%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV218+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 01:08:24 PM UTC 2026
% Result : Theorem 2.80s 1.19s
% Output : Refutation 2.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 12 unt; 2 def)
% Number of atoms : 381 ( 344 equ)
% Maximal formula atoms : 71 ( 15 avg)
% Number of connectives : 619 ( 262 ~; 98 |; 253 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 44 ( 10 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn 6 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f53,conjecture,
! [X0,X1] :
( ( leq(n0,X0)
& leq(n0,X1)
& leq(X0,n5)
& leq(X1,n5) )
=> ( ( ~ ( n0 = X0
& n5 = X1 )
& ~ ( n0 = X1
& n1 = X0 )
& ~ ( n0 = X1
& n2 = X0 )
& ~ ( n0 = X1
& n3 = X0 )
& ~ ( n0 = X1
& n4 = X0 )
& ~ ( n0 = X1
& n5 = X0 )
& ~ ( n1 = X0
& n1 = X1 )
& ~ ( n1 = X0
& n2 = X1 )
& ~ ( n1 = X0
& n3 = X1 )
& ~ ( n1 = X0
& n4 = X1 )
& ~ ( n1 = X0
& n5 = X1 )
& ~ ( n1 = X1
& n2 = X0 )
& ~ ( n1 = X1
& n3 = X0 )
& ~ ( n1 = X1
& n4 = X0 )
& ~ ( n1 = X1
& n5 = X0 )
& ~ ( n2 = X0
& n2 = X1 )
& ~ ( n2 = X0
& n3 = X1 )
& ~ ( n2 = X0
& n4 = X1 )
& ~ ( n2 = X0
& n5 = X1 )
& ~ ( n2 = X1
& n3 = X0 )
& ~ ( n2 = X1
& n4 = X0 )
& ~ ( n2 = X1
& n5 = X0 )
& ~ ( n3 = X0
& n3 = X1 )
& ~ ( n3 = X0
& n4 = X1 )
& ~ ( n3 = X0
& n5 = X1 )
& ~ ( n3 = X1
& n4 = X0 )
& ~ ( n3 = X1
& n5 = X0 )
& ~ ( n4 = X0
& n4 = X1 )
& ~ ( n4 = X0
& n5 = X1 )
& ~ ( n4 = X1
& n5 = X0 )
& ~ ( n5 = X0
& n5 = X1 )
& n0 = X0
& n4 = X1
& n5 = X0
& n5 = X1 )
=> n0 = times(divide(n1,n400),a_select2(sigma,n5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_symm_0281) ).
fof(f54,negated_conjecture,
~ ! [X0,X1] :
( ( leq(n0,X0)
& leq(n0,X1)
& leq(X0,n5)
& leq(X1,n5) )
=> ( ( ~ ( n0 = X0
& n5 = X1 )
& ~ ( n0 = X1
& n1 = X0 )
& ~ ( n0 = X1
& n2 = X0 )
& ~ ( n0 = X1
& n3 = X0 )
& ~ ( n0 = X1
& n4 = X0 )
& ~ ( n0 = X1
& n5 = X0 )
& ~ ( n1 = X0
& n1 = X1 )
& ~ ( n1 = X0
& n2 = X1 )
& ~ ( n1 = X0
& n3 = X1 )
& ~ ( n1 = X0
& n4 = X1 )
& ~ ( n1 = X0
& n5 = X1 )
& ~ ( n1 = X1
& n2 = X0 )
& ~ ( n1 = X1
& n3 = X0 )
& ~ ( n1 = X1
& n4 = X0 )
& ~ ( n1 = X1
& n5 = X0 )
& ~ ( n2 = X0
& n2 = X1 )
& ~ ( n2 = X0
& n3 = X1 )
& ~ ( n2 = X0
& n4 = X1 )
& ~ ( n2 = X0
& n5 = X1 )
& ~ ( n2 = X1
& n3 = X0 )
& ~ ( n2 = X1
& n4 = X0 )
& ~ ( n2 = X1
& n5 = X0 )
& ~ ( n3 = X0
& n3 = X1 )
& ~ ( n3 = X0
& n4 = X1 )
& ~ ( n3 = X0
& n5 = X1 )
& ~ ( n3 = X1
& n4 = X0 )
& ~ ( n3 = X1
& n5 = X0 )
& ~ ( n4 = X0
& n4 = X1 )
& ~ ( n4 = X0
& n5 = X1 )
& ~ ( n4 = X1
& n5 = X0 )
& ~ ( n5 = X0
& n5 = X1 )
& n0 = X0
& n4 = X1
& n5 = X0
& n5 = X1 )
=> n0 = times(divide(n1,n400),a_select2(sigma,n5)) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f98,plain,
? [X0,X1] :
( n0 != times(divide(n1,n400),a_select2(sigma,n5))
& ( n0 != X0
| n5 != X1 )
& ( n0 != X1
| n1 != X0 )
& ( n0 != X1
| n2 != X0 )
& ( n0 != X1
| n3 != X0 )
& ( n0 != X1
| n4 != X0 )
& ( n0 != X1
| n5 != X0 )
& ( n1 != X0
| n1 != X1 )
& ( n1 != X0
| n2 != X1 )
& ( n1 != X0
| n3 != X1 )
& ( n1 != X0
| n4 != X1 )
& ( n1 != X0
| n5 != X1 )
& ( n1 != X1
| n2 != X0 )
& ( n1 != X1
| n3 != X0 )
& ( n1 != X1
| n4 != X0 )
& ( n1 != X1
| n5 != X0 )
& ( n2 != X0
| n2 != X1 )
& ( n2 != X0
| n3 != X1 )
& ( n2 != X0
| n4 != X1 )
& ( n2 != X0
| n5 != X1 )
& ( n2 != X1
| n3 != X0 )
& ( n2 != X1
| n4 != X0 )
& ( n2 != X1
| n5 != X0 )
& ( n3 != X0
| n3 != X1 )
& ( n3 != X0
| n4 != X1 )
& ( n3 != X0
| n5 != X1 )
& ( n3 != X1
| n4 != X0 )
& ( n3 != X1
| n5 != X0 )
& ( n4 != X0
| n4 != X1 )
& ( n4 != X0
| n5 != X1 )
& ( n4 != X1
| n5 != X0 )
& ( n5 != X0
| n5 != X1 )
& n0 = X0
& n4 = X1
& n5 = X0
& n5 = X1
& leq(n0,X0)
& leq(n0,X1)
& leq(X0,n5)
& leq(X1,n5) ),
inference(ennf_transformation,[],[f54]) ).
fof(f99,plain,
? [X0,X1] :
( n0 != times(divide(n1,n400),a_select2(sigma,n5))
& ( n0 != X0
| n5 != X1 )
& ( n0 != X1
| n1 != X0 )
& ( n0 != X1
| n2 != X0 )
& ( n0 != X1
| n3 != X0 )
& ( n0 != X1
| n4 != X0 )
& ( n0 != X1
| n5 != X0 )
& ( n1 != X0
| n1 != X1 )
& ( n1 != X0
| n2 != X1 )
& ( n1 != X0
| n3 != X1 )
& ( n1 != X0
| n4 != X1 )
& ( n1 != X0
| n5 != X1 )
& ( n1 != X1
| n2 != X0 )
& ( n1 != X1
| n3 != X0 )
& ( n1 != X1
| n4 != X0 )
& ( n1 != X1
| n5 != X0 )
& ( n2 != X0
| n2 != X1 )
& ( n2 != X0
| n3 != X1 )
& ( n2 != X0
| n4 != X1 )
& ( n2 != X0
| n5 != X1 )
& ( n2 != X1
| n3 != X0 )
& ( n2 != X1
| n4 != X0 )
& ( n2 != X1
| n5 != X0 )
& ( n3 != X0
| n3 != X1 )
& ( n3 != X0
| n4 != X1 )
& ( n3 != X0
| n5 != X1 )
& ( n3 != X1
| n4 != X0 )
& ( n3 != X1
| n5 != X0 )
& ( n4 != X0
| n4 != X1 )
& ( n4 != X0
| n5 != X1 )
& ( n4 != X1
| n5 != X0 )
& ( n5 != X0
| n5 != X1 )
& n0 = X0
& n4 = X1
& n5 = X0
& n5 = X1
& leq(n0,X0)
& leq(n0,X1)
& leq(X0,n5)
& leq(X1,n5) ),
inference(flattening,[],[f98]) ).
fof(f141,plain,
( n0 != times(divide(n1,n400),a_select2(sigma,n5))
& ( n0 != sK0
| n5 != sK1 )
& ( n0 != sK1
| n1 != sK0 )
& ( n0 != sK1
| n2 != sK0 )
& ( n0 != sK1
| n3 != sK0 )
& ( n0 != sK1
| n4 != sK0 )
& ( n0 != sK1
| n5 != sK0 )
& ( n1 != sK0
| n1 != sK1 )
& ( n1 != sK0
| n2 != sK1 )
& ( n1 != sK0
| n3 != sK1 )
& ( n1 != sK0
| n4 != sK1 )
& ( n1 != sK0
| n5 != sK1 )
& ( n1 != sK1
| n2 != sK0 )
& ( n1 != sK1
| n3 != sK0 )
& ( n1 != sK1
| n4 != sK0 )
& ( n1 != sK1
| n5 != sK0 )
& ( n2 != sK0
| n2 != sK1 )
& ( n2 != sK0
| n3 != sK1 )
& ( n2 != sK0
| n4 != sK1 )
& ( n2 != sK0
| n5 != sK1 )
& ( n2 != sK1
| n3 != sK0 )
& ( n2 != sK1
| n4 != sK0 )
& ( n2 != sK1
| n5 != sK0 )
& ( n3 != sK0
| n3 != sK1 )
& ( n3 != sK0
| n4 != sK1 )
& ( n3 != sK0
| n5 != sK1 )
& ( n3 != sK1
| n4 != sK0 )
& ( n3 != sK1
| n5 != sK0 )
& ( n4 != sK0
| n4 != sK1 )
& ( n4 != sK0
| n5 != sK1 )
& ( n4 != sK1
| n5 != sK0 )
& ( n5 != sK0
| n5 != sK1 )
& n0 = sK0
& n4 = sK1
& n5 = sK0
& n5 = sK1
& leq(n0,sK0)
& leq(n0,sK1)
& leq(sK0,n5)
& leq(sK1,n5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f99]) ).
fof(f158,plain,
n5 = sK1,
inference(cnf_transformation,[],[f141]) ).
fof(f159,plain,
n5 = sK0,
inference(cnf_transformation,[],[f141]) ).
fof(f160,plain,
n4 = sK1,
inference(cnf_transformation,[],[f141]) ).
fof(f164,plain,
( n4 != sK0
| n5 != sK1 ),
inference(cnf_transformation,[],[f141]) ).
fof(f314,plain,
( sK0 != sK1
| sK0 != sK1 ),
inference(definition_unfolding,[],[f164,f160,f159]) ).
fof(f317,plain,
sK0 = sK1,
inference(definition_unfolding,[],[f158,f159]) ).
fof(f401,definition,
! [X0,X1] :
( sQ13_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ13_eqProxy])],[equality_proxy_definition]) ).
fof(f431,plain,
( ~ sQ13_eqProxy(sK0,sK1)
| ~ sQ13_eqProxy(sK0,sK1) ),
inference(equality_proxy_replacement,[],[f314,f401,f401]) ).
fof(f434,plain,
sQ13_eqProxy(sK0,sK1),
inference(equality_proxy_replacement,[],[f317,f401]) ).
fof(f497,plain,
~ sQ13_eqProxy(sK0,sK1),
inference(duplicate_literal_removal,[],[f431]) ).
fof(f500,definition,
( spl14_1
<=> sQ13_eqProxy(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
fof(f501,plain,
( ~ sQ13_eqProxy(sK0,sK1)
| spl14_1 ),
inference(avatar_component_clause,[],[f500]) ).
fof(f510,plain,
~ spl14_1,
inference(avatar_split_clause,[],[f497,f500]) ).
fof(f556,plain,
( $false
| spl14_1 ),
inference(resolution,[],[f434,f501]) ).
fof(f557,plain,
spl14_1,
inference(avatar_contradiction_clause,[],[f556]) ).
cnf(s3,plain,
~ spl14_1,
inference(sat_conversion,[],[f510]) ).
cnf(s32,plain,
spl14_1,
inference(sat_conversion,[],[f557]) ).
cnf(s41,plain,
$false,
inference(rat,[],[s3,s32]) ).
fof(f558,plain,
$false,
inference(avatar_sat_refutation,[],[s41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV218+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n017.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 10:08:51 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 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
% 2.80/1.19 % (3448713)Detected formulas, will run a generic FOF schedule.
% 2.80/1.19 % (3448724)dis-21_1_sil=8000:lcm=predicate:random_seed=4020596959: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)
% 2.80/1.19 % (3448724)First to succeed.
% 2.80/1.19 % (3448724)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3448713"
% 2.80/1.19 % (3448723)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4088794431:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.80/1.19 % (3448718)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=3821625053:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.80/1.19 % (3448720)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=3622107535:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.80/1.19 % (3448722)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1809049802:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.80/1.19 % (3448719)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=1528231330:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.80/1.19 % (3448721)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1907936990:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.80/1.19 % (3448722)Also succeeded, but the first one will report.
% 2.80/1.19 % (3448721)Also succeeded, but the first one will report.
% 2.80/1.19 % (3448723)Also succeeded, but the first one will report.
% 2.80/1.19 % (3448724)Refutation found. Thanks to Tanya!
% 2.80/1.19 % SZS status Theorem for theBenchmark
% 2.80/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 2.80/1.19 % (3448724)------------------------------
% 2.80/1.19 % (3448724)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.19 % (3448724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.19 % (3448724)CaDiCaL version: 2.1.3
% 2.80/1.19 % (3448724)Termination reason: Refutation
% 2.80/1.19 % (3448724)Time elapsed: 0.004 s
% 2.80/1.19 % (3448724)Peak memory usage: 89 MB
% 2.80/1.19 % (3448724)Instructions burned: 10 (million)
% 2.80/1.19 % (3448724)------------------------------
% 2.80/1.19 % (3448724)------------------------------
% 2.80/1.19 % (3448713)Success in time 0.312 s
% 2.80/1.19 % Vampire exiting
%------------------------------------------------------------------------------