%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HEN002-4 : 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 10:19:03 AM UTC 2026
% Result : Unsatisfiable 2.33s 0.92s
% Output : Refutation 2.33s
% 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 : 3 ( 3 usr; 2 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(f5,axiom,
! [X0] : less_equal(zero,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_is_smallest) ).
fof(f10,negated_conjecture,
divide(zero,a) != zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_zero_over_a_is_zero) ).
fof(f11,plain,
zero != divide(zero,a),
inference(reorient_equations,[],[f10]) ).
fof(f12,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f14,plain,
~ sQ0_eqProxy(zero,divide(zero,a)),
inference(equality_proxy_replacement,[],[f11,f12]) ).
fof(f17,plain,
! [X0,X1] :
( sQ0_eqProxy(divide(X0,X1),zero)
| ~ less_equal(X0,X1) ),
inference(equality_proxy_replacement,[],[f1,f12]) ).
fof(f19,plain,
! [X0,X1] :
( sQ0_eqProxy(X1,X0)
| ~ sQ0_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f12]) ).
fof(f20,plain,
~ sQ0_eqProxy(divide(zero,a),zero),
inference(resolution,[],[f19,f14]) ).
fof(f24,plain,
~ less_equal(zero,a),
inference(resolution,[],[f17,f20]) ).
fof(f25,plain,
$false,
inference(resolution,[],[f24,f5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : HEN002-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 27 10:49:04 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 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
% 2.33/0.92 % (2200965)Input is clausal, will run a generic CNF schedule.
% 2.33/0.92 % (2200976)dis-21_1_sil=8000:lcm=predicate:random_seed=3597654730:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.33/0.92 % (2200975)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3631260735:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.33/0.92 % (2200974)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1256440329:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.33/0.92 % (2200970)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=269074837:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.33/0.92 % (2200972)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2938994633:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.33/0.92 % (2200973)lrs+10_1_sil=8000:sp=occurrence:random_seed=1624078724:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.33/0.92 % (2200971)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1681548683:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.33/0.92 % (2200974)Also succeeded, but the first one will report.
% 2.33/0.92 % (2200976)First to succeed.
% 2.33/0.92 % (2200973)Also succeeded, but the first one will report.
% 2.33/0.92 % (2200975)Also succeeded, but the first one will report.
% 2.33/0.92 % (2200976)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2200965"
% 2.33/0.92 % (2200976)Refutation found. Thanks to Tanya!
% 2.33/0.92 % SZS status Unsatisfiable for theBenchmark
% 2.33/0.92 % SZS output start Proof for theBenchmark
% See solution above
% 2.33/0.92 % (2200976)------------------------------
% 2.33/0.92 % (2200976)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.33/0.92 % (2200976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.33/0.92 % (2200976)CaDiCaL version: 2.1.3
% 2.33/0.92 % (2200976)Termination reason: Refutation
% 2.33/0.92 % (2200976)Time elapsed: 0.001 s
% 2.33/0.92 % (2200976)Peak memory usage: 88 MB
% 2.33/0.92 % (2200976)------------------------------
% 2.33/0.92 % (2200976)------------------------------
% 2.33/0.92 % (2200965)Success in time 0.299 s
% 2.33/0.92 % Vampire exiting
%------------------------------------------------------------------------------