%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN919+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 2.63s 1.15s
% Output : Refutation 2.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 4 unt; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 71 ( 25 ~; 16 |; 18 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 54 ( 48 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ! [X0,X1] :
( r(X0,X1)
=> r(X1,X0) )
& ! [X0,X1,X2] :
( ( r(X0,X1)
& r(X1,X2) )
=> r(X0,X2) ) )
=> ! [X0,X1] :
( r(X0,X1)
=> r(X0,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f2,negated_conjecture,
~ ( ( ! [X0,X1] :
( r(X0,X1)
=> r(X1,X0) )
& ! [X0,X1,X2] :
( ( r(X0,X1)
& r(X1,X2) )
=> r(X0,X2) ) )
=> ! [X0,X1] :
( r(X0,X1)
=> r(X0,X0) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ( ! [X0,X1] :
( r(X0,X1)
=> r(X1,X0) )
& ! [X2,X3,X4] :
( ( r(X2,X3)
& r(X3,X4) )
=> r(X2,X4) ) )
=> ! [X5,X6] :
( r(X5,X6)
=> r(X5,X5) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ? [X5,X6] :
( ~ r(X5,X5)
& r(X5,X6) )
& ! [X0,X1] :
( r(X1,X0)
| ~ r(X0,X1) )
& ! [X2,X3,X4] :
( r(X2,X4)
| ~ r(X2,X3)
| ~ r(X3,X4) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
( ? [X5,X6] :
( ~ r(X5,X5)
& r(X5,X6) )
& ! [X0,X1] :
( r(X1,X0)
| ~ r(X0,X1) )
& ! [X2,X3,X4] :
( r(X2,X4)
| ~ r(X2,X3)
| ~ r(X3,X4) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
( ? [X0,X1] :
( ~ r(X0,X0)
& r(X0,X1) )
& ! [X2,X3] :
( r(X3,X2)
| ~ r(X2,X3) )
& ! [X4,X5,X6] :
( r(X4,X6)
| ~ r(X4,X5)
| ~ r(X5,X6) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
( ~ r(sK0,sK0)
& r(sK0,sK1)
& ! [X2,X3] :
( r(X3,X2)
| ~ r(X2,X3) )
& ! [X4,X5,X6] :
( r(X4,X6)
| ~ r(X4,X5)
| ~ r(X5,X6) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f6]) ).
fof(f8,plain,
! [X6,X4,X5] :
( r(X4,X6)
| ~ r(X4,X5)
| ~ r(X5,X6) ),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
! [X2,X3] :
( r(X3,X2)
| ~ r(X2,X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f10,plain,
r(sK0,sK1),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
~ r(sK0,sK0),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
! [X0] :
( ~ r(sK0,X0)
| ~ r(X0,sK0) ),
inference(resolution,[],[f8,f11]) ).
fof(f14,plain,
! [X0] : ~ r(sK0,X0),
inference(forward_subsumption_resolution,[],[f13,f9]) ).
fof(f15,plain,
$false,
inference(resolution,[],[f14,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN919+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n007.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 17:10:56 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 2.63/1.15 % (2566986)Detected formulas, will run a generic FOF schedule.
% 2.63/1.15 % (2566995)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=313369784:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.63/1.15 % (2566995)First to succeed.
% 2.63/1.15 % (2566995)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2566986"
% 2.63/1.15 % (2566991)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=2745593509:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.63/1.15 % (2566994)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4092102695:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.63/1.15 % (2566993)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=414026149:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.63/1.15 % (2566992)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=1265303549:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.63/1.15 % (2566994)Also succeeded, but the first one will report.
% 2.63/1.15 % (2566997)dis-21_1_sil=8000:lcm=predicate:random_seed=3789143873: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)
% 2.63/1.15 % (2566996)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=591519978:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.63/1.15 % (2566996)Also succeeded, but the first one will report.
% 2.63/1.15 % (2566997)Also succeeded, but the first one will report.
% 2.63/1.15 % (2566995)Refutation found. Thanks to Tanya!
% 2.63/1.15 % SZS status Theorem for theBenchmark
% 2.63/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 2.63/1.15 % (2566995)------------------------------
% 2.63/1.15 % (2566995)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.15 % (2566995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.15 % (2566995)CaDiCaL version: 2.1.3
% 2.63/1.15 % (2566995)Termination reason: Refutation
% 2.63/1.15 % (2566995)Time elapsed: 0.001 s
% 2.63/1.15 % (2566995)Peak memory usage: 88 MB
% 2.63/1.15 % (2566995)------------------------------
% 2.63/1.15 % (2566995)------------------------------
% 2.63/1.15 % (2566986)Success in time 0.278 s
% 2.63/1.15 % Vampire exiting
%------------------------------------------------------------------------------