%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU212+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 12:52:24 PM UTC 2026
% Result : Theorem 0.08s 0.45s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 76 ( 11 unt; 3 def)
% Number of atoms : 280 ( 54 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 338 ( 134 ~; 143 |; 38 &)
% ( 15 <=>; 6 =>; 0 <=; 2 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 103 ( 0 sgn 83 !; 20 ?)
% 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(f5,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1,X2] :
( ( in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) )
& ( ~ in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> X2 = empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f7,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(f35,conjecture,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(ordered_pair(X0,X1),X2)
<=> ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_1) ).
fof(f36,negated_conjecture,
~ ! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(ordered_pair(X0,X1),X2)
<=> ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f44,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) )
& ( ( X2 = apply(X0,X1)
<=> X2 = empty_set )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f45,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) )
& ( ( X2 = apply(X0,X1)
<=> X2 = empty_set )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f61,plain,
? [X0,X1,X2] :
( ( in(ordered_pair(X0,X1),X2)
<~> ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) ) )
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f36]) ).
fof(f62,plain,
? [X0,X1,X2] :
( ( in(ordered_pair(X0,X1),X2)
<~> ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) ) )
& relation(X2)
& function(X2) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0] :
( ! [X1,X2] :
( ( ( ( X2 = apply(X0,X1)
| ~ in(ordered_pair(X1,X2),X0) )
& ( in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2 ) )
| ~ in(X1,relation_dom(X0)) )
& ( ( ( X2 = apply(X0,X1)
| empty_set != X2 )
& ( X2 = empty_set
| apply(X0,X1) != X2 ) )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f45]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f46]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f64]) ).
fof(f66,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ( ( ! [X3] : ~ in(ordered_pair(sK0(X0,X1),X3),X0)
| ~ in(sK0(X0,X1),X1) )
& ( in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK2(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X2,sK0(X0,X1)),skolemize(X4,sK1(X0,X1)),skolemize(X7,sK2(X0,X5))],[f65]) ).
fof(f76,plain,
? [X0,X1,X2] :
( ( ~ in(X0,relation_dom(X2))
| apply(X2,X0) != X1
| ~ in(ordered_pair(X0,X1),X2) )
& ( ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) )
| in(ordered_pair(X0,X1),X2) )
& relation(X2)
& function(X2) ),
inference(nnf_transformation,[],[f62]) ).
fof(f77,plain,
? [X0,X1,X2] :
( ( ~ in(X0,relation_dom(X2))
| apply(X2,X0) != X1
| ~ in(ordered_pair(X0,X1),X2) )
& ( ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) )
| in(ordered_pair(X0,X1),X2) )
& relation(X2)
& function(X2) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
( ( ~ in(sK12,relation_dom(sK14))
| sK13 != apply(sK14,sK12)
| ~ in(ordered_pair(sK12,sK13),sK14) )
& ( ( in(sK12,relation_dom(sK14))
& sK13 = apply(sK14,sK12) )
| in(ordered_pair(sK12,sK13),sK14) )
& relation(sK14)
& function(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14]),skolemize(X0,sK12),skolemize(X1,sK13),skolemize(X2,sK14)],[f77]) ).
fof(f82,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f85,plain,
! [X2,X0,X1] :
( in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f86,plain,
! [X2,X0,X1] :
( apply(X0,X1) = X2
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f88,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f91,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f127,plain,
function(sK14),
inference(cnf_transformation,[],[f78]) ).
fof(f128,plain,
relation(sK14),
inference(cnf_transformation,[],[f78]) ).
fof(f129,plain,
( sK13 = apply(sK14,sK12)
| in(ordered_pair(sK12,sK13),sK14) ),
inference(cnf_transformation,[],[f78]) ).
fof(f130,plain,
( in(sK12,relation_dom(sK14))
| in(ordered_pair(sK12,sK13),sK14) ),
inference(cnf_transformation,[],[f78]) ).
fof(f131,plain,
( ~ in(sK12,relation_dom(sK14))
| sK13 != apply(sK14,sK12)
| ~ in(ordered_pair(sK12,sK13),sK14) ),
inference(cnf_transformation,[],[f78]) ).
fof(f132,plain,
! [X2,X0,X1] :
( apply(X0,X1) = X2
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(definition_unfolding,[],[f86,f91]) ).
fof(f133,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
| apply(X0,X1) != X2
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(definition_unfolding,[],[f85,f91]) ).
fof(f136,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f88,f91]) ).
fof(f139,plain,
( ~ in(sK12,relation_dom(sK14))
| sK13 != apply(sK14,sK12)
| ~ in(unordered_pair(unordered_pair(sK12,sK13),singleton(sK12)),sK14) ),
inference(definition_unfolding,[],[f131,f91]) ).
fof(f140,plain,
( in(sK12,relation_dom(sK14))
| in(unordered_pair(unordered_pair(sK12,sK13),singleton(sK12)),sK14) ),
inference(definition_unfolding,[],[f130,f91]) ).
fof(f141,plain,
( sK13 = apply(sK14,sK12)
| in(unordered_pair(unordered_pair(sK12,sK13),singleton(sK12)),sK14) ),
inference(definition_unfolding,[],[f129,f91]) ).
fof(f142,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X1,apply(X0,X1)),singleton(X1)),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f133]) ).
fof(f145,plain,
! [X0,X6,X5] :
( in(X5,relation_dom(X0))
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f136]) ).
fof(f148,definition,
( spl15_1
<=> in(unordered_pair(unordered_pair(sK12,sK13),singleton(sK12)),sK14) ),
introduced(definition,[new_symbols(definition,[spl15_1])],[avatar_definition]) ).
fof(f149,plain,
( ~ in(unordered_pair(unordered_pair(sK12,sK13),singleton(sK12)),sK14)
| spl15_1 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f150,plain,
( in(unordered_pair(unordered_pair(sK12,sK13),singleton(sK12)),sK14)
| ~ spl15_1 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f152,definition,
( spl15_2
<=> sK13 = apply(sK14,sK12) ),
introduced(definition,[new_symbols(definition,[spl15_2])],[avatar_definition]) ).
fof(f154,plain,
( sK13 = apply(sK14,sK12)
| ~ spl15_2 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f155,plain,
( spl15_1
| spl15_2 ),
inference(avatar_split_clause,[],[f141,f152,f148]) ).
fof(f157,definition,
( spl15_3
<=> in(sK12,relation_dom(sK14)) ),
introduced(definition,[new_symbols(definition,[spl15_3])],[avatar_definition]) ).
fof(f159,plain,
( in(sK12,relation_dom(sK14))
| ~ spl15_3 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f160,plain,
( spl15_1
| spl15_3 ),
inference(avatar_split_clause,[],[f140,f157,f148]) ).
fof(f161,plain,
( ~ spl15_1
| ~ spl15_2
| ~ spl15_3 ),
inference(avatar_split_clause,[],[f139,f157,f152,f148]) ).
fof(f184,plain,
( ~ in(unordered_pair(singleton(sK12),unordered_pair(sK12,sK13)),sK14)
| spl15_1 ),
inference(superposition,[],[f149,f82]) ).
fof(f249,plain,
! [X0,X6,X5] :
( ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),X0)
| in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(forward_demodulation,[],[f145,f82]) ).
fof(f279,plain,
! [X0,X1] :
( in(unordered_pair(singleton(X1),unordered_pair(X1,apply(X0,X1))),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_demodulation,[],[f142,f82]) ).
fof(f285,plain,
( in(unordered_pair(singleton(sK12),unordered_pair(sK12,sK13)),sK14)
| ~ in(sK12,relation_dom(sK14))
| ~ relation(sK14)
| ~ function(sK14)
| ~ spl15_2 ),
inference(superposition,[],[f279,f154]) ).
fof(f287,plain,
( ~ in(sK12,relation_dom(sK14))
| ~ relation(sK14)
| ~ function(sK14)
| spl15_1
| ~ spl15_2 ),
inference(forward_subsumption_resolution,[],[f285,f184]) ).
fof(f290,plain,
( ~ relation(sK14)
| ~ function(sK14)
| spl15_1
| ~ spl15_2
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f287,f159]) ).
fof(f293,plain,
( ~ function(sK14)
| spl15_1
| ~ spl15_2
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f290,f128]) ).
fof(f295,plain,
( $false
| spl15_1
| ~ spl15_2
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f293,f127]) ).
fof(f296,plain,
( spl15_1
| ~ spl15_2
| ~ spl15_3 ),
inference(avatar_contradiction_clause,[],[f295]) ).
fof(f297,plain,
( in(unordered_pair(singleton(sK12),unordered_pair(sK12,sK13)),sK14)
| ~ spl15_1 ),
inference(forward_demodulation,[],[f150,f82]) ).
fof(f298,plain,
( in(sK12,relation_dom(sK14))
| ~ relation(sK14)
| ~ spl15_1 ),
inference(resolution,[],[f297,f249]) ).
fof(f303,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X0)
| apply(X0,X1) = X2
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_demodulation,[],[f132,f82]) ).
fof(f304,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X0)
| apply(X0,X1) = X2
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f303,f249]) ).
fof(f307,plain,
( sK13 = apply(sK14,sK12)
| ~ relation(sK14)
| ~ function(sK14)
| ~ spl15_1 ),
inference(resolution,[],[f304,f297]) ).
fof(f317,plain,
( in(sK12,relation_dom(sK14))
| ~ spl15_1 ),
inference(forward_subsumption_resolution,[],[f298,f128]) ).
fof(f318,plain,
( sK13 = apply(sK14,sK12)
| ~ function(sK14)
| ~ spl15_1 ),
inference(forward_subsumption_resolution,[],[f307,f128]) ).
fof(f319,plain,
( spl15_3
| ~ spl15_1 ),
inference(avatar_split_clause,[],[f317,f148,f157]) ).
fof(f320,plain,
( sK13 = apply(sK14,sK12)
| ~ spl15_1 ),
inference(forward_subsumption_resolution,[],[f318,f127]) ).
fof(f321,plain,
( spl15_2
| ~ spl15_1 ),
inference(avatar_split_clause,[],[f320,f148,f152]) ).
cnf(s1,plain,
( spl15_1
| spl15_2 ),
inference(sat_conversion,[],[f155]) ).
cnf(s2,plain,
( spl15_1
| spl15_3 ),
inference(sat_conversion,[],[f160]) ).
cnf(s3,plain,
( ~ spl15_1
| ~ spl15_2
| ~ spl15_3 ),
inference(sat_conversion,[],[f161]) ).
cnf(s10,plain,
( spl15_1
| ~ spl15_2
| ~ spl15_3 ),
inference(sat_conversion,[],[f296]) ).
cnf(s12,plain,
( ~ spl15_1
| spl15_3 ),
inference(sat_conversion,[],[f319]) ).
cnf(s13,plain,
( ~ spl15_1
| spl15_2 ),
inference(sat_conversion,[],[f321]) ).
cnf(s15,plain,
spl15_1,
inference(rat,[],[s10,s1,s2]) ).
cnf(s16,plain,
spl15_2,
inference(rat,[],[s13,s15]) ).
cnf(s17,plain,
spl15_3,
inference(rat,[],[s12,s15]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s3,s16,s17,s15]) ).
fof(f322,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU212+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.37 % Computer : n026.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Mon Sep 28 04:07:12 UTC 2026
% 0.08/0.38 % CPUTime :
% 0.08/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.40 Running first-order model finding
% 0.08/0.40 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
% 0.08/0.45 % (3448723)Will run a generic schedule for satisfiability detection.
% 0.08/0.45 % (3448731)dis+10_1_sil=32000:sp=arity:random_seed=733622289:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.45 % (3448729)% WARNING: option uhcvi not known.
% 0.08/0.45 % (3448731) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3448723-3448731"...
% 0.08/0.45 % (3448731)...printing done.
% 0.08/0.45 % (3448731)Refutation found. Thanks to Tanya!
% 0.08/0.45 % SZS status Theorem for theBenchmark
% 0.08/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.45 % (3448731)------------------------------
% 0.08/0.45 % (3448731)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.45 % (3448731)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.45 % (3448731)CaDiCaL version: 2.1.3
% 0.08/0.45 % (3448731)Termination reason: Refutation
% 0.08/0.45 % (3448731)Time elapsed: 0.004 s
% 0.08/0.45 % (3448731)Peak memory usage: 12 MB
% 0.08/0.45 % (3448731)Instructions burned: 9 (million)
% 0.08/0.45 % (3448723)Success in time 0.034 s
% 0.08/0.45 % Vampire exiting
%------------------------------------------------------------------------------