%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN408+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 : 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 01:50:32 PM UTC 2026
% Result : Theorem 5.61s 1.85s
% Output : Refutation 5.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 9 ( 3 unt; 0 def)
% Number of atoms : 17 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 0 |; 3 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 12 ( 7 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ~ ? [X0] : f(X0)
=> ! [X1] :
( f(X1)
=> g(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kalish244) ).
fof(f2,negated_conjecture,
~ ( ~ ? [X0] : f(X0)
=> ! [X1] :
( f(X1)
=> g(X1) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ~ ? [X0] : f(X0)
=> ! [X1] : ~ f(X1) ),
inference(pure_predicate_removal,[],[f2]) ).
fof(f4,plain,
( ? [X1] : f(X1)
& ! [X0] : ~ f(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
( ? [X0] : f(X0)
& ! [X1] : ~ f(X1) ),
inference(rectify,[],[f4]) ).
fof(f6,plain,
( f(sK0)
& ! [X1] : ~ f(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f5]) ).
fof(f7,plain,
! [X1] : ~ f(X1),
inference(cnf_transformation,[],[f6]) ).
fof(f8,plain,
f(sK0),
inference(cnf_transformation,[],[f6]) ).
fof(f9,plain,
$false,
inference(forward_subsumption_resolution,[],[f8,f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYN408+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.27 % Computer : n018.cluster.edu
% 0.10/0.27 % Model : x86_64 x86_64
% 0.10/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.27 % Memory : 8046.5625MB
% 0.10/0.27 % OS : Linux 6.8.0-71-generic
% 0.10/0.27 % CPULimit : 300
% 0.10/0.27 % WCLimit : 300
% 0.10/0.27 % DateTime : Mon Sep 28 15:56:40 UTC 2026
% 0.10/0.27 % CPUTime :
% 0.26/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.32 Running first-order theorem proving
% 0.26/0.32 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
% 5.61/1.85 % (3504662)Detected formulas, will run a generic FOF schedule.
% 5.61/1.85 % (3504671)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=1287546871:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.61/1.85 % (3504676)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3516946309:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.61/1.85 % (3504676)First to succeed.
% 5.61/1.85 % (3504676)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3504662"
% 5.61/1.85 % (3504673)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=1941291433:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.61/1.85 % (3504670)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=2898667483:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.61/1.85 % (3504675)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1850602015:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.61/1.85 % (3504674)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1490473184:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.61/1.85 % (3504675)Also succeeded, but the first one will report.
% 5.61/1.85 % (3504674)Also succeeded, but the first one will report.
% 5.61/1.85 % (3504677)dis-21_1_sil=8000:lcm=predicate:random_seed=3551214732: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)
% 5.61/1.85 % (3504677)Also succeeded, but the first one will report.
% 5.61/1.85 % (3504676)Refutation found. Thanks to Tanya!
% 5.61/1.85 % SZS status Theorem for theBenchmark
% 5.61/1.85 % SZS output start Proof for theBenchmark
% See solution above
% 5.61/1.85 % (3504676)------------------------------
% 5.61/1.85 % (3504676)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.61/1.85 % (3504676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.61/1.85 % (3504676)CaDiCaL version: 2.1.3
% 5.61/1.85 % (3504676)Termination reason: Refutation
% 5.61/1.85 % (3504676)Time elapsed: 0.001 s
% 5.61/1.85 % (3504676)Peak memory usage: 88 MB
% 5.61/1.85 % (3504676)------------------------------
% 5.61/1.85 % (3504676)------------------------------
% 5.61/1.85 % (3504662)Success in time 0.67 s
% 5.61/1.85 % Vampire exiting
%------------------------------------------------------------------------------