenceInvExistence(X0)
& natureConcOnlyByExistence(X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/PHI002+0.ax',self_caused) ).
fof(f3,axiom,
! [X0] :
( substance(X0)
<=> ( inItself(X0)
& conceivedThruItself(X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/PHI002+0.ax',substance) ).
fof(f5,axiom,
! [X0,X1,X2] :
( mode(X0)
<=> ( ( modification(X0,X1)
& substance(X1) )
| ( existsIn(X0,X2)
& conceivedThru(X0,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/PHI002+0.ax',mode) ).
fof(f6,axiom,
! [X0] :
( god(X0)
<=> ( being(X0)
& absolutelyInfinite(X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/PHI002+0.ax',god) ).
fof(f7,axiom,
! [X0,X1] :
( absolutelyInfinite(X0)
<=> ( substance(X0)
& constInInfAttributes(X0)
& ( attributeOf(X1,X0)
=> ( expressesEternalEssentiality(X1)
& expressesInfiniteEssentiality(X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/PHI002+0.ax',absolutely_infinite) ).
fof(f11,axiom,
! [X0,X1] :
( exists(X0)
<=> ( existsIn(X0,X0)
| ( existsIn(X0,X1)
& X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/PHI002+1.ax',exists) ).
fof(f12,axiom,
! [X0,X1] :
( ~ conceivedThru(X0,X0)
=> ( conceivedThru(X0,X1)
& X0 != X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/PHI002+1.ax',conceived_through) ).
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(f31,plain,
! [X0] :
( essenceInvExistence(X0)
| ~ selfCaused(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f32,plain,
! [X0] :
( ( being(X0)
& absolutelyInfinite(X0) )
| ~ god(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f33,plain,
! [X0,X1] :
( absolutelyInfinite(X0)
<=> ( substance(X0)
& constInInfAttributes(X0)
& ( ( expressesEternalEssentiality(X1)
& expressesInfiniteEssentiality(X1) )
| ~ attributeOf(X1,X0) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f35,plain,
! [X0,X1] :
( ( conceivedThru(X0,X1)
& X0 != X1 )
| conceivedThru(X0,X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f37,plain,
! [X0] :
( selfCaused(X0)
| ~ inItself(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f38,plain,
! [X0] :
( hasEssence(X0)
| ~ being(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f39,plain,
! [X0] :
( exists(X0)
| ~ essenceInvExistence(X0)
| ~ hasEssence(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f40,plain,
! [X0] :
( exists(X0)
| ~ essenceInvExistence(X0)
| ~ hasEssence(X0) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
? [X0] :
( ~ exists(X0)
& god(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f44,plain,
! [X0] :
( ( substance(X0)
| ~ inItself(X0)
| ~ conceivedThruItself(X0) )
& ( ( inItself(X0)
& conceivedThruItself(X0) )
| ~ substance(X0) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f45,plain,
! [X0] :
( ( substance(X0)
| ~ inItself(X0)
| ~ conceivedThruItself(X0) )
& ( ( inItself(X0)
& conceivedThruItself(X0) )
| ~ substance(X0) ) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ( mode(X0)
| ( ( ~ modification(X0,X1)
| ~ substance(X1) )
& ( ~ existsIn(X0,X2)
| ~ conceivedThru(X0,X2) ) ) )
& ( ( modification(X0,X1)
& substance(X1) )
| ( existsIn(X0,X2)
& conceivedThru(X0,X2) )
| ~ mode(X0) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ( mode(X0)
| ( ( ~ modification(X0,X1)
| ~ substance(X1) )
& ( ~ existsIn(X0,X2)
| ~ conceivedThru(X0,X2) ) ) )
& ( ( modification(X0,X1)
& substance(X1) )
| ( existsIn(X0,X2)
& conceivedThru(X0,X2) )
| ~ mode(X0) ) ),
inference(flattening,[],[f46]) ).
fof(f48,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,[],[f33]) ).
fof(f49,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,[],[f48]) ).
fof(f54,plain,
! [X0,X1] :
( ( exists(X0)
| ( ~ existsIn(X0,X0)
& ( ~ existsIn(X0,X1)
| X0 = X1 ) ) )
& ( existsIn(X0,X0)
| ( existsIn(X0,X1)
& X0 != X1 )
| ~ exists(X0) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f55,plain,
! [X0,X1] :
( ( exists(X0)
| ( ~ existsIn(X0,X0)
& ( ~ existsIn(X0,X1)
| X0 = X1 ) ) )
& ( existsIn(X0,X0)
| ( existsIn(X0,X1)
& X0 != X1 )
| ~ exists(X0) ) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
( ~ exists(sK0)
& god(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f41]) ).
fof(f57,plain,
! [X0] :
( essenceInvExistence(X0)
| ~ selfCaused(X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f62,plain,
! [X0] :
( inItself(X0)
| ~ substance(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f65,plain,
! [X2,X0,X1] :
( substance(X1)
| existsIn(X0,X2)
| ~ mode(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f68,plain,
! [X2,X0] :
( mode(X0)
| ~ existsIn(X0,X2)
| ~ conceivedThru(X0,X2) ),
inference(cnf_transformation,[],[f47]) ).
fof(f70,plain,
! [X0] :
( absolutelyInfinite(X0)
| ~ god(X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f71,plain,
! [X0] :
( being(X0)
| ~ god(X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f75,plain,
! [X0] :
( substance(X0)
| ~ absolutelyInfinite(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f88,plain,
! [X0,X1] :
( existsIn(X0,X0)
| X0 != X1
| ~ exists(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f89,plain,
! [X0,X1] :
( existsIn(X0,X0)
| existsIn(X0,X1)
| ~ exists(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f90,plain,
! [X0,X1] :
( exists(X0)
| ~ existsIn(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f55]) ).
fof(f91,plain,
! [X0] :
( exists(X0)
| ~ existsIn(X0,X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f92,plain,
! [X0,X1] :
( X0 != X1
| conceivedThru(X0,X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f93,plain,
! [X0,X1] :
( conceivedThru(X0,X1)
| conceivedThru(X0,X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f96,plain,
! [X0] :
( selfCaused(X0)
| ~ inItself(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f97,plain,
! [X0] :
( hasEssence(X0)
| ~ being(X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f98,plain,
! [X0] :
( exists(X0)
| ~ essenceInvExistence(X0)
| ~ hasEssence(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f99,plain,
god(sK0),
inference(cnf_transformation,[],[f56]) ).
fof(f100,plain,
~ exists(sK0),
inference(cnf_transformation,[],[f56]) ).
fof(f101,plain,
! [X1] :
( existsIn(X1,X1)
| ~ exists(X1) ),
inference(equality_resolution,[],[f88]) ).
fof(f102,plain,
! [X1] : conceivedThru(X1,X1),
inference(equality_resolution,[],[f92]) ).
fof(f103,plain,
! [X0] :
( ~ essenceInvExistence(X0)
| ~ selfCaused(X0) ),
inference(consistent_polarity_flipping,[],[f57]) ).
fof(f104,plain,
! [X0,X1] :
( ~ mode(X0)
| existsIn(X0,X1)
| conceivedThru(X0,X1) ),
inference(consistent_polarity_flipping,[],[f68]) ).
fof(f105,plain,
! [X2,X0,X1] :
( substance(X1)
| ~ existsIn(X0,X2)
| mode(X0) ),
inference(consistent_polarity_flipping,[],[f65]) ).
fof(f106,plain,
! [X0] :
( ~ being(X0)
| god(X0) ),
inference(consistent_polarity_flipping,[],[f71]) ).
fof(f107,plain,
! [X0] :
( ~ absolutelyInfinite(X0)
| god(X0) ),
inference(consistent_polarity_flipping,[],[f70]) ).
fof(f108,plain,
! [X0] :
( substance(X0)
| absolutelyInfinite(X0) ),
inference(consistent_polarity_flipping,[],[f75]) ).
fof(f109,plain,
! [X0] :
( exists(X0)
| existsIn(X0,X0) ),
inference(consistent_polarity_flipping,[],[f91]) ).
fof(f110,plain,
! [X0,X1] :
( exists(X0)
| existsIn(X0,X1)
| X0 = X1 ),
inference(consistent_polarity_flipping,[],[f90]) ).
fof(f111,plain,
! [X0,X1] :
( ~ existsIn(X0,X0)
| ~ existsIn(X0,X1)
| ~ exists(X0) ),
inference(consistent_polarity_flipping,[],[f89]) ).
fof(f112,plain,
! [X0] :
( ~ existsIn(X0,X0)
| ~ exists(X0) ),
inference(consistent_polarity_flipping,[],[f101]) ).
fof(f113,plain,
! [X0,X1] :
( ~ conceivedThru(X0,X1)
| ~ conceivedThru(X0,X0) ),
inference(consistent_polarity_flipping,[],[f93]) ).
fof(f114,plain,
! [X0] : ~ conceivedThru(X0,X0),
inference(consistent_polarity_flipping,[],[f102]) ).
fof(f115,plain,
! [X0] :
( ~ hasEssence(X0)
| being(X0) ),
inference(consistent_polarity_flipping,[],[f97]) ).
fof(f116,plain,
! [X0] :
( exists(X0)
| essenceInvExistence(X0)
| hasEssence(X0) ),
inference(consistent_polarity_flipping,[],[f98]) ).
fof(f117,plain,
~ god(sK0),
inference(consistent_polarity_flipping,[],[f99]) ).
fof(f122,plain,
$false,
inference(finite_model_not_found_(exhaustively_excluded_all_possible_domain_size_assignments),[],[f103,f62,f104,f105,f106,f107,f108,f109,f110,f111,f112,f113,f114,f96,f115,f116,f100,f117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : PHI023+1 : TPTP v9.3.1. Released v7.4.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 27 22:07:04 UTC 2026
% 0.04/0.32 % CPUTime :
% 0.04/0.32 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.33 Running first-order model finding
% 0.07/0.33 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.36 % (2799009)Will run a generic schedule for satisfiability detection.
% 0.07/0.36 % (2799015)% WARNING: option uhcvi not known.
% 0.07/0.36 % (2799015)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1015447626:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.36 % (2799016)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=718950992:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.36 % (2799014)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1091749895_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.36 % (2799017)dis+10_1_sil=32000:sp=arity:random_seed=1339280784:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.36 % (2799019)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2512548244:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.36 % (2799018)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2788762274:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.36 % Detected minimum model sizes of [1]
% 0.07/0.36 % Detected maximum model sizes of [1]
% 0.07/0.36 % TRYING [1]
% 0.07/0.36 % (2799014) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2799009-2799014"...
% 0.07/0.36 % (2799020)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1784381194:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.36 % (2799017) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2799009-2799017"...
% 0.07/0.36 % (2799019) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2799009-2799019"...
% 0.07/0.36 % (2799018) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2799009-2799018"...
% 0.07/0.36 % (2799015) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2799009-2799015"...
% 0.07/0.36 % (2799019)...printing done.
% 0.07/0.36 % (2799017)...printing done.
% 0.07/0.36 % (2799014)...printing done.
% 0.07/0.36 % (2799016) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2799009-2799016"...
% 0.07/0.36 % (2799015)...printing done.
% 0.07/0.36 % (2799018)...printing done.
% 0.07/0.36 % (2799014)Refutation found. Thanks to Tanya!
% 0.07/0.36 % SZS status Theorem for theBenchmark
% 0.07/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.36 % (2799014)------------------------------
% 0.07/0.36 % (2799014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.36 % (2799014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.36 % (2799014)CaDiCaL version: 2.1.3
% 0.07/0.36 % (2799014)Termination reason: Refutation
% 0.07/0.36 % (2799014)Time elapsed: 0.001 s
% 0.07/0.36 % (2799014)Peak memory usage: 11 MB
% 0.07/0.36 % (2799014)Instructions burned: 3 (million)
% 0.07/0.36 % (2799009)Success in time 0.026 s
% 0.07/0.36 % Vampire exiting
%------------------------------------------------------------------------------