%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN409+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 01:50:32 PM UTC 2026
% Result : Theorem 0.16s 1.13s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 3 unt; 0 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 47 ( 19 ~; 16 |; 9 &)
% ( 2 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 29 ( 23 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X0] : f(X0)
<=> ! [X1,X2] :
( f(X1)
& f(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kalish246) ).
fof(f2,negated_conjecture,
~ ( ! [X0] : f(X0)
<=> ! [X1,X2] :
( f(X1)
& f(X2) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ! [X0] : f(X0)
<~> ! [X1,X2] :
( f(X1)
& f(X2) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
( ( ? [X1,X2] :
( ~ f(X1)
| ~ f(X2) )
| ? [X0] : ~ f(X0) )
& ( ! [X1,X2] :
( f(X1)
& f(X2) )
| ! [X0] : f(X0) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f5,plain,
( ( ? [X0,X1] :
( ~ f(X0)
| ~ f(X1) )
| ? [X2] : ~ f(X2) )
& ( ! [X3,X4] :
( f(X3)
& f(X4) )
| ! [X5] : f(X5) ) ),
inference(rectify,[],[f4]) ).
fof(f6,plain,
( ( ~ f(sK0)
| ~ f(sK1)
| ~ f(sK2) )
& ( ! [X3,X4] :
( f(X3)
& f(X4) )
| ! [X5] : f(X5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f5]) ).
fof(f7,plain,
! [X4,X5] :
( f(X5)
| f(X4) ),
inference(cnf_transformation,[],[f6]) ).
fof(f9,plain,
( ~ f(sK2)
| ~ f(sK1)
| ~ f(sK0) ),
inference(cnf_transformation,[],[f6]) ).
fof(f10,plain,
! [X0] :
( ~ f(sK1)
| ~ f(sK0)
| f(X0) ),
inference(resolution,[],[f9,f7]) ).
fof(f11,plain,
! [X0] :
( ~ f(sK1)
| f(X0) ),
inference(forward_subsumption_resolution,[],[f10,f7]) ).
fof(f12,plain,
! [X0] : f(X0),
inference(forward_subsumption_resolution,[],[f11,f7]) ).
fof(f13,plain,
( ~ f(sK1)
| ~ f(sK0) ),
inference(resolution,[],[f12,f9]) ).
fof(f14,plain,
~ f(sK0),
inference(forward_subsumption_resolution,[],[f13,f12]) ).
fof(f15,plain,
$false,
inference(forward_subsumption_resolution,[],[f14,f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN409+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.16 % Computer : n016.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Mon Sep 28 15:59:33 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running first-order theorem proving
% 0.08/0.20 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
% 0.16/1.13 % (3731970)Detected formulas, will run a generic FOF schedule.
% 0.16/1.13 % (3731979)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3240384729:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.16/1.13 % (3731979)First to succeed.
% 0.16/1.13 % (3731979)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3731970"
% 0.16/1.13 % (3731976)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=793648733:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.16/1.13 % (3731975)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=119355574:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.16/1.13 % (3731977)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=4217149243:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.16/1.13 % (3731980)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3114063680:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.16/1.13 % (3731981)dis-21_1_sil=8000:lcm=predicate:random_seed=3265116621: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)
% 0.16/1.13 % (3731978)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2467847900:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.16/1.13 % (3731980)Also succeeded, but the first one will report.
% 0.16/1.13 % (3731981)Also succeeded, but the first one will report.
% 0.16/1.13 % (3731978)Also succeeded, but the first one will report.
% 0.16/1.13 % (3731979)Refutation found. Thanks to Tanya!
% 0.16/1.13 % SZS status Theorem for theBenchmark
% 0.16/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.13 % (3731979)------------------------------
% 0.16/1.13 % (3731979)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.13 % (3731979)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.13 % (3731979)CaDiCaL version: 2.1.3
% 0.16/1.13 % (3731979)Termination reason: Refutation
% 0.16/1.13 % (3731979)Time elapsed: 0.001 s
% 0.16/1.13 % (3731979)Peak memory usage: 88 MB
% 0.16/1.13 % (3731979)------------------------------
% 0.16/1.13 % (3731979)------------------------------
% 0.16/1.13 % (3731970)Success in time 0.29 s
% 0.16/1.13 % Vampire exiting
%------------------------------------------------------------------------------