%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN550+1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 02:00:56 PM UTC 2026
% Result : Theorem 2.48s 1.12s
% Output : Refutation 2.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 4
% Syntax : Number of formulae : 48 ( 6 unt; 1 def)
% Number of atoms : 209 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 265 ( 104 ~; 105 |; 40 &)
% ( 4 <=>; 10 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-1 aty)
% Number of variables : 103 ( 76 !; 27 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : reachable(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_reachable) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( reachable(X0,X1)
& reachable(X1,X2) )
=> reachable(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_reachable) ).
fof(f3,conjecture,
( ? [X0] :
( reachable(initial_world,X0)
& ! [X1] :
( reachable(X0,X1)
=> p(X1) ) )
<=> ? [X0] :
( reachable(initial_world,X0)
& ! [X1] :
( reachable(X0,X1)
=> ? [X2] :
( reachable(X1,X2)
& ! [X3] :
( reachable(X2,X3)
=> p(X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f4,negated_conjecture,
~ ( ? [X0] :
( reachable(initial_world,X0)
& ! [X1] :
( reachable(X0,X1)
=> p(X1) ) )
<=> ? [X0] :
( reachable(initial_world,X0)
& ! [X1] :
( reachable(X0,X1)
=> ? [X2] :
( reachable(X1,X2)
& ! [X3] :
( reachable(X2,X3)
=> p(X3) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
~ ( ? [X0] :
( reachable(initial_world,X0)
& ! [X1] :
( reachable(X0,X1)
=> p(X1) ) )
<=> ? [X2] :
( reachable(initial_world,X2)
& ! [X3] :
( reachable(X2,X3)
=> ? [X4] :
( reachable(X3,X4)
& ! [X5] :
( reachable(X4,X5)
=> p(X5) ) ) ) ) ),
inference(rectify,[],[f4]) ).
fof(f6,plain,
( ? [X0] :
( reachable(initial_world,X0)
& ! [X1] :
( p(X1)
| ~ reachable(X0,X1) ) )
<~> ? [X2] :
( reachable(initial_world,X2)
& ! [X3] :
( ? [X4] :
( reachable(X3,X4)
& ! [X5] :
( p(X5)
| ~ reachable(X4,X5) ) )
| ~ reachable(X2,X3) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f7,plain,
! [X0,X1,X2] :
( reachable(X0,X2)
| ~ reachable(X0,X1)
| ~ reachable(X1,X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f8,plain,
! [X0,X1,X2] :
( reachable(X0,X2)
| ~ reachable(X0,X1)
| ~ reachable(X1,X2) ),
inference(flattening,[],[f7]) ).
fof(f9,definition,
( sP0
<=> ? [X2] :
( reachable(initial_world,X2)
& ! [X3] :
( ? [X4] :
( reachable(X3,X4)
& ! [X5] :
( p(X5)
| ~ reachable(X4,X5) ) )
| ~ reachable(X2,X3) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f10,plain,
( ? [X0] :
( reachable(initial_world,X0)
& ! [X1] :
( p(X1)
| ~ reachable(X0,X1) ) )
<~> sP0 ),
inference(definition_folding,[],[f6,f9]) ).
fof(f11,plain,
( ( sP0
| ! [X2] :
( ~ reachable(initial_world,X2)
| ? [X3] :
( ! [X4] :
( ~ reachable(X3,X4)
| ? [X5] :
( ~ p(X5)
& reachable(X4,X5) ) )
& reachable(X2,X3) ) ) )
& ( ? [X2] :
( reachable(initial_world,X2)
& ! [X3] :
( ? [X4] :
( reachable(X3,X4)
& ! [X5] :
( p(X5)
| ~ reachable(X4,X5) ) )
| ~ reachable(X2,X3) ) )
| ~ sP0 ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f12,plain,
( ( sP0
| ! [X0] :
( ~ reachable(initial_world,X0)
| ? [X1] :
( ! [X2] :
( ~ reachable(X1,X2)
| ? [X3] :
( ~ p(X3)
& reachable(X2,X3) ) )
& reachable(X0,X1) ) ) )
& ( ? [X4] :
( reachable(initial_world,X4)
& ! [X5] :
( ? [X6] :
( reachable(X5,X6)
& ! [X7] :
( p(X7)
| ~ reachable(X6,X7) ) )
| ~ reachable(X4,X5) ) )
| ~ sP0 ) ),
inference(rectify,[],[f11]) ).
fof(f13,plain,
( ( sP0
| ! [X0] :
( ~ reachable(initial_world,X0)
| ( ! [X2] :
( ~ reachable(sK1(X0),X2)
| ( ~ p(sK2(X2))
& reachable(X2,sK2(X2)) ) )
& reachable(X0,sK1(X0)) ) ) )
& ( ( reachable(initial_world,sK3)
& ! [X5] :
( ( reachable(X5,sK4(X5))
& ! [X7] :
( p(X7)
| ~ reachable(sK4(X5),X7) ) )
| ~ reachable(sK3,X5) ) )
| ~ sP0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(X1,sK1(X0)),skolemize(X3,sK2(X2)),skolemize(X4,sK3),skolemize(X6,sK4(X5))],[f12]) ).
fof(f14,plain,
( ( ~ sP0
| ! [X0] :
( ~ reachable(initial_world,X0)
| ? [X1] :
( ~ p(X1)
& reachable(X0,X1) ) ) )
& ( sP0
| ? [X0] :
( reachable(initial_world,X0)
& ! [X1] :
( p(X1)
| ~ reachable(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f15,plain,
( ( ~ sP0
| ! [X0] :
( ~ reachable(initial_world,X0)
| ? [X1] :
( ~ p(X1)
& reachable(X0,X1) ) ) )
& ( sP0
| ? [X2] :
( reachable(initial_world,X2)
& ! [X3] :
( p(X3)
| ~ reachable(X2,X3) ) ) ) ),
inference(rectify,[],[f14]) ).
fof(f16,plain,
( ( ~ sP0
| ! [X0] :
( ~ reachable(initial_world,X0)
| ( ~ p(sK5(X0))
& reachable(X0,sK5(X0)) ) ) )
& ( sP0
| ( reachable(initial_world,sK6)
& ! [X3] :
( p(X3)
| ~ reachable(sK6,X3) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X1,sK5(X0)),skolemize(X2,sK6)],[f15]) ).
fof(f17,plain,
! [X7,X5] :
( ~ reachable(sK4(X5),X7)
| p(X7)
| ~ reachable(sK3,X5)
| ~ sP0 ),
inference(cnf_transformation,[],[f13]) ).
fof(f18,plain,
! [X5] :
( reachable(X5,sK4(X5))
| ~ reachable(sK3,X5)
| ~ sP0 ),
inference(cnf_transformation,[],[f13]) ).
fof(f19,plain,
( reachable(initial_world,sK3)
| ~ sP0 ),
inference(cnf_transformation,[],[f13]) ).
fof(f20,plain,
! [X0] :
( reachable(X0,sK1(X0))
| ~ reachable(initial_world,X0)
| sP0 ),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
! [X2,X0] :
( reachable(X2,sK2(X2))
| ~ reachable(initial_world,X0)
| ~ reachable(sK1(X0),X2)
| sP0 ),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
! [X2,X0] :
( ~ reachable(sK1(X0),X2)
| ~ reachable(initial_world,X0)
| sP0
| ~ p(sK2(X2)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f23,plain,
! [X3] :
( ~ reachable(sK6,X3)
| p(X3)
| sP0 ),
inference(cnf_transformation,[],[f16]) ).
fof(f24,plain,
( reachable(initial_world,sK6)
| sP0 ),
inference(cnf_transformation,[],[f16]) ).
fof(f25,plain,
! [X0] :
( reachable(X0,sK5(X0))
| ~ reachable(initial_world,X0)
| ~ sP0 ),
inference(cnf_transformation,[],[f16]) ).
fof(f26,plain,
! [X0] :
( ~ p(sK5(X0))
| ~ reachable(initial_world,X0)
| ~ sP0 ),
inference(cnf_transformation,[],[f16]) ).
fof(f27,plain,
! [X2,X0,X1] :
( reachable(X0,X2)
| ~ reachable(X0,X1)
| ~ reachable(X1,X2) ),
inference(cnf_transformation,[],[f8]) ).
fof(f28,plain,
! [X0] : reachable(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f35,plain,
! [X0,X1] :
( ~ reachable(sK6,X0)
| ~ reachable(X0,X1)
| p(X1)
| sP0 ),
inference(resolution,[],[f27,f23]) ).
fof(f40,plain,
! [X0] :
( p(sK5(sK4(X0)))
| ~ reachable(sK3,X0)
| ~ sP0
| ~ reachable(initial_world,sK4(X0))
| ~ sP0 ),
inference(resolution,[],[f17,f25]) ).
fof(f41,plain,
! [X0] :
( p(sK5(sK4(X0)))
| ~ reachable(sK3,X0)
| ~ sP0
| ~ reachable(initial_world,sK4(X0)) ),
inference(duplicate_literal_removal,[],[f40]) ).
fof(f43,plain,
! [X0] :
( ~ reachable(initial_world,sK4(X0))
| ~ sP0
| ~ reachable(sK3,X0) ),
inference(forward_subsumption_resolution,[],[f41,f26]) ).
fof(f45,plain,
! [X0,X1] :
( ~ sP0
| ~ reachable(sK3,X0)
| ~ reachable(initial_world,X1)
| ~ reachable(X1,sK4(X0)) ),
inference(resolution,[],[f43,f27]) ).
fof(f83,plain,
! [X0] :
( ~ reachable(sK1(sK6),X0)
| p(X0)
| sP0
| ~ reachable(initial_world,sK6)
| sP0 ),
inference(resolution,[],[f35,f20]) ).
fof(f89,plain,
! [X0] :
( ~ reachable(sK1(sK6),X0)
| p(X0)
| sP0
| ~ reachable(initial_world,sK6) ),
inference(duplicate_literal_removal,[],[f83]) ).
fof(f90,plain,
! [X0] :
( ~ reachable(sK1(sK6),X0)
| p(X0)
| sP0 ),
inference(forward_subsumption_resolution,[],[f89,f24]) ).
fof(f94,plain,
! [X0] :
( p(sK2(sK1(sK6)))
| sP0
| ~ reachable(initial_world,X0)
| ~ reachable(sK1(X0),sK1(sK6))
| sP0 ),
inference(resolution,[],[f90,f21]) ).
fof(f97,plain,
! [X0] :
( p(sK2(sK1(sK6)))
| sP0
| ~ reachable(initial_world,X0)
| ~ reachable(sK1(X0),sK1(sK6)) ),
inference(duplicate_literal_removal,[],[f94]) ).
fof(f99,plain,
! [X0] :
( ~ reachable(sK1(X0),sK1(sK6))
| ~ reachable(initial_world,X0)
| sP0 ),
inference(forward_subsumption_resolution,[],[f97,f22]) ).
fof(f108,plain,
( ~ reachable(initial_world,sK6)
| sP0 ),
inference(resolution,[],[f99,f28]) ).
fof(f110,plain,
sP0,
inference(forward_subsumption_resolution,[],[f108,f24]) ).
fof(f144,plain,
! [X0,X1] :
( ~ reachable(X1,sK4(X0))
| ~ reachable(initial_world,X1)
| ~ reachable(sK3,X0) ),
inference(forward_subsumption_resolution,[],[f45,f110]) ).
fof(f145,plain,
! [X0] :
( ~ reachable(initial_world,X0)
| ~ reachable(sK3,X0)
| ~ reachable(sK3,X0)
| ~ sP0 ),
inference(resolution,[],[f144,f18]) ).
fof(f148,plain,
! [X0] :
( ~ reachable(initial_world,X0)
| ~ reachable(sK3,X0)
| ~ sP0 ),
inference(duplicate_literal_removal,[],[f145]) ).
fof(f149,plain,
! [X0] :
( ~ reachable(sK3,X0)
| ~ reachable(initial_world,X0) ),
inference(forward_subsumption_resolution,[],[f148,f110]) ).
fof(f150,plain,
~ reachable(initial_world,sK3),
inference(resolution,[],[f149,f28]) ).
fof(f158,plain,
~ sP0,
inference(resolution,[],[f150,f19]) ).
fof(f160,plain,
$false,
inference(forward_subsumption_resolution,[],[f158,f110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN550+1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n004.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 16:28:07 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 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
% 2.48/1.12 % (503365)Detected formulas, will run a generic FOF schedule.
% 2.48/1.12 % (503374)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4204264663:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.48/1.12 % (503374)First to succeed.
% 2.48/1.12 % (503374)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-503365"
% 2.48/1.12 % (503371)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=2939985489:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.48/1.12 % (503373)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=880359703:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.48/1.12 % (503370)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=979463540:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.48/1.12 % (503372)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=3898605757:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.48/1.12 % (503375)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3301719032:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.48/1.12 % (503375)Also succeeded, but the first one will report.
% 2.48/1.12 % (503376)dis-21_1_sil=8000:lcm=predicate:random_seed=998455777: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)
% 2.48/1.12 % (503376)Also succeeded, but the first one will report.
% 2.48/1.12 % (503373)Instruction limit reached!
% 2.48/1.12 % (503373)------------------------------
% 2.48/1.12 % (503373)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.48/1.12 % (503373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.48/1.12 % (503373)CaDiCaL version: 2.1.3
% 2.48/1.12 % (503373)Termination reason: Instruction limit
% 2.48/1.12 % (503373)Termination phase: Saturation
% 2.48/1.12 % (503373)Time elapsed: 0.044 s
% 2.48/1.12 % (503373)Peak memory usage: 88 MB
% 2.48/1.12 % (503373)Instructions burned: 109 (million)
% 2.48/1.12 % (503374)Refutation found. Thanks to Tanya!
% 2.48/1.12 % SZS status Theorem for theBenchmark
% 2.48/1.12 % SZS output start Proof for theBenchmark
% See solution above
% 2.48/1.12 % (503374)------------------------------
% 2.48/1.12 % (503374)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.48/1.12 % (503374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.48/1.12 % (503374)CaDiCaL version: 2.1.3
% 2.48/1.12 % (503374)Termination reason: Refutation
% 2.48/1.12 % (503374)Time elapsed: 0.002 s
% 2.48/1.12 % (503374)Peak memory usage: 88 MB
% 2.48/1.12 % (503374)Instructions burned: 4 (million)
% 2.48/1.12 % (503374)------------------------------
% 2.48/1.12 % (503374)------------------------------
% 2.48/1.12 % (503365)Success in time 0.266 s
% 2.48/1.12 % Vampire exiting
%------------------------------------------------------------------------------