%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU284+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:48:09 PM UTC 2026
% Result : Theorem 3.53s 1.45s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 44 ( 4 unt; 1 def)
% Number of atoms : 187 ( 77 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 223 ( 80 ~; 78 |; 57 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 97 ( 71 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
? [X1] :
( relation(X1)
& function(X1)
& relation_dom(X1) = X0
& ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = singleton(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_funct_1__e16_22__wellord2) ).
fof(f2,negated_conjecture,
~ ! [X0] :
? [X1] :
( relation(X1)
& function(X1)
& relation_dom(X1) = X0
& ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = singleton(X2) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f8,axiom,
! [X0] :
( ( ! [X1,X2,X3] :
( ( in(X1,X0)
& X2 = singleton(X1)
& X3 = singleton(X1) )
=> X2 = X3 )
& ! [X1] :
~ ( in(X1,X0)
& ! [X2] : X2 != singleton(X1) ) )
=> ? [X1] :
( relation(X1)
& function(X1)
& relation_dom(X1) = X0
& ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = singleton(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_funct_1__e16_22__wellord2__1) ).
fof(f29,plain,
! [X0] :
( ( ! [X1,X2,X3] :
( ( in(X1,X0)
& X2 = singleton(X1)
& X3 = singleton(X1) )
=> X2 = X3 )
& ! [X4] :
~ ( in(X4,X0)
& ! [X5] : singleton(X4) != X5 ) )
=> ? [X6] :
( relation(X6)
& function(X6)
& relation_dom(X6) = X0
& ! [X7] :
( in(X7,X0)
=> apply(X6,X7) = singleton(X7) ) ) ),
inference(rectify,[],[f8]) ).
fof(f30,plain,
? [X0] :
! [X1] :
( ~ relation(X1)
| ~ function(X1)
| relation_dom(X1) != X0
| ? [X2] :
( apply(X1,X2) != singleton(X2)
& in(X2,X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f37,plain,
! [X0] :
( ? [X6] :
( relation(X6)
& function(X6)
& relation_dom(X6) = X0
& ! [X7] :
( apply(X6,X7) = singleton(X7)
| ~ in(X7,X0) ) )
| ? [X1,X2,X3] :
( X2 != X3
& in(X1,X0)
& X2 = singleton(X1)
& X3 = singleton(X1) )
| ? [X4] :
( in(X4,X0)
& ! [X5] : singleton(X4) != X5 ) ),
inference(ennf_transformation,[],[f29]) ).
fof(f38,plain,
! [X0] :
( ? [X6] :
( relation(X6)
& function(X6)
& relation_dom(X6) = X0
& ! [X7] :
( apply(X6,X7) = singleton(X7)
| ~ in(X7,X0) ) )
| ? [X1,X2,X3] :
( X2 != X3
& in(X1,X0)
& X2 = singleton(X1)
& X3 = singleton(X1) )
| ? [X4] :
( in(X4,X0)
& ! [X5] : singleton(X4) != X5 ) ),
inference(flattening,[],[f37]) ).
fof(f42,definition,
! [X0] :
( ? [X1,X2,X3] :
( X2 != X3
& in(X1,X0)
& X2 = singleton(X1)
& X3 = singleton(X1) )
| ~ sP0(X0) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f43,plain,
! [X0] :
( ? [X6] :
( relation(X6)
& function(X6)
& relation_dom(X6) = X0
& ! [X7] :
( apply(X6,X7) = singleton(X7)
| ~ in(X7,X0) ) )
| sP0(X0)
| ? [X4] :
( in(X4,X0)
& ! [X5] : singleton(X4) != X5 ) ),
inference(definition_folding,[],[f38,f42]) ).
fof(f44,plain,
! [X1] :
( ~ relation(X1)
| ~ function(X1)
| relation_dom(X1) != sK1
| ( apply(X1,sK2(X1)) != singleton(sK2(X1))
& in(sK2(X1),sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X2,sK2(X1))],[f30]) ).
fof(f47,plain,
! [X0] :
( ? [X1,X2,X3] :
( X2 != X3
& in(X1,X0)
& X2 = singleton(X1)
& X3 = singleton(X1) )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f42]) ).
fof(f48,plain,
! [X0] :
( ( sK6(X0) != sK7(X0)
& in(sK5(X0),X0)
& sK6(X0) = singleton(sK5(X0))
& sK7(X0) = singleton(sK5(X0)) )
| ~ sP0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X1,sK5(X0)),skolemize(X2,sK6(X0)),skolemize(X3,sK7(X0))],[f47]) ).
fof(f49,plain,
! [X0] :
( ? [X1] :
( relation(X1)
& function(X1)
& relation_dom(X1) = X0
& ! [X2] :
( apply(X1,X2) = singleton(X2)
| ~ in(X2,X0) ) )
| sP0(X0)
| ? [X3] :
( in(X3,X0)
& ! [X4] : singleton(X3) != X4 ) ),
inference(rectify,[],[f43]) ).
fof(f50,plain,
! [X0] :
( ( relation(sK8(X0))
& function(sK8(X0))
& relation_dom(sK8(X0)) = X0
& ! [X2] :
( singleton(X2) = apply(sK8(X0),X2)
| ~ in(X2,X0) ) )
| sP0(X0)
| ( in(sK9(X0),X0)
& ! [X4] : singleton(sK9(X0)) != X4 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X1,sK8(X0)),skolemize(X3,sK9(X0))],[f49]) ).
fof(f54,plain,
! [X1] :
( relation_dom(X1) != sK1
| ~ function(X1)
| ~ relation(X1)
| in(sK2(X1),sK1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f55,plain,
! [X1] :
( apply(X1,sK2(X1)) != singleton(sK2(X1))
| ~ function(X1)
| relation_dom(X1) != sK1
| ~ relation(X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f66,plain,
! [X0] :
( sK7(X0) = singleton(sK5(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f67,plain,
! [X0] :
( sK6(X0) = singleton(sK5(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f69,plain,
! [X0] :
( sK6(X0) != sK7(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f70,plain,
! [X2,X0,X4] :
( singleton(X2) = apply(sK8(X0),X2)
| ~ in(X2,X0)
| sP0(X0)
| singleton(sK9(X0)) != X4 ),
inference(cnf_transformation,[],[f50]) ).
fof(f72,plain,
! [X0,X4] :
( relation_dom(sK8(X0)) = X0
| sP0(X0)
| singleton(sK9(X0)) != X4 ),
inference(cnf_transformation,[],[f50]) ).
fof(f74,plain,
! [X0,X4] :
( function(sK8(X0))
| sP0(X0)
| singleton(sK9(X0)) != X4 ),
inference(cnf_transformation,[],[f50]) ).
fof(f76,plain,
! [X0,X4] :
( relation(sK8(X0))
| sP0(X0)
| singleton(sK9(X0)) != X4 ),
inference(cnf_transformation,[],[f50]) ).
fof(f88,plain,
! [X0] :
( relation(sK8(X0))
| sP0(X0) ),
inference(equality_resolution,[],[f76]) ).
fof(f89,plain,
! [X0] :
( function(sK8(X0))
| sP0(X0) ),
inference(equality_resolution,[],[f74]) ).
fof(f90,plain,
! [X0] :
( relation_dom(sK8(X0)) = X0
| sP0(X0) ),
inference(equality_resolution,[],[f72]) ).
fof(f91,plain,
! [X2,X0] :
( singleton(X2) = apply(sK8(X0),X2)
| ~ in(X2,X0)
| sP0(X0) ),
inference(equality_resolution,[],[f70]) ).
fof(f102,plain,
! [X0] :
( sK1 != X0
| ~ function(sK8(X0))
| ~ relation(sK8(X0))
| in(sK2(sK8(X0)),sK1)
| sP0(X0) ),
inference(superposition,[],[f54,f90]) ).
fof(f103,plain,
! [X0] :
( sK1 != X0
| ~ relation(sK8(X0))
| in(sK2(sK8(X0)),sK1)
| sP0(X0) ),
inference(forward_subsumption_resolution,[],[f102,f89]) ).
fof(f105,plain,
! [X0] :
( sK1 != X0
| in(sK2(sK8(X0)),sK1)
| sP0(X0) ),
inference(forward_subsumption_resolution,[],[f103,f88]) ).
fof(f106,plain,
( in(sK2(sK8(sK1)),sK1)
| sP0(sK1) ),
inference(equality_resolution,[],[f105]) ).
fof(f111,plain,
! [X0] :
( sK6(X0) = sK7(X0)
| ~ sP0(X0)
| ~ sP0(X0) ),
inference(superposition,[],[f66,f67]) ).
fof(f112,plain,
! [X0] :
( sK6(X0) = sK7(X0)
| ~ sP0(X0) ),
inference(duplicate_literal_removal,[],[f111]) ).
fof(f114,plain,
! [X0] : ~ sP0(X0),
inference(forward_subsumption_resolution,[],[f112,f69]) ).
fof(f117,plain,
! [X2,X0] :
( singleton(X2) = apply(sK8(X0),X2)
| ~ in(X2,X0) ),
inference(forward_subsumption_resolution,[],[f91,f114]) ).
fof(f119,plain,
! [X0] :
( singleton(sK2(sK8(X0))) != singleton(sK2(sK8(X0)))
| ~ function(sK8(X0))
| sK1 != relation_dom(sK8(X0))
| ~ relation(sK8(X0))
| ~ in(sK2(sK8(X0)),X0) ),
inference(superposition,[],[f55,f117]) ).
fof(f120,plain,
! [X0] :
( sK1 != relation_dom(sK8(X0))
| ~ function(sK8(X0))
| ~ relation(sK8(X0))
| ~ in(sK2(sK8(X0)),X0) ),
inference(trivial_inequality_removal,[],[f119]) ).
fof(f121,plain,
! [X0] :
( sK1 != X0
| ~ function(sK8(X0))
| ~ relation(sK8(X0))
| ~ in(sK2(sK8(X0)),X0)
| sP0(X0) ),
inference(superposition,[],[f120,f90]) ).
fof(f122,plain,
! [X0] :
( sK1 != X0
| ~ relation(sK8(X0))
| ~ in(sK2(sK8(X0)),X0)
| sP0(X0) ),
inference(forward_subsumption_resolution,[],[f121,f89]) ).
fof(f123,plain,
! [X0] :
( sK1 != X0
| ~ in(sK2(sK8(X0)),X0)
| sP0(X0) ),
inference(forward_subsumption_resolution,[],[f122,f88]) ).
fof(f124,plain,
! [X0] :
( sK1 != X0
| ~ in(sK2(sK8(X0)),X0) ),
inference(forward_subsumption_resolution,[],[f123,f114]) ).
fof(f125,plain,
~ in(sK2(sK8(sK1)),sK1),
inference(equality_resolution,[],[f124]) ).
fof(f126,plain,
sP0(sK1),
inference(resolution,[],[f125,f106]) ).
fof(f127,plain,
$false,
inference(forward_subsumption_resolution,[],[f126,f114]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU284+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n008.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 04:30:10 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.53/1.45 % (1875413)Detected formulas, will run a generic FOF schedule.
% 3.53/1.45 % (1875423)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2427174100:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.53/1.45 % (1875424)dis-21_1_sil=8000:lcm=predicate:random_seed=1770762496: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)
% 3.53/1.45 % (1875420)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=505745807:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.53/1.45 % (1875419)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=2840646139:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.53/1.45 % (1875421)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1199471412:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.53/1.45 % (1875418)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=1457616137:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.53/1.45 % (1875421)Refutation not found, incomplete strategy
% 3.53/1.45 % (1875421)------------------------------
% 3.53/1.45 % (1875421)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.45 % (1875421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.45 % (1875421)CaDiCaL version: 2.1.3
% 3.53/1.45 % (1875421)Termination reason: Refutation not found, incomplete strategy
% 3.53/1.45 % (1875421)Time elapsed: 0.003 s
% 3.53/1.45 % (1875421)Peak memory usage: 88 MB
% 3.53/1.45 % (1875421)Instructions burned: 2 (million)
% 3.53/1.45 % (1875424)Refutation not found, incomplete strategy
% 3.53/1.45 % (1875424)------------------------------
% 3.53/1.45 % (1875424)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.45 % (1875424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.45 % (1875424)CaDiCaL version: 2.1.3
% 3.53/1.45 % (1875424)Termination reason: Refutation not found, incomplete strategy
% 3.53/1.45 % (1875424)Time elapsed: 0.003 s
% 3.53/1.45 % (1875424)Peak memory usage: 88 MB
% 3.53/1.45 % (1875424)Instructions burned: 3 (million)
% 3.53/1.45 % (1875423)Instruction limit reached!
% 3.53/1.45 % (1875423)------------------------------
% 3.53/1.45 % (1875423)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.45 % (1875423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.45 % (1875423)CaDiCaL version: 2.1.3
% 3.53/1.45 % (1875423)Termination reason: Instruction limit
% 3.53/1.45 % (1875423)Termination phase: Saturation
% 3.53/1.45 % (1875423)Time elapsed: 0.033 s
% 3.53/1.45 % (1875423)Peak memory usage: 88 MB
% 3.53/1.45 % (1875423)Instructions burned: 140 (million)
% 3.53/1.45 % (1875422)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2327845614:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.53/1.45 % (1875422)First to succeed.
% 3.53/1.45 % (1875422)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1875413"
% 3.53/1.45 % (1875432)lrs+10_1_sil=8000:sp=occurrence:random_seed=1366072666:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.53/1.45 % (1875432)Also succeeded, but the first one will report.
% 3.53/1.45 % (1875424)------------------------------
% 3.53/1.45 % (1875424)------------------------------
% 3.53/1.45 % (1875421)------------------------------
% 3.53/1.45 % (1875421)------------------------------
% 3.53/1.45 % (1875422)Refutation found. Thanks to Tanya!
% 3.53/1.45 % SZS status Theorem for theBenchmark
% 3.53/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 3.53/1.45 % (1875422)------------------------------
% 3.53/1.45 % (1875422)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.45 % (1875422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.45 % (1875422)CaDiCaL version: 2.1.3
% 3.53/1.45 % (1875422)Termination reason: Refutation
% 3.53/1.45 % (1875422)Time elapsed: 0.004 s
% 3.53/1.45 % (1875422)Peak memory usage: 88 MB
% 3.53/1.45 % (1875422)Instructions burned: 4 (million)
% 3.53/1.45 % (1875422)------------------------------
% 3.53/1.45 % (1875422)------------------------------
% 3.53/1.45 % (1875413)Success in time 0.412 s
% 3.53/1.45 % Vampire exiting
%------------------------------------------------------------------------------