%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN406+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 01:50:31 PM UTC 2026
% Result : Theorem 2.74s 0.94s
% Output : Refutation 2.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 5 unt; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 50 ( 18 ~; 10 |; 18 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-1 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 19 ( 12 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ! [X0] :
( f(X0)
=> g(X0) )
& ? [X1] :
( f(X1)
& h(X1) ) )
=> ? [X2] :
( g(X2)
& h(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kalish240) ).
fof(f2,negated_conjecture,
~ ( ( ! [X0] :
( f(X0)
=> g(X0) )
& ? [X1] :
( f(X1)
& h(X1) ) )
=> ? [X2] :
( g(X2)
& h(X2) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ! [X2] :
( ~ g(X2)
| ~ h(X2) )
& ! [X0] :
( g(X0)
| ~ f(X0) )
& ? [X1] :
( f(X1)
& h(X1) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
( ! [X2] :
( ~ g(X2)
| ~ h(X2) )
& ! [X0] :
( g(X0)
| ~ f(X0) )
& ? [X1] :
( f(X1)
& h(X1) ) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
( ! [X0] :
( ~ g(X0)
| ~ h(X0) )
& ! [X1] :
( g(X1)
| ~ f(X1) )
& ? [X2] :
( f(X2)
& h(X2) ) ),
inference(rectify,[],[f4]) ).
fof(f6,plain,
( ! [X0] :
( ~ g(X0)
| ~ h(X0) )
& ! [X1] :
( g(X1)
| ~ f(X1) )
& f(sK0)
& h(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0)],[f5]) ).
fof(f7,plain,
h(sK0),
inference(cnf_transformation,[],[f6]) ).
fof(f8,plain,
f(sK0),
inference(cnf_transformation,[],[f6]) ).
fof(f9,plain,
! [X1] :
( g(X1)
| ~ f(X1) ),
inference(cnf_transformation,[],[f6]) ).
fof(f10,plain,
! [X0] :
( ~ h(X0)
| ~ g(X0) ),
inference(cnf_transformation,[],[f6]) ).
fof(f11,plain,
~ g(sK0),
inference(resolution,[],[f10,f7]) ).
fof(f12,plain,
~ f(sK0),
inference(resolution,[],[f11,f9]) ).
fof(f13,plain,
$false,
inference(forward_subsumption_resolution,[],[f12,f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN406+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n001.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 16:00:33 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running first-order theorem proving
% 0.09/0.20 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.74/0.94 % (456385)Detected formulas, will run a generic FOF schedule.
% 2.74/0.94 % (456395)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1363121621:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.74/0.94 % (456395)First to succeed.
% 2.74/0.94 % (456395)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-456385"
% 2.74/0.94 % (456394)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3458019350:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.74/0.94 % (456390)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=4170191165:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.74/0.94 % (456393)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2964930580:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.74/0.94 % (456396)dis-21_1_sil=8000:lcm=predicate:random_seed=2932212200: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)
% 2.74/0.94 % (456391)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=3293162375:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.74/0.94 % (456392)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=3781839488:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.74/0.94 % (456394)Also succeeded, but the first one will report.
% 2.74/0.94 % (456393)Also succeeded, but the first one will report.
% 2.74/0.94 % (456396)Also succeeded, but the first one will report.
% 2.74/0.94 % (456395)Refutation found. Thanks to Tanya!
% 2.74/0.94 % SZS status Theorem for theBenchmark
% 2.74/0.94 % SZS output start Proof for theBenchmark
% See solution above
% 2.74/0.94 % (456395)------------------------------
% 2.74/0.94 % (456395)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/0.94 % (456395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/0.94 % (456395)CaDiCaL version: 2.1.3
% 2.74/0.94 % (456395)Termination reason: Refutation
% 2.74/0.94 % (456395)Time elapsed: 0.001 s
% 2.74/0.94 % (456395)Peak memory usage: 88 MB
% 2.74/0.94 % (456395)------------------------------
% 2.74/0.94 % (456395)------------------------------
% 2.74/0.94 % (456385)Success in time 0.335 s
% 2.74/0.94 % Vampire exiting
%------------------------------------------------------------------------------