%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET793+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 : n002.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 3.60s 1.49s
% Output : Refutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 60 ( 10 unt; 2 def)
% Number of atoms : 205 ( 14 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 247 ( 102 ~; 103 |; 24 &)
% ( 5 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 3 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 98 ( 0 sgn 90 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( total_order(X0,X1)
<=> ( order(X0,X1)
& ! [X2,X3] :
( ( member(X2,X1)
& member(X3,X1) )
=> ( apply(X0,X2,X3)
| apply(X0,X3,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_order) ).
fof(f5,axiom,
! [X0,X1,X2] :
( greatest(X2,X0,X1)
<=> ( member(X2,X1)
& ! [X3] :
( member(X3,X1)
=> apply(X0,X3,X2) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',max) ).
fof(f11,conjecture,
! [X0,X1,X2] :
( ( total_order(X0,X1)
& max(X2,X0,X1) )
=> greatest(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV5) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2] :
( ( total_order(X0,X1)
& max(X2,X0,X1) )
=> greatest(X2,X0,X1) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,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(f14,plain,
! [X0,X1,X2] :
( ( member(X2,X1)
& ! [X3] :
( member(X3,X1)
=> apply(X0,X3,X2) ) )
=> greatest(X2,X0,X1) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f15,plain,
! [X0,X1] :
( total_order(X0,X1)
=> ( order(X0,X1)
& ! [X2,X3] :
( ( member(X2,X1)
& member(X3,X1) )
=> ( apply(X0,X2,X3)
| apply(X0,X3,X2) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f16,plain,
! [X0,X1] :
( total_order(X0,X1)
=> ! [X2,X3] :
( ( member(X2,X1)
& member(X3,X1) )
=> ( apply(X0,X2,X3)
| apply(X0,X3,X2) ) ) ),
inference(pure_predicate_removal,[],[f15]) ).
fof(f17,plain,
? [X0,X1,X2] :
( ~ greatest(X2,X0,X1)
& total_order(X0,X1)
& max(X2,X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f18,plain,
? [X0,X1,X2] :
( ~ greatest(X2,X0,X1)
& total_order(X0,X1)
& max(X2,X0,X1) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ! [X2,X3] :
( apply(X0,X2,X3)
| apply(X0,X3,X2)
| ~ member(X2,X1)
| ~ member(X3,X1) )
| ~ total_order(X0,X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f20,plain,
! [X0,X1] :
( ! [X2,X3] :
( apply(X0,X2,X3)
| apply(X0,X3,X2)
| ~ member(X2,X1)
| ~ member(X3,X1) )
| ~ total_order(X0,X1) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( greatest(X2,X0,X1)
| ~ member(X2,X1)
| ? [X3] :
( ~ apply(X0,X3,X2)
& member(X3,X1) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f22,plain,
! [X0,X1,X2] :
( greatest(X2,X0,X1)
| ~ member(X2,X1)
| ? [X3] :
( ~ apply(X0,X3,X2)
& member(X3,X1) ) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( member(X2,X1)
& ! [X3] :
( X2 = X3
| ~ member(X3,X1)
| ~ apply(X0,X2,X3) ) )
| ~ max(X2,X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( member(X2,X1)
& ! [X3] :
( X2 = X3
| ~ member(X3,X1)
| ~ apply(X0,X2,X3) ) )
| ~ max(X2,X0,X1) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
( ~ greatest(sK2,sK0,sK1)
& total_order(sK0,sK1)
& max(sK2,sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f18]) ).
fof(f26,plain,
! [X0,X1,X2] :
( greatest(X2,X0,X1)
| ~ member(X2,X1)
| ( ~ apply(X0,sK3(X0,X1,X2),X2)
& member(sK3(X0,X1,X2),X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f22]) ).
fof(f27,plain,
max(sK2,sK0,sK1),
inference(cnf_transformation,[],[f25]) ).
fof(f28,plain,
total_order(sK0,sK1),
inference(cnf_transformation,[],[f25]) ).
fof(f29,plain,
~ greatest(sK2,sK0,sK1),
inference(cnf_transformation,[],[f25]) ).
fof(f30,plain,
! [X2,X3,X0,X1] :
( apply(X0,X3,X2)
| apply(X0,X2,X3)
| ~ member(X2,X1)
| ~ member(X3,X1)
| ~ total_order(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f31,plain,
! [X2,X0,X1] :
( member(sK3(X0,X1,X2),X1)
| ~ member(X2,X1)
| greatest(X2,X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f32,plain,
! [X2,X0,X1] :
( ~ apply(X0,sK3(X0,X1,X2),X2)
| ~ member(X2,X1)
| greatest(X2,X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f33,plain,
! [X2,X3,X0,X1] :
( ~ max(X2,X0,X1)
| ~ member(X3,X1)
| ~ apply(X0,X2,X3)
| X2 = X3 ),
inference(cnf_transformation,[],[f24]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ max(X2,X0,X1)
| member(X2,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f35,plain,
! [X0] :
( ~ apply(sK0,sK2,X0)
| ~ member(X0,sK1)
| sK2 = X0 ),
inference(resolution,[],[f27,f33]) ).
fof(f36,plain,
member(sK2,sK1),
inference(resolution,[],[f27,f34]) ).
fof(f37,plain,
! [X0,X1] :
( apply(sK0,X0,sK2)
| sK2 = X0
| ~ member(X0,sK1)
| ~ member(X0,X1)
| ~ member(sK2,X1)
| ~ total_order(sK0,X1) ),
inference(resolution,[],[f35,f30]) ).
fof(f39,plain,
! [X0,X1] :
( ~ member(sK3(sK0,X0,sK2),sK1)
| sK2 = sK3(sK0,X0,sK2)
| ~ member(sK3(sK0,X0,sK2),X1)
| ~ member(sK2,X1)
| ~ total_order(sK0,X1)
| ~ member(sK2,X0)
| greatest(sK2,sK0,X0) ),
inference(resolution,[],[f37,f32]) ).
fof(f41,plain,
! [X0] :
( sK2 = sK3(sK0,sK1,sK2)
| ~ member(sK3(sK0,sK1,sK2),X0)
| ~ member(sK2,X0)
| ~ total_order(sK0,X0)
| ~ member(sK2,sK1)
| greatest(sK2,sK0,sK1)
| ~ member(sK2,sK1)
| greatest(sK2,sK0,sK1) ),
inference(resolution,[],[f39,f31]) ).
fof(f42,plain,
! [X0] :
( sK2 = sK3(sK0,sK1,sK2)
| ~ member(sK3(sK0,sK1,sK2),X0)
| ~ member(sK2,X0)
| ~ total_order(sK0,X0)
| ~ member(sK2,sK1)
| greatest(sK2,sK0,sK1) ),
inference(duplicate_literal_removal,[],[f41]) ).
fof(f43,plain,
! [X0] :
( sK2 = sK3(sK0,sK1,sK2)
| ~ member(sK3(sK0,sK1,sK2),X0)
| ~ member(sK2,X0)
| ~ total_order(sK0,X0)
| greatest(sK2,sK0,sK1) ),
inference(forward_subsumption_resolution,[],[f42,f36]) ).
fof(f44,plain,
! [X0] :
( sK2 = sK3(sK0,sK1,sK2)
| ~ member(sK3(sK0,sK1,sK2),X0)
| ~ member(sK2,X0)
| ~ total_order(sK0,X0) ),
inference(forward_subsumption_resolution,[],[f43,f29]) ).
fof(f46,definition,
( spl4_1
<=> ! [X0] :
( ~ member(sK3(sK0,sK1,sK2),X0)
| ~ total_order(sK0,X0)
| ~ member(sK2,X0) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f47,plain,
( ! [X0] :
( ~ member(sK3(sK0,sK1,sK2),X0)
| ~ total_order(sK0,X0)
| ~ member(sK2,X0) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f49,definition,
( spl4_2
<=> sK2 = sK3(sK0,sK1,sK2) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f51,plain,
( sK2 = sK3(sK0,sK1,sK2)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f52,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f44,f49,f46]) ).
fof(f54,plain,
( ~ apply(sK0,sK2,sK2)
| ~ member(sK2,sK1)
| greatest(sK2,sK0,sK1)
| ~ spl4_2 ),
inference(superposition,[],[f32,f51]) ).
fof(f55,plain,
( ~ apply(sK0,sK2,sK2)
| greatest(sK2,sK0,sK1)
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f54,f36]) ).
fof(f56,plain,
( ~ apply(sK0,sK2,sK2)
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f55,f29]) ).
fof(f58,plain,
( ! [X0] :
( apply(sK0,sK2,sK2)
| ~ member(sK2,X0)
| ~ member(sK2,X0)
| ~ total_order(sK0,X0) )
| ~ spl4_2 ),
inference(resolution,[],[f56,f30]) ).
fof(f59,plain,
( ! [X0] :
( apply(sK0,sK2,sK2)
| ~ member(sK2,X0)
| ~ total_order(sK0,X0) )
| ~ spl4_2 ),
inference(duplicate_literal_removal,[],[f58]) ).
fof(f61,plain,
( ! [X0] :
( ~ total_order(sK0,X0)
| ~ member(sK2,X0) )
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f59,f56]) ).
fof(f62,plain,
( ~ member(sK2,sK1)
| ~ spl4_2 ),
inference(resolution,[],[f61,f28]) ).
fof(f63,plain,
( $false
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f62,f36]) ).
fof(f64,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f63]) ).
fof(f65,plain,
( ~ total_order(sK0,sK1)
| ~ member(sK2,sK1)
| ~ member(sK2,sK1)
| greatest(sK2,sK0,sK1)
| ~ spl4_1 ),
inference(resolution,[],[f47,f31]) ).
fof(f66,plain,
( ~ total_order(sK0,sK1)
| ~ member(sK2,sK1)
| greatest(sK2,sK0,sK1)
| ~ spl4_1 ),
inference(duplicate_literal_removal,[],[f65]) ).
fof(f67,plain,
( ~ member(sK2,sK1)
| greatest(sK2,sK0,sK1)
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f66,f28]) ).
fof(f68,plain,
( greatest(sK2,sK0,sK1)
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f67,f36]) ).
fof(f69,plain,
( $false
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f68,f29]) ).
fof(f70,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f69]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f52]) ).
cnf(s2,plain,
~ spl4_2,
inference(sat_conversion,[],[f64]) ).
cnf(s3,plain,
~ spl4_1,
inference(sat_conversion,[],[f70]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f71,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET793+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n002.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 02:52:37 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 3.60/1.49 % (4107321)Detected formulas, will run a generic FOF schedule.
% 3.60/1.49 % (4107414)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=3946836123:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.60/1.49 % (4107419)dis-21_1_sil=8000:lcm=predicate:random_seed=2087388920: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)
% 3.60/1.49 % (4107413)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=4197186862:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.60/1.49 % (4107415)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=948668597:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.60/1.49 % (4107416)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3000364766:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.60/1.49 % (4107417)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1065946335:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.60/1.49 % (4107416)First to succeed.
% 3.60/1.49 % (4107417)Also succeeded, but the first one will report.
% 3.60/1.49 % (4107416)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4107321"
% 3.60/1.49 % (4107419)Instruction limit reached!
% 3.60/1.49 % (4107419)------------------------------
% 3.60/1.49 % (4107419)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.49 % (4107419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.49 % (4107419)CaDiCaL version: 2.1.3
% 3.60/1.49 % (4107419)Termination reason: Instruction limit
% 3.60/1.49 % (4107419)Termination phase: Saturation
% 3.60/1.49 % (4107419)Time elapsed: 0.057 s
% 3.60/1.49 % (4107419)Peak memory usage: 88 MB
% 3.60/1.49 % (4107419)Instructions burned: 131 (million)
% 3.60/1.49 % (4107418)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2966045229:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.60/1.49 % (4107418)Also succeeded, but the first one will report.
% 3.60/1.49 % (4107440)lrs+10_1_sil=8000:sp=occurrence:random_seed=118206705:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.60/1.49 % (4107440)Also succeeded, but the first one will report.
% 3.60/1.49 % (4107416)Refutation found. Thanks to Tanya!
% 3.60/1.49 % SZS status Theorem for theBenchmark
% 3.60/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.60/1.49 % (4107416)------------------------------
% 3.60/1.49 % (4107416)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.49 % (4107416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.49 % (4107416)CaDiCaL version: 2.1.3
% 3.60/1.49 % (4107416)Termination reason: Refutation
% 3.60/1.49 % (4107416)Time elapsed: 0.004 s
% 3.60/1.49 % (4107416)Peak memory usage: 89 MB
% 3.60/1.49 % (4107416)Instructions burned: 3 (million)
% 3.60/1.49 % (4107416)------------------------------
% 3.60/1.49 % (4107416)------------------------------
% 3.60/1.49 % (4107321)Success in time 0.431 s
% 3.60/1.49 % Vampire exiting
%------------------------------------------------------------------------------