%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWV204+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 : n011.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 01:20:27 PM UTC 2026
% Result : Theorem 0.20s 0.30s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 46 ( 15 unt; 3 def)
% Number of atoms : 326 ( 214 equ)
% Maximal formula atoms : 40 ( 7 avg)
% Number of connectives : 347 ( 67 ~; 73 |; 195 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 16 con; 0-3 aty)
% Number of variables : 33 ( 0 sgn 30 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f53,conjecture,
( ( a_select2(rho_defuse,n0) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n2) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n5) = use
& a_select3(u_defuse,n0,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n2,n0) = use
& a_select2(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n5) = use
& ! [X0,X1] :
( ( leq(n0,X0)
& leq(n0,X1)
& leq(X0,n2)
& leq(X1,n998) )
=> a_select3(u_defuse,X0,X1) = use )
& ! [X2,X3] :
( ( leq(n0,X2)
& leq(n0,X3)
& leq(X2,n2)
& leq(X3,n998) )
=> a_select3(z_defuse,X2,X3) = use ) )
=> ! [X4] :
( ( leq(n0,X4)
& leq(X4,n2) )
=> a_select2(rho_defuse,X4) = use ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_inuse_0015) ).
fof(f54,negated_conjecture,
~ ( ( a_select2(rho_defuse,n0) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n2) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n5) = use
& a_select3(u_defuse,n0,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n2,n0) = use
& a_select2(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n5) = use
& ! [X0,X1] :
( ( leq(n0,X0)
& leq(n0,X1)
& leq(X0,n2)
& leq(X1,n998) )
=> a_select3(u_defuse,X0,X1) = use )
& ! [X2,X3] :
( ( leq(n0,X2)
& leq(n0,X3)
& leq(X2,n2)
& leq(X3,n998) )
=> a_select3(z_defuse,X2,X3) = use ) )
=> ! [X4] :
( ( leq(n0,X4)
& leq(X4,n2) )
=> a_select2(rho_defuse,X4) = use ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f87,axiom,
! [X0] :
( ( leq(n0,X0)
& leq(X0,n2) )
=> ( X0 = n0
| X0 = n1
| X0 = n2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_2) ).
fof(f143,plain,
( ? [X4] :
( use != a_select2(rho_defuse,X4)
& leq(n0,X4)
& leq(X4,n2) )
& a_select2(rho_defuse,n0) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n2) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n5) = use
& a_select3(u_defuse,n0,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n2,n0) = use
& a_select2(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n5) = use
& ! [X0,X1] :
( a_select3(u_defuse,X0,X1) = use
| ~ leq(n0,X0)
| ~ leq(n0,X1)
| ~ leq(X0,n2)
| ~ leq(X1,n998) )
& ! [X2,X3] :
( a_select3(z_defuse,X2,X3) = use
| ~ leq(n0,X2)
| ~ leq(n0,X3)
| ~ leq(X2,n2)
| ~ leq(X3,n998) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f144,plain,
( ? [X4] :
( use != a_select2(rho_defuse,X4)
& leq(n0,X4)
& leq(X4,n2) )
& a_select2(rho_defuse,n0) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n2) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n5) = use
& a_select3(u_defuse,n0,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n2,n0) = use
& a_select2(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n5) = use
& ! [X0,X1] :
( a_select3(u_defuse,X0,X1) = use
| ~ leq(n0,X0)
| ~ leq(n0,X1)
| ~ leq(X0,n2)
| ~ leq(X1,n998) )
& ! [X2,X3] :
( a_select3(z_defuse,X2,X3) = use
| ~ leq(n0,X2)
| ~ leq(n0,X3)
| ~ leq(X2,n2)
| ~ leq(X3,n998) ) ),
inference(flattening,[],[f143]) ).
fof(f153,plain,
! [X0] :
( X0 = n0
| X0 = n1
| X0 = n2
| ~ leq(n0,X0)
| ~ leq(X0,n2) ),
inference(ennf_transformation,[],[f87]) ).
fof(f154,plain,
! [X0] :
( X0 = n0
| X0 = n1
| X0 = n2
| ~ leq(n0,X0)
| ~ leq(X0,n2) ),
inference(flattening,[],[f153]) ).
fof(f197,plain,
( ? [X0] :
( use != a_select2(rho_defuse,X0)
& leq(n0,X0)
& leq(X0,n2) )
& a_select2(rho_defuse,n0) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n2) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n5) = use
& a_select3(u_defuse,n0,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n2,n0) = use
& a_select2(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n5) = use
& ! [X1,X2] :
( use = a_select3(u_defuse,X1,X2)
| ~ leq(n0,X1)
| ~ leq(n0,X2)
| ~ leq(X1,n2)
| ~ leq(X2,n998) )
& ! [X3,X4] :
( use = a_select3(z_defuse,X3,X4)
| ~ leq(n0,X3)
| ~ leq(n0,X4)
| ~ leq(X3,n2)
| ~ leq(X4,n998) ) ),
inference(rectify,[],[f144]) ).
fof(f198,plain,
( use != a_select2(rho_defuse,sK31)
& leq(n0,sK31)
& leq(sK31,n2)
& a_select2(rho_defuse,n0) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n2) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n5) = use
& a_select3(u_defuse,n0,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n2,n0) = use
& a_select2(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n5) = use
& ! [X1,X2] :
( use = a_select3(u_defuse,X1,X2)
| ~ leq(n0,X1)
| ~ leq(n0,X2)
| ~ leq(X1,n2)
| ~ leq(X2,n998) )
& ! [X3,X4] :
( use = a_select3(z_defuse,X3,X4)
| ~ leq(n0,X3)
| ~ leq(n0,X4)
| ~ leq(X3,n2)
| ~ leq(X4,n998) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(X0,sK31)],[f197]) ).
fof(f335,plain,
use = a_select2(rho_defuse,n2),
inference(cnf_transformation,[],[f198]) ).
fof(f336,plain,
use = a_select2(rho_defuse,n1),
inference(cnf_transformation,[],[f198]) ).
fof(f337,plain,
use = a_select2(rho_defuse,n0),
inference(cnf_transformation,[],[f198]) ).
fof(f338,plain,
leq(sK31,n2),
inference(cnf_transformation,[],[f198]) ).
fof(f339,plain,
leq(n0,sK31),
inference(cnf_transformation,[],[f198]) ).
fof(f340,plain,
use != a_select2(rho_defuse,sK31),
inference(cnf_transformation,[],[f198]) ).
fof(f373,plain,
! [X0] :
( ~ leq(n0,X0)
| n1 = X0
| n2 = X0
| n0 = X0
| ~ leq(X0,n2) ),
inference(cnf_transformation,[],[f154]) ).
fof(f758,definition,
( spl32_13
<=> n2 = sK31 ),
introduced(definition,[new_symbols(definition,[spl32_13])],[avatar_definition]) ).
fof(f759,plain,
( n2 != sK31
| spl32_13 ),
inference(avatar_component_clause,[],[f758]) ).
fof(f760,plain,
( n2 = sK31
| ~ spl32_13 ),
inference(avatar_component_clause,[],[f758]) ).
fof(f767,definition,
( spl32_15
<=> n0 = sK31 ),
introduced(definition,[new_symbols(definition,[spl32_15])],[avatar_definition]) ).
fof(f768,plain,
( n0 != sK31
| spl32_15 ),
inference(avatar_component_clause,[],[f767]) ).
fof(f769,plain,
( n0 = sK31
| ~ spl32_15 ),
inference(avatar_component_clause,[],[f767]) ).
fof(f777,plain,
( use != a_select2(rho_defuse,n2)
| ~ spl32_13 ),
inference(superposition,[],[f340,f760]) ).
fof(f783,plain,
( $false
| ~ spl32_13 ),
inference(forward_subsumption_resolution,[],[f777,f335]) ).
fof(f784,plain,
~ spl32_13,
inference(avatar_contradiction_clause,[],[f783]) ).
fof(f821,plain,
( use != a_select2(rho_defuse,n0)
| ~ spl32_15 ),
inference(superposition,[],[f340,f769]) ).
fof(f832,plain,
( $false
| ~ spl32_15 ),
inference(forward_subsumption_resolution,[],[f821,f337]) ).
fof(f833,plain,
~ spl32_15,
inference(avatar_contradiction_clause,[],[f832]) ).
fof(f1031,definition,
( spl32_34
<=> n1 = sK31 ),
introduced(definition,[new_symbols(definition,[spl32_34])],[avatar_definition]) ).
fof(f1033,plain,
( n1 = sK31
| ~ spl32_34 ),
inference(avatar_component_clause,[],[f1031]) ).
fof(f1123,plain,
( n1 = sK31
| n2 = sK31
| n0 = sK31
| ~ leq(sK31,n2) ),
inference(resolution,[],[f373,f339]) ).
fof(f1127,plain,
( n1 = sK31
| n0 = sK31
| ~ leq(sK31,n2)
| spl32_13 ),
inference(forward_subsumption_resolution,[],[f1123,f759]) ).
fof(f1128,plain,
( n1 = sK31
| ~ leq(sK31,n2)
| spl32_13
| spl32_15 ),
inference(forward_subsumption_resolution,[],[f1127,f768]) ).
fof(f1129,plain,
( n1 = sK31
| spl32_13
| spl32_15 ),
inference(forward_subsumption_resolution,[],[f1128,f338]) ).
fof(f1130,plain,
( spl32_34
| spl32_13
| spl32_15 ),
inference(avatar_split_clause,[],[f1129,f767,f758,f1031]) ).
fof(f1140,plain,
( use != a_select2(rho_defuse,n1)
| ~ spl32_34 ),
inference(superposition,[],[f340,f1033]) ).
fof(f1162,plain,
( $false
| ~ spl32_34 ),
inference(forward_subsumption_resolution,[],[f1140,f336]) ).
fof(f1163,plain,
~ spl32_34,
inference(avatar_contradiction_clause,[],[f1162]) ).
cnf(s12,plain,
~ spl32_13,
inference(sat_conversion,[],[f784]) ).
cnf(s18,plain,
~ spl32_15,
inference(sat_conversion,[],[f833]) ).
cnf(s34,plain,
( spl32_13
| spl32_15
| spl32_34 ),
inference(sat_conversion,[],[f1130]) ).
cnf(s37,plain,
~ spl32_34,
inference(sat_conversion,[],[f1163]) ).
cnf(s39,plain,
( spl32_13
| spl32_15 ),
inference(rat,[],[s34,s37]) ).
cnf(s45,plain,
spl32_13,
inference(rat,[],[s39,s18]) ).
cnf(s48,plain,
$false,
inference(rat,[],[s12,s45]) ).
fof(f1165,plain,
$false,
inference(avatar_sat_refutation,[],[s48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV204+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n011.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 10:09:31 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.20/0.30 % (3298818)Will run a generic schedule for satisfiability detection.
% 0.20/0.30 % (3298829)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3724452367:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.30 % (3298824)% WARNING: option uhcvi not known.
% 0.20/0.30 % (3298823)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4205751727_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.30 % (3298825)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=901192366:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.30 % (3298824)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1777985761:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.30 % (3298826)dis+10_1_sil=32000:sp=arity:random_seed=3659276367:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.30 % (3298827)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=941783128:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.30 % (3298828)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2123472051:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.30 % (3298826) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3298818-3298826"...
% 0.20/0.30 % (3298826)...printing done.
% 0.20/0.30 % (3298824) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3298818-3298824"...
% 0.20/0.30 % (3298826)Refutation found. Thanks to Tanya!
% 0.20/0.30 % SZS status Theorem for theBenchmark
% 0.20/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.30 % (3298826)------------------------------
% 0.20/0.30 % (3298826)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (3298826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (3298826)CaDiCaL version: 2.1.3
% 0.20/0.30 % (3298826)Termination reason: Refutation
% 0.20/0.30 % (3298826)Time elapsed: 0.026 s
% 0.20/0.30 % (3298826)Peak memory usage: 13 MB
% 0.20/0.30 % (3298826)Instructions burned: 42 (million)
% 0.20/0.30 % (3298818)Success in time 0.061 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------