%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HEN001-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 10:19:02 AM UTC 2026
% Result : Unsatisfiable 3.28s 1.35s
% Output : Refutation 3.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 7 unt; 1 def)
% Number of atoms : 15 ( 4 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 8 ~; 3 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 9 ( 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ less_equal(X0,X1)
| divide(X0,X1) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_less_equal1) ).
fof(f7,axiom,
! [X0] : less_equal(X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_is_largest) ).
fof(f8,negated_conjecture,
divide(a,identity) != zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_divide_id_is_zero) ).
fof(f9,plain,
zero != divide(a,identity),
inference(reorient_equations,[],[f8]) ).
fof(f10,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f11,plain,
~ sQ0_eqProxy(zero,divide(a,identity)),
inference(equality_proxy_replacement,[],[f9,f10]) ).
fof(f14,plain,
! [X0,X1] :
( sQ0_eqProxy(divide(X0,X1),zero)
| ~ less_equal(X0,X1) ),
inference(equality_proxy_replacement,[],[f1,f10]) ).
fof(f16,plain,
! [X0,X1] :
( sQ0_eqProxy(X1,X0)
| ~ sQ0_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f10]) ).
fof(f17,plain,
~ sQ0_eqProxy(divide(a,identity),zero),
inference(resolution,[],[f16,f11]) ).
fof(f20,plain,
~ less_equal(a,identity),
inference(resolution,[],[f14,f17]) ).
fof(f33,plain,
$false,
inference(resolution,[],[f20,f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : HEN001-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.33 % Computer : n012.cluster.edu
% 0.06/0.33 % Model : x86_64 x86_64
% 0.06/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.33 % Memory : 8046.5625MB
% 0.06/0.33 % OS : Linux 6.8.0-71-generic
% 0.06/0.33 % CPULimit : 300
% 0.06/0.33 % WCLimit : 300
% 0.06/0.33 % DateTime : Sun Sep 27 10:48:35 UTC 2026
% 0.06/0.34 % CPUTime :
% 0.06/0.34 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 Running first-order theorem proving
% 0.10/0.37 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
% 3.28/1.35 % (2199885)Input is clausal, will run a generic CNF schedule.
% 3.28/1.35 % (2199900)dis-21_1_sil=8000:lcm=predicate:random_seed=2394715089:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/117Mi)
% 3.28/1.35 % (2199897)lrs+10_1_sil=8000:sp=occurrence:random_seed=674054968:i=107:sd=3:ss=axioms:sgt=8_3000 on theBenchmark for (3000ds/107Mi)
% 3.28/1.35 % (2199899)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2681353717:s2a=on:i=180:gtg=position_3000 on theBenchmark for (3000ds/180Mi)
% 3.28/1.35 % (2199896)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3144921113:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_3000 on theBenchmark for (3000ds/137899Mi)
% 3.28/1.35 % (2199898)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=757456801:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_3000 on theBenchmark for (3000ds/114Mi)
% 3.28/1.35 % (2199894)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=709831550:i=140167_3000 on theBenchmark for (3000ds/140167Mi)
% 3.28/1.35 % (2199900)First to succeed.
% 3.28/1.35 % (2199895)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=295026880:i=132376:av=off_3000 on theBenchmark for (3000ds/132376Mi)
% 3.28/1.35 % (2199900)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2199885"
% 3.28/1.35 % (2199899)Also succeeded, but the first one will report.
% 3.28/1.35 % (2199897)Also succeeded, but the first one will report.
% 3.28/1.35 % (2199898)Also succeeded, but the first one will report.
% 3.28/1.35 % (2199900)Refutation found. Thanks to Tanya!
% 3.28/1.35 % SZS status Unsatisfiable for theBenchmark
% 3.28/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.28/1.35 % (2199900)------------------------------
% 3.28/1.35 % (2199900)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.28/1.35 % (2199900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.28/1.35 % (2199900)CaDiCaL version: 2.1.3
% 3.28/1.35 % (2199900)Termination reason: Refutation
% 3.28/1.35 % (2199900)Time elapsed: 0.001 s
% 3.28/1.35 % (2199900)Peak memory usage: 88 MB
% 3.28/1.35 % (2199900)------------------------------
% 3.28/1.35 % (2199900)------------------------------
% 3.28/1.35 % (2199885)Success in time 0.388 s
% 3.28/1.35 % Vampire exiting
%------------------------------------------------------------------------------