%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PHI010+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 : n014.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 2.60s 1.12s
% Output : Refutation 2.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 49 ( 12 unt; 4 def)
% Number of atoms : 201 ( 39 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 234 ( 82 ~; 75 |; 63 &)
% ( 7 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 3 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 60 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( ( property(X0)
& object(X1)
& object(X2) )
=> ( ( is_the(X1,X0)
& X1 = X2 )
<=> ? [X3] :
( object(X3)
& exemplifies_property(X0,X3)
& ! [X4] :
( object(X4)
=> ( exemplifies_property(X0,X4)
=> X4 = X3 ) )
& X3 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',description_axiom_identity_instance) ).
fof(f5,conjecture,
! [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(f6,negated_conjecture,
~ ! [X0,X1,X2] :
( ( object(X0)
& property(X1)
& object(X2) )
=> ( ( is_the(X0,X1)
& X0 = X2 )
=> exemplifies_property(X1,X2) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f10,plain,
! [X0,X1,X2] :
( ( ( is_the(X1,X0)
& X1 = X2 )
<=> ? [X3] :
( object(X3)
& exemplifies_property(X0,X3)
& ! [X4] :
( X4 = X3
| ~ exemplifies_property(X0,X4)
| ~ object(X4) )
& X3 = X2 ) )
| ~ property(X0)
| ~ object(X1)
| ~ object(X2) ),
inference(ennf_transformation,[],[f4]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ( ( is_the(X1,X0)
& X1 = X2 )
<=> ? [X3] :
( object(X3)
& exemplifies_property(X0,X3)
& ! [X4] :
( X4 = X3
| ~ exemplifies_property(X0,X4)
| ~ object(X4) )
& X3 = X2 ) )
| ~ property(X0)
| ~ object(X1)
| ~ object(X2) ),
inference(flattening,[],[f10]) ).
fof(f12,plain,
? [X0,X1,X2] :
( ~ exemplifies_property(X1,X2)
& is_the(X0,X1)
& X0 = X2
& object(X0)
& property(X1)
& object(X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f13,plain,
? [X0,X1,X2] :
( ~ exemplifies_property(X1,X2)
& is_the(X0,X1)
& X0 = X2
& object(X0)
& property(X1)
& object(X2) ),
inference(flattening,[],[f12]) ).
fof(f14,definition,
! [X0,X2] :
( sP0(X0,X2)
<=> ? [X3] :
( object(X3)
& exemplifies_property(X0,X3)
& ! [X4] :
( X4 = X3
| ~ exemplifies_property(X0,X4)
| ~ object(X4) )
& X3 = X2 ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f15,definition,
! [X2,X0,X1] :
( ( ( is_the(X1,X0)
& X1 = X2 )
<=> sP0(X0,X2) )
| ~ sP1(X2,X0,X1) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f16,plain,
! [X0,X1,X2] :
( sP1(X2,X0,X1)
| ~ property(X0)
| ~ object(X1)
| ~ object(X2) ),
inference(definition_folding,[],[f11,f15,f14]) ).
fof(f17,plain,
! [X2,X0,X1] :
( ( ( ( is_the(X1,X0)
& X1 = X2 )
| ~ sP0(X0,X2) )
& ( sP0(X0,X2)
| ~ is_the(X1,X0)
| X1 != X2 ) )
| ~ sP1(X2,X0,X1) ),
inference(nnf_transformation,[],[f15]) ).
fof(f18,plain,
! [X2,X0,X1] :
( ( ( ( is_the(X1,X0)
& X1 = X2 )
| ~ sP0(X0,X2) )
& ( sP0(X0,X2)
| ~ is_the(X1,X0)
| X1 != X2 ) )
| ~ sP1(X2,X0,X1) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( ( ( is_the(X2,X1)
& X0 = X2 )
| ~ sP0(X1,X0) )
& ( sP0(X1,X0)
| ~ is_the(X2,X1)
| X0 != X2 ) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f18]) ).
fof(f20,plain,
! [X0,X2] :
( ( sP0(X0,X2)
| ! [X3] :
( ~ object(X3)
| ~ exemplifies_property(X0,X3)
| ? [X4] :
( X3 != X4
& exemplifies_property(X0,X4)
& object(X4) )
| X2 != X3 ) )
& ( ? [X3] :
( object(X3)
& exemplifies_property(X0,X3)
& ! [X4] :
( X4 = X3
| ~ exemplifies_property(X0,X4)
| ~ object(X4) )
& X3 = X2 )
| ~ sP0(X0,X2) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f21,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ! [X2] :
( ~ object(X2)
| ~ exemplifies_property(X0,X2)
| ? [X3] :
( X2 != X3
& exemplifies_property(X0,X3)
& object(X3) )
| X1 != X2 ) )
& ( ? [X4] :
( object(X4)
& exemplifies_property(X0,X4)
& ! [X5] :
( X4 = X5
| ~ exemplifies_property(X0,X5)
| ~ object(X5) )
& X1 = X4 )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ! [X2] :
( ~ object(X2)
| ~ exemplifies_property(X0,X2)
| ( sK2(X0,X2) != X2
& exemplifies_property(X0,sK2(X0,X2))
& object(sK2(X0,X2)) )
| X1 != X2 ) )
& ( ( object(sK3(X0,X1))
& exemplifies_property(X0,sK3(X0,X1))
& ! [X5] :
( sK3(X0,X1) = X5
| ~ exemplifies_property(X0,X5)
| ~ object(X5) )
& sK3(X0,X1) = X1 )
| ~ sP0(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X3,sK2(X0,X2)),skolemize(X4,sK3(X0,X1))],[f21]) ).
fof(f23,plain,
( ~ exemplifies_property(sK5,sK6)
& is_the(sK4,sK5)
& sK4 = sK6
& object(sK4)
& property(sK5)
& object(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6)],[f13]) ).
fof(f29,plain,
! [X2,X0,X1] :
( sP0(X1,X0)
| ~ is_the(X2,X1)
| X0 != X2
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f19]) ).
fof(f32,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK3(X0,X1) = X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f34,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| exemplifies_property(X0,sK3(X0,X1)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f39,plain,
! [X2,X0,X1] :
( sP1(X2,X0,X1)
| ~ property(X0)
| ~ object(X1)
| ~ object(X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f41,plain,
property(sK5),
inference(cnf_transformation,[],[f23]) ).
fof(f42,plain,
object(sK4),
inference(cnf_transformation,[],[f23]) ).
fof(f43,plain,
sK4 = sK6,
inference(cnf_transformation,[],[f23]) ).
fof(f44,plain,
is_the(sK4,sK5),
inference(cnf_transformation,[],[f23]) ).
fof(f45,plain,
~ exemplifies_property(sK5,sK6),
inference(cnf_transformation,[],[f23]) ).
fof(f46,plain,
! [X2,X1] :
( ~ is_the(X2,X1)
| sP0(X1,X2)
| ~ sP1(X2,X1,X2) ),
inference(equality_resolution,[],[f29]) ).
fof(f51,plain,
~ exemplifies_property(sK5,sK4),
inference(forward_demodulation,[],[f45,f43]) ).
fof(f56,plain,
( sP0(sK5,sK4)
| ~ sP1(sK4,sK5,sK4) ),
inference(resolution,[],[f46,f44]) ).
fof(f58,definition,
( spl7_1
<=> sP1(sK4,sK5,sK4) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
fof(f60,plain,
( ~ sP1(sK4,sK5,sK4)
| spl7_1 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f62,definition,
( spl7_2
<=> sP0(sK5,sK4) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
fof(f64,plain,
( sP0(sK5,sK4)
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f65,plain,
( ~ spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f56,f62,f58]) ).
fof(f66,plain,
( ~ property(sK5)
| ~ object(sK4)
| ~ object(sK4)
| spl7_1 ),
inference(resolution,[],[f60,f39]) ).
fof(f67,plain,
( ~ property(sK5)
| ~ object(sK4)
| spl7_1 ),
inference(duplicate_literal_removal,[],[f66]) ).
fof(f68,plain,
( ~ object(sK4)
| spl7_1 ),
inference(forward_subsumption_resolution,[],[f67,f41]) ).
fof(f69,plain,
( $false
| spl7_1 ),
inference(forward_subsumption_resolution,[],[f68,f42]) ).
fof(f70,plain,
spl7_1,
inference(avatar_contradiction_clause,[],[f69]) ).
fof(f74,plain,
( exemplifies_property(sK5,sK3(sK5,sK4))
| ~ spl7_2 ),
inference(resolution,[],[f64,f34]) ).
fof(f75,plain,
( sK4 = sK3(sK5,sK4)
| ~ spl7_2 ),
inference(resolution,[],[f64,f32]) ).
fof(f82,plain,
( exemplifies_property(sK5,sK4)
| ~ spl7_2 ),
inference(superposition,[],[f74,f75]) ).
fof(f84,plain,
( $false
| ~ spl7_2 ),
inference(forward_subsumption_resolution,[],[f82,f51]) ).
fof(f85,plain,
~ spl7_2,
inference(avatar_contradiction_clause,[],[f84]) ).
cnf(s1,plain,
( ~ spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f65]) ).
cnf(s2,plain,
spl7_1,
inference(sat_conversion,[],[f70]) ).
cnf(s3,plain,
~ spl7_2,
inference(sat_conversion,[],[f85]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f86,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI010+1 : TPTP v9.3.1. Released v7.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n014.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 22:07:01 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.39 Running first-order theorem proving
% 0.15/0.39 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
% 2.60/1.12 % (1218587)Detected formulas, will run a generic FOF schedule.
% 2.60/1.12 % (1218597)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=529025357:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.60/1.12 % (1218597)First to succeed.
% 2.60/1.12 % (1218594)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=4234999763:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.60/1.12 % (1218598)dis-21_1_sil=8000:lcm=predicate:random_seed=3700110094: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)
% 2.60/1.12 % (1218592)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=3372223185:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.60/1.12 % (1218596)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2207775170:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.60/1.12 % (1218595)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3948616890:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.60/1.12 % (1218593)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=1380283337:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.60/1.12 % (1218597)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1218587"
% 2.60/1.12 % (1218595)Refutation not found, incomplete strategy
% 2.60/1.12 % (1218595)------------------------------
% 2.60/1.12 % (1218595)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.12 % (1218595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.12 % (1218596)Also succeeded, but the first one will report.
% 2.60/1.12 % (1218595)CaDiCaL version: 2.1.3
% 2.60/1.12 % (1218595)Termination reason: Refutation not found, incomplete strategy
% 2.60/1.12 % (1218595)Time elapsed: 0.002 s
% 2.60/1.12 % (1218595)Peak memory usage: 88 MB
% 2.60/1.12 % (1218595)Instructions burned: 1 (million)
% 2.60/1.12 % (1218598)Instruction limit reached!
% 2.60/1.12 % (1218598)------------------------------
% 2.60/1.12 % (1218598)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.12 % (1218598)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.12 % (1218598)CaDiCaL version: 2.1.3
% 2.60/1.12 % (1218598)Termination reason: Instruction limit
% 2.60/1.12 % (1218598)Termination phase: Saturation
% 2.60/1.12 % (1218598)Time elapsed: 0.070 s
% 2.60/1.12 % (1218598)Peak memory usage: 88 MB
% 2.60/1.12 % (1218598)Instructions burned: 130 (million)
% 2.60/1.12 % (1218597)Refutation found. Thanks to Tanya!
% 2.60/1.12 % SZS status Theorem for theBenchmark
% 2.60/1.12 % SZS output start Proof for theBenchmark
% See solution above
% 2.60/1.12 % (1218597)------------------------------
% 2.60/1.12 % (1218597)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.12 % (1218597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.12 % (1218597)CaDiCaL version: 2.1.3
% 2.60/1.12 % (1218597)Termination reason: Refutation
% 2.60/1.12 % (1218597)Time elapsed: 0.003 s
% 2.60/1.12 % (1218597)Peak memory usage: 89 MB
% 2.60/1.12 % (1218597)Instructions burned: 3 (million)
% 2.60/1.12 % (1218597)------------------------------
% 2.60/1.12 % (1218597)------------------------------
% 2.60/1.12 % (1218587)Success in time 0.32 s
% 2.60/1.12 % Vampire exiting
%------------------------------------------------------------------------------