%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN721+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 02:01:20 PM UTC 2026
% Result : Theorem 2.71s 1.15s
% Output : Refutation 2.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 6 unt; 2 def)
% Number of atoms : 71 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 75 ( 30 ~; 22 |; 15 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 43 ( 0 sgn 39 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( r(a,b)
& ! [X0] :
( ? [X1] : r(X0,X1)
=> q(X0,X0) )
& ! [X2,X3] :
( q(X2,X3)
=> ! [X4] : r(X4,X3) ) )
=> ? [X5] :
( r(b,X5)
& q(X5,a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lx1) ).
fof(f2,negated_conjecture,
~ ( ( r(a,b)
& ! [X0] :
( ? [X1] : r(X0,X1)
=> q(X0,X0) )
& ! [X2,X3] :
( q(X2,X3)
=> ! [X4] : r(X4,X3) ) )
=> ? [X5] :
( r(b,X5)
& q(X5,a) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ! [X5] :
( ~ r(b,X5)
| ~ q(X5,a) )
& r(a,b)
& ! [X0] :
( q(X0,X0)
| ! [X1] : ~ r(X0,X1) )
& ! [X2,X3] :
( ! [X4] : r(X4,X3)
| ~ q(X2,X3) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
( ! [X5] :
( ~ r(b,X5)
| ~ q(X5,a) )
& r(a,b)
& ! [X0] :
( q(X0,X0)
| ! [X1] : ~ r(X0,X1) )
& ! [X2,X3] :
( ! [X4] : r(X4,X3)
| ~ q(X2,X3) ) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
( ! [X0] :
( ~ r(b,X0)
| ~ q(X0,a) )
& r(a,b)
& ! [X1] :
( q(X1,X1)
| ! [X2] : ~ r(X1,X2) )
& ! [X3,X4] :
( ! [X5] : r(X5,X4)
| ~ q(X3,X4) ) ),
inference(rectify,[],[f4]) ).
fof(f6,plain,
! [X3,X4,X5] :
( ~ q(X3,X4)
| r(X5,X4) ),
inference(cnf_transformation,[],[f5]) ).
fof(f7,plain,
! [X2,X1] :
( q(X1,X1)
| ~ r(X1,X2) ),
inference(cnf_transformation,[],[f5]) ).
fof(f8,plain,
r(a,b),
inference(cnf_transformation,[],[f5]) ).
fof(f9,plain,
! [X0] :
( ~ q(X0,a)
| ~ r(b,X0) ),
inference(cnf_transformation,[],[f5]) ).
fof(f10,plain,
! [X2,X0,X1] :
( r(X2,X0)
| ~ r(X0,X1) ),
inference(resolution,[],[f7,f6]) ).
fof(f11,plain,
! [X0] :
( ~ r(b,a)
| ~ r(a,X0) ),
inference(resolution,[],[f9,f7]) ).
fof(f13,definition,
( spl0_1
<=> ! [X0] : ~ r(a,X0) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f14,plain,
( ! [X0] : ~ r(a,X0)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f13]) ).
fof(f16,definition,
( spl0_2
<=> r(b,a) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f17,plain,
( ~ r(b,a)
| spl0_2 ),
inference(avatar_component_clause,[],[f16]) ).
fof(f18,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f11,f16,f13]) ).
fof(f19,plain,
( ! [X0] : ~ r(a,X0)
| spl0_2 ),
inference(resolution,[],[f10,f17]) ).
fof(f20,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f19,f16,f13]) ).
fof(f21,plain,
( $false
| ~ spl0_1 ),
inference(resolution,[],[f14,f8]) ).
fof(f23,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f21]) ).
cnf(s1,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f18]) ).
cnf(s2,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f20]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f23]) ).
cnf(s4,plain,
spl0_2,
inference(rat,[],[s2,s3]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4,s3]) ).
fof(f24,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN721+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n018.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 16:51:10 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 2.71/1.15 % (3536456)Detected formulas, will run a generic FOF schedule.
% 2.71/1.15 % (3536467)dis-21_1_sil=8000:lcm=predicate:random_seed=631275270: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)
% 2.71/1.15 % (3536467)First to succeed.
% 2.71/1.15 % (3536467)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3536456"
% 2.71/1.15 % (3536462)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=2434037292:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.71/1.15 % (3536461)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=1095337671:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.71/1.15 % (3536463)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=867752240:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.71/1.15 % (3536464)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=58796221:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.71/1.15 % (3536464)Also succeeded, but the first one will report.
% 2.71/1.15 % (3536465)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1656831196:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.71/1.15 % (3536466)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2850327885:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.71/1.15 % (3536465)Also succeeded, but the first one will report.
% 2.71/1.15 % (3536466)Also succeeded, but the first one will report.
% 2.71/1.15 % (3536467)Refutation found. Thanks to Tanya!
% 2.71/1.15 % SZS status Theorem for theBenchmark
% 2.71/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 2.71/1.15 % (3536467)------------------------------
% 2.71/1.15 % (3536467)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.15 % (3536467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.15 % (3536467)CaDiCaL version: 2.1.3
% 2.71/1.15 % (3536467)Termination reason: Refutation
% 2.71/1.15 % (3536467)Time elapsed: 0.001 s
% 2.71/1.15 % (3536467)Peak memory usage: 89 MB
% 2.71/1.15 % (3536467)Instructions burned: 1 (million)
% 2.71/1.15 % (3536467)------------------------------
% 2.71/1.15 % (3536467)------------------------------
% 2.71/1.15 % (3536456)Success in time 0.288 s
% 2.71/1.15 % Vampire exiting
%------------------------------------------------------------------------------