%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET994+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 : n004.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 12:45:09 PM UTC 2026
% Result : Theorem 0.14s 0.45s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of formulae : 68 ( 23 unt; 1 def)
% Number of atoms : 189 ( 73 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 196 ( 75 ~; 78 |; 30 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 2 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 75 ( 0 sgn 68 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f5,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(f20,axiom,
! [X0] :
? [X1] :
( relation(X1)
& function(X1)
& relation_dom(X1) = X0
& ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_funct_1__e4_14__funct_1) ).
fof(f21,axiom,
! [X0] :
? [X1] :
( relation(X1)
& function(X1)
& relation_dom(X1) = X0
& ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = n1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_funct_1__e7_14__funct_1) ).
fof(f22,axiom,
empty(n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',spc0_boole) ).
fof(f23,axiom,
~ empty(n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',spc1_boole) ).
fof(f24,conjecture,
! [X0] :
( ! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( ( relation_dom(X1) = X0
& relation_dom(X2) = X0 )
=> X1 = X2 ) ) )
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_funct_1) ).
fof(f25,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( ( relation_dom(X1) = X0
& relation_dom(X2) = X0 )
=> X1 = X2 ) ) )
=> X0 = empty_set ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f27,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f31,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f36,plain,
( empty(empty_set)
& relation(empty_set) ),
inference(pure_predicate_removal,[],[f5]) ).
fof(f45,plain,
! [X0] :
? [X1] :
( relation(X1)
& function(X1)
& relation_dom(X1) = X0
& ! [X2] :
( apply(X1,X2) = n0
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f46,plain,
! [X0] :
? [X1] :
( relation(X1)
& function(X1)
& relation_dom(X1) = X0
& ! [X2] :
( apply(X1,X2) = n1
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f47,plain,
? [X0] :
( empty_set != X0
& ! [X1] :
( ! [X2] :
( X1 = X2
| relation_dom(X1) != X0
| relation_dom(X2) != X0
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f48,plain,
? [X0] :
( empty_set != X0
& ! [X1] :
( ! [X2] :
( X1 = X2
| relation_dom(X1) != X0
| relation_dom(X2) != X0
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ) ),
inference(flattening,[],[f47]) ).
fof(f50,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f51,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f50]) ).
fof(f56,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f59,plain,
! [X0] : element(sK0(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f4]) ).
fof(f68,plain,
! [X0] :
( relation(sK9(X0))
& function(sK9(X0))
& relation_dom(sK9(X0)) = X0
& ! [X2] :
( n0 = apply(sK9(X0),X2)
| ~ in(X2,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X1,sK9(X0))],[f45]) ).
fof(f69,plain,
! [X0] :
( relation(sK10(X0))
& function(sK10(X0))
& relation_dom(sK10(X0)) = X0
& ! [X2] :
( n1 = apply(sK10(X0),X2)
| ~ in(X2,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X1,sK10(X0))],[f46]) ).
fof(f70,plain,
( empty_set != sK11
& ! [X1] :
( ! [X2] :
( X1 = X2
| relation_dom(X1) != sK11
| relation_dom(X2) != sK11
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X0,sK11)],[f48]) ).
fof(f74,plain,
! [X0] : element(sK0(X0),X0),
inference(cnf_transformation,[],[f59]) ).
fof(f76,plain,
empty(empty_set),
inference(cnf_transformation,[],[f36]) ).
fof(f98,plain,
! [X2,X0] :
( n0 = apply(sK9(X0),X2)
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f99,plain,
! [X0] : relation_dom(sK9(X0)) = X0,
inference(cnf_transformation,[],[f68]) ).
fof(f100,plain,
! [X0] : function(sK9(X0)),
inference(cnf_transformation,[],[f68]) ).
fof(f101,plain,
! [X0] : relation(sK9(X0)),
inference(cnf_transformation,[],[f68]) ).
fof(f102,plain,
! [X2,X0] :
( ~ in(X2,X0)
| n1 = apply(sK10(X0),X2) ),
inference(cnf_transformation,[],[f69]) ).
fof(f103,plain,
! [X0] : relation_dom(sK10(X0)) = X0,
inference(cnf_transformation,[],[f69]) ).
fof(f104,plain,
! [X0] : function(sK10(X0)),
inference(cnf_transformation,[],[f69]) ).
fof(f105,plain,
! [X0] : relation(sK10(X0)),
inference(cnf_transformation,[],[f69]) ).
fof(f106,plain,
empty(n0),
inference(cnf_transformation,[],[f22]) ).
fof(f107,plain,
~ empty(n1),
inference(cnf_transformation,[],[f23]) ).
fof(f108,plain,
! [X2,X1] :
( relation_dom(X2) != sK11
| relation_dom(X1) != sK11
| X1 = X2
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f109,plain,
empty_set != sK11,
inference(cnf_transformation,[],[f70]) ).
fof(f111,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f115,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f56]) ).
fof(f132,plain,
! [X0,X1] :
( sK11 != X0
| relation_dom(X1) != sK11
| sK9(X0) = X1
| ~ relation(sK9(X0))
| ~ function(sK9(X0))
| ~ relation(X1)
| ~ function(X1) ),
inference(superposition,[],[f108,f99]) ).
fof(f133,plain,
! [X0,X1] :
( sK11 != X0
| relation_dom(X1) != sK11
| sK9(X0) = X1
| ~ function(sK9(X0))
| ~ relation(X1)
| ~ function(X1) ),
inference(forward_subsumption_resolution,[],[f132,f101]) ).
fof(f134,plain,
! [X0,X1] :
( relation_dom(X1) != sK11
| sK11 != X0
| sK9(X0) = X1
| ~ relation(X1)
| ~ function(X1) ),
inference(forward_subsumption_resolution,[],[f133,f100]) ).
fof(f138,plain,
! [X0,X1] :
( sK11 != X0
| sK11 != X1
| sK10(X0) = sK9(X1)
| ~ relation(sK10(X0))
| ~ function(sK10(X0)) ),
inference(superposition,[],[f134,f103]) ).
fof(f143,plain,
! [X0,X1] :
( sK11 != X0
| sK11 != X1
| sK10(X0) = sK9(X1)
| ~ function(sK10(X0)) ),
inference(forward_subsumption_resolution,[],[f138,f105]) ).
fof(f145,plain,
! [X0,X1] :
( sK11 != X1
| sK11 != X0
| sK10(X0) = sK9(X1) ),
inference(forward_subsumption_resolution,[],[f143,f104]) ).
fof(f149,plain,
empty_set = n0,
inference(resolution,[],[f115,f106]) ).
fof(f154,plain,
! [X0] :
( sK11 != X0
| sK10(X0) = sK9(sK11) ),
inference(equality_resolution,[],[f145]) ).
fof(f155,plain,
sK9(sK11) = sK10(sK11),
inference(equality_resolution,[],[f154]) ).
fof(f180,plain,
! [X0] :
( in(sK0(X0),X0)
| empty(X0) ),
inference(resolution,[],[f111,f74]) ).
fof(f189,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set = apply(sK9(X0),X2) ),
inference(forward_demodulation,[],[f98,f149]) ).
fof(f235,definition,
( spl12_3
<=> empty(sK11) ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
fof(f236,plain,
( empty(sK11)
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f237,plain,
( ~ empty(sK11)
| spl12_3 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f275,plain,
! [X0] :
( empty(X0)
| empty_set = apply(sK9(X0),sK0(X0)) ),
inference(resolution,[],[f180,f189]) ).
fof(f276,plain,
! [X0] :
( empty(X0)
| n1 = apply(sK10(X0),sK0(X0)) ),
inference(resolution,[],[f180,f102]) ).
fof(f441,plain,
( empty_set = apply(sK9(sK11),sK0(sK11))
| spl12_3 ),
inference(resolution,[],[f275,f237]) ).
fof(f465,plain,
( n1 = apply(sK10(sK11),sK0(sK11))
| spl12_3 ),
inference(resolution,[],[f276,f237]) ).
fof(f466,plain,
( n1 = apply(sK9(sK11),sK0(sK11))
| spl12_3 ),
inference(forward_demodulation,[],[f465,f155]) ).
fof(f467,plain,
( empty_set = n1
| spl12_3 ),
inference(forward_demodulation,[],[f466,f441]) ).
fof(f468,plain,
( ~ empty(empty_set)
| spl12_3 ),
inference(superposition,[],[f107,f467]) ).
fof(f469,plain,
( $false
| spl12_3 ),
inference(forward_subsumption_resolution,[],[f468,f76]) ).
fof(f470,plain,
spl12_3,
inference(avatar_contradiction_clause,[],[f469]) ).
fof(f500,plain,
( empty_set = sK11
| ~ spl12_3 ),
inference(resolution,[],[f236,f115]) ).
fof(f510,plain,
( $false
| ~ spl12_3 ),
inference(forward_subsumption_resolution,[],[f500,f109]) ).
fof(f511,plain,
~ spl12_3,
inference(avatar_contradiction_clause,[],[f510]) ).
cnf(s3,plain,
spl12_3,
inference(sat_conversion,[],[f470]) ).
cnf(s4,plain,
~ spl12_3,
inference(sat_conversion,[],[f511]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s3,s4]) ).
fof(f512,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET994+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 03:20:52 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.39 Running first-order model finding
% 0.14/0.39 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
% 0.14/0.45 % (4118423)Will run a generic schedule for satisfiability detection.
% 0.14/0.45 % (4118429)% WARNING: option uhcvi not known.
% 0.14/0.45 % (4118431)dis+10_1_sil=32000:sp=arity:random_seed=1802990562:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.14/0.45 % (4118428)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1675243132_2999 on theBenchmark for (2999ds/0Mi)
% 0.14/0.45 % (4118429)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2293145253:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.14/0.45 % (4118430)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=164558307:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.14/0.45 % (4118432)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1269329254:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.14/0.45 % (4118433)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=350859107:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.14/0.45 % (4118434)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1249981514:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.14/0.45 % TRYING [1]
% 0.14/0.45 % TRYING [2]
% 0.14/0.45 % TRYING [3]
% 0.14/0.45 % TRYING [4]
% 0.14/0.45 % TRYING [5]
% 0.14/0.45 % (4118431) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4118423-4118431"...
% 0.14/0.45 % TRYING [6]
% 0.14/0.45 % (4118431)...printing done.
% 0.14/0.45 % (4118431)Refutation found. Thanks to Tanya!
% 0.14/0.45 % SZS status Theorem for theBenchmark
% 0.14/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.45 % (4118431)------------------------------
% 0.14/0.45 % (4118431)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.45 % (4118431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.45 % (4118431)CaDiCaL version: 2.1.3
% 0.14/0.45 % (4118431)Termination reason: Refutation
% 0.14/0.45 % (4118431)Time elapsed: 0.010 s
% 0.14/0.45 % (4118431)Peak memory usage: 12 MB
% 0.14/0.45 % (4118431)Instructions burned: 15 (million)
% 0.14/0.45 % (4118423)Success in time 0.046 s
% 0.14/0.45 % Vampire exiting
%------------------------------------------------------------------------------