%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW469+1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 01:30:23 PM UTC 2026
% Result : Theorem 3.61s 1.28s
% Output : Refutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 9 unt; 4 def)
% Number of atoms : 82 ( 14 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 78 ( 34 ~; 24 |; 10 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 14 ( 0 sgn 7 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
( hoare_165779456gleton
<=> ? [X0,X1] :
( is_state(X0)
& is_state(X1)
& X0 != X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_state__not__singleton__def) ).
fof(f6,axiom,
hoare_165779456gleton,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f7,conjecture,
! [X0] :
( is_state(X0)
=> ~ ! [X1] :
( is_state(X1)
=> X1 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(f8,negated_conjecture,
~ ! [X0] :
( is_state(X0)
=> ~ ! [X1] :
( is_state(X1)
=> X1 = X0 ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
( hoare_165779456gleton
=> ? [X0,X1] :
( is_state(X0)
& is_state(X1)
& X0 != X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f13,plain,
( ? [X0,X1] :
( is_state(X0)
& is_state(X1)
& X0 != X1 )
| ~ hoare_165779456gleton ),
inference(ennf_transformation,[],[f9]) ).
fof(f14,plain,
? [X0] :
( ! [X1] :
( X1 = X0
| ~ is_state(X1) )
& is_state(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f15,plain,
( ( is_state(sK0)
& is_state(sK1)
& sK0 != sK1 )
| ~ hoare_165779456gleton ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f13]) ).
fof(f16,plain,
( ! [X1] :
( sK2 = X1
| ~ is_state(X1) )
& is_state(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f14]) ).
fof(f18,plain,
( sK0 != sK1
| ~ hoare_165779456gleton ),
inference(cnf_transformation,[],[f15]) ).
fof(f19,plain,
( is_state(sK1)
| ~ hoare_165779456gleton ),
inference(cnf_transformation,[],[f15]) ).
fof(f20,plain,
( is_state(sK0)
| ~ hoare_165779456gleton ),
inference(cnf_transformation,[],[f15]) ).
fof(f21,plain,
hoare_165779456gleton,
inference(cnf_transformation,[],[f6]) ).
fof(f23,plain,
! [X1] :
( ~ is_state(X1)
| sK2 = X1 ),
inference(cnf_transformation,[],[f16]) ).
fof(f25,definition,
( spl3_1
<=> hoare_165779456gleton ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f29,definition,
( spl3_2
<=> sK0 = sK1 ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f32,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f18,f29,f25]) ).
fof(f34,definition,
( spl3_3
<=> is_state(sK1) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f36,plain,
( is_state(sK1)
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f37,plain,
( ~ spl3_1
| spl3_3 ),
inference(avatar_split_clause,[],[f19,f34,f25]) ).
fof(f39,definition,
( spl3_4
<=> is_state(sK0) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f41,plain,
( is_state(sK0)
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f42,plain,
( ~ spl3_1
| spl3_4 ),
inference(avatar_split_clause,[],[f20,f39,f25]) ).
fof(f48,plain,
spl3_1,
inference(avatar_split_clause,[],[f21,f25]) ).
fof(f49,plain,
( sK1 = sK2
| ~ spl3_3 ),
inference(resolution,[],[f36,f23]) ).
fof(f51,plain,
( sK0 = sK2
| ~ spl3_4 ),
inference(resolution,[],[f41,f23]) ).
fof(f53,plain,
( sK0 = sK1
| ~ spl3_3
| ~ spl3_4 ),
inference(superposition,[],[f49,f51]) ).
fof(f55,plain,
( spl3_2
| ~ spl3_3
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f53,f39,f34,f29]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f32]) ).
cnf(s2,plain,
( ~ spl3_1
| spl3_3 ),
inference(sat_conversion,[],[f37]) ).
cnf(s3,plain,
( ~ spl3_1
| spl3_4 ),
inference(sat_conversion,[],[f42]) ).
cnf(s5,plain,
spl3_1,
inference(sat_conversion,[],[f48]) ).
cnf(s6,plain,
( spl3_2
| ~ spl3_3
| ~ spl3_4 ),
inference(sat_conversion,[],[f55]) ).
cnf(s8,plain,
spl3_4,
inference(rat,[],[s3,s5]) ).
cnf(s9,plain,
spl3_3,
inference(rat,[],[s2,s5]) ).
cnf(s10,plain,
spl3_2,
inference(rat,[],[s6,s8,s9]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s1,s10,s5]) ).
fof(f56,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW469+1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n003.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 14:02:42 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 3.61/1.28 % (1592786)Detected formulas, will run a generic FOF schedule.
% 3.61/1.28 % (1592794)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4107497274:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.61/1.28 % (1592794)Refutation not found, incomplete strategy
% 3.61/1.28 % (1592794)------------------------------
% 3.61/1.28 % (1592794)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.28 % (1592794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.28 % (1592794)CaDiCaL version: 2.1.3
% 3.61/1.28 % (1592794)Termination reason: Refutation not found, incomplete strategy
% 3.61/1.28 % (1592794)Time elapsed: 0.001 s
% 3.61/1.28 % (1592794)Peak memory usage: 88 MB
% 3.61/1.28 % (1592792)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=3076114593:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.61/1.28 % (1592793)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=1315550549:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.61/1.28 % (1592791)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=3915729029:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.61/1.28 % (1592797)dis-21_1_sil=8000:lcm=predicate:random_seed=18312980: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)
% 3.61/1.28 % (1592796)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=217647228:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.61/1.28 % (1592795)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3463343233:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.61/1.28 % (1592795)Refutation not found, incomplete strategy
% 3.61/1.28 % (1592795)------------------------------
% 3.61/1.28 % (1592795)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.28 % (1592795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.28 % (1592795)CaDiCaL version: 2.1.3
% 3.61/1.28 % (1592795)Termination reason: Refutation not found, incomplete strategy
% 3.61/1.28 % (1592795)Time elapsed: 0.001 s
% 3.61/1.28 % (1592795)Peak memory usage: 87 MB
% 3.61/1.28 % (1592797)Refutation not found, incomplete strategy
% 3.61/1.28 % (1592797)------------------------------
% 3.61/1.28 % (1592797)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.28 % (1592797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.28 % (1592797)CaDiCaL version: 2.1.3
% 3.61/1.28 % (1592797)Termination reason: Refutation not found, incomplete strategy
% 3.61/1.28 % (1592797)Time elapsed: 0.001 s
% 3.61/1.28 % (1592797)Peak memory usage: 88 MB
% 3.61/1.28 % (1592796)First to succeed.
% 3.61/1.28 % (1592796)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1592786"
% 3.61/1.28 % (1592794)------------------------------
% 3.61/1.28 % (1592794)------------------------------
% 3.61/1.28 % (1592805)lrs+10_1_sil=8000:sp=occurrence:random_seed=3763530639:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.61/1.28 % (1592805)Also succeeded, but the first one will report.
% 3.61/1.28 % (1592797)------------------------------
% 3.61/1.28 % (1592797)------------------------------
% 3.61/1.28 % (1592795)------------------------------
% 3.61/1.28 % (1592795)------------------------------
% 3.61/1.28 % (1592796)Refutation found. Thanks to Tanya!
% 3.61/1.28 % SZS status Theorem for theBenchmark
% 3.61/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.61/1.28 % (1592796)------------------------------
% 3.61/1.28 % (1592796)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.28 % (1592796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.28 % (1592796)CaDiCaL version: 2.1.3
% 3.61/1.28 % (1592796)Termination reason: Refutation
% 3.61/1.28 % (1592796)Time elapsed: 0.002 s
% 3.61/1.28 % (1592796)Peak memory usage: 89 MB
% 3.61/1.28 % (1592796)Instructions burned: 1 (million)
% 3.61/1.28 % (1592796)------------------------------
% 3.61/1.28 % (1592796)------------------------------
% 3.61/1.28 % (1592786)Success in time 0.421 s
% 3.61/1.28 % Vampire exiting
%------------------------------------------------------------------------------