%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN954+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 02:06:03 PM UTC 2026
% Result : Theorem 2.64s 1.23s
% Output : Refutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 7 unt; 3 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 70 ( 26 ~; 22 |; 11 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 23 ( 0 sgn 17 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
( ! [X2] :
( q(X2)
=> p(X2) )
=> ? [X3] :
( ( p(X3)
=> p(X0) )
& ( q(X3)
=> p(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( ! [X2] :
( q(X2)
=> p(X2) )
=> ? [X3] :
( ( p(X3)
=> p(X0) )
& ( q(X3)
=> p(X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X0,X1] :
( ! [X3] :
( ( ~ p(X0)
& p(X3) )
| ( ~ p(X1)
& q(X3) ) )
& ! [X2] :
( p(X2)
| ~ q(X2) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
? [X0,X1] :
( ! [X2] :
( ( ~ p(X0)
& p(X2) )
| ( ~ p(X1)
& q(X2) ) )
& ! [X3] :
( p(X3)
| ~ q(X3) ) ),
inference(rectify,[],[f3]) ).
fof(f5,plain,
( ! [X2] :
( ( ~ p(sK0)
& p(X2) )
| ( ~ p(sK1)
& q(X2) ) )
& ! [X3] :
( p(X3)
| ~ q(X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f4]) ).
fof(f6,plain,
! [X3] :
( p(X3)
| ~ q(X3) ),
inference(cnf_transformation,[],[f5]) ).
fof(f7,plain,
! [X2] :
( p(X2)
| q(X2) ),
inference(cnf_transformation,[],[f5]) ).
fof(f10,plain,
( ~ p(sK0)
| ~ p(sK1) ),
inference(cnf_transformation,[],[f5]) ).
fof(f11,plain,
! [X2] : p(X2),
inference(forward_subsumption_resolution,[],[f7,f6]) ).
fof(f13,definition,
( spl2_1
<=> p(sK1) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f15,plain,
( ~ p(sK1)
| spl2_1 ),
inference(avatar_component_clause,[],[f13]) ).
fof(f17,definition,
( spl2_2
<=> ! [X2] : p(X2) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f18,plain,
( ! [X2] : p(X2)
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f17]) ).
fof(f24,definition,
( spl2_4
<=> p(sK0) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f26,plain,
( ~ p(sK0)
| spl2_4 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f28,plain,
( ~ spl2_1
| ~ spl2_4 ),
inference(avatar_split_clause,[],[f10,f24,f13]) ).
fof(f29,plain,
spl2_2,
inference(avatar_split_clause,[],[f11,f17]) ).
fof(f30,plain,
( $false
| ~ spl2_2
| spl2_4 ),
inference(forward_subsumption_resolution,[],[f26,f18]) ).
fof(f31,plain,
( ~ spl2_2
| spl2_4 ),
inference(avatar_contradiction_clause,[],[f30]) ).
fof(f32,plain,
( $false
| spl2_1
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f15,f18]) ).
fof(f33,plain,
( spl2_1
| ~ spl2_2 ),
inference(avatar_contradiction_clause,[],[f32]) ).
cnf(s3,plain,
( ~ spl2_1
| ~ spl2_4 ),
inference(sat_conversion,[],[f28]) ).
cnf(s4,plain,
spl2_2,
inference(sat_conversion,[],[f29]) ).
cnf(s5,plain,
( ~ spl2_2
| spl2_4 ),
inference(sat_conversion,[],[f31]) ).
cnf(s6,plain,
( spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f33]) ).
cnf(s7,plain,
spl2_1,
inference(rat,[],[s6,s4]) ).
cnf(s8,plain,
spl2_4,
inference(rat,[],[s5,s4]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s3,s8,s7]) ).
fof(f34,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN954+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.18 % Computer : n026.cluster.edu
% 0.13/0.18 % Model : x86_64 x86_64
% 0.13/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.18 % Memory : 8046.5625MB
% 0.13/0.18 % OS : Linux 6.8.0-71-generic
% 0.13/0.18 % CPULimit : 300
% 0.13/0.18 % WCLimit : 300
% 0.13/0.18 % DateTime : Mon Sep 28 17:19:12 UTC 2026
% 0.13/0.18 % CPUTime :
% 0.13/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.21 Running first-order theorem proving
% 0.13/0.21 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
% 2.64/1.23 % (4029448)Detected formulas, will run a generic FOF schedule.
% 2.64/1.23 % (4029471)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3612653279:i=109:sd=1:ins=1:gsp=on:ss=axioms_3000 on theBenchmark for (3000ds/109Mi)
% 2.64/1.23 % (4029471)First to succeed.
% 2.64/1.23 % (4029471)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4029448"
% 2.64/1.23 % (4029474)dis-21_1_sil=8000:lcm=predicate:random_seed=4144355852:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/129Mi)
% 2.64/1.23 % (4029473)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=439386050:s2a=on:i=139:gtg=position_3000 on theBenchmark for (3000ds/139Mi)
% 2.64/1.23 % (4029468)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=2382938155:i=141193_3000 on theBenchmark for (3000ds/141193Mi)
% 2.64/1.23 % (4029469)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=3810842454:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/134677Mi)
% 2.64/1.23 % (4029470)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=2717681734:i=141695:sd=1:nm=32:gsp=on:ss=included_3000 on theBenchmark for (3000ds/141695Mi)
% 2.64/1.23 % (4029474)Also succeeded, but the first one will report.
% 2.64/1.23 % (4029473)Also succeeded, but the first one will report.
% 2.64/1.23 % (4029472)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=958126411:i=119:av=off:ss=axioms_3000 on theBenchmark for (3000ds/119Mi)
% 2.64/1.23 % (4029472)Also succeeded, but the first one will report.
% 2.64/1.23 % (4029471)Refutation found. Thanks to Tanya!
% 2.64/1.23 % SZS status Theorem for theBenchmark
% 2.64/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 2.64/1.23 % (4029471)------------------------------
% 2.64/1.23 % (4029471)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.23 % (4029471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.23 % (4029471)CaDiCaL version: 2.1.3
% 2.64/1.23 % (4029471)Termination reason: Refutation
% 2.64/1.23 % (4029471)Time elapsed: 0.001 s
% 2.64/1.23 % (4029471)Peak memory usage: 89 MB
% 2.64/1.23 % (4029471)------------------------------
% 2.64/1.23 % (4029471)------------------------------
% 2.64/1.23 % (4029448)Success in time 0.259 s
% 2.64/1.23 % Vampire exiting
%------------------------------------------------------------------------------