%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET994+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 12:42:29 PM UTC 2026
% Result : Theorem 2.88s 1.25s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 68 ( 23 unt; 1 def)
% Number of atoms : 189 ( 70 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 194 ( 73 ~; 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 : 71 ( 0 sgn 64 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f5,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',s3_funct_1__e7_14__funct_1) ).
fof(f22,axiom,
empty(n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',spc0_boole) ).
fof(f23,axiom,
~ empty(n1),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f31,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/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] :
( ~ in(X2,X0)
| n0 = apply(sK9(X0),X2) ),
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(X1) != sK11
| X1 = X2
| relation_dom(X2) != sK11
| ~ 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(f120,plain,
! [X0,X1] :
( sK11 != X0
| sK9(X0) = X1
| relation_dom(X1) != sK11
| ~ relation(X1)
| ~ function(X1)
| ~ relation(sK9(X0))
| ~ function(sK9(X0)) ),
inference(superposition,[],[f108,f99]) ).
fof(f121,plain,
! [X0,X1] :
( sK11 != X0
| sK9(X0) = X1
| relation_dom(X1) != sK11
| ~ relation(X1)
| ~ function(X1)
| ~ function(sK9(X0)) ),
inference(forward_subsumption_resolution,[],[f120,f101]) ).
fof(f122,plain,
! [X0,X1] :
( sK11 != X0
| sK9(X0) = X1
| relation_dom(X1) != sK11
| ~ relation(X1)
| ~ function(X1) ),
inference(forward_subsumption_resolution,[],[f121,f100]) ).
fof(f128,plain,
! [X0] :
( relation_dom(X0) != sK11
| sK9(sK11) = X0
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f122]) ).
fof(f131,plain,
empty_set = n0,
inference(resolution,[],[f115,f106]) ).
fof(f136,plain,
! [X0] :
( sK11 != X0
| sK10(X0) = sK9(sK11)
| ~ relation(sK10(X0))
| ~ function(sK10(X0)) ),
inference(superposition,[],[f128,f103]) ).
fof(f137,plain,
! [X0] :
( sK11 != X0
| sK10(X0) = sK9(sK11)
| ~ function(sK10(X0)) ),
inference(forward_subsumption_resolution,[],[f136,f105]) ).
fof(f139,plain,
! [X0] :
( sK11 != X0
| sK10(X0) = sK9(sK11) ),
inference(forward_subsumption_resolution,[],[f137,f104]) ).
fof(f146,plain,
sK9(sK11) = sK10(sK11),
inference(equality_resolution,[],[f139]) ).
fof(f172,definition,
( spl12_1
<=> empty(sK11) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f173,plain,
( empty(sK11)
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f174,plain,
( ~ empty(sK11)
| spl12_1 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f208,plain,
! [X0] :
( in(sK0(X0),X0)
| empty(X0) ),
inference(resolution,[],[f111,f74]) ).
fof(f294,plain,
! [X0] :
( n1 = apply(sK10(X0),sK0(X0))
| empty(X0) ),
inference(resolution,[],[f208,f102]) ).
fof(f295,plain,
! [X0] :
( empty(X0)
| n0 = apply(sK9(X0),sK0(X0)) ),
inference(resolution,[],[f208,f98]) ).
fof(f296,plain,
! [X0] :
( empty_set = apply(sK9(X0),sK0(X0))
| empty(X0) ),
inference(forward_demodulation,[],[f295,f131]) ).
fof(f1134,plain,
( n1 = apply(sK9(sK11),sK0(sK11))
| empty(sK11) ),
inference(superposition,[],[f294,f146]) ).
fof(f1138,plain,
( n1 = apply(sK9(sK11),sK0(sK11))
| spl12_1 ),
inference(forward_subsumption_resolution,[],[f1134,f174]) ).
fof(f1144,plain,
( empty_set = n1
| empty(sK11)
| spl12_1 ),
inference(superposition,[],[f1138,f296]) ).
fof(f1145,plain,
( empty_set = n1
| spl12_1 ),
inference(forward_subsumption_resolution,[],[f1144,f174]) ).
fof(f1147,plain,
( ~ empty(empty_set)
| spl12_1 ),
inference(superposition,[],[f107,f1145]) ).
fof(f1148,plain,
( $false
| spl12_1 ),
inference(forward_subsumption_resolution,[],[f1147,f76]) ).
fof(f1149,plain,
spl12_1,
inference(avatar_contradiction_clause,[],[f1148]) ).
fof(f1183,plain,
( empty_set = sK11
| ~ spl12_1 ),
inference(resolution,[],[f173,f115]) ).
fof(f1239,plain,
( $false
| ~ spl12_1 ),
inference(forward_subsumption_resolution,[],[f1183,f109]) ).
fof(f1240,plain,
~ spl12_1,
inference(avatar_contradiction_clause,[],[f1239]) ).
cnf(s9,plain,
spl12_1,
inference(sat_conversion,[],[f1149]) ).
cnf(s11,plain,
~ spl12_1,
inference(sat_conversion,[],[f1240]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s9,s11]) ).
fof(f1241,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----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/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n013.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 28 03:20:22 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 Running first-order theorem proving
% 0.11/0.39 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.88/1.25 % (774524)Detected formulas, will run a generic FOF schedule.
% 2.88/1.25 % (774529)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3578734352:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.88/1.25 % (774534)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3454331379:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.88/1.25 % (774532)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=520667919:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.88/1.25 % (774533)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=247040970:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.88/1.25 % (774530)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=449020325:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.88/1.25 % (774531)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3437136607:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.88/1.25 % (774532)Refutation not found, incomplete strategy
% 2.88/1.25 % (774532)------------------------------
% 2.88/1.25 % (774532)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.88/1.25 % (774533)Refutation not found, incomplete strategy
% 2.88/1.25 % (774533)------------------------------
% 2.88/1.25 % (774533)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.88/1.25 % (774532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.88/1.25 % (774533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.88/1.25 % (774532)CaDiCaL version: 2.1.3
% 2.88/1.25 % (774532)Termination reason: Refutation not found, incomplete strategy
% 2.88/1.25 % (774532)Time elapsed: 0.001 s
% 2.88/1.25 % (774533)CaDiCaL version: 2.1.3
% 2.88/1.25 % (774533)Termination reason: Refutation not found, incomplete strategy
% 2.88/1.25 % (774533)Time elapsed: 0.002 s
% 2.88/1.25 % (774532)Peak memory usage: 88 MB
% 2.88/1.25 % (774533)Peak memory usage: 88 MB
% 2.88/1.25 % (774532)Instructions burned: 1 (million)
% 2.88/1.25 % (774533)Instructions burned: 1 (million)
% 2.88/1.25 % (774535)dis-21_1_sil=8000:lcm=predicate:random_seed=3024624514:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.88/1.25 % (774534)First to succeed.
% 2.88/1.25 % (774534)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-774524"
% 2.88/1.25 % (774535)Instruction limit reached!
% 2.88/1.25 % (774535)------------------------------
% 2.88/1.25 % (774535)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.88/1.25 % (774535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.88/1.25 % (774535)CaDiCaL version: 2.1.3
% 2.88/1.25 % (774535)Termination reason: Instruction limit
% 2.88/1.25 % (774535)Termination phase: Saturation
% 2.88/1.25 % (774535)Time elapsed: 0.080 s
% 2.88/1.25 % (774535)Peak memory usage: 90 MB
% 2.88/1.25 % (774535)Instructions burned: 130 (million)
% 2.88/1.25 % (774543)lrs+10_1_sil=8000:sp=occurrence:random_seed=3465623091:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.88/1.25 % (774532)------------------------------
% 2.88/1.25 % (774532)------------------------------
% 2.88/1.25 % (774533)------------------------------
% 2.88/1.25 % (774533)------------------------------
% 2.88/1.25 % (774543)Also succeeded, but the first one will report.
% 2.88/1.25 % (774534)Refutation found. Thanks to Tanya!
% 2.88/1.25 % SZS status Theorem for theBenchmark
% 2.88/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 3.55/1.45 % (774534)------------------------------
% 3.55/1.45 % (774534)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.45 % (774534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.45 % (774534)CaDiCaL version: 2.1.3
% 3.55/1.45 % (774534)Termination reason: Refutation
% 3.55/1.45 % (774534)Time elapsed: 0.021 s
% 3.55/1.45 % (774534)Peak memory usage: 90 MB
% 3.55/1.45 % (774534)Instructions burned: 33 (million)
% 3.55/1.45 % (774534)------------------------------
% 3.55/1.45 % (774534)------------------------------
% 3.55/1.45 % (774524)Success in time 0.416 s
% 3.55/1.45 % Vampire exiting
%------------------------------------------------------------------------------