%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET809+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 12:44:40 PM UTC 2026
% Result : Theorem 0.15s 0.50s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 6 unt; 1 def)
% Number of atoms : 260 ( 0 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 347 ( 131 ~; 116 |; 78 &)
% ( 12 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 144 ( 121 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0] :
( member(X0,on)
<=> ( set(X0)
& strict_well_order(member_predicate,X0)
& ! [X1] :
( member(X1,X0)
=> subset(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+4.ax',ordinal_number) ).
fof(f13,axiom,
! [X0,X1] :
( strict_well_order(X0,X1)
<=> ( strict_order(X0,X1)
& ! [X2] :
( ( subset(X2,X1)
& ? [X3] : member(X3,X2) )
=> ? [X4] : least(X4,X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+4.ax',strict_well_order) ).
fof(f15,axiom,
! [X0,X1] :
( apply(member_predicate,X0,X1)
<=> member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+4.ax',rel_member) ).
fof(f16,axiom,
! [X0,X1] :
( strict_order(X0,X1)
<=> ( ! [X2,X3] :
( ( member(X2,X1)
& member(X3,X1) )
=> ~ ( apply(X0,X2,X3)
& apply(X0,X3,X2) ) )
& ! [X2,X3,X4] :
( ( member(X2,X1)
& member(X3,X1)
& member(X4,X1) )
=> ( ( apply(X0,X2,X3)
& apply(X0,X3,X4) )
=> apply(X0,X2,X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+4.ax',strict_order) ).
fof(f20,conjecture,
! [X0] :
( member(X0,on)
=> ~ member(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thV2) ).
fof(f21,negated_conjecture,
~ ! [X0] :
( member(X0,on)
=> ~ member(X0,X0) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( strict_order(X0,X1)
<=> ( ! [X2,X3] :
( ( member(X2,X1)
& member(X3,X1) )
=> ~ ( apply(X0,X2,X3)
& apply(X0,X3,X2) ) )
& ! [X4,X5,X6] :
( ( member(X4,X1)
& member(X5,X1)
& member(X6,X1) )
=> ( ( apply(X0,X4,X5)
& apply(X0,X5,X6) )
=> apply(X0,X4,X6) ) ) ) ),
inference(rectify,[],[f16]) ).
fof(f25,plain,
! [X0] :
( member(X0,on)
<=> ( set(X0)
& strict_well_order(member_predicate,X0)
& ! [X1] :
( subset(X1,X0)
| ~ member(X1,X0) ) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f26,plain,
! [X0,X1] :
( strict_well_order(X0,X1)
<=> ( strict_order(X0,X1)
& ! [X2] :
( ? [X4] : least(X4,X0,X2)
| ~ subset(X2,X1)
| ! [X3] : ~ member(X3,X2) ) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f27,plain,
! [X0,X1] :
( strict_well_order(X0,X1)
<=> ( strict_order(X0,X1)
& ! [X2] :
( ? [X4] : least(X4,X0,X2)
| ~ subset(X2,X1)
| ! [X3] : ~ member(X3,X2) ) ) ),
inference(flattening,[],[f26]) ).
fof(f30,plain,
! [X0,X1] :
( strict_order(X0,X1)
<=> ( ! [X2,X3] :
( ~ apply(X0,X2,X3)
| ~ apply(X0,X3,X2)
| ~ member(X2,X1)
| ~ member(X3,X1) )
& ! [X4,X5,X6] :
( apply(X0,X4,X6)
| ~ apply(X0,X4,X5)
| ~ apply(X0,X5,X6)
| ~ member(X4,X1)
| ~ member(X5,X1)
| ~ member(X6,X1) ) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f31,plain,
! [X0,X1] :
( strict_order(X0,X1)
<=> ( ! [X2,X3] :
( ~ apply(X0,X2,X3)
| ~ apply(X0,X3,X2)
| ~ member(X2,X1)
| ~ member(X3,X1) )
& ! [X4,X5,X6] :
( apply(X0,X4,X6)
| ~ apply(X0,X4,X5)
| ~ apply(X0,X5,X6)
| ~ member(X4,X1)
| ~ member(X5,X1)
| ~ member(X6,X1) ) ) ),
inference(flattening,[],[f30]) ).
fof(f33,plain,
? [X0] :
( member(X0,X0)
& member(X0,on) ),
inference(ennf_transformation,[],[f21]) ).
fof(f34,definition,
! [X0,X1] :
( sP0(X0,X1)
<=> ! [X4,X5,X6] :
( apply(X0,X4,X6)
| ~ apply(X0,X4,X5)
| ~ apply(X0,X5,X6)
| ~ member(X4,X1)
| ~ member(X5,X1)
| ~ member(X6,X1) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f35,plain,
! [X0,X1] :
( strict_order(X0,X1)
<=> ( ! [X2,X3] :
( ~ apply(X0,X2,X3)
| ~ apply(X0,X3,X2)
| ~ member(X2,X1)
| ~ member(X3,X1) )
& sP0(X0,X1) ) ),
inference(definition_folding,[],[f31,f34]) ).
fof(f55,plain,
! [X0] :
( ( member(X0,on)
| ~ set(X0)
| ~ strict_well_order(member_predicate,X0)
| ? [X1] :
( ~ subset(X1,X0)
& member(X1,X0) ) )
& ( ( set(X0)
& strict_well_order(member_predicate,X0)
& ! [X1] :
( subset(X1,X0)
| ~ member(X1,X0) ) )
| ~ member(X0,on) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f56,plain,
! [X0] :
( ( member(X0,on)
| ~ set(X0)
| ~ strict_well_order(member_predicate,X0)
| ? [X1] :
( ~ subset(X1,X0)
& member(X1,X0) ) )
& ( ( set(X0)
& strict_well_order(member_predicate,X0)
& ! [X1] :
( subset(X1,X0)
| ~ member(X1,X0) ) )
| ~ member(X0,on) ) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0] :
( ( member(X0,on)
| ~ set(X0)
| ~ strict_well_order(member_predicate,X0)
| ? [X1] :
( ~ subset(X1,X0)
& member(X1,X0) ) )
& ( ( set(X0)
& strict_well_order(member_predicate,X0)
& ! [X2] :
( subset(X2,X0)
| ~ member(X2,X0) ) )
| ~ member(X0,on) ) ),
inference(rectify,[],[f56]) ).
fof(f58,plain,
! [X0] :
( ( member(X0,on)
| ~ set(X0)
| ~ strict_well_order(member_predicate,X0)
| ( ~ subset(sK4(X0),X0)
& member(sK4(X0),X0) ) )
& ( ( set(X0)
& strict_well_order(member_predicate,X0)
& ! [X2] :
( subset(X2,X0)
| ~ member(X2,X0) ) )
| ~ member(X0,on) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f57]) ).
fof(f59,plain,
! [X0,X1] :
( ( strict_well_order(X0,X1)
| ~ strict_order(X0,X1)
| ? [X2] :
( ! [X4] : ~ least(X4,X0,X2)
& subset(X2,X1)
& ? [X3] : member(X3,X2) ) )
& ( ( strict_order(X0,X1)
& ! [X2] :
( ? [X4] : least(X4,X0,X2)
| ~ subset(X2,X1)
| ! [X3] : ~ member(X3,X2) ) )
| ~ strict_well_order(X0,X1) ) ),
inference(nnf_transformation,[],[f27]) ).
fof(f60,plain,
! [X0,X1] :
( ( strict_well_order(X0,X1)
| ~ strict_order(X0,X1)
| ? [X2] :
( ! [X4] : ~ least(X4,X0,X2)
& subset(X2,X1)
& ? [X3] : member(X3,X2) ) )
& ( ( strict_order(X0,X1)
& ! [X2] :
( ? [X4] : least(X4,X0,X2)
| ~ subset(X2,X1)
| ! [X3] : ~ member(X3,X2) ) )
| ~ strict_well_order(X0,X1) ) ),
inference(flattening,[],[f59]) ).
fof(f61,plain,
! [X0,X1] :
( ( strict_well_order(X0,X1)
| ~ strict_order(X0,X1)
| ? [X2] :
( ! [X3] : ~ least(X3,X0,X2)
& subset(X2,X1)
& ? [X4] : member(X4,X2) ) )
& ( ( strict_order(X0,X1)
& ! [X5] :
( ? [X6] : least(X6,X0,X5)
| ~ subset(X5,X1)
| ! [X7] : ~ member(X7,X5) ) )
| ~ strict_well_order(X0,X1) ) ),
inference(rectify,[],[f60]) ).
fof(f62,plain,
! [X0,X1] :
( ( strict_well_order(X0,X1)
| ~ strict_order(X0,X1)
| ( ! [X3] : ~ least(X3,X0,sK5(X0,X1))
& subset(sK5(X0,X1),X1)
& member(sK6(X0,X1),sK5(X0,X1)) ) )
& ( ( strict_order(X0,X1)
& ! [X5] :
( least(sK7(X0,X5),X0,X5)
| ~ subset(X5,X1)
| ! [X7] : ~ member(X7,X5) ) )
| ~ strict_well_order(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X2,sK5(X0,X1)),skolemize(X4,sK6(X0,X1)),skolemize(X6,sK7(X0,X5))],[f61]) ).
fof(f67,plain,
! [X0,X1] :
( ( apply(member_predicate,X0,X1)
| ~ member(X0,X1) )
& ( member(X0,X1)
| ~ apply(member_predicate,X0,X1) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f71,plain,
! [X0,X1] :
( ( strict_order(X0,X1)
| ? [X2,X3] :
( apply(X0,X2,X3)
& apply(X0,X3,X2)
& member(X2,X1)
& member(X3,X1) )
| ~ sP0(X0,X1) )
& ( ( ! [X2,X3] :
( ~ apply(X0,X2,X3)
| ~ apply(X0,X3,X2)
| ~ member(X2,X1)
| ~ member(X3,X1) )
& sP0(X0,X1) )
| ~ strict_order(X0,X1) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f72,plain,
! [X0,X1] :
( ( strict_order(X0,X1)
| ? [X2,X3] :
( apply(X0,X2,X3)
& apply(X0,X3,X2)
& member(X2,X1)
& member(X3,X1) )
| ~ sP0(X0,X1) )
& ( ( ! [X2,X3] :
( ~ apply(X0,X2,X3)
| ~ apply(X0,X3,X2)
| ~ member(X2,X1)
| ~ member(X3,X1) )
& sP0(X0,X1) )
| ~ strict_order(X0,X1) ) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0,X1] :
( ( strict_order(X0,X1)
| ? [X2,X3] :
( apply(X0,X2,X3)
& apply(X0,X3,X2)
& member(X2,X1)
& member(X3,X1) )
| ~ sP0(X0,X1) )
& ( ( ! [X4,X5] :
( ~ apply(X0,X4,X5)
| ~ apply(X0,X5,X4)
| ~ member(X4,X1)
| ~ member(X5,X1) )
& sP0(X0,X1) )
| ~ strict_order(X0,X1) ) ),
inference(rectify,[],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( ( strict_order(X0,X1)
| ( apply(X0,sK12(X0,X1),sK13(X0,X1))
& apply(X0,sK13(X0,X1),sK12(X0,X1))
& member(sK12(X0,X1),X1)
& member(sK13(X0,X1),X1) )
| ~ sP0(X0,X1) )
& ( ( ! [X4,X5] :
( ~ apply(X0,X4,X5)
| ~ apply(X0,X5,X4)
| ~ member(X4,X1)
| ~ member(X5,X1) )
& sP0(X0,X1) )
| ~ strict_order(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X2,sK12(X0,X1)),skolemize(X3,sK13(X0,X1))],[f73]) ).
fof(f78,plain,
( member(sK14,sK14)
& member(sK14,on) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X0,sK14)],[f33]) ).
fof(f106,plain,
! [X0] :
( ~ member(X0,on)
| strict_well_order(member_predicate,X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f111,plain,
! [X0,X1] :
( ~ strict_well_order(X0,X1)
| strict_order(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f121,plain,
! [X0,X1] :
( apply(member_predicate,X0,X1)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f130,plain,
! [X0,X1,X4,X5] :
( ~ apply(X0,X5,X4)
| ~ apply(X0,X4,X5)
| ~ member(X4,X1)
| ~ member(X5,X1)
| ~ strict_order(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f141,plain,
member(sK14,on),
inference(cnf_transformation,[],[f78]) ).
fof(f142,plain,
member(sK14,sK14),
inference(cnf_transformation,[],[f78]) ).
fof(f172,plain,
strict_well_order(member_predicate,sK14),
inference(resolution,[],[f106,f141]) ).
fof(f184,plain,
strict_order(member_predicate,sK14),
inference(resolution,[],[f111,f172]) ).
fof(f320,plain,
! [X2,X0,X1] :
( ~ apply(member_predicate,X1,X0)
| ~ member(X0,X1)
| ~ member(X1,X2)
| ~ member(X0,X2)
| ~ strict_order(member_predicate,X2) ),
inference(resolution,[],[f121,f130]) ).
fof(f358,plain,
! [X2,X0,X1] :
( ~ strict_order(member_predicate,X2)
| ~ member(X1,X2)
| ~ member(X0,X2)
| ~ member(X0,X1)
| ~ member(X1,X0) ),
inference(resolution,[],[f320,f121]) ).
fof(f361,plain,
! [X0,X1] :
( ~ member(X1,sK14)
| ~ member(X0,sK14)
| ~ member(X1,X0)
| ~ member(X0,X1) ),
inference(resolution,[],[f358,f184]) ).
fof(f362,plain,
! [X0] :
( ~ member(X0,sK14)
| ~ member(sK14,X0)
| ~ member(X0,sK14) ),
inference(resolution,[],[f361,f142]) ).
fof(f363,plain,
! [X0] :
( ~ member(sK14,X0)
| ~ member(X0,sK14) ),
inference(duplicate_literal_removal,[],[f362]) ).
fof(f365,plain,
~ member(sK14,sK14),
inference(resolution,[],[f363,f142]) ).
fof(f369,plain,
$false,
inference(forward_subsumption_resolution,[],[f365,f142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET809+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.41 % Computer : n019.cluster.edu
% 0.08/0.41 % Model : x86_64 x86_64
% 0.08/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.41 % Memory : 8046.5625MB
% 0.08/0.41 % OS : Linux 6.8.0-71-generic
% 0.08/0.41 % CPULimit : 300
% 0.08/0.41 % WCLimit : 300
% 0.08/0.41 % DateTime : Mon Sep 28 02:52:55 UTC 2026
% 0.08/0.41 % CPUTime :
% 0.08/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.44 Running first-order model finding
% 0.08/0.44 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.50 % (3619256)Will run a generic schedule for satisfiability detection.
% 0.15/0.50 % (3619264)dis+10_1_sil=32000:sp=arity:random_seed=1076751936:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.50 % (3619262)% WARNING: option uhcvi not known.
% 0.15/0.50 % (3619263)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=721275799:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.50 % (3619262)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1878820760:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.50 % (3619261)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=534687610_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.50 % (3619267)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=825565592:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.50 % (3619265)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4290504323:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.50 % (3619266)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2905923461:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.50 % TRYING [1]
% 0.15/0.50 % TRYING [2]
% 0.15/0.50 % TRYING [3]
% 0.15/0.50 % (3619263) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3619256-3619263"...
% 0.15/0.50 % (3619263)...printing done.
% 0.15/0.50 % (3619263)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 % (3619263)------------------------------
% 0.15/0.50 % (3619263)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.50 % (3619263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.50 % (3619263)CaDiCaL version: 2.1.3
% 0.15/0.50 % (3619263)Termination reason: Refutation
% 0.15/0.50 % (3619263)Time elapsed: 0.007 s
% 0.15/0.50 % (3619263)Peak memory usage: 12 MB
% 0.15/0.50 % (3619263)Instructions burned: 9 (million)
% 0.15/0.50 % (3619256)Success in time 0.041 s
% 0.15/0.50 % Vampire exiting
%------------------------------------------------------------------------------