%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWV228+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 01:20:30 PM UTC 2026
% Result : Theorem 0.09s 0.26s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 19 ( 10 unt; 1 def)
% Number of atoms : 400 ( 321 equ)
% Maximal formula atoms : 64 ( 21 avg)
% Number of connectives : 655 ( 274 ~; 126 |; 244 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 12 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-3 aty)
% Number of variables : 34 ( 0 sgn 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
& n4 = X5 )
& ~ ( n0 = X4
& n5 = X5 )
& ~ ( n0 = X5
& n4 = X4 )
& ~ ( n0 = X5
& n5 = X4 )
& ~ ( n1 = X4
& n4 = X5 )
& ~ ( n1 = X4
& n5 = X5 )
& ~ ( n1 = X5
& n3 = X4 )
& ~ ( n1 = X5
& n4 = X4 )
& ~ ( n1 = X5
& n5 = X4 )
& ~ ( 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 )
& n0 = X5
& n3 = X4
& n3 = X5 )
=> n0 = a_select2(xinit_noise,n3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_symm_0681) ).
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
& n4 = X5 )
& ~ ( n0 = X4
& n5 = X5 )
& ~ ( n0 = X5
& n4 = X4 )
& ~ ( n0 = X5
& n5 = X4 )
& ~ ( n1 = X4
& n4 = X5 )
& ~ ( n1 = X4
& n5 = X5 )
& ~ ( n1 = X5
& n3 = X4 )
& ~ ( n1 = X5
& n4 = X4 )
& ~ ( n1 = X5
& n5 = X4 )
& ~ ( 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 )
& n0 = X5
& n3 = X4
& n3 = X5 )
=> n0 = a_select2(xinit_noise,n3) ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f136,plain,
( ? [X4,X5] :
( n0 != a_select2(xinit_noise,n3)
& ( n0 != X4
| n4 != X5 )
& ( n0 != X4
| n5 != X5 )
& ( n0 != X5
| n4 != X4 )
& ( n0 != X5
| n5 != X4 )
& ( n1 != X4
| n4 != X5 )
& ( n1 != X4
| n5 != X5 )
& ( n1 != X5
| n3 != X4 )
& ( n1 != X5
| n4 != X4 )
& ( n1 != X5
| n5 != X4 )
& ( 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 )
& n0 = X5
& n3 = X4
& n3 = 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(f137,plain,
( ? [X4,X5] :
( n0 != a_select2(xinit_noise,n3)
& ( n0 != X4
| n4 != X5 )
& ( n0 != X4
| n5 != X5 )
& ( n0 != X5
| n4 != X4 )
& ( n0 != X5
| n5 != X4 )
& ( n1 != X4
| n4 != X5 )
& ( n1 != X4
| n5 != X5 )
& ( n1 != X5
| n3 != X4 )
& ( n1 != X5
| n4 != X4 )
& ( n1 != X5
| n5 != X4 )
& ( 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 )
& n0 = X5
& n3 = X4
& n3 = 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,[],[f136]) ).
fof(f190,plain,
( ? [X0,X1] :
( n0 != a_select2(xinit_noise,n3)
& ( n0 != X0
| n4 != X1 )
& ( n0 != X0
| n5 != X1 )
& ( n0 != X1
| n4 != X0 )
& ( n0 != X1
| n5 != X0 )
& ( n1 != X0
| n4 != X1 )
& ( n1 != X0
| n5 != X1 )
& ( n1 != X1
| n3 != X0 )
& ( n1 != X1
| n4 != X0 )
& ( n1 != X1
| n5 != X0 )
& ( 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 = X1
& n3 = X0
& n3 = 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,[],[f137]) ).
fof(f191,plain,
( n0 != a_select2(xinit_noise,n3)
& ( n0 != sK31
| n4 != sK32 )
& ( n0 != sK31
| n5 != sK32 )
& ( n0 != sK32
| n4 != sK31 )
& ( n0 != sK32
| n5 != sK31 )
& ( n1 != sK31
| n4 != sK32 )
& ( n1 != sK31
| n5 != sK32 )
& ( n1 != sK32
| n3 != sK31 )
& ( n1 != sK32
| n4 != sK31 )
& ( n1 != sK32
| n5 != sK31 )
& ( n2 != sK31
| n4 != sK32 )
& ( n2 != sK31
| n5 != sK32 )
& ( n2 != sK32
| n3 != sK31 )
& ( n2 != sK32
| n4 != sK31 )
& ( n2 != sK32
| n5 != sK31 )
& ( n3 != sK31
| n3 != sK32 )
& ( n3 != sK31
| n4 != sK32 )
& ( n3 != sK31
| n5 != sK32 )
& ( n3 != sK32
| n4 != sK31 )
& ( n3 != sK32
| n5 != sK31 )
& ( n4 != sK31
| n4 != sK32 )
& ( n4 != sK31
| n5 != sK32 )
& ( n4 != sK32
| n5 != sK31 )
& ( n5 != sK31
| n5 != sK32 )
& n0 = sK32
& n3 = sK31
& n3 = sK32
& leq(n0,sK31)
& leq(n0,sK32)
& leq(sK31,n5)
& leq(sK32,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,[sK31,sK32]),skolemize(X0,sK31),skolemize(X1,sK32)],[f190]) ).
fof(f308,plain,
n3 = sK32,
inference(cnf_transformation,[],[f191]) ).
fof(f309,plain,
n3 = sK31,
inference(cnf_transformation,[],[f191]) ).
fof(f319,plain,
( n3 != sK31
| n3 != sK32 ),
inference(cnf_transformation,[],[f191]) ).
fof(f456,plain,
( sK31 != sK31
| sK31 != sK32 ),
inference(definition_unfolding,[],[f319,f309,f309]) ).
fof(f461,plain,
sK31 = sK32,
inference(definition_unfolding,[],[f308,f309]) ).
fof(f493,plain,
sK31 != sK32,
inference(trivial_inequality_removal,[],[f456]) ).
fof(f519,definition,
( spl33_5
<=> sK31 = sK32 ),
introduced(definition,[new_symbols(definition,[spl33_5])],[avatar_definition]) ).
fof(f526,plain,
~ spl33_5,
inference(avatar_split_clause,[],[f493,f519]) ).
fof(f557,plain,
spl33_5,
inference(avatar_split_clause,[],[f461,f519]) ).
cnf(s9,plain,
~ spl33_5,
inference(sat_conversion,[],[f526]) ).
cnf(s24,plain,
spl33_5,
inference(sat_conversion,[],[f557]) ).
cnf(s27,plain,
$false,
inference(rat,[],[s9,s24]) ).
fof(f558,plain,
$false,
inference(avatar_sat_refutation,[],[s27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV228+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n002.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 10:16:37 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.26 % (252248)Will run a generic schedule for satisfiability detection.
% 0.09/0.26 % (252256)dis+10_1_sil=32000:sp=arity:random_seed=2221188239:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.26 % (252256) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-252248-252256"...
% 0.09/0.26 % (252254)% WARNING: option uhcvi not known.
% 0.09/0.26 % (252256)...printing done.
% 0.09/0.26 % (252256)Refutation found. Thanks to Tanya!
% 0.09/0.26 % SZS status Theorem for theBenchmark
% 0.09/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.26 % (252256)------------------------------
% 0.09/0.26 % (252256)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.26 % (252256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.26 % (252256)CaDiCaL version: 2.1.3
% 0.09/0.26 % (252256)Termination reason: Refutation
% 0.09/0.26 % (252256)Time elapsed: 0.004 s
% 0.09/0.26 % (252256)Peak memory usage: 12 MB
% 0.09/0.26 % (252256)Instructions burned: 12 (million)
% 0.09/0.26 % (252248)Success in time 0.033 s
% 0.19/0.26 % Vampire exiting
%------------------------------------------------------------------------------