%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU406+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 12:53:09 PM UTC 2026
% Result : Theorem 0.20s 0.55s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 59 ( 16 unt; 4 def)
% Number of atoms : 140 ( 6 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 146 ( 65 ~; 52 |; 23 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 32 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1,X2,X3] :
~ ( r2_hidden(X0,k2_xboole_0(X2,X3))
& r2_hidden(X1,k2_xboole_0(X2,X3))
& ~ ( r2_hidden(X0,k4_xboole_0(X2,X3))
& r2_hidden(X1,k4_xboole_0(X2,X3)) )
& ~ ( r2_hidden(X0,X3)
& r2_hidden(X1,X3) )
& ~ ( r2_hidden(X0,k4_xboole_0(X2,X3))
& r2_hidden(X1,X3) )
& ~ ( r2_hidden(X0,X3)
& r2_hidden(X1,k4_xboole_0(X2,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_latsum_1) ).
fof(f2,negated_conjecture,
~ ! [X0,X1,X2,X3] :
~ ( r2_hidden(X0,k2_xboole_0(X2,X3))
& r2_hidden(X1,k2_xboole_0(X2,X3))
& ~ ( r2_hidden(X0,k4_xboole_0(X2,X3))
& r2_hidden(X1,k4_xboole_0(X2,X3)) )
& ~ ( r2_hidden(X0,X3)
& r2_hidden(X1,X3) )
& ~ ( r2_hidden(X0,k4_xboole_0(X2,X3))
& r2_hidden(X1,X3) )
& ~ ( r2_hidden(X0,X3)
& r2_hidden(X1,k4_xboole_0(X2,X3)) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f4,axiom,
! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f5,axiom,
! [X0,X1,X2] :
( X2 = k2_xboole_0(X0,X1)
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> ( r2_hidden(X3,X0)
| r2_hidden(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f20,axiom,
! [X0,X1] : k2_xboole_0(X0,k4_xboole_0(X1,X0)) = k2_xboole_0(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(f27,plain,
? [X0,X1,X2,X3] :
( r2_hidden(X0,k2_xboole_0(X2,X3))
& r2_hidden(X1,k2_xboole_0(X2,X3))
& ( ~ r2_hidden(X0,k4_xboole_0(X2,X3))
| ~ r2_hidden(X1,k4_xboole_0(X2,X3)) )
& ( ~ r2_hidden(X0,X3)
| ~ r2_hidden(X1,X3) )
& ( ~ r2_hidden(X0,k4_xboole_0(X2,X3))
| ~ r2_hidden(X1,X3) )
& ( ~ r2_hidden(X0,X3)
| ~ r2_hidden(X1,k4_xboole_0(X2,X3)) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f37,plain,
( ~ r2_hidden(sK1,k4_xboole_0(sK2,sK3))
| ~ r2_hidden(sK0,k4_xboole_0(sK2,sK3)) ),
inference(cnf_transformation,[],[f27]) ).
fof(f38,plain,
( ~ r2_hidden(sK1,sK3)
| ~ r2_hidden(sK0,sK3) ),
inference(cnf_transformation,[],[f27]) ).
fof(f39,plain,
( ~ r2_hidden(sK1,sK3)
| ~ r2_hidden(sK0,k4_xboole_0(sK2,sK3)) ),
inference(cnf_transformation,[],[f27]) ).
fof(f40,plain,
( ~ r2_hidden(sK1,k4_xboole_0(sK2,sK3))
| ~ r2_hidden(sK0,sK3) ),
inference(cnf_transformation,[],[f27]) ).
fof(f41,plain,
r2_hidden(sK1,k2_xboole_0(sK2,sK3)),
inference(cnf_transformation,[],[f27]) ).
fof(f42,plain,
r2_hidden(sK0,k2_xboole_0(sK2,sK3)),
inference(cnf_transformation,[],[f27]) ).
fof(f44,plain,
! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f48,plain,
! [X2,X3,X0,X1] :
( r2_hidden(X3,X1)
| r2_hidden(X3,X0)
| ~ r2_hidden(X3,X2)
| k2_xboole_0(X0,X1) != X2 ),
inference(cnf_transformation,[],[f5]) ).
fof(f61,plain,
! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X0,k4_xboole_0(X1,X0)),
inference(cnf_transformation,[],[f20]) ).
fof(f69,plain,
! [X3,X0,X1] :
( r2_hidden(X3,X1)
| r2_hidden(X3,X0)
| ~ r2_hidden(X3,k2_xboole_0(X0,X1)) ),
inference(equality_resolution,[],[f48]) ).
fof(f70,plain,
~ r2_hidden(sK0,k2_xboole_0(sK2,sK3)),
inference(consistent_polarity_flipping,[],[f42]) ).
fof(f71,plain,
~ r2_hidden(sK1,k2_xboole_0(sK2,sK3)),
inference(consistent_polarity_flipping,[],[f41]) ).
fof(f72,plain,
( r2_hidden(sK1,k4_xboole_0(sK2,sK3))
| r2_hidden(sK0,sK3) ),
inference(consistent_polarity_flipping,[],[f40]) ).
fof(f73,plain,
( r2_hidden(sK1,sK3)
| r2_hidden(sK0,k4_xboole_0(sK2,sK3)) ),
inference(consistent_polarity_flipping,[],[f39]) ).
fof(f74,plain,
( r2_hidden(sK1,sK3)
| r2_hidden(sK0,sK3) ),
inference(consistent_polarity_flipping,[],[f38]) ).
fof(f75,plain,
( r2_hidden(sK1,k4_xboole_0(sK2,sK3))
| r2_hidden(sK0,k4_xboole_0(sK2,sK3)) ),
inference(consistent_polarity_flipping,[],[f37]) ).
fof(f79,plain,
! [X3,X0,X1] :
( ~ r2_hidden(X3,X0)
| ~ r2_hidden(X3,X1)
| r2_hidden(X3,k2_xboole_0(X0,X1)) ),
inference(consistent_polarity_flipping,[],[f69]) ).
fof(f88,definition,
( spl8_1
<=> r2_hidden(sK0,k4_xboole_0(sK2,sK3)) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
fof(f90,plain,
( r2_hidden(sK0,k4_xboole_0(sK2,sK3))
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f92,definition,
( spl8_2
<=> r2_hidden(sK1,k4_xboole_0(sK2,sK3)) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
fof(f94,plain,
( r2_hidden(sK1,k4_xboole_0(sK2,sK3))
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f95,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f75,f92,f88]) ).
fof(f97,definition,
( spl8_3
<=> r2_hidden(sK0,sK3) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
fof(f99,plain,
( r2_hidden(sK0,sK3)
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f101,definition,
( spl8_4
<=> r2_hidden(sK1,sK3) ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
fof(f103,plain,
( r2_hidden(sK1,sK3)
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f104,plain,
( spl8_3
| spl8_4 ),
inference(avatar_split_clause,[],[f74,f101,f97]) ).
fof(f105,plain,
( spl8_1
| spl8_4 ),
inference(avatar_split_clause,[],[f73,f101,f88]) ).
fof(f106,plain,
( spl8_3
| spl8_2 ),
inference(avatar_split_clause,[],[f72,f92,f97]) ).
fof(f120,plain,
~ r2_hidden(sK1,k2_xboole_0(sK3,sK2)),
inference(superposition,[],[f71,f44]) ).
fof(f121,plain,
~ r2_hidden(sK0,k2_xboole_0(sK3,sK2)),
inference(superposition,[],[f70,f44]) ).
fof(f156,plain,
( ! [X0] :
( ~ r2_hidden(sK1,X0)
| r2_hidden(sK1,k2_xboole_0(sK3,X0)) )
| ~ spl8_4 ),
inference(resolution,[],[f79,f103]) ).
fof(f186,plain,
( r2_hidden(sK1,k2_xboole_0(sK3,k4_xboole_0(sK2,sK3)))
| ~ spl8_2
| ~ spl8_4 ),
inference(resolution,[],[f156,f94]) ).
fof(f191,plain,
( r2_hidden(sK1,k2_xboole_0(sK3,sK2))
| ~ spl8_2
| ~ spl8_4 ),
inference(forward_demodulation,[],[f186,f61]) ).
fof(f193,plain,
( $false
| ~ spl8_2
| ~ spl8_4 ),
inference(forward_subsumption_resolution,[],[f191,f120]) ).
fof(f194,plain,
( ~ spl8_2
| ~ spl8_4 ),
inference(avatar_contradiction_clause,[],[f193]) ).
fof(f195,plain,
( ! [X0] :
( ~ r2_hidden(sK0,X0)
| r2_hidden(sK0,k2_xboole_0(sK3,X0)) )
| ~ spl8_3 ),
inference(resolution,[],[f99,f79]) ).
fof(f202,plain,
( r2_hidden(sK0,k2_xboole_0(sK3,k4_xboole_0(sK2,sK3)))
| ~ spl8_1
| ~ spl8_3 ),
inference(resolution,[],[f195,f90]) ).
fof(f207,plain,
( r2_hidden(sK0,k2_xboole_0(sK3,sK2))
| ~ spl8_1
| ~ spl8_3 ),
inference(forward_demodulation,[],[f202,f61]) ).
fof(f209,plain,
( $false
| ~ spl8_1
| ~ spl8_3 ),
inference(forward_subsumption_resolution,[],[f207,f121]) ).
fof(f210,plain,
( ~ spl8_1
| ~ spl8_3 ),
inference(avatar_contradiction_clause,[],[f209]) ).
cnf(s1,plain,
( spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f95]) ).
cnf(s2,plain,
( spl8_3
| spl8_4 ),
inference(sat_conversion,[],[f104]) ).
cnf(s3,plain,
( spl8_1
| spl8_4 ),
inference(sat_conversion,[],[f105]) ).
cnf(s4,plain,
( spl8_2
| spl8_3 ),
inference(sat_conversion,[],[f106]) ).
cnf(s5,plain,
( ~ spl8_2
| ~ spl8_4 ),
inference(sat_conversion,[],[f194]) ).
cnf(s6,plain,
( ~ spl8_1
| ~ spl8_3 ),
inference(sat_conversion,[],[f210]) ).
cnf(s7,plain,
spl8_1,
inference(rat,[],[s5,s1,s3]) ).
cnf(s8,plain,
~ spl8_3,
inference(rat,[],[s6,s7]) ).
cnf(s9,plain,
spl8_2,
inference(rat,[],[s4,s8]) ).
cnf(s10,plain,
spl8_4,
inference(rat,[],[s2,s8]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s5,s10,s9]) ).
fof(f211,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU406+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.15/0.43 % Computer : n009.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Mon Sep 28 05:09:45 UTC 2026
% 0.15/0.44 % CPUTime :
% 0.15/0.44 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.20/0.49 Running first-order model finding
% 0.20/0.49 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
% 0.20/0.55 % (2673969)Will run a generic schedule for satisfiability detection.
% 0.20/0.55 % (2673974)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2691981882_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.55 % TRYING [1]
% 0.20/0.55 % TRYING [2]
% 0.20/0.55 % TRYING [3]
% 0.20/0.55 % TRYING [4]
% 0.20/0.55 % (2673976)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1206302842:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.55 % (2673975)% WARNING: option uhcvi not known.
% 0.20/0.55 % (2673977)dis+10_1_sil=32000:sp=arity:random_seed=1929077947:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.55 % (2673978)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3161798752:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.55 % (2673979)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4030229051:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.55 % (2673980)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4204055913:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.55 % TRYING [5]
% 0.20/0.55 % (2673975)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=948880298:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.55 % (2673975) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2673969-2673975"...
% 0.20/0.55 % (2673978) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2673969-2673978"...
% 0.20/0.55 % (2673975)...printing done.
% 0.20/0.55 % (2673978)...printing done.
% 0.20/0.55 % (2673975)Refutation found. Thanks to Tanya!
% 0.20/0.55 % SZS status Theorem for theBenchmark
% 0.20/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.55 % (2673975)------------------------------
% 0.20/0.55 % (2673975)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.55 % (2673975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.55 % (2673975)CaDiCaL version: 2.1.3
% 0.20/0.55 % (2673975)Termination reason: Refutation
% 0.20/0.55 % (2673975)Time elapsed: 0.010 s
% 0.20/0.55 % (2673975)Peak memory usage: 13 MB
% 0.20/0.55 % (2673975)Instructions burned: 7 (million)
% 0.20/0.55 % (2673969)Success in time 0.051 s
% 0.20/0.55 % Vampire exiting
%------------------------------------------------------------------------------