%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV232+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 01:08:26 PM UTC 2026
% Result : Theorem 2.65s 1.05s
% Output : Refutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 13 unt; 2 def)
% Number of atoms : 195 ( 130 equ)
% Maximal formula atoms : 28 ( 7 avg)
% Number of connectives : 270 ( 101 ~; 49 |; 110 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-3 aty)
% Number of variables : 24 ( 0 sgn 18 !; 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) )
=> ( ( ~ ( n0 = X2
& n1 = X3 )
& ~ ( n0 = X2
& n2 = X3 )
& ~ ( n0 = X3
& n2 = X2 )
& ~ ( n1 = X2
& n1 = X3 )
& ~ ( n1 = X2
& n2 = X3 )
& ~ ( n1 = X3
& n2 = X2 )
& ~ ( n2 = X2
& n2 = X3 )
& n0 = X3
& n1 = X2
& n1 = X3
& n2 = X2 )
=> a_select2(rho,n1) = n0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_symm_0841) ).
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) )
=> ( ( ~ ( n0 = X2
& n1 = X3 )
& ~ ( n0 = X2
& n2 = X3 )
& ~ ( n0 = X3
& n2 = X2 )
& ~ ( n1 = X2
& n1 = X3 )
& ~ ( n1 = X2
& n2 = X3 )
& ~ ( n1 = X3
& n2 = X2 )
& ~ ( n2 = X2
& n2 = X3 )
& n0 = X3
& n1 = X2
& n1 = X3
& n2 = X2 )
=> a_select2(rho,n1) = n0 ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f93,plain,
( ? [X2,X3] :
( n0 != a_select2(rho,n1)
& ( n0 != X2
| n1 != X3 )
& ( n0 != X2
| n2 != X3 )
& ( n0 != X3
| n2 != X2 )
& ( n1 != X2
| n1 != X3 )
& ( n1 != X2
| n2 != X3 )
& ( n1 != X3
| n2 != X2 )
& ( n2 != X2
| n2 != X3 )
& n0 = X3
& n1 = X2
& n1 = X3
& n2 = X2
& leq(n0,X2)
& leq(n0,X3)
& leq(X2,n2)
& leq(X3,n2) )
& ! [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) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f94,plain,
( ? [X2,X3] :
( n0 != a_select2(rho,n1)
& ( n0 != X2
| n1 != X3 )
& ( n0 != X2
| n2 != X3 )
& ( n0 != X3
| n2 != X2 )
& ( n1 != X2
| n1 != X3 )
& ( n1 != X2
| n2 != X3 )
& ( n1 != X3
| n2 != X2 )
& ( n2 != X2
| n2 != X3 )
& n0 = X3
& n1 = X2
& n1 = X3
& n2 = X2
& leq(n0,X2)
& leq(n0,X3)
& leq(X2,n2)
& leq(X3,n2) )
& ! [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) ) ),
inference(flattening,[],[f93]) ).
fof(f145,plain,
( ? [X0,X1] :
( n0 != a_select2(rho,n1)
& ( n0 != X0
| n1 != X1 )
& ( n0 != X0
| n2 != X1 )
& ( n0 != X1
| n2 != X0 )
& ( n1 != X0
| n1 != X1 )
& ( n1 != X0
| n2 != X1 )
& ( n1 != X1
| n2 != X0 )
& ( n2 != X0
| n2 != X1 )
& n0 = X1
& n1 = X0
& n1 = X1
& n2 = X0
& leq(n0,X0)
& leq(n0,X1)
& leq(X0,n2)
& leq(X1,n2) )
& ! [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) ) ),
inference(rectify,[],[f94]) ).
fof(f146,plain,
( n0 != a_select2(rho,n1)
& ( n0 != sK3
| n1 != sK4 )
& ( n0 != sK3
| n2 != sK4 )
& ( n0 != sK4
| n2 != sK3 )
& ( n1 != sK3
| n1 != sK4 )
& ( n1 != sK3
| n2 != sK4 )
& ( n1 != sK4
| n2 != sK3 )
& ( n2 != sK3
| n2 != sK4 )
& n0 = sK4
& n1 = sK3
& n1 = sK4
& n2 = sK3
& leq(n0,sK3)
& leq(n0,sK4)
& leq(sK3,n2)
& leq(sK4,n2)
& ! [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) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f145]) ).
fof(f177,plain,
n2 = sK3,
inference(cnf_transformation,[],[f146]) ).
fof(f178,plain,
n1 = sK4,
inference(cnf_transformation,[],[f146]) ).
fof(f179,plain,
n1 = sK3,
inference(cnf_transformation,[],[f146]) ).
fof(f180,plain,
n0 = sK4,
inference(cnf_transformation,[],[f146]) ).
fof(f186,plain,
( n0 != sK3
| n2 != sK4 ),
inference(cnf_transformation,[],[f146]) ).
fof(f310,plain,
( sK3 != sK4
| sK3 != sK4 ),
inference(definition_unfolding,[],[f186,f180,f177]) ).
fof(f316,plain,
sK3 = sK4,
inference(definition_unfolding,[],[f178,f179]) ).
fof(f414,definition,
! [X0,X1] :
( sQ26_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ26_eqProxy])],[equality_proxy_definition]) ).
fof(f417,plain,
( ~ sQ26_eqProxy(sK3,sK4)
| ~ sQ26_eqProxy(sK3,sK4) ),
inference(equality_proxy_replacement,[],[f310,f414,f414]) ).
fof(f423,plain,
sQ26_eqProxy(sK3,sK4),
inference(equality_proxy_replacement,[],[f316,f414]) ).
fof(f503,plain,
~ sQ26_eqProxy(sK3,sK4),
inference(duplicate_literal_removal,[],[f417]) ).
fof(f506,definition,
( spl27_1
<=> sQ26_eqProxy(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl27_1])],[avatar_definition]) ).
fof(f507,plain,
( ~ sQ26_eqProxy(sK3,sK4)
| spl27_1 ),
inference(avatar_component_clause,[],[f506]) ).
fof(f519,plain,
~ spl27_1,
inference(avatar_split_clause,[],[f503,f506]) ).
fof(f520,plain,
( $false
| spl27_1 ),
inference(resolution,[],[f423,f507]) ).
fof(f521,plain,
spl27_1,
inference(avatar_contradiction_clause,[],[f520]) ).
cnf(s6,plain,
~ spl27_1,
inference(sat_conversion,[],[f519]) ).
cnf(s8,plain,
spl27_1,
inference(sat_conversion,[],[f521]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s6,s8]) ).
fof(f522,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV232+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n018.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 10:16:25 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.23 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
% 2.65/1.05 % (3278560)Detected formulas, will run a generic FOF schedule.
% 2.65/1.05 % (3278571)dis-21_1_sil=8000:lcm=predicate:random_seed=4058843146: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)
% 2.65/1.05 % (3278571)First to succeed.
% 2.65/1.05 % (3278571)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3278560"
% 2.65/1.05 % (3278568)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=552169333:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.65/1.05 % (3278570)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3744915449:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.65/1.05 % (3278567)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=2487167822:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.65/1.05 % (3278565)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=3229163397:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.65/1.05 % (3278566)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=2122395990:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.65/1.05 % (3278569)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3194301556:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.65/1.05 % (3278569)Also succeeded, but the first one will report.
% 2.65/1.05 % (3278568)Also succeeded, but the first one will report.
% 2.65/1.05 % (3278570)Also succeeded, but the first one will report.
% 2.65/1.05 % (3278571)Refutation found. Thanks to Tanya!
% 2.65/1.05 % SZS status Theorem for theBenchmark
% 2.65/1.05 % SZS output start Proof for theBenchmark
% See solution above
% 2.65/1.05 % (3278571)------------------------------
% 2.65/1.05 % (3278571)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.05 % (3278571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.05 % (3278571)CaDiCaL version: 2.1.3
% 2.65/1.05 % (3278571)Termination reason: Refutation
% 2.65/1.05 % (3278571)Time elapsed: 0.004 s
% 2.65/1.05 % (3278571)Peak memory usage: 89 MB
% 2.65/1.05 % (3278571)Instructions burned: 10 (million)
% 2.65/1.05 % (3278571)------------------------------
% 2.65/1.05 % (3278571)------------------------------
% 2.65/1.05 % (3278560)Success in time 0.3 s
% 2.65/1.06 % Vampire exiting
%------------------------------------------------------------------------------