%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN731+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 : n017.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 02:01:22 PM UTC 2026
% Result : Theorem 3.49s 1.23s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 8 ( 3 unt; 0 def)
% Number of atoms : 13 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 5 ~; 0 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 23 ( 15 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [X0] :
( ! [X1] :
? [X2] : p(X0,X1,X2)
=> ? [X3] : p(X3,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x2150) ).
fof(f2,negated_conjecture,
~ ? [X0] :
( ! [X1] :
? [X2] : p(X0,X1,X2)
=> ? [X3] : p(X3,X3,X0) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
! [X0] :
( ! [X3] : ~ p(X3,X3,X0)
& ! [X1] :
? [X2] : p(X0,X1,X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
! [X0] :
( ! [X1] : ~ p(X1,X1,X0)
& ! [X2] :
? [X3] : p(X0,X2,X3) ),
inference(rectify,[],[f3]) ).
fof(f5,plain,
! [X0] :
( ! [X1] : ~ p(X1,X1,X0)
& ! [X2] : p(X0,X2,sK0(X0,X2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X2))],[f4]) ).
fof(f6,plain,
! [X2,X0] : p(X0,X2,sK0(X0,X2)),
inference(cnf_transformation,[],[f5]) ).
fof(f7,plain,
! [X0,X1] : ~ p(X1,X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f8,plain,
$false,
inference(resolution,[],[f6,f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN731+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.25 % Computer : n017.cluster.edu
% 0.11/0.25 % Model : x86_64 x86_64
% 0.11/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.25 % Memory : 8046.5625MB
% 0.11/0.25 % OS : Linux 6.8.0-71-generic
% 0.11/0.26 % CPULimit : 300
% 0.11/0.26 % WCLimit : 300
% 0.11/0.26 % DateTime : Mon Sep 28 16:45:37 UTC 2026
% 0.11/0.26 % CPUTime :
% 0.11/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.29 Running first-order theorem proving
% 0.11/0.29 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
% 3.49/1.23 % (3702020)Detected formulas, will run a generic FOF schedule.
% 3.49/1.23 % (3702079)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=1386278536:i=141193_3000 on theBenchmark for (3000ds/141193Mi)
% 3.49/1.23 % (3702084)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=237334829:i=109:sd=1:ins=1:gsp=on:ss=axioms_3000 on theBenchmark for (3000ds/109Mi)
% 3.49/1.23 % (3702088)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1421540343:s2a=on:i=139:gtg=position_3000 on theBenchmark for (3000ds/139Mi)
% 3.49/1.23 % (3702086)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=327595247:i=119:av=off:ss=axioms_3000 on theBenchmark for (3000ds/119Mi)
% 3.49/1.23 % (3702089)dis-21_1_sil=8000:lcm=predicate:random_seed=819086723: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)
% 3.49/1.23 % (3702082)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=2739453660:i=141695:sd=1:nm=32:gsp=on:ss=included_3000 on theBenchmark for (3000ds/141695Mi)
% 3.49/1.23 % (3702081)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=1432719676:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/134677Mi)
% 3.49/1.23 % (3702084)Also succeeded, but the first one will report.
% 3.49/1.23 % (3702089)Also succeeded, but the first one will report.
% 3.49/1.23 % (3702088)Also succeeded, but the first one will report.
% 3.49/1.23 % (3702086)First to succeed.
% 3.49/1.23 % (3702086)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3702020"
% 3.49/1.23 % (3702086)Refutation found. Thanks to Tanya!
% 3.49/1.23 % SZS status Theorem for theBenchmark
% 3.49/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 3.49/1.23 % (3702086)------------------------------
% 3.49/1.23 % (3702086)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.23 % (3702086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.23 % (3702086)CaDiCaL version: 2.1.3
% 3.49/1.23 % (3702086)Termination reason: Refutation
% 3.49/1.23 % (3702086)Time elapsed: 0.001 s
% 3.49/1.23 % (3702086)Peak memory usage: 88 MB
% 3.49/1.23 % (3702086)------------------------------
% 3.49/1.23 % (3702086)------------------------------
% 3.49/1.23 % (3702020)Success in time 0.398 s
% 3.49/1.23 % Vampire exiting
%------------------------------------------------------------------------------