%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU255+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 12:52:37 PM UTC 2026
% Result : Theorem 0.11s 0.46s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 7
% Syntax : Number of formulae : 62 ( 15 unt; 1 def)
% Number of atoms : 199 ( 26 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 231 ( 94 ~; 101 |; 22 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 96 ( 0 sgn 88 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f6,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f11,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(f20,axiom,
! [X0] :
( relation(X0)
=> ( antisymmetric(X0)
<=> ! [X1,X2] :
( ( in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X2,X1),X0) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_wellord1) ).
fof(f26,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,X2)
& in(X0,cartesian_product2(X1,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_wellord1) ).
fof(f28,conjecture,
! [X0,X1] :
( relation(X1)
=> ( antisymmetric(X1)
=> antisymmetric(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_wellord1) ).
fof(f29,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ( antisymmetric(X1)
=> antisymmetric(relation_restriction(X1,X0)) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f43,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f44,plain,
! [X0] :
( ( antisymmetric(X0)
<=> ! [X1,X2] :
( X1 = X2
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X2,X1),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f45,plain,
! [X0] :
( ( antisymmetric(X0)
<=> ! [X1,X2] :
( X1 = X2
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X2,X1),X0) ) )
| ~ relation(X0) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,X2)
& in(X0,cartesian_product2(X1,X1)) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f26]) ).
fof(f48,plain,
? [X0,X1] :
( ~ antisymmetric(relation_restriction(X1,X0))
& antisymmetric(X1)
& relation(X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f49,plain,
? [X0,X1] :
( ~ antisymmetric(relation_restriction(X1,X0))
& antisymmetric(X1)
& relation(X1) ),
inference(flattening,[],[f48]) ).
fof(f56,plain,
! [X0] :
( ( ( antisymmetric(X0)
| ? [X1,X2] :
( X1 != X2
& in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X2,X1),X0) ) )
& ( ! [X1,X2] :
( X1 = X2
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X2,X1),X0) )
| ~ antisymmetric(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f45]) ).
fof(f57,plain,
! [X0] :
( ( ( antisymmetric(X0)
| ? [X1,X2] :
( X1 != X2
& in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X2,X1),X0) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X4,X3),X0) )
| ~ antisymmetric(X0) ) )
| ~ relation(X0) ),
inference(rectify,[],[f56]) ).
fof(f58,plain,
! [X0] :
( ( ( antisymmetric(X0)
| ( sK1(X0) != sK2(X0)
& in(ordered_pair(sK1(X0),sK2(X0)),X0)
& in(ordered_pair(sK2(X0),sK1(X0)),X0) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X4,X3),X0) )
| ~ antisymmetric(X0) ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X1,sK1(X0)),skolemize(X2,sK2(X0))],[f57]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_restriction(X2,X1))
| ~ in(X0,X2)
| ~ in(X0,cartesian_product2(X1,X1)) )
& ( ( in(X0,X2)
& in(X0,cartesian_product2(X1,X1)) )
| ~ in(X0,relation_restriction(X2,X1)) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f46]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_restriction(X2,X1))
| ~ in(X0,X2)
| ~ in(X0,cartesian_product2(X1,X1)) )
& ( ( in(X0,X2)
& in(X0,cartesian_product2(X1,X1)) )
| ~ in(X0,relation_restriction(X2,X1)) ) )
| ~ relation(X2) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
( ~ antisymmetric(relation_restriction(sK9,sK8))
& antisymmetric(sK9)
& relation(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X0,sK8),skolemize(X1,sK9)],[f49]) ).
fof(f71,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f73,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f75,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f80,plain,
! [X3,X0,X4] :
( X3 = X4
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X4,X3),X0)
| ~ antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f81,plain,
! [X0] :
( antisymmetric(X0)
| in(ordered_pair(sK2(X0),sK1(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f82,plain,
! [X0] :
( antisymmetric(X0)
| in(ordered_pair(sK1(X0),sK2(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f83,plain,
! [X0] :
( sK1(X0) != sK2(X0)
| antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f94,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_restriction(X2,X1))
| in(X0,X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f65]) ).
fof(f97,plain,
relation(sK9),
inference(cnf_transformation,[],[f66]) ).
fof(f98,plain,
antisymmetric(sK9),
inference(cnf_transformation,[],[f66]) ).
fof(f99,plain,
~ antisymmetric(relation_restriction(sK9,sK8)),
inference(cnf_transformation,[],[f66]) ).
fof(f106,plain,
! [X0] :
( antisymmetric(X0)
| in(unordered_pair(unordered_pair(sK1(X0),sK2(X0)),singleton(sK1(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f82,f73]) ).
fof(f107,plain,
! [X0] :
( antisymmetric(X0)
| in(unordered_pair(unordered_pair(sK2(X0),sK1(X0)),singleton(sK2(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f81,f73]) ).
fof(f108,plain,
! [X3,X0,X4] :
( X3 = X4
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),X0)
| ~ in(unordered_pair(unordered_pair(X4,X3),singleton(X4)),X0)
| ~ antisymmetric(X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f80,f73,f73]) ).
fof(f156,plain,
! [X0] :
( in(unordered_pair(singleton(sK1(X0)),unordered_pair(sK1(X0),sK2(X0))),X0)
| antisymmetric(X0)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f106,f71]) ).
fof(f159,plain,
! [X0] :
( in(unordered_pair(singleton(sK2(X0)),unordered_pair(sK2(X0),sK1(X0))),X0)
| antisymmetric(X0)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f107,f71]) ).
fof(f160,plain,
! [X0] :
( in(unordered_pair(singleton(sK2(X0)),unordered_pair(sK1(X0),sK2(X0))),X0)
| antisymmetric(X0)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f159,f71]) ).
fof(f165,plain,
! [X0,X1] :
( antisymmetric(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1))
| in(unordered_pair(singleton(sK1(relation_restriction(X0,X1))),unordered_pair(sK1(relation_restriction(X0,X1)),sK2(relation_restriction(X0,X1)))),X0)
| ~ relation(X0) ),
inference(resolution,[],[f156,f94]) ).
fof(f167,plain,
! [X0,X1] :
( in(unordered_pair(singleton(sK1(relation_restriction(X0,X1))),unordered_pair(sK1(relation_restriction(X0,X1)),sK2(relation_restriction(X0,X1)))),X0)
| antisymmetric(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[],[f165,f75]) ).
fof(f200,plain,
! [X0,X1] :
( antisymmetric(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1))
| in(unordered_pair(singleton(sK2(relation_restriction(X0,X1))),unordered_pair(sK1(relation_restriction(X0,X1)),sK2(relation_restriction(X0,X1)))),X0)
| ~ relation(X0) ),
inference(resolution,[],[f160,f94]) ).
fof(f202,plain,
! [X0,X1] :
( in(unordered_pair(singleton(sK2(relation_restriction(X0,X1))),unordered_pair(sK1(relation_restriction(X0,X1)),sK2(relation_restriction(X0,X1)))),X0)
| antisymmetric(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[],[f200,f75]) ).
fof(f204,plain,
! [X3,X0,X4] :
( ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X4)),X0)
| X3 = X4
| ~ in(unordered_pair(unordered_pair(X4,X3),singleton(X4)),X0)
| ~ antisymmetric(X0)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f108,f71]) ).
fof(f205,plain,
! [X3,X0,X4] :
( ~ in(unordered_pair(singleton(X4),unordered_pair(X4,X3)),X0)
| ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X4)),X0)
| X3 = X4
| ~ antisymmetric(X0)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f204,f71]) ).
fof(f207,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2)
| X0 = X1
| ~ antisymmetric(X2)
| ~ relation(X2) ),
inference(superposition,[],[f205,f71]) ).
fof(f268,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(sK1(relation_restriction(X0,X1))),unordered_pair(sK1(relation_restriction(X0,X1)),sK2(relation_restriction(X0,X1)))),X0)
| sK1(relation_restriction(X0,X1)) = sK2(relation_restriction(X0,X1))
| ~ antisymmetric(X0)
| ~ relation(X0)
| antisymmetric(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(resolution,[],[f207,f202]) ).
fof(f272,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(sK1(relation_restriction(X0,X1))),unordered_pair(sK1(relation_restriction(X0,X1)),sK2(relation_restriction(X0,X1)))),X0)
| sK1(relation_restriction(X0,X1)) = sK2(relation_restriction(X0,X1))
| ~ antisymmetric(X0)
| ~ relation(X0)
| antisymmetric(relation_restriction(X0,X1)) ),
inference(duplicate_literal_removal,[],[f268]) ).
fof(f274,plain,
! [X0,X1] :
( antisymmetric(relation_restriction(X0,X1))
| ~ antisymmetric(X0)
| ~ relation(X0)
| sK1(relation_restriction(X0,X1)) = sK2(relation_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f272,f167]) ).
fof(f367,plain,
( ~ antisymmetric(sK9)
| ~ relation(sK9)
| sK1(relation_restriction(sK9,sK8)) = sK2(relation_restriction(sK9,sK8)) ),
inference(resolution,[],[f274,f99]) ).
fof(f369,plain,
( ~ relation(sK9)
| sK1(relation_restriction(sK9,sK8)) = sK2(relation_restriction(sK9,sK8)) ),
inference(forward_subsumption_resolution,[],[f367,f98]) ).
fof(f370,plain,
sK1(relation_restriction(sK9,sK8)) = sK2(relation_restriction(sK9,sK8)),
inference(forward_subsumption_resolution,[],[f369,f97]) ).
fof(f375,plain,
( sK1(relation_restriction(sK9,sK8)) != sK1(relation_restriction(sK9,sK8))
| antisymmetric(relation_restriction(sK9,sK8))
| ~ relation(relation_restriction(sK9,sK8)) ),
inference(superposition,[],[f83,f370]) ).
fof(f382,plain,
( antisymmetric(relation_restriction(sK9,sK8))
| ~ relation(relation_restriction(sK9,sK8)) ),
inference(trivial_inequality_removal,[],[f375]) ).
fof(f389,plain,
~ relation(relation_restriction(sK9,sK8)),
inference(forward_subsumption_resolution,[],[f382,f99]) ).
fof(f395,definition,
( spl10_8
<=> relation(relation_restriction(sK9,sK8)) ),
introduced(definition,[new_symbols(definition,[spl10_8])],[avatar_definition]) ).
fof(f397,plain,
( ~ relation(relation_restriction(sK9,sK8))
| spl10_8 ),
inference(avatar_component_clause,[],[f395]) ).
fof(f416,plain,
~ spl10_8,
inference(avatar_split_clause,[],[f389,f395]) ).
fof(f434,plain,
( ~ relation(sK9)
| spl10_8 ),
inference(resolution,[],[f397,f75]) ).
fof(f435,plain,
( $false
| spl10_8 ),
inference(forward_subsumption_resolution,[],[f434,f97]) ).
fof(f436,plain,
spl10_8,
inference(avatar_contradiction_clause,[],[f435]) ).
cnf(s12,plain,
~ spl10_8,
inference(sat_conversion,[],[f416]) ).
cnf(s13,plain,
spl10_8,
inference(sat_conversion,[],[f436]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s12,s13]) ).
fof(f437,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU255+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 04:22:12 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.46 % (1184602)Will run a generic schedule for satisfiability detection.
% 0.11/0.46 % (1184613)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2811416979:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.46 % (1184607)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=446039561_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.46 % (1184610)dis+10_1_sil=32000:sp=arity:random_seed=691253559:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.46 % (1184609)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2861798564:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.46 % (1184611)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3173787376:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.46 % (1184612)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3087340402:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.46 % TRYING [1]
% 0.11/0.46 % TRYING [2]
% 0.11/0.46 % TRYING [3]
% 0.11/0.46 % (1184608)% WARNING: option uhcvi not known.
% 0.11/0.46 % (1184608)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2008008135:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.46 % (1184610) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1184602-1184610"...
% 0.11/0.46 % (1184610)...printing done.
% 0.11/0.46 % (1184610)Refutation found. Thanks to Tanya!
% 0.11/0.46 % SZS status Theorem for theBenchmark
% 0.11/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.46 % (1184610)------------------------------
% 0.11/0.46 % (1184610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.46 % (1184610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.46 % (1184610)CaDiCaL version: 2.1.3
% 0.11/0.46 % (1184610)Termination reason: Refutation
% 0.11/0.46 % (1184610)Time elapsed: 0.012 s
% 0.11/0.46 % (1184610)Peak memory usage: 12 MB
% 0.11/0.46 % (1184610)Instructions burned: 17 (million)
% 0.11/0.46 % (1184602)Success in time 0.051 s
% 0.11/0.46 % Vampire exiting
%------------------------------------------------------------------------------