%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PUZ092^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 : Wed Sep 30 08:20:52 AM UTC 2026
% Result : Theorem 0.08s 0.27s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 59 ( 10 unt; 4 def)
% Number of atoms : 292 ( 248 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 389 ( 156 ~; 144 |; 71 &)
% ( 4 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 12 con; 0-0 aty)
% Number of variables : 48 ( 0 sgn 24 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ( ( ( X8 != X11
& X4 = X2
& X4 = X5
& X2 = X3 )
=> X6 = X9 )
& ( ( X4 = X7
& X10 = X11
& X8 = X9 )
=> X0 != X3 )
& ( ( X2 != X5
& X6 = X7
& X0 = X1 )
=> X8 = X11 )
& ( ( X0 != X3
& X6 = X4
& X6 = X7
& X4 = X5 )
=> X8 != X11 )
& ( ( X2 = X5
& X10 = X11
& X0 = X1 )
=> X6 != X9 )
& ( ( X8 = X11
& X2 = X3
& X0 = X1 )
=> X4 = X7 ) )
=> ( X10 != X11
| X8 != X9
| X6 != X7
| X4 != X5
| X2 != X3
| X0 != X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cSIXFRIENDS_EASIER) ).
fof(f2,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ( ( ( X8 != X11
& X4 = X2
& X4 = X5
& X2 = X3 )
=> X6 = X9 )
& ( ( X4 = X7
& X10 = X11
& X8 = X9 )
=> X0 != X3 )
& ( ( X2 != X5
& X6 = X7
& X0 = X1 )
=> X8 = X11 )
& ( ( X0 != X3
& X6 = X4
& X6 = X7
& X4 = X5 )
=> X8 != X11 )
& ( ( X2 = X5
& X10 = X11
& X0 = X1 )
=> X6 != X9 )
& ( ( X8 = X11
& X2 = X3
& X0 = X1 )
=> X4 = X7 ) )
=> ( X10 != X11
| X8 != X9
| X6 != X7
| X4 != X5
| X2 != X3
| X0 != X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( X10 = X11
& X8 = X9
& X6 = X7
& X4 = X5
& X2 = X3
& X0 = X1
& ( X6 = X9
| X8 = X11
| X2 != X4
| X4 != X5
| X2 != X3 )
& ( X0 != X3
| X4 != X7
| X10 != X11
| X8 != X9 )
& ( X8 = X11
| X2 = X5
| X6 != X7
| X0 != X1 )
& ( X8 != X11
| X0 = X3
| X4 != X6
| X6 != X7
| X4 != X5 )
& ( X6 != X9
| X2 != X5
| X10 != X11
| X0 != X1 )
& ( X4 = X7
| X8 != X11
| X2 != X3
| X0 != X1 ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( X10 = X11
& X8 = X9
& X6 = X7
& X4 = X5
& X2 = X3
& X0 = X1
& ( X6 = X9
| X8 = X11
| X2 != X4
| X4 != X5
| X2 != X3 )
& ( X0 != X3
| X4 != X7
| X10 != X11
| X8 != X9 )
& ( X8 = X11
| X2 = X5
| X6 != X7
| X0 != X1 )
& ( X8 != X11
| X0 = X3
| X4 != X6
| X6 != X7
| X4 != X5 )
& ( X6 != X9
| X2 != X5
| X10 != X11
| X0 != X1 )
& ( X4 = X7
| X8 != X11
| X2 != X3
| X0 != X1 ) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
( sK10 = sK11
& sK8 = sK9
& sK6 = sK7
& sK4 = sK5
& sK2 = sK3
& sK0 = sK1
& ( sK6 = sK9
| sK8 = sK11
| sK2 != sK4
| sK4 != sK5
| sK2 != sK3 )
& ( sK0 != sK3
| sK4 != sK7
| sK10 != sK11
| sK8 != sK9 )
& ( sK8 = sK11
| sK2 = sK5
| sK6 != sK7
| sK0 != sK1 )
& ( sK8 != sK11
| sK0 = sK3
| sK4 != sK6
| sK6 != sK7
| sK4 != sK5 )
& ( sK6 != sK9
| sK2 != sK5
| sK10 != sK11
| sK0 != sK1 )
& ( sK4 = sK7
| sK8 != sK11
| sK2 != sK3
| sK0 != sK1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6),skolemize(X7,sK7),skolemize(X8,sK8),skolemize(X9,sK9),skolemize(X10,sK10),skolemize(X11,sK11)],[f4]) ).
fof(f6,plain,
( sK4 = sK7
| sK8 != sK11
| sK2 != sK3
| sK0 != sK1 ),
inference(cnf_transformation,[],[f5]) ).
fof(f7,plain,
( sK6 != sK9
| sK2 != sK5
| sK10 != sK11
| sK0 != sK1 ),
inference(cnf_transformation,[],[f5]) ).
fof(f8,plain,
( sK8 != sK11
| sK0 = sK3
| sK4 != sK6
| sK6 != sK7
| sK4 != sK5 ),
inference(cnf_transformation,[],[f5]) ).
fof(f9,plain,
( sK8 = sK11
| sK2 = sK5
| sK6 != sK7
| sK0 != sK1 ),
inference(cnf_transformation,[],[f5]) ).
fof(f10,plain,
( sK0 != sK3
| sK4 != sK7
| sK10 != sK11
| sK8 != sK9 ),
inference(cnf_transformation,[],[f5]) ).
fof(f11,plain,
( sK6 = sK9
| sK8 = sK11
| sK2 != sK4
| sK4 != sK5
| sK2 != sK3 ),
inference(cnf_transformation,[],[f5]) ).
fof(f12,plain,
sK0 = sK1,
inference(cnf_transformation,[],[f5]) ).
fof(f13,plain,
sK2 = sK3,
inference(cnf_transformation,[],[f5]) ).
fof(f14,plain,
sK4 = sK5,
inference(cnf_transformation,[],[f5]) ).
fof(f15,plain,
sK6 = sK7,
inference(cnf_transformation,[],[f5]) ).
fof(f16,plain,
sK8 = sK9,
inference(cnf_transformation,[],[f5]) ).
fof(f17,plain,
sK10 = sK11,
inference(cnf_transformation,[],[f5]) ).
fof(f18,plain,
( sK7 = sK9
| sK9 = sK11
| sK3 != sK5
| sK5 != sK5
| sK3 != sK3 ),
inference(definition_unfolding,[],[f11,f15,f16,f13,f14,f14,f13]) ).
fof(f19,plain,
( sK1 != sK3
| sK5 != sK7
| sK11 != sK11
| sK9 != sK9 ),
inference(definition_unfolding,[],[f10,f12,f14,f17,f16]) ).
fof(f20,plain,
( sK9 = sK11
| sK3 = sK5
| sK7 != sK7
| sK1 != sK1 ),
inference(definition_unfolding,[],[f9,f16,f13,f15,f12]) ).
fof(f21,plain,
( sK9 != sK11
| sK1 = sK3
| sK5 != sK7
| sK7 != sK7
| sK5 != sK5 ),
inference(definition_unfolding,[],[f8,f16,f12,f14,f15,f15,f14]) ).
fof(f22,plain,
( sK7 != sK9
| sK3 != sK5
| sK11 != sK11
| sK1 != sK1 ),
inference(definition_unfolding,[],[f7,f15,f13,f17,f12]) ).
fof(f23,plain,
( sK5 = sK7
| sK9 != sK11
| sK3 != sK3
| sK1 != sK1 ),
inference(definition_unfolding,[],[f6,f14,f16,f13,f12]) ).
fof(f24,plain,
( sK5 = sK7
| sK9 != sK11 ),
inference(trivial_inequality_removal,[],[f23]) ).
fof(f25,plain,
( sK7 != sK9
| sK3 != sK5 ),
inference(trivial_inequality_removal,[],[f22]) ).
fof(f26,plain,
( sK9 != sK11
| sK1 = sK3
| sK5 != sK7 ),
inference(trivial_inequality_removal,[],[f21]) ).
fof(f27,plain,
( sK9 = sK11
| sK3 = sK5 ),
inference(trivial_inequality_removal,[],[f20]) ).
fof(f28,plain,
( sK1 != sK3
| sK5 != sK7 ),
inference(trivial_inequality_removal,[],[f19]) ).
fof(f29,plain,
( sK7 = sK9
| sK9 = sK11
| sK3 != sK5 ),
inference(trivial_inequality_removal,[],[f18]) ).
fof(f31,definition,
( spl12_1
<=> sK9 = sK11 ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f32,plain,
( sK9 != sK11
| spl12_1 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f34,definition,
( spl12_2
<=> sK5 = sK7 ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f35,plain,
( sK5 = sK7
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f36,plain,
( ~ spl12_1
| spl12_2 ),
inference(avatar_split_clause,[],[f24,f34,f31]) ).
fof(f38,definition,
( spl12_3
<=> sK3 = sK5 ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
fof(f39,plain,
( sK3 != sK5
| spl12_3 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f41,definition,
( spl12_4
<=> sK7 = sK9 ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
fof(f42,plain,
( sK7 != sK9
| spl12_4 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f43,plain,
( ~ spl12_3
| ~ spl12_4 ),
inference(avatar_split_clause,[],[f25,f41,f38]) ).
fof(f44,plain,
( sK3 = sK5
| spl12_1 ),
inference(forward_subsumption_resolution,[],[f27,f32]) ).
fof(f45,plain,
( $false
| spl12_1
| spl12_3 ),
inference(forward_subsumption_resolution,[],[f44,f39]) ).
fof(f46,plain,
( spl12_1
| spl12_3 ),
inference(avatar_contradiction_clause,[],[f45]) ).
fof(f48,plain,
( sK1 != sK3
| ~ spl12_2 ),
inference(forward_subsumption_resolution,[],[f28,f35]) ).
fof(f54,plain,
( sK9 != sK11
| sK5 != sK7
| ~ spl12_2 ),
inference(forward_subsumption_resolution,[],[f26,f48]) ).
fof(f55,plain,
( sK9 != sK11
| ~ spl12_2 ),
inference(forward_subsumption_resolution,[],[f54,f35]) ).
fof(f56,plain,
( ~ spl12_1
| ~ spl12_2 ),
inference(avatar_split_clause,[],[f55,f34,f31]) ).
fof(f57,plain,
( sK7 = sK9
| sK3 != sK5
| spl12_1 ),
inference(forward_subsumption_resolution,[],[f29,f32]) ).
fof(f58,plain,
( sK7 = sK9
| spl12_1 ),
inference(forward_subsumption_resolution,[],[f57,f44]) ).
fof(f63,plain,
( $false
| spl12_1
| spl12_4 ),
inference(forward_subsumption_resolution,[],[f58,f42]) ).
fof(f64,plain,
( spl12_1
| spl12_4 ),
inference(avatar_contradiction_clause,[],[f63]) ).
cnf(s1,plain,
( ~ spl12_1
| spl12_2 ),
inference(sat_conversion,[],[f36]) ).
cnf(s2,plain,
( ~ spl12_3
| ~ spl12_4 ),
inference(sat_conversion,[],[f43]) ).
cnf(s3,plain,
( spl12_1
| spl12_3 ),
inference(sat_conversion,[],[f46]) ).
cnf(s5,plain,
( ~ spl12_1
| ~ spl12_2 ),
inference(sat_conversion,[],[f56]) ).
cnf(s7,plain,
( spl12_1
| spl12_4 ),
inference(sat_conversion,[],[f64]) ).
cnf(s8,plain,
spl12_1,
inference(rat,[],[s2,s3,s7]) ).
cnf(s9,plain,
~ spl12_2,
inference(rat,[],[s5,s8]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s9,s8]) ).
fof(f65,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ092^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n010.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:22:33 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.27 % (2835585)Detected 'Essentially Bernays–Schönfinkel–Ramsey OR Essentially ground' problem, will run a specialized EPR schedule (with support for satisfiability detection).
% 0.08/0.27 % (2835594)dis+10_1_sil=2000:bsr=unit_only:sac=on:avsqc=5:random_seed=1992481667:avsq=on:i=109:aac=none:nicw=on_2999 on theBenchmark for (2999ds/109Mi)
% 0.08/0.27 % (2835594) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2835585-2835594"...
% 0.08/0.27 % (2835594)...printing done.
% 0.08/0.27 % (2835590)lrs+1_1024_to=lpo:sp=weighted_frequency:random_seed=868806074:amm=off_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.27 % (2835593)ott+21_1_sil=128000:fs=off:lcm=predicate:random_seed=3781411617:i=102:av=off:fsr=off_2999 on theBenchmark for (2999ds/102Mi)
% 0.08/0.27 % (2835594)Refutation found. Thanks to Tanya!
% 0.08/0.27 % SZS status Theorem for theBenchmark
% 0.08/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.27 % (2835594)------------------------------
% 0.08/0.27 % (2835594)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.27 % (2835594)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.27 % (2835594)CaDiCaL version: 2.1.3
% 0.08/0.27 % (2835594)Termination reason: Refutation
% 0.08/0.27 % (2835594)Time elapsed: 0.002 s
% 0.08/0.27 % (2835594)Peak memory usage: 12 MB
% 0.08/0.27 % (2835594)Instructions burned: 3 (million)
% 0.08/0.27 % (2835585)Success in time 0.03 s
% 0.08/0.27 % Vampire exiting
%------------------------------------------------------------------------------