%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET790+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 12:41:56 PM UTC 2026
% Result : Theorem 2.64s 1.32s
% Output : Refutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 47 ( 14 unt; 3 def)
% Number of atoms : 179 ( 18 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 209 ( 77 ~; 65 |; 39 &)
% ( 5 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 88 ( 0 sgn 80 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( order(X0,X1)
<=> ( ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) )
& ! [X2,X3] :
( ( member(X2,X1)
& member(X3,X1) )
=> ( ( apply(X0,X2,X3)
& apply(X0,X3,X2) )
=> X2 = X3 ) )
& ! [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/sandbox/benchmark/theBenchmark.p',order) ).
fof(f6,axiom,
! [X0,X1,X2] :
( least(X2,X0,X1)
<=> ( member(X2,X1)
& ! [X3] :
( member(X3,X1)
=> apply(X0,X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',least) ).
fof(f11,conjecture,
! [X0,X1,X2] :
( ( order(X0,X1)
& least(X2,X0,X1) )
=> ! [X3] :
( least(X3,X0,X1)
=> X2 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV2) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2] :
( ( order(X0,X1)
& least(X2,X0,X1) )
=> ! [X3] :
( least(X3,X0,X1)
=> X2 = X3 ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( order(X0,X1)
<=> ( ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) )
& ! [X3,X4] :
( ( member(X3,X1)
& member(X4,X1) )
=> ( ( apply(X0,X3,X4)
& apply(X0,X4,X3) )
=> X3 = X4 ) )
& ! [X5,X6,X7] :
( ( member(X5,X1)
& member(X6,X1)
& member(X7,X1) )
=> ( ( apply(X0,X5,X6)
& apply(X0,X6,X7) )
=> apply(X0,X5,X7) ) ) ) ),
inference(rectify,[],[f1]) ).
fof(f14,plain,
! [X0,X1,X2] :
( least(X2,X0,X1)
=> ( member(X2,X1)
& ! [X3] :
( member(X3,X1)
=> apply(X0,X2,X3) ) ) ),
inference(unused_predicate_definition_removal,[],[f6]) ).
fof(f15,plain,
! [X0,X1] :
( order(X0,X1)
=> ( ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) )
& ! [X3,X4] :
( ( member(X3,X1)
& member(X4,X1) )
=> ( ( apply(X0,X3,X4)
& apply(X0,X4,X3) )
=> X3 = X4 ) )
& ! [X5,X6,X7] :
( ( member(X5,X1)
& member(X6,X1)
& member(X7,X1) )
=> ( ( apply(X0,X5,X6)
& apply(X0,X6,X7) )
=> apply(X0,X5,X7) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f13]) ).
fof(f16,plain,
? [X0,X1,X2] :
( ? [X3] :
( X2 != X3
& least(X3,X0,X1) )
& order(X0,X1)
& least(X2,X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f17,plain,
? [X0,X1,X2] :
( ? [X3] :
( X2 != X3
& least(X3,X0,X1) )
& order(X0,X1)
& least(X2,X0,X1) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ( ! [X2] :
( apply(X0,X2,X2)
| ~ member(X2,X1) )
& ! [X3,X4] :
( X3 = X4
| ~ apply(X0,X3,X4)
| ~ apply(X0,X4,X3)
| ~ member(X3,X1)
| ~ member(X4,X1) )
& ! [X5,X6,X7] :
( apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| ~ apply(X0,X6,X7)
| ~ member(X5,X1)
| ~ member(X6,X1)
| ~ member(X7,X1) ) )
| ~ order(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f19,plain,
! [X0,X1] :
( ( ! [X2] :
( apply(X0,X2,X2)
| ~ member(X2,X1) )
& ! [X3,X4] :
( X3 = X4
| ~ apply(X0,X3,X4)
| ~ apply(X0,X4,X3)
| ~ member(X3,X1)
| ~ member(X4,X1) )
& ! [X5,X6,X7] :
( apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| ~ apply(X0,X6,X7)
| ~ member(X5,X1)
| ~ member(X6,X1)
| ~ member(X7,X1) ) )
| ~ order(X0,X1) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( member(X2,X1)
& ! [X3] :
( apply(X0,X2,X3)
| ~ member(X3,X1) ) )
| ~ least(X2,X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f21,plain,
( sK2 != sK3
& least(sK3,sK0,sK1)
& order(sK0,sK1)
& least(sK2,sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f17]) ).
fof(f22,plain,
least(sK2,sK0,sK1),
inference(cnf_transformation,[],[f21]) ).
fof(f23,plain,
order(sK0,sK1),
inference(cnf_transformation,[],[f21]) ).
fof(f24,plain,
least(sK3,sK0,sK1),
inference(cnf_transformation,[],[f21]) ).
fof(f25,plain,
sK2 != sK3,
inference(cnf_transformation,[],[f21]) ).
fof(f27,plain,
! [X3,X0,X1,X4] :
( ~ apply(X0,X4,X3)
| ~ apply(X0,X3,X4)
| X3 = X4
| ~ member(X3,X1)
| ~ member(X4,X1)
| ~ order(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f29,plain,
! [X2,X3,X0,X1] :
( ~ least(X2,X0,X1)
| ~ member(X3,X1)
| apply(X0,X2,X3) ),
inference(cnf_transformation,[],[f20]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ least(X2,X0,X1)
| member(X2,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f31,definition,
~ sP4(sK2),
introduced(definition,[new_symbols(definition,[sP4])],[inequality_splitting_name_introduction]) ).
fof(f32,plain,
sP4(sK3),
inference(inequality_splitting,[],[f25,f31]) ).
fof(f33,plain,
! [X0] :
( apply(sK0,sK2,X0)
| ~ member(X0,sK1) ),
inference(resolution,[],[f22,f29]) ).
fof(f34,plain,
member(sK2,sK1),
inference(resolution,[],[f22,f30]) ).
fof(f35,plain,
! [X0] :
( apply(sK0,sK3,X0)
| ~ member(X0,sK1) ),
inference(resolution,[],[f24,f29]) ).
fof(f36,plain,
member(sK3,sK1),
inference(resolution,[],[f24,f30]) ).
fof(f38,plain,
! [X0,X1] :
( ~ apply(sK0,X0,sK2)
| ~ member(X0,sK1)
| sK2 = X0
| ~ member(X0,X1)
| ~ member(sK2,X1)
| ~ order(sK0,X1) ),
inference(resolution,[],[f33,f27]) ).
fof(f42,plain,
! [X0] :
( ~ member(sK3,sK1)
| sK2 = sK3
| ~ member(sK3,X0)
| ~ member(sK2,X0)
| ~ order(sK0,X0)
| ~ member(sK2,sK1) ),
inference(resolution,[],[f38,f35]) ).
fof(f46,plain,
! [X0] :
( sK2 = sK3
| ~ member(sK3,X0)
| ~ member(sK2,X0)
| ~ order(sK0,X0)
| ~ member(sK2,sK1) ),
inference(forward_subsumption_resolution,[],[f42,f36]) ).
fof(f47,plain,
! [X0] :
( sK2 = sK3
| ~ member(sK3,X0)
| ~ member(sK2,X0)
| ~ order(sK0,X0) ),
inference(forward_subsumption_resolution,[],[f46,f34]) ).
fof(f49,definition,
( spl5_1
<=> ! [X0] :
( ~ member(sK3,X0)
| ~ order(sK0,X0)
| ~ member(sK2,X0) ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f50,plain,
( ! [X0] :
( ~ member(sK3,X0)
| ~ order(sK0,X0)
| ~ member(sK2,X0) )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f52,definition,
( spl5_2
<=> sK2 = sK3 ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f54,plain,
( sK2 = sK3
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f55,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f47,f52,f49]) ).
fof(f59,plain,
( sP4(sK2)
| ~ spl5_2 ),
inference(superposition,[],[f32,f54]) ).
fof(f60,plain,
( $false
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f59,f31]) ).
fof(f61,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f60]) ).
fof(f72,plain,
( ~ order(sK0,sK1)
| ~ member(sK2,sK1)
| ~ spl5_1 ),
inference(resolution,[],[f50,f36]) ).
fof(f73,plain,
( ~ member(sK2,sK1)
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f72,f23]) ).
fof(f74,plain,
( $false
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f73,f34]) ).
fof(f75,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[],[f74]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f55]) ).
cnf(s2,plain,
~ spl5_2,
inference(sat_conversion,[],[f61]) ).
cnf(s3,plain,
~ spl5_1,
inference(sat_conversion,[],[f75]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f76,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET790+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 02:49:45 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.64/1.32 % (2617856)Detected formulas, will run a generic FOF schedule.
% 2.64/1.32 % (2617864)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=883746112:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.64/1.32 % (2617864)First to succeed.
% 2.64/1.32 % (2617864)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2617856"
% 2.64/1.32 % (2617863)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=2493424105:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.64/1.32 % (2617865)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4177962166:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.64/1.32 % (2617861)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=3483091180:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.64/1.32 % (2617867)dis-21_1_sil=8000:lcm=predicate:random_seed=1299441745: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)
% 2.64/1.32 % (2617866)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2604008247:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.64/1.32 % (2617862)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=155991759:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.64/1.32 % (2617867)Also succeeded, but the first one will report.
% 2.64/1.32 % (2617865)Also succeeded, but the first one will report.
% 2.64/1.32 % (2617866)Also succeeded, but the first one will report.
% 2.64/1.32 % (2617864)Refutation found. Thanks to Tanya!
% 2.64/1.32 % SZS status Theorem for theBenchmark
% 2.64/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.64/1.33 % (2617864)------------------------------
% 2.64/1.33 % (2617864)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.33 % (2617864)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.33 % (2617864)CaDiCaL version: 2.1.3
% 2.64/1.33 % (2617864)Termination reason: Refutation
% 2.64/1.33 % (2617864)Time elapsed: 0.002 s
% 2.64/1.33 % (2617864)Peak memory usage: 89 MB
% 2.64/1.33 % (2617864)Instructions burned: 3 (million)
% 2.64/1.33 % (2617864)------------------------------
% 2.64/1.33 % (2617864)------------------------------
% 2.64/1.33 % (2617856)Success in time 0.286 s
% 2.64/1.33 % Vampire exiting
%------------------------------------------------------------------------------