%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU243+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 : 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 12:52:34 PM UTC 2026
% Result : Theorem 0.12s 5.48s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 56 ( 5 unt; 2 def)
% Number of atoms : 184 ( 16 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 223 ( 95 ~; 106 |; 9 &)
% ( 8 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 51 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( relation(X0)
=> ( well_founded_relation(X0)
<=> ! [X1] :
~ ( subset(X1,relation_field(X0))
& X1 != empty_set
& ! [X2] :
~ ( in(X2,X1)
& disjoint(fiber(X0,X2),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_wellord1) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_well_founded_in(X0,X1)
<=> ! [X2] :
~ ( subset(X2,X1)
& X2 != empty_set
& ! [X3] :
~ ( in(X3,X2)
& disjoint(fiber(X0,X3),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_wellord1) ).
fof(f34,conjecture,
! [X0] :
( relation(X0)
=> ( well_founded_relation(X0)
<=> is_well_founded_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_wellord1) ).
fof(f35,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( well_founded_relation(X0)
<=> is_well_founded_in(X0,relation_field(X0)) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
fof(f47,plain,
! [X0] :
( ( well_founded_relation(X0)
<=> ! [X1] :
( ~ subset(X1,relation_field(X0))
| empty_set = X1
| ? [X2] :
( in(X2,X1)
& disjoint(fiber(X0,X2),X1) ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f48,plain,
! [X0] :
( ! [X1] :
( is_well_founded_in(X0,X1)
<=> ! [X2] :
( ~ subset(X2,X1)
| empty_set = X2
| ? [X3] :
( in(X3,X2)
& disjoint(fiber(X0,X3),X2) ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f59,plain,
? [X0] :
( ( well_founded_relation(X0)
<~> is_well_founded_in(X0,relation_field(X0)) )
& relation(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f66,plain,
! [X2,X0] :
( ~ disjoint(fiber(X0,X2),sK0(X0))
| ~ relation(X0)
| ~ in(X2,sK0(X0))
| well_founded_relation(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f67,plain,
! [X0,X1] :
( disjoint(fiber(X0,sK1(X0,X1)),X1)
| ~ relation(X0)
| empty_set = X1
| ~ subset(X1,relation_field(X0))
| ~ well_founded_relation(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f68,plain,
! [X0,X1] :
( ~ well_founded_relation(X0)
| in(sK1(X0,X1),X1)
| empty_set = X1
| ~ subset(X1,relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f69,plain,
! [X0] :
( well_founded_relation(X0)
| empty_set != sK0(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f70,plain,
! [X0] :
( well_founded_relation(X0)
| subset(sK0(X0),relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f71,plain,
! [X3,X0,X1] :
( ~ disjoint(fiber(X0,X3),sK2(X0,X1))
| ~ relation(X0)
| ~ in(X3,sK2(X0,X1))
| is_well_founded_in(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f72,plain,
! [X2,X0,X1] :
( disjoint(fiber(X0,sK3(X0,X2)),X2)
| ~ relation(X0)
| empty_set = X2
| ~ subset(X2,X1)
| ~ is_well_founded_in(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f73,plain,
! [X2,X0,X1] :
( ~ is_well_founded_in(X0,X1)
| in(sK3(X0,X2),X2)
| empty_set = X2
| ~ subset(X2,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f74,plain,
! [X0,X1] :
( is_well_founded_in(X0,X1)
| empty_set != sK2(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f75,plain,
! [X0,X1] :
( is_well_founded_in(X0,X1)
| subset(sK2(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f100,plain,
( is_well_founded_in(sK10,relation_field(sK10))
| well_founded_relation(sK10) ),
inference(cnf_transformation,[],[f59]) ).
fof(f101,plain,
( ~ is_well_founded_in(sK10,relation_field(sK10))
| ~ well_founded_relation(sK10) ),
inference(cnf_transformation,[],[f59]) ).
fof(f102,plain,
relation(sK10),
inference(cnf_transformation,[],[f59]) ).
fof(f107,definition,
( spl11_1
<=> well_founded_relation(sK10) ),
introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition]) ).
fof(f108,plain,
( ~ well_founded_relation(sK10)
| spl11_1 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f109,plain,
( well_founded_relation(sK10)
| ~ spl11_1 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f111,definition,
( spl11_2
<=> is_well_founded_in(sK10,relation_field(sK10)) ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
fof(f112,plain,
( ~ is_well_founded_in(sK10,relation_field(sK10))
| spl11_2 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f113,plain,
( is_well_founded_in(sK10,relation_field(sK10))
| ~ spl11_2 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f114,plain,
( spl11_1
| spl11_2 ),
inference(avatar_split_clause,[],[f100,f111,f107]) ).
fof(f115,plain,
( ~ spl11_1
| ~ spl11_2 ),
inference(avatar_split_clause,[],[f101,f111,f107]) ).
fof(f271,plain,
! [X0,X1] :
( ~ relation(X0)
| empty_set = sK2(X0,X1)
| ~ subset(sK2(X0,X1),relation_field(X0))
| ~ well_founded_relation(X0)
| ~ relation(X0)
| ~ in(sK1(X0,sK2(X0,X1)),sK2(X0,X1))
| is_well_founded_in(X0,X1) ),
inference(resolution,[],[f67,f71]) ).
fof(f273,plain,
! [X0,X1] :
( ~ relation(X0)
| empty_set = sK2(X0,X1)
| ~ subset(sK2(X0,X1),relation_field(X0))
| ~ well_founded_relation(X0)
| ~ in(sK1(X0,sK2(X0,X1)),sK2(X0,X1))
| is_well_founded_in(X0,X1) ),
inference(duplicate_literal_removal,[],[f271]) ).
fof(f275,plain,
! [X0,X1] :
( ~ relation(X0)
| empty_set = sK2(X0,X1)
| ~ subset(sK2(X0,X1),relation_field(X0))
| ~ well_founded_relation(X0)
| is_well_founded_in(X0,X1) ),
inference(forward_subsumption_resolution,[],[f273,f68]) ).
fof(f276,plain,
! [X0,X1] :
( is_well_founded_in(X0,X1)
| ~ subset(sK2(X0,X1),relation_field(X0))
| ~ well_founded_relation(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[],[f275,f74]) ).
fof(f277,plain,
! [X0,X1] :
( ~ relation(X0)
| empty_set = sK0(X0)
| ~ subset(sK0(X0),X1)
| ~ is_well_founded_in(X0,X1)
| ~ relation(X0)
| ~ in(sK3(X0,sK0(X0)),sK0(X0))
| well_founded_relation(X0) ),
inference(resolution,[],[f72,f66]) ).
fof(f281,plain,
! [X0,X1] :
( ~ relation(X0)
| empty_set = sK0(X0)
| ~ subset(sK0(X0),X1)
| ~ is_well_founded_in(X0,X1)
| ~ in(sK3(X0,sK0(X0)),sK0(X0))
| well_founded_relation(X0) ),
inference(duplicate_literal_removal,[],[f277]) ).
fof(f283,plain,
! [X0,X1] :
( ~ relation(X0)
| empty_set = sK0(X0)
| ~ subset(sK0(X0),X1)
| ~ is_well_founded_in(X0,X1)
| well_founded_relation(X0) ),
inference(forward_subsumption_resolution,[],[f281,f73]) ).
fof(f285,plain,
! [X0,X1] :
( ~ is_well_founded_in(X0,X1)
| ~ subset(sK0(X0),X1)
| ~ relation(X0)
| well_founded_relation(X0) ),
inference(forward_subsumption_resolution,[],[f283,f69]) ).
fof(f457,plain,
( ~ subset(sK0(sK10),relation_field(sK10))
| ~ relation(sK10)
| well_founded_relation(sK10)
| ~ spl11_2 ),
inference(resolution,[],[f285,f113]) ).
fof(f460,plain,
( ~ relation(sK10)
| well_founded_relation(sK10)
| ~ spl11_2 ),
inference(forward_subsumption_resolution,[],[f457,f70]) ).
fof(f461,plain,
( well_founded_relation(sK10)
| ~ spl11_2 ),
inference(forward_subsumption_resolution,[],[f460,f102]) ).
fof(f462,plain,
( $false
| spl11_1
| ~ spl11_2 ),
inference(forward_subsumption_resolution,[],[f461,f108]) ).
fof(f463,plain,
( spl11_1
| ~ spl11_2 ),
inference(avatar_contradiction_clause,[],[f462]) ).
fof(f466,plain,
( subset(sK2(sK10,relation_field(sK10)),relation_field(sK10))
| ~ relation(sK10)
| spl11_2 ),
inference(resolution,[],[f112,f75]) ).
fof(f469,plain,
( subset(sK2(sK10,relation_field(sK10)),relation_field(sK10))
| spl11_2 ),
inference(forward_subsumption_resolution,[],[f466,f102]) ).
fof(f517,plain,
( ~ subset(sK2(sK10,relation_field(sK10)),relation_field(sK10))
| ~ well_founded_relation(sK10)
| ~ relation(sK10)
| spl11_2 ),
inference(resolution,[],[f276,f112]) ).
fof(f520,plain,
( ~ well_founded_relation(sK10)
| ~ relation(sK10)
| spl11_2 ),
inference(forward_subsumption_resolution,[],[f517,f469]) ).
fof(f521,plain,
( ~ relation(sK10)
| ~ spl11_1
| spl11_2 ),
inference(forward_subsumption_resolution,[],[f520,f109]) ).
fof(f522,plain,
( $false
| ~ spl11_1
| spl11_2 ),
inference(forward_subsumption_resolution,[],[f521,f102]) ).
fof(f523,plain,
( ~ spl11_1
| spl11_2 ),
inference(avatar_contradiction_clause,[],[f522]) ).
cnf(s1,plain,
( spl11_1
| spl11_2 ),
inference(sat_conversion,[],[f114]) ).
cnf(s2,plain,
( ~ spl11_1
| ~ spl11_2 ),
inference(sat_conversion,[],[f115]) ).
cnf(s21,plain,
( spl11_1
| ~ spl11_2 ),
inference(sat_conversion,[],[f463]) ).
cnf(s22,plain,
( ~ spl11_1
| spl11_2 ),
inference(sat_conversion,[],[f523]) ).
cnf(s23,plain,
spl11_1,
inference(rat,[],[s1,s21]) ).
cnf(s24,plain,
spl11_2,
inference(rat,[],[s22,s23]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s2,s24,s23]) ).
fof(f524,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU243+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/5.40 % Computer : n026.cluster.edu
% 0.12/5.40 % Model : x86_64 x86_64
% 0.12/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.40 % Memory : 8046.5625MB
% 0.12/5.40 % OS : Linux 6.8.0-71-generic
% 0.12/5.40 % CPULimit : 300
% 0.12/5.40 % WCLimit : 300
% 0.12/5.40 % DateTime : Mon Sep 28 04:19:33 UTC 2026
% 0.12/5.40 % CPUTime :
% 0.12/5.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/5.44 Running first-order model finding
% 0.12/5.44 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
% 0.12/5.48 % (3454758)Will run a generic schedule for satisfiability detection.
% 0.12/5.48 % (3454767)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3480534822:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/5.48 % (3454764)% WARNING: option uhcvi not known.
% 0.12/5.48 % (3454765)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2261587323:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/5.48 % (3454763)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3758521333_2999 on theBenchmark for (2999ds/0Mi)
% 0.12/5.48 % (3454767) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3454758-3454767"...
% 0.12/5.48 % (3454764)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=496870969:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/5.48 % (3454769)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3193109480:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/5.48 % (3454766)dis+10_1_sil=32000:sp=arity:random_seed=1856396739:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/5.48 % (3454768)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=112194180:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/5.48 % (3454767)...printing done.
% 0.12/5.48 % (3454767)Refutation found. Thanks to Tanya!
% 0.12/5.48 % SZS status Theorem for theBenchmark
% 0.12/5.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/5.48 % (3454767)------------------------------
% 0.12/5.48 % (3454767)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/5.48 % (3454767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/5.48 % (3454767)CaDiCaL version: 2.1.3
% 0.12/5.48 % (3454767)Termination reason: Refutation
% 0.12/5.48 % (3454767)Time elapsed: 0.007 s
% 0.12/5.48 % (3454767)Peak memory usage: 12 MB
% 0.12/5.48 % (3454767)Instructions burned: 15 (million)
% 0.12/5.48 % (3454758)Success in time 0.037 s
% 0.12/5.48 % Vampire exiting
%------------------------------------------------------------------------------