%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV226+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 : 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 01:08:25 PM UTC 2026
% Result : Theorem 3.67s 1.22s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 5 unt; 0 def)
% Number of atoms : 491 ( 418 equ)
% Maximal formula atoms : 81 ( 44 avg)
% Number of connectives : 829 ( 349 ~; 156 |; 314 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 46 ( 25 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-3 aty)
% Number of variables : 34 ( 28 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f53,conjecture,
( ( ! [X0,X1] :
( ( leq(n0,X0)
& leq(n0,X1)
& leq(X0,n5)
& leq(X1,n5) )
=> a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0) )
& ! [X2,X3] :
( ( leq(n0,X2)
& leq(n0,X3)
& leq(X2,n2)
& leq(X3,n2) )
=> a_select3(r_ds1_filter,X2,X3) = a_select3(r_ds1_filter,X3,X2) ) )
=> ! [X4,X5] :
( ( leq(n0,X4)
& leq(n0,X5)
& leq(X4,n5)
& leq(X5,n5) )
=> ( ( ~ ( n0 = X4
& n3 = X5 )
& ~ ( n0 = X4
& n4 = X5 )
& ~ ( n0 = X4
& n5 = X5 )
& ~ ( n0 = X5
& n2 = X4 )
& ~ ( n0 = X5
& n3 = X4 )
& ~ ( n0 = X5
& n4 = X4 )
& ~ ( n0 = X5
& n5 = X4 )
& ~ ( n1 = X4
& n2 = X5 )
& ~ ( n1 = X4
& n3 = X5 )
& ~ ( n1 = X4
& n4 = X5 )
& ~ ( n1 = X4
& n5 = X5 )
& ~ ( n1 = X5
& n2 = X4 )
& ~ ( n1 = X5
& n3 = X4 )
& ~ ( n1 = X5
& n4 = X4 )
& ~ ( n1 = X5
& n5 = X4 )
& ~ ( n2 = X4
& n2 = X5 )
& ~ ( n2 = X4
& n3 = X5 )
& ~ ( n2 = X4
& n4 = X5 )
& ~ ( n2 = X4
& n5 = X5 )
& ~ ( n2 = X5
& n3 = X4 )
& ~ ( n2 = X5
& n4 = X4 )
& ~ ( n2 = X5
& n5 = X4 )
& ~ ( n3 = X4
& n3 = X5 )
& ~ ( n3 = X4
& n4 = X5 )
& ~ ( n3 = X4
& n5 = X5 )
& ~ ( n3 = X5
& n4 = X4 )
& ~ ( n3 = X5
& n5 = X4 )
& ~ ( n4 = X4
& n4 = X5 )
& ~ ( n4 = X4
& n5 = X5 )
& ~ ( n4 = X5
& n5 = X4 )
& ~ ( n5 = X4
& n5 = X5 )
& n1 = X4
& n1 = X5
& n2 = X4
& n2 = X5 )
=> a_select2(xinit_noise,n1) = a_select2(xinit_noise,n2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_symm_0601) ).
fof(f54,negated_conjecture,
~ ( ( ! [X0,X1] :
( ( leq(n0,X0)
& leq(n0,X1)
& leq(X0,n5)
& leq(X1,n5) )
=> a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0) )
& ! [X2,X3] :
( ( leq(n0,X2)
& leq(n0,X3)
& leq(X2,n2)
& leq(X3,n2) )
=> a_select3(r_ds1_filter,X2,X3) = a_select3(r_ds1_filter,X3,X2) ) )
=> ! [X4,X5] :
( ( leq(n0,X4)
& leq(n0,X5)
& leq(X4,n5)
& leq(X5,n5) )
=> ( ( ~ ( n0 = X4
& n3 = X5 )
& ~ ( n0 = X4
& n4 = X5 )
& ~ ( n0 = X4
& n5 = X5 )
& ~ ( n0 = X5
& n2 = X4 )
& ~ ( n0 = X5
& n3 = X4 )
& ~ ( n0 = X5
& n4 = X4 )
& ~ ( n0 = X5
& n5 = X4 )
& ~ ( n1 = X4
& n2 = X5 )
& ~ ( n1 = X4
& n3 = X5 )
& ~ ( n1 = X4
& n4 = X5 )
& ~ ( n1 = X4
& n5 = X5 )
& ~ ( n1 = X5
& n2 = X4 )
& ~ ( n1 = X5
& n3 = X4 )
& ~ ( n1 = X5
& n4 = X4 )
& ~ ( n1 = X5
& n5 = X4 )
& ~ ( n2 = X4
& n2 = X5 )
& ~ ( n2 = X4
& n3 = X5 )
& ~ ( n2 = X4
& n4 = X5 )
& ~ ( n2 = X4
& n5 = X5 )
& ~ ( n2 = X5
& n3 = X4 )
& ~ ( n2 = X5
& n4 = X4 )
& ~ ( n2 = X5
& n5 = X4 )
& ~ ( n3 = X4
& n3 = X5 )
& ~ ( n3 = X4
& n4 = X5 )
& ~ ( n3 = X4
& n5 = X5 )
& ~ ( n3 = X5
& n4 = X4 )
& ~ ( n3 = X5
& n5 = X4 )
& ~ ( n4 = X4
& n4 = X5 )
& ~ ( n4 = X4
& n5 = X5 )
& ~ ( n4 = X5
& n5 = X4 )
& ~ ( n5 = X4
& n5 = X5 )
& n1 = X4
& n1 = X5
& n2 = X4
& n2 = X5 )
=> a_select2(xinit_noise,n1) = a_select2(xinit_noise,n2) ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f87,plain,
( ? [X4,X5] :
( a_select2(xinit_noise,n1) != a_select2(xinit_noise,n2)
& ( n0 != X4
| n3 != X5 )
& ( n0 != X4
| n4 != X5 )
& ( n0 != X4
| n5 != X5 )
& ( n0 != X5
| n2 != X4 )
& ( n0 != X5
| n3 != X4 )
& ( n0 != X5
| n4 != X4 )
& ( n0 != X5
| n5 != X4 )
& ( n1 != X4
| n2 != X5 )
& ( n1 != X4
| n3 != X5 )
& ( n1 != X4
| n4 != X5 )
& ( n1 != X4
| n5 != X5 )
& ( n1 != X5
| n2 != X4 )
& ( n1 != X5
| n3 != X4 )
& ( n1 != X5
| n4 != X4 )
& ( n1 != X5
| n5 != X4 )
& ( n2 != X4
| n2 != X5 )
& ( n2 != X4
| n3 != X5 )
& ( n2 != X4
| n4 != X5 )
& ( n2 != X4
| n5 != X5 )
& ( n2 != X5
| n3 != X4 )
& ( n2 != X5
| n4 != X4 )
& ( n2 != X5
| n5 != X4 )
& ( n3 != X4
| n3 != X5 )
& ( n3 != X4
| n4 != X5 )
& ( n3 != X4
| n5 != X5 )
& ( n3 != X5
| n4 != X4 )
& ( n3 != X5
| n5 != X4 )
& ( n4 != X4
| n4 != X5 )
& ( n4 != X4
| n5 != X5 )
& ( n4 != X5
| n5 != X4 )
& ( n5 != X4
| n5 != X5 )
& n1 = X4
& n1 = X5
& n2 = X4
& n2 = X5
& leq(n0,X4)
& leq(n0,X5)
& leq(X4,n5)
& leq(X5,n5) )
& ! [X0,X1] :
( a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0)
| ~ leq(n0,X0)
| ~ leq(n0,X1)
| ~ leq(X0,n5)
| ~ leq(X1,n5) )
& ! [X2,X3] :
( a_select3(r_ds1_filter,X2,X3) = a_select3(r_ds1_filter,X3,X2)
| ~ leq(n0,X2)
| ~ leq(n0,X3)
| ~ leq(X2,n2)
| ~ leq(X3,n2) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f88,plain,
( ? [X4,X5] :
( a_select2(xinit_noise,n1) != a_select2(xinit_noise,n2)
& ( n0 != X4
| n3 != X5 )
& ( n0 != X4
| n4 != X5 )
& ( n0 != X4
| n5 != X5 )
& ( n0 != X5
| n2 != X4 )
& ( n0 != X5
| n3 != X4 )
& ( n0 != X5
| n4 != X4 )
& ( n0 != X5
| n5 != X4 )
& ( n1 != X4
| n2 != X5 )
& ( n1 != X4
| n3 != X5 )
& ( n1 != X4
| n4 != X5 )
& ( n1 != X4
| n5 != X5 )
& ( n1 != X5
| n2 != X4 )
& ( n1 != X5
| n3 != X4 )
& ( n1 != X5
| n4 != X4 )
& ( n1 != X5
| n5 != X4 )
& ( n2 != X4
| n2 != X5 )
& ( n2 != X4
| n3 != X5 )
& ( n2 != X4
| n4 != X5 )
& ( n2 != X4
| n5 != X5 )
& ( n2 != X5
| n3 != X4 )
& ( n2 != X5
| n4 != X4 )
& ( n2 != X5
| n5 != X4 )
& ( n3 != X4
| n3 != X5 )
& ( n3 != X4
| n4 != X5 )
& ( n3 != X4
| n5 != X5 )
& ( n3 != X5
| n4 != X4 )
& ( n3 != X5
| n5 != X4 )
& ( n4 != X4
| n4 != X5 )
& ( n4 != X4
| n5 != X5 )
& ( n4 != X5
| n5 != X4 )
& ( n5 != X4
| n5 != X5 )
& n1 = X4
& n1 = X5
& n2 = X4
& n2 = X5
& leq(n0,X4)
& leq(n0,X5)
& leq(X4,n5)
& leq(X5,n5) )
& ! [X0,X1] :
( a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0)
| ~ leq(n0,X0)
| ~ leq(n0,X1)
| ~ leq(X0,n5)
| ~ leq(X1,n5) )
& ! [X2,X3] :
( a_select3(r_ds1_filter,X2,X3) = a_select3(r_ds1_filter,X3,X2)
| ~ leq(n0,X2)
| ~ leq(n0,X3)
| ~ leq(X2,n2)
| ~ leq(X3,n2) ) ),
inference(flattening,[],[f87]) ).
fof(f110,plain,
( ? [X0,X1] :
( a_select2(xinit_noise,n1) != a_select2(xinit_noise,n2)
& ( n0 != X0
| n3 != X1 )
& ( n0 != X0
| n4 != X1 )
& ( n0 != X0
| n5 != X1 )
& ( n0 != X1
| n2 != X0 )
& ( n0 != X1
| n3 != X0 )
& ( n0 != X1
| n4 != X0 )
& ( n0 != X1
| n5 != X0 )
& ( 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 )
& n1 = X0
& n1 = X1
& n2 = X0
& n2 = X1
& leq(n0,X0)
& leq(n0,X1)
& leq(X0,n5)
& leq(X1,n5) )
& ! [X2,X3] :
( a_select3(q_ds1_filter,X2,X3) = a_select3(q_ds1_filter,X3,X2)
| ~ leq(n0,X2)
| ~ leq(n0,X3)
| ~ leq(X2,n5)
| ~ leq(X3,n5) )
& ! [X4,X5] :
( a_select3(r_ds1_filter,X4,X5) = a_select3(r_ds1_filter,X5,X4)
| ~ leq(n0,X4)
| ~ leq(n0,X5)
| ~ leq(X4,n2)
| ~ leq(X5,n2) ) ),
inference(rectify,[],[f88]) ).
fof(f111,plain,
( a_select2(xinit_noise,n1) != a_select2(xinit_noise,n2)
& ( n0 != sK0
| n3 != sK1 )
& ( n0 != sK0
| n4 != sK1 )
& ( n0 != sK0
| n5 != sK1 )
& ( n0 != sK1
| n2 != sK0 )
& ( n0 != sK1
| n3 != sK0 )
& ( n0 != sK1
| n4 != sK0 )
& ( n0 != sK1
| n5 != sK0 )
& ( 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 )
& n1 = sK0
& n1 = sK1
& n2 = sK0
& n2 = sK1
& leq(n0,sK0)
& leq(n0,sK1)
& leq(sK0,n5)
& leq(sK1,n5)
& ! [X2,X3] :
( a_select3(q_ds1_filter,X2,X3) = a_select3(q_ds1_filter,X3,X2)
| ~ leq(n0,X2)
| ~ leq(n0,X3)
| ~ leq(X2,n5)
| ~ leq(X3,n5) )
& ! [X4,X5] :
( a_select3(r_ds1_filter,X4,X5) = a_select3(r_ds1_filter,X5,X4)
| ~ leq(n0,X4)
| ~ leq(n0,X5)
| ~ leq(X4,n2)
| ~ leq(X5,n2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f110]) ).
fof(f121,plain,
n2 = sK0,
inference(cnf_transformation,[],[f111]) ).
fof(f123,plain,
n1 = sK0,
inference(cnf_transformation,[],[f111]) ).
fof(f155,plain,
a_select2(xinit_noise,n1) != a_select2(xinit_noise,n2),
inference(cnf_transformation,[],[f111]) ).
fof(f196,plain,
a_select2(xinit_noise,sK0) != a_select2(xinit_noise,sK0),
inference(definition_unfolding,[],[f155,f123,f121]) ).
fof(f246,plain,
$false,
inference(trivial_inequality_removal,[],[f196]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV226+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 % Computer : n018.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Mon Sep 28 10:15:55 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 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
% 3.67/1.22 % (3277531)Detected formulas, will run a generic FOF schedule.
% 3.67/1.22 % (3277536)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=2097124104:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.67/1.22 % (3277541)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3744095382:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.67/1.22 % (3277542)dis-21_1_sil=8000:lcm=predicate:random_seed=2031983912: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)
% 3.67/1.22 % (3277537)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=2731825887:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.67/1.22 % (3277538)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=3234607466:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.67/1.22 % (3277539)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3833771759:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.67/1.22 % (3277540)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4009793864:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.67/1.22 % (3277540)First to succeed.
% 3.67/1.22 % (3277539)Also succeeded, but the first one will report.
% 3.67/1.22 % (3277540)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3277531"
% 3.67/1.22 % (3277541)Also succeeded, but the first one will report.
% 3.67/1.22 % (3277542)Also succeeded, but the first one will report.
% 3.67/1.22 % (3277540)Refutation found. Thanks to Tanya!
% 3.67/1.22 % SZS status Theorem for theBenchmark
% 3.67/1.22 % SZS output start Proof for theBenchmark
% See solution above
% 3.67/1.22 % (3277540)------------------------------
% 3.67/1.22 % (3277540)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.22 % (3277540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.22 % (3277540)CaDiCaL version: 2.1.3
% 3.67/1.22 % (3277540)Termination reason: Refutation
% 3.67/1.22 % (3277540)Time elapsed: 0.003 s
% 3.67/1.22 % (3277540)Peak memory usage: 88 MB
% 3.67/1.22 % (3277540)Instructions burned: 5 (million)
% 3.67/1.22 % (3277540)------------------------------
% 3.67/1.22 % (3277540)------------------------------
% 3.67/1.22 % (3277531)Success in time 0.438 s
% 3.67/1.22 % Vampire exiting
%------------------------------------------------------------------------------