%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET803+4 : 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 : n016.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 12:41:58 PM UTC 2026
% Result : Theorem 3.33s 1.35s
% Output : Refutation 3.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 64 ( 13 unt; 5 def)
% Number of atoms : 167 ( 23 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 178 ( 75 ~; 61 |; 25 &)
% ( 7 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 6 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 86 ( 0 sgn 74 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1,X2] :
( greatest(X2,X0,X1)
<=> ( member(X2,X1)
& ! [X3] :
( member(X3,X1)
=> apply(X0,X3,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',greatest) ).
fof(f7,axiom,
! [X0,X1,X2] :
( max(X2,X0,X1)
<=> ( member(X2,X1)
& ! [X3] :
( ( member(X3,X1)
& apply(X0,X2,X3) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',max) ).
fof(f11,conjecture,
! [X0,X1] :
( order(X0,X1)
=> ! [X2,X3] :
( ( max(X2,X0,X1)
& max(X3,X0,X1)
& X2 != X3 )
=> ~ ? [X4] : greatest(X4,X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV15) ).
fof(f12,negated_conjecture,
~ ! [X0,X1] :
( order(X0,X1)
=> ! [X2,X3] :
( ( max(X2,X0,X1)
& max(X3,X0,X1)
& X2 != X3 )
=> ~ ? [X4] : greatest(X4,X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f14,plain,
! [X0,X1,X2] :
( max(X2,X0,X1)
=> ( member(X2,X1)
& ! [X3] :
( ( member(X3,X1)
& apply(X0,X2,X3) )
=> X2 = X3 ) ) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f15,plain,
! [X0,X1,X2] :
( greatest(X2,X0,X1)
=> ( member(X2,X1)
& ! [X3] :
( member(X3,X1)
=> apply(X0,X3,X2) ) ) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( member(X2,X1)
& ! [X3] :
( apply(X0,X3,X2)
| ~ member(X3,X1) ) )
| ~ greatest(X2,X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( member(X2,X1)
& ! [X3] :
( X2 = X3
| ~ member(X3,X1)
| ~ apply(X0,X2,X3) ) )
| ~ max(X2,X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( member(X2,X1)
& ! [X3] :
( X2 = X3
| ~ member(X3,X1)
| ~ apply(X0,X2,X3) ) )
| ~ max(X2,X0,X1) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
? [X0,X1] :
( ? [X2,X3] :
( ? [X4] : greatest(X4,X0,X1)
& max(X2,X0,X1)
& max(X3,X0,X1)
& X2 != X3 )
& order(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f23,plain,
? [X0,X1] :
( ? [X2,X3] :
( ? [X4] : greatest(X4,X0,X1)
& max(X2,X0,X1)
& max(X3,X0,X1)
& X2 != X3 )
& order(X0,X1) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
( greatest(sK4,sK0,sK1)
& max(sK2,sK0,sK1)
& max(sK3,sK0,sK1)
& sK2 != sK3
& order(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f23]) ).
fof(f28,plain,
! [X2,X3,X0,X1] :
( apply(X0,X3,X2)
| ~ member(X3,X1)
| ~ greatest(X2,X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f29,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ greatest(X2,X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f30,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,X1)
| X2 = X3
| ~ apply(X0,X2,X3)
| ~ max(X2,X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f31,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ max(X2,X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f33,plain,
sK2 != sK3,
inference(cnf_transformation,[],[f24]) ).
fof(f34,plain,
max(sK3,sK0,sK1),
inference(cnf_transformation,[],[f24]) ).
fof(f35,plain,
max(sK2,sK0,sK1),
inference(cnf_transformation,[],[f24]) ).
fof(f36,plain,
greatest(sK4,sK0,sK1),
inference(cnf_transformation,[],[f24]) ).
fof(f37,plain,
! [X2,X3,X0,X1,X4] :
( ~ max(X0,X2,X3)
| ~ apply(X2,X0,X1)
| X0 = X1
| ~ max(X1,X4,X3) ),
inference(resolution,[],[f30,f31]) ).
fof(f38,plain,
! [X2,X3,X0,X1,X4] :
( ~ greatest(X1,X4,X3)
| ~ apply(X2,X0,X1)
| ~ max(X0,X2,X3)
| X0 = X1 ),
inference(resolution,[],[f30,f29]) ).
fof(f39,plain,
! [X0,X1] :
( ~ apply(sK0,sK3,X0)
| sK3 = X0
| ~ max(X0,X1,sK1) ),
inference(resolution,[],[f37,f34]) ).
fof(f44,plain,
! [X2,X0,X1] :
( ~ greatest(X0,sK0,X2)
| ~ max(X0,X1,sK1)
| ~ member(sK3,X2)
| sK3 = X0 ),
inference(resolution,[],[f39,f28]) ).
fof(f52,plain,
! [X0] :
( ~ max(sK4,X0,sK1)
| ~ member(sK3,sK1)
| sK3 = sK4 ),
inference(resolution,[],[f44,f36]) ).
fof(f54,definition,
( spl5_1
<=> sK3 = sK4 ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f56,plain,
( sK3 = sK4
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f58,definition,
( spl5_2
<=> member(sK3,sK1) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f60,plain,
( ~ member(sK3,sK1)
| spl5_2 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f62,definition,
( spl5_3
<=> ! [X0] : ~ max(sK4,X0,sK1) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f63,plain,
( ! [X0] : ~ max(sK4,X0,sK1)
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f64,plain,
( spl5_1
| ~ spl5_2
| spl5_3 ),
inference(avatar_split_clause,[],[f52,f62,f58,f54]) ).
fof(f69,plain,
( ! [X0] : ~ max(sK3,X0,sK1)
| spl5_2 ),
inference(resolution,[],[f60,f31]) ).
fof(f71,plain,
! [X0,X1] :
( ~ max(X1,X0,sK1)
| ~ apply(X0,X1,sK4)
| sK4 = X1 ),
inference(resolution,[],[f38,f36]) ).
fof(f72,plain,
( $false
| spl5_2 ),
inference(resolution,[],[f69,f34]) ).
fof(f73,plain,
spl5_2,
inference(avatar_contradiction_clause,[],[f72]) ).
fof(f75,plain,
( ~ apply(sK0,sK2,sK4)
| sK2 = sK4 ),
inference(resolution,[],[f71,f35]) ).
fof(f77,definition,
( spl5_4
<=> sK2 = sK4 ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
fof(f79,plain,
( sK2 = sK4
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f81,definition,
( spl5_5
<=> apply(sK0,sK2,sK4) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
fof(f83,plain,
( ~ apply(sK0,sK2,sK4)
| spl5_5 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f84,plain,
( spl5_4
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f75,f81,f77]) ).
fof(f95,plain,
( ! [X0] :
( ~ greatest(sK4,sK0,X0)
| ~ member(sK2,X0) )
| spl5_5 ),
inference(resolution,[],[f83,f28]) ).
fof(f102,plain,
( ~ member(sK2,sK1)
| spl5_5 ),
inference(resolution,[],[f95,f36]) ).
fof(f104,plain,
( ! [X0] : ~ max(sK2,X0,sK1)
| spl5_5 ),
inference(resolution,[],[f102,f31]) ).
fof(f107,plain,
( $false
| spl5_5 ),
inference(resolution,[],[f104,f35]) ).
fof(f108,plain,
spl5_5,
inference(avatar_contradiction_clause,[],[f107]) ).
fof(f109,plain,
( ! [X0] : ~ max(sK2,X0,sK1)
| ~ spl5_3
| ~ spl5_4 ),
inference(superposition,[],[f63,f79]) ).
fof(f130,plain,
( $false
| ~ spl5_3
| ~ spl5_4 ),
inference(resolution,[],[f109,f35]) ).
fof(f131,plain,
( ~ spl5_3
| ~ spl5_4 ),
inference(avatar_contradiction_clause,[],[f130]) ).
fof(f132,plain,
( sK2 = sK3
| ~ spl5_1
| ~ spl5_4 ),
inference(forward_demodulation,[],[f56,f79]) ).
fof(f133,plain,
( $false
| ~ spl5_1
| ~ spl5_4 ),
inference(forward_subsumption_resolution,[],[f132,f33]) ).
fof(f134,plain,
( ~ spl5_1
| ~ spl5_4 ),
inference(avatar_contradiction_clause,[],[f133]) ).
cnf(s1,plain,
( spl5_1
| ~ spl5_2
| spl5_3 ),
inference(sat_conversion,[],[f64]) ).
cnf(s2,plain,
spl5_2,
inference(sat_conversion,[],[f73]) ).
cnf(s3,plain,
( spl5_4
| ~ spl5_5 ),
inference(sat_conversion,[],[f84]) ).
cnf(s5,plain,
spl5_5,
inference(sat_conversion,[],[f108]) ).
cnf(s6,plain,
( ~ spl5_3
| ~ spl5_4 ),
inference(sat_conversion,[],[f131]) ).
cnf(s7,plain,
( ~ spl5_1
| ~ spl5_4 ),
inference(sat_conversion,[],[f134]) ).
cnf(s8,plain,
spl5_4,
inference(rat,[],[s3,s5]) ).
cnf(s9,plain,
~ spl5_1,
inference(rat,[],[s7,s8]) ).
cnf(s10,plain,
~ spl5_3,
inference(rat,[],[s6,s8]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s1,s10,s2,s9]) ).
fof(f135,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET803+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n016.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 02:55:18 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 3.33/1.35 % (3214724)Detected formulas, will run a generic FOF schedule.
% 3.33/1.35 % (3214847)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=1095979833:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.33/1.35 % (3214849)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=1261217279:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.33/1.35 % (3214844)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=2794217074:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.33/1.35 % (3214854)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=380832593:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.33/1.35 % (3214854)First to succeed.
% 3.33/1.35 % (3214851)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2125012524:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.33/1.35 % (3214856)dis-21_1_sil=8000:lcm=predicate:random_seed=3541849574: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)
% 3.33/1.35 % (3214854)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3214724"
% 3.33/1.35 % (3214851)Also succeeded, but the first one will report.
% 3.33/1.35 % (3214852)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2522732440:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.33/1.35 % (3214852)Also succeeded, but the first one will report.
% 3.33/1.35 % (3214856)Instruction limit reached!
% 3.33/1.35 % (3214856)------------------------------
% 3.33/1.35 % (3214856)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.33/1.35 % (3214856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.33/1.35 % (3214856)CaDiCaL version: 2.1.3
% 3.33/1.35 % (3214856)Termination reason: Instruction limit
% 3.33/1.35 % (3214856)Termination phase: Saturation
% 3.33/1.35 % (3214856)Time elapsed: 0.062 s
% 3.33/1.35 % (3214856)Peak memory usage: 88 MB
% 3.33/1.35 % (3214856)Instructions burned: 129 (million)
% 3.33/1.35 % (3214895)lrs+10_1_sil=8000:sp=occurrence:random_seed=2134075226:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.33/1.35 % (3214895)Also succeeded, but the first one will report.
% 3.33/1.35 % (3214854)Refutation found. Thanks to Tanya!
% 3.33/1.35 % SZS status Theorem for theBenchmark
% 3.33/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.33/1.35 % (3214854)------------------------------
% 3.33/1.35 % (3214854)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.33/1.35 % (3214854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.33/1.35 % (3214854)CaDiCaL version: 2.1.3
% 3.33/1.35 % (3214854)Termination reason: Refutation
% 3.33/1.35 % (3214854)Time elapsed: 0.006 s
% 3.33/1.35 % (3214854)Peak memory usage: 90 MB
% 3.33/1.35 % (3214854)Instructions burned: 6 (million)
% 3.33/1.35 % (3214854)------------------------------
% 3.33/1.35 % (3214854)------------------------------
% 3.33/1.35 % (3214724)Success in time 0.406 s
% 3.33/1.35 % Vampire exiting
%------------------------------------------------------------------------------