%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN926+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 : n007.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 02:05:59 PM UTC 2026
% Result : Theorem 0.19s 1.14s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 9 unt; 4 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 63 ( 30 ~; 14 |; 12 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 5 prp; 0-1 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 26 ( 0 sgn 15 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ? [X0] :
( p(X0)
& q(X0) )
=> ( ? [X0] : p(X0)
& ? [X0] : q(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f2,negated_conjecture,
~ ( ? [X0] :
( p(X0)
& q(X0) )
=> ( ? [X0] : p(X0)
& ? [X0] : q(X0) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ? [X0] :
( p(X0)
& q(X0) )
=> ( ? [X1] : p(X1)
& ? [X2] : q(X2) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ( ! [X1] : ~ p(X1)
| ! [X2] : ~ q(X2) )
& ? [X0] :
( p(X0)
& q(X0) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
( ( ! [X0] : ~ p(X0)
| ! [X1] : ~ q(X1) )
& ? [X2] :
( p(X2)
& q(X2) ) ),
inference(rectify,[],[f4]) ).
fof(f6,plain,
( ( ! [X0] : ~ p(X0)
| ! [X1] : ~ q(X1) )
& p(sK0)
& q(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0)],[f5]) ).
fof(f7,plain,
q(sK0),
inference(cnf_transformation,[],[f6]) ).
fof(f8,plain,
p(sK0),
inference(cnf_transformation,[],[f6]) ).
fof(f9,plain,
! [X0,X1] :
( ~ p(X0)
| ~ q(X1) ),
inference(cnf_transformation,[],[f6]) ).
fof(f10,plain,
! [X0] :
( ~ p(X0)
| sP1 ),
inference(cnf_transformation,[],[f10_D]) ).
fof(f10_D,definition,
( ! [X0] : ~ p(X0)
<=> ~ sP1 ),
introduced(definition,[new_symbols(definition,[sP1])],[general_splitting_component_introduction]) ).
fof(f11,plain,
! [X1] :
( ~ q(X1)
| ~ sP1 ),
inference(general_splitting,[],[f9,f10_D]) ).
fof(f13,definition,
( spl2_1
<=> sP1 ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f17,definition,
( spl2_2
<=> ! [X0] : ~ p(X0) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f18,plain,
( ! [X0] : ~ p(X0)
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f17]) ).
fof(f19,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f10,f17,f13]) ).
fof(f21,definition,
( spl2_3
<=> ! [X1] : ~ q(X1) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f22,plain,
( ! [X1] : ~ q(X1)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f23,plain,
( ~ spl2_1
| spl2_3 ),
inference(avatar_split_clause,[],[f11,f21,f13]) ).
fof(f24,plain,
( $false
| ~ spl2_2 ),
inference(resolution,[],[f18,f8]) ).
fof(f25,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f24]) ).
fof(f26,plain,
( $false
| ~ spl2_3 ),
inference(resolution,[],[f22,f7]) ).
fof(f27,plain,
~ spl2_3,
inference(avatar_contradiction_clause,[],[f26]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f19]) ).
cnf(s2,plain,
( ~ spl2_1
| spl2_3 ),
inference(sat_conversion,[],[f23]) ).
cnf(s3,plain,
~ spl2_2,
inference(sat_conversion,[],[f25]) ).
cnf(s4,plain,
~ spl2_3,
inference(sat_conversion,[],[f27]) ).
cnf(s5,plain,
~ spl2_1,
inference(rat,[],[s2,s4]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s3,s5]) ).
fof(f28,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN926+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n007.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Mon Sep 28 17:11:11 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running first-order theorem proving
% 0.10/0.22 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
% 0.19/1.14 % (2567668)Detected formulas, will run a generic FOF schedule.
% 0.19/1.14 % (2567685)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1972848774:i=109:sd=1:ins=1:gsp=on:ss=axioms_3000 on theBenchmark for (3000ds/109Mi)
% 0.19/1.14 % (2567685)First to succeed.
% 0.19/1.14 % (2567685)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2567668"
% 0.19/1.14 % (2567683)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=1557776785:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/134677Mi)
% 0.19/1.14 % (2567684)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=3666773328:i=141695:sd=1:nm=32:gsp=on:ss=included_3000 on theBenchmark for (3000ds/141695Mi)
% 0.19/1.14 % (2567682)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=1058224683:i=141193_3000 on theBenchmark for (3000ds/141193Mi)
% 0.19/1.14 % (2567687)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1954677069:s2a=on:i=139:gtg=position_3000 on theBenchmark for (3000ds/139Mi)
% 0.19/1.14 % (2567688)dis-21_1_sil=8000:lcm=predicate:random_seed=1688909743: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)
% 0.19/1.14 % (2567687)Also succeeded, but the first one will report.
% 0.19/1.14 % (2567688)Also succeeded, but the first one will report.
% 0.19/1.14 % (2567686)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=436862248:i=119:av=off:ss=axioms_3000 on theBenchmark for (3000ds/119Mi)
% 0.19/1.14 % (2567686)Also succeeded, but the first one will report.
% 0.19/1.14 % (2567685)Refutation found. Thanks to Tanya!
% 0.19/1.14 % SZS status Theorem for theBenchmark
% 0.19/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.14 % (2567685)------------------------------
% 0.19/1.14 % (2567685)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.14 % (2567685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.14 % (2567685)CaDiCaL version: 2.1.3
% 0.19/1.14 % (2567685)Termination reason: Refutation
% 0.19/1.14 % (2567685)Time elapsed: 0.001 s
% 0.19/1.14 % (2567685)Peak memory usage: 89 MB
% 0.19/1.14 % (2567685)------------------------------
% 0.19/1.14 % (2567685)------------------------------
% 0.19/1.14 % (2567668)Success in time 0.25 s
% 0.19/1.14 % Vampire exiting
%------------------------------------------------------------------------------