%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU098+1 : 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 : n001.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 12:51:55 PM UTC 2026
% Result : Theorem 0.15s 0.50s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 85 ( 17 unt; 2 def)
% Number of atoms : 226 ( 16 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 238 ( 97 ~; 97 |; 27 &)
% ( 5 <=>; 10 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 3 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-4 aty)
% Number of variables : 97 ( 0 sgn 93 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0,X1] :
( relation(first_projection(X0,X1))
& function(first_projection(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_funct_3) ).
fof(f16,axiom,
! [X0,X1] :
( function(first_projection_as_func_of(X0,X1))
& quasi_total(first_projection_as_func_of(X0,X1),cartesian_product2(X0,X1),X0)
& relation_of2_as_subset(first_projection_as_func_of(X0,X1),cartesian_product2(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_funct_3) ).
fof(f22,axiom,
! [X0,X1] :
( ( relation(X0)
& function(X0)
& finite(X1) )
=> finite(relation_image(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc13_finset_1) ).
fof(f23,axiom,
! [X0,X1] :
( ( finite(X0)
& finite(X1) )
=> finite(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc14_finset_1) ).
fof(f62,axiom,
! [X0,X1,X2,X3] :
( ( function(X2)
& quasi_total(X2,X0,X1)
& relation_of2(X2,X0,X1) )
=> function_image(X0,X1,X2,X3) = relation_image(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).
fof(f63,axiom,
! [X0,X1] : first_projection_as_func_of(X0,X1) = first_projection(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_funct_3) ).
fof(f64,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f66,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> function_image(cartesian_product2(relation_dom(X0),relation_rng(X0)),relation_dom(X0),first_projection_as_func_of(relation_dom(X0),relation_rng(X0)),X0) = relation_dom(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_funct_3) ).
fof(f67,axiom,
! [X0,X1] :
( ( subset(X0,X1)
& finite(X1) )
=> finite(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finset_1) ).
fof(f71,axiom,
! [X0] :
( relation(X0)
=> subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relat_1) ).
fof(f72,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( finite(relation_dom(X0))
=> finite(relation_rng(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finset_1) ).
fof(f73,conjecture,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( finite(relation_dom(X0))
<=> finite(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_finset_1) ).
fof(f74,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ( finite(relation_dom(X0))
<=> finite(X0) ) ),
inference(negated_conjecture,[status(cth)],[f73]) ).
fof(f122,plain,
! [X0,X1] :
( finite(relation_image(X0,X1))
| ~ relation(X0)
| ~ function(X0)
| ~ finite(X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f123,plain,
! [X0,X1] :
( finite(relation_image(X0,X1))
| ~ relation(X0)
| ~ function(X0)
| ~ finite(X1) ),
inference(flattening,[],[f122]) ).
fof(f124,plain,
! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X0)
| ~ finite(X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f125,plain,
! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X0)
| ~ finite(X1) ),
inference(flattening,[],[f124]) ).
fof(f139,plain,
! [X0,X1,X2,X3] :
( function_image(X0,X1,X2,X3) = relation_image(X2,X3)
| ~ function(X2)
| ~ quasi_total(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f62]) ).
fof(f140,plain,
! [X0,X1,X2,X3] :
( function_image(X0,X1,X2,X3) = relation_image(X2,X3)
| ~ function(X2)
| ~ quasi_total(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ),
inference(flattening,[],[f139]) ).
fof(f141,plain,
! [X0] :
( function_image(cartesian_product2(relation_dom(X0),relation_rng(X0)),relation_dom(X0),first_projection_as_func_of(relation_dom(X0),relation_rng(X0)),X0) = relation_dom(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f66]) ).
fof(f142,plain,
! [X0] :
( function_image(cartesian_product2(relation_dom(X0),relation_rng(X0)),relation_dom(X0),first_projection_as_func_of(relation_dom(X0),relation_rng(X0)),X0) = relation_dom(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f141]) ).
fof(f143,plain,
! [X0,X1] :
( finite(X0)
| ~ subset(X0,X1)
| ~ finite(X1) ),
inference(ennf_transformation,[],[f67]) ).
fof(f144,plain,
! [X0,X1] :
( finite(X0)
| ~ subset(X0,X1)
| ~ finite(X1) ),
inference(flattening,[],[f143]) ).
fof(f150,plain,
! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f71]) ).
fof(f151,plain,
! [X0] :
( finite(relation_rng(X0))
| ~ finite(relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f72]) ).
fof(f152,plain,
! [X0] :
( finite(relation_rng(X0))
| ~ finite(relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f151]) ).
fof(f153,plain,
? [X0] :
( ( finite(relation_dom(X0))
<~> finite(X0) )
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f74]) ).
fof(f154,plain,
? [X0] :
( ( finite(relation_dom(X0))
<~> finite(X0) )
& relation(X0)
& function(X0) ),
inference(flattening,[],[f153]) ).
fof(f192,plain,
! [X0,X1,X2] :
( ( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) )
& ( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f64]) ).
fof(f193,plain,
? [X0] :
( ( ~ finite(X0)
| ~ finite(relation_dom(X0)) )
& ( finite(X0)
| finite(relation_dom(X0)) )
& relation(X0)
& function(X0) ),
inference(nnf_transformation,[],[f154]) ).
fof(f194,plain,
? [X0] :
( ( ~ finite(X0)
| ~ finite(relation_dom(X0)) )
& ( finite(X0)
| finite(relation_dom(X0)) )
& relation(X0)
& function(X0) ),
inference(flattening,[],[f193]) ).
fof(f195,plain,
( ( ~ finite(sK29)
| ~ finite(relation_dom(sK29)) )
& ( finite(sK29)
| finite(relation_dom(sK29)) )
& relation(sK29)
& function(sK29) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(X0,sK29)],[f194]) ).
fof(f222,plain,
! [X0,X1] : relation(first_projection(X0,X1)),
inference(cnf_transformation,[],[f15]) ).
fof(f223,plain,
! [X0,X1] : relation_of2_as_subset(first_projection_as_func_of(X0,X1),cartesian_product2(X0,X1),X0),
inference(cnf_transformation,[],[f16]) ).
fof(f224,plain,
! [X0,X1] : quasi_total(first_projection_as_func_of(X0,X1),cartesian_product2(X0,X1),X0),
inference(cnf_transformation,[],[f16]) ).
fof(f225,plain,
! [X0,X1] : function(first_projection_as_func_of(X0,X1)),
inference(cnf_transformation,[],[f16]) ).
fof(f232,plain,
! [X0,X1] :
( finite(relation_image(X0,X1))
| ~ relation(X0)
| ~ function(X0)
| ~ finite(X1) ),
inference(cnf_transformation,[],[f123]) ).
fof(f233,plain,
! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X0)
| ~ finite(X1) ),
inference(cnf_transformation,[],[f125]) ).
fof(f331,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| ~ function(X2)
| ~ quasi_total(X2,X0,X1)
| function_image(X0,X1,X2,X3) = relation_image(X2,X3) ),
inference(cnf_transformation,[],[f140]) ).
fof(f332,plain,
! [X0,X1] : first_projection(X0,X1) = first_projection_as_func_of(X0,X1),
inference(cnf_transformation,[],[f63]) ).
fof(f333,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f192]) ).
fof(f336,plain,
! [X0] :
( ~ relation(X0)
| relation_dom(X0) = function_image(cartesian_product2(relation_dom(X0),relation_rng(X0)),relation_dom(X0),first_projection_as_func_of(relation_dom(X0),relation_rng(X0)),X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f337,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| finite(X0)
| ~ finite(X1) ),
inference(cnf_transformation,[],[f144]) ).
fof(f341,plain,
! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f150]) ).
fof(f342,plain,
! [X0] :
( ~ finite(relation_dom(X0))
| finite(relation_rng(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f152]) ).
fof(f343,plain,
function(sK29),
inference(cnf_transformation,[],[f195]) ).
fof(f344,plain,
relation(sK29),
inference(cnf_transformation,[],[f195]) ).
fof(f345,plain,
( finite(sK29)
| finite(relation_dom(sK29)) ),
inference(cnf_transformation,[],[f195]) ).
fof(f346,plain,
( ~ finite(sK29)
| ~ finite(relation_dom(sK29)) ),
inference(cnf_transformation,[],[f195]) ).
fof(f355,plain,
! [X0,X1] : relation(first_projection_as_func_of(X0,X1)),
inference(definition_unfolding,[],[f222,f332]) ).
fof(f358,definition,
( spl30_1
<=> finite(relation_dom(sK29)) ),
introduced(definition,[new_symbols(definition,[spl30_1])],[avatar_definition]) ).
fof(f360,plain,
( finite(relation_dom(sK29))
| ~ spl30_1 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f362,definition,
( spl30_2
<=> finite(sK29) ),
introduced(definition,[new_symbols(definition,[spl30_2])],[avatar_definition]) ).
fof(f363,plain,
( ~ finite(sK29)
| spl30_2 ),
inference(avatar_component_clause,[],[f362]) ).
fof(f365,plain,
( spl30_1
| spl30_2 ),
inference(avatar_split_clause,[],[f345,f362,f358]) ).
fof(f366,plain,
( ~ spl30_1
| ~ spl30_2 ),
inference(avatar_split_clause,[],[f346,f362,f358]) ).
fof(f614,plain,
! [X0,X1] : relation_of2(first_projection_as_func_of(X0,X1),cartesian_product2(X0,X1),X0),
inference(resolution,[],[f333,f223]) ).
fof(f651,plain,
! [X0] :
( ~ finite(cartesian_product2(relation_dom(X0),relation_rng(X0)))
| finite(X0)
| ~ relation(X0) ),
inference(resolution,[],[f341,f337]) ).
fof(f748,plain,
( relation_dom(sK29) = function_image(cartesian_product2(relation_dom(sK29),relation_rng(sK29)),relation_dom(sK29),first_projection_as_func_of(relation_dom(sK29),relation_rng(sK29)),sK29)
| ~ function(sK29) ),
inference(resolution,[],[f336,f344]) ).
fof(f749,plain,
relation_dom(sK29) = function_image(cartesian_product2(relation_dom(sK29),relation_rng(sK29)),relation_dom(sK29),first_projection_as_func_of(relation_dom(sK29),relation_rng(sK29)),sK29),
inference(forward_subsumption_resolution,[],[f748,f343]) ).
fof(f990,plain,
! [X2,X0,X1] :
( ~ function(first_projection_as_func_of(X0,X1))
| ~ quasi_total(first_projection_as_func_of(X0,X1),cartesian_product2(X0,X1),X0)
| function_image(cartesian_product2(X0,X1),X0,first_projection_as_func_of(X0,X1),X2) = relation_image(first_projection_as_func_of(X0,X1),X2) ),
inference(resolution,[],[f614,f331]) ).
fof(f993,plain,
! [X2,X0,X1] :
( ~ quasi_total(first_projection_as_func_of(X0,X1),cartesian_product2(X0,X1),X0)
| function_image(cartesian_product2(X0,X1),X0,first_projection_as_func_of(X0,X1),X2) = relation_image(first_projection_as_func_of(X0,X1),X2) ),
inference(forward_subsumption_resolution,[],[f990,f225]) ).
fof(f994,plain,
! [X2,X0,X1] : function_image(cartesian_product2(X0,X1),X0,first_projection_as_func_of(X0,X1),X2) = relation_image(first_projection_as_func_of(X0,X1),X2),
inference(forward_subsumption_resolution,[],[f993,f224]) ).
fof(f1147,plain,
! [X0] :
( ~ finite(relation_rng(X0))
| ~ relation(X0)
| ~ finite(relation_dom(X0))
| finite(X0) ),
inference(resolution,[],[f651,f233]) ).
fof(f2053,plain,
relation_dom(sK29) = relation_image(first_projection_as_func_of(relation_dom(sK29),relation_rng(sK29)),sK29),
inference(superposition,[],[f994,f749]) ).
fof(f2105,plain,
( finite(relation_dom(sK29))
| ~ relation(first_projection_as_func_of(relation_dom(sK29),relation_rng(sK29)))
| ~ function(first_projection_as_func_of(relation_dom(sK29),relation_rng(sK29)))
| ~ finite(sK29) ),
inference(superposition,[],[f232,f2053]) ).
fof(f2111,plain,
( finite(relation_dom(sK29))
| ~ function(first_projection_as_func_of(relation_dom(sK29),relation_rng(sK29)))
| ~ finite(sK29) ),
inference(forward_subsumption_resolution,[],[f2105,f355]) ).
fof(f2112,plain,
( finite(relation_dom(sK29))
| ~ finite(sK29) ),
inference(forward_subsumption_resolution,[],[f2111,f225]) ).
fof(f2113,plain,
( ~ spl30_2
| spl30_1 ),
inference(avatar_split_clause,[],[f2112,f358,f362]) ).
fof(f2114,plain,
( finite(relation_rng(sK29))
| ~ relation(sK29)
| ~ function(sK29)
| ~ spl30_1 ),
inference(resolution,[],[f360,f342]) ).
fof(f2115,plain,
( finite(relation_rng(sK29))
| ~ function(sK29)
| ~ spl30_1 ),
inference(forward_subsumption_resolution,[],[f2114,f344]) ).
fof(f2116,plain,
( finite(relation_rng(sK29))
| ~ spl30_1 ),
inference(forward_subsumption_resolution,[],[f2115,f343]) ).
fof(f2117,plain,
( ~ relation(sK29)
| ~ finite(relation_dom(sK29))
| finite(sK29)
| ~ spl30_1 ),
inference(resolution,[],[f2116,f1147]) ).
fof(f2118,plain,
( ~ finite(relation_dom(sK29))
| finite(sK29)
| ~ spl30_1 ),
inference(forward_subsumption_resolution,[],[f2117,f344]) ).
fof(f2119,plain,
( finite(sK29)
| ~ spl30_1 ),
inference(forward_subsumption_resolution,[],[f2118,f360]) ).
fof(f2120,plain,
( $false
| ~ spl30_1
| spl30_2 ),
inference(forward_subsumption_resolution,[],[f2119,f363]) ).
fof(f2121,plain,
( ~ spl30_1
| spl30_2 ),
inference(avatar_contradiction_clause,[],[f2120]) ).
cnf(s1,plain,
( spl30_1
| spl30_2 ),
inference(sat_conversion,[],[f365]) ).
cnf(s2,plain,
( ~ spl30_1
| ~ spl30_2 ),
inference(sat_conversion,[],[f366]) ).
cnf(s19,plain,
( spl30_1
| ~ spl30_2 ),
inference(sat_conversion,[],[f2113]) ).
cnf(s20,plain,
( ~ spl30_1
| spl30_2 ),
inference(sat_conversion,[],[f2121]) ).
cnf(s23,plain,
spl30_1,
inference(rat,[],[s1,s19]) ).
cnf(s24,plain,
spl30_2,
inference(rat,[],[s20,s23]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s2,s24,s23]) ).
fof(f2122,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU098+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 % Computer : n001.cluster.edu
% 0.10/0.41 % Model : x86_64 x86_64
% 0.10/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.41 % Memory : 8046.5625MB
% 0.10/0.41 % OS : Linux 6.8.0-71-generic
% 0.10/0.41 % CPULimit : 300
% 0.10/0.41 % WCLimit : 300
% 0.10/0.41 % DateTime : Mon Sep 28 03:39:17 UTC 2026
% 0.10/0.41 % CPUTime :
% 0.10/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.44 Running first-order model finding
% 0.10/0.44 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
% 0.15/0.50 % (4183873)Will run a generic schedule for satisfiability detection.
% 0.15/0.50 % (4183881)dis+10_1_sil=32000:sp=arity:random_seed=526257019:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.50 % (4183879)% WARNING: option uhcvi not known.
% 0.15/0.50 % (4183882)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2389657017:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.50 % (4183880)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=685877621:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.50 % (4183878)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2123223109_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.50 % (4183879)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=190220059:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.50 % (4183883)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2656201844:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.50 % (4183884)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=108836427:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.50 % TRYING [1]
% 0.15/0.50 % TRYING [2]
% 0.15/0.50 % TRYING [3]
% 0.15/0.50 % TRYING [4]
% 0.15/0.50 % (4183881) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4183873-4183881"...
% 0.15/0.50 % (4183881)...printing done.
% 0.15/0.50 % (4183881)Refutation found. Thanks to Tanya!
% 0.15/0.50 % SZS status Theorem for theBenchmark
% 0.15/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.50 % (4183881)------------------------------
% 0.15/0.50 % (4183881)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.50 % (4183881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.50 % (4183881)CaDiCaL version: 2.1.3
% 0.15/0.50 % (4183881)Termination reason: Refutation
% 0.15/0.50 % (4183881)Time elapsed: 0.019 s
% 0.15/0.50 % (4183881)Peak memory usage: 13 MB
% 0.15/0.50 % (4183881)Instructions burned: 54 (million)
% 0.15/0.50 % (4183873)Success in time 0.052 s
% 0.15/0.50 % Vampire exiting
%------------------------------------------------------------------------------