%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET804+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 : 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 3.62s 1.41s
% Output : Refutation 3.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 37 ( 14 unt; 1 def)
% Number of atoms : 100 ( 20 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 99 ( 36 ~; 26 |; 25 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 65 ( 53 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
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(f8,axiom,
! [X0,X1,X2] :
( min(X2,X0,X1)
<=> ( member(X2,X1)
& ! [X3] :
( ( member(X3,X1)
& apply(X0,X3,X2) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',min) ).
fof(f11,conjecture,
! [X0,X1] :
( order(X0,X1)
=> ! [X2,X3] :
( ( min(X2,X0,X1)
& min(X3,X0,X1)
& X2 != X3 )
=> ~ ? [X4] : least(X4,X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV16) ).
fof(f12,negated_conjecture,
~ ! [X0,X1] :
( order(X0,X1)
=> ! [X2,X3] :
( ( min(X2,X0,X1)
& min(X3,X0,X1)
& X2 != X3 )
=> ~ ? [X4] : least(X4,X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f14,plain,
! [X0,X1,X2] :
( min(X2,X0,X1)
=> ( member(X2,X1)
& ! [X3] :
( ( member(X3,X1)
& apply(X0,X3,X2) )
=> X2 = X3 ) ) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f15,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(f17,plain,
? [X0,X1] :
( ? [X2,X3] :
( ? [X4] : least(X4,X0,X1)
& min(X2,X0,X1)
& min(X3,X0,X1)
& X2 != X3 )
& order(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f18,plain,
? [X0,X1] :
( ? [X2,X3] :
( ? [X4] : least(X4,X0,X1)
& min(X2,X0,X1)
& min(X3,X0,X1)
& X2 != X3 )
& order(X0,X1) ),
inference(flattening,[],[f17]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( member(X2,X1)
& ! [X3] :
( apply(X0,X2,X3)
| ~ member(X3,X1) ) )
| ~ least(X2,X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( member(X2,X1)
& ! [X3] :
( X2 = X3
| ~ member(X3,X1)
| ~ apply(X0,X3,X2) ) )
| ~ min(X2,X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( member(X2,X1)
& ! [X3] :
( X2 = X3
| ~ member(X3,X1)
| ~ apply(X0,X3,X2) ) )
| ~ min(X2,X0,X1) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
( least(sK4,sK0,sK1)
& min(sK2,sK0,sK1)
& min(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)],[f18]) ).
fof(f26,plain,
sK2 != sK3,
inference(cnf_transformation,[],[f24]) ).
fof(f27,plain,
min(sK3,sK0,sK1),
inference(cnf_transformation,[],[f24]) ).
fof(f28,plain,
min(sK2,sK0,sK1),
inference(cnf_transformation,[],[f24]) ).
fof(f29,plain,
least(sK4,sK0,sK1),
inference(cnf_transformation,[],[f24]) ).
fof(f33,plain,
! [X2,X3,X0,X1] :
( ~ least(X2,X0,X1)
| ~ member(X3,X1)
| apply(X0,X2,X3) ),
inference(cnf_transformation,[],[f21]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ least(X2,X0,X1)
| member(X2,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f35,plain,
! [X2,X3,X0,X1] :
( ~ min(X2,X0,X1)
| ~ member(X3,X1)
| ~ apply(X0,X3,X2)
| X2 = X3 ),
inference(cnf_transformation,[],[f23]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ min(X2,X0,X1)
| member(X2,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f37,definition,
~ sP5(sK2),
introduced(definition,[new_symbols(definition,[sP5])],[inequality_splitting_name_introduction]) ).
fof(f38,plain,
sP5(sK3),
inference(inequality_splitting,[],[f26,f37]) ).
fof(f39,plain,
! [X0] :
( ~ apply(sK0,X0,sK3)
| ~ member(X0,sK1)
| sK3 = X0 ),
inference(resolution,[],[f27,f35]) ).
fof(f40,plain,
member(sK3,sK1),
inference(resolution,[],[f27,f36]) ).
fof(f41,plain,
! [X0] :
( ~ apply(sK0,X0,sK2)
| ~ member(X0,sK1)
| sK2 = X0 ),
inference(resolution,[],[f28,f35]) ).
fof(f42,plain,
member(sK2,sK1),
inference(resolution,[],[f28,f36]) ).
fof(f43,plain,
! [X0] :
( apply(sK0,sK4,X0)
| ~ member(X0,sK1) ),
inference(resolution,[],[f29,f33]) ).
fof(f44,plain,
member(sK4,sK1),
inference(resolution,[],[f29,f34]) ).
fof(f47,plain,
( ~ member(sK4,sK1)
| sK3 = sK4
| ~ member(sK3,sK1) ),
inference(resolution,[],[f39,f43]) ).
fof(f49,plain,
( sK3 = sK4
| ~ member(sK3,sK1) ),
inference(forward_subsumption_resolution,[],[f47,f44]) ).
fof(f50,plain,
sK3 = sK4,
inference(forward_subsumption_resolution,[],[f49,f40]) ).
fof(f51,plain,
( ~ member(sK4,sK1)
| sK2 = sK4
| ~ member(sK2,sK1) ),
inference(resolution,[],[f41,f43]) ).
fof(f53,plain,
( sK2 = sK4
| ~ member(sK2,sK1) ),
inference(forward_subsumption_resolution,[],[f51,f44]) ).
fof(f54,plain,
sK2 = sK4,
inference(forward_subsumption_resolution,[],[f53,f42]) ).
fof(f59,plain,
sK2 = sK3,
inference(superposition,[],[f50,f54]) ).
fof(f66,plain,
sP5(sK2),
inference(superposition,[],[f38,f59]) ).
fof(f67,plain,
$false,
inference(forward_subsumption_resolution,[],[f66,f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET804+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n016.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 02:55:32 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 3.62/1.41 % (3215505)Detected formulas, will run a generic FOF schedule.
% 3.62/1.41 % (3215512)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=707027563:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.62/1.41 % (3215511)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=2895932620:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.62/1.41 % (3215510)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=602541376:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.62/1.41 % (3215514)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2895246934:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.62/1.41 % (3215516)dis-21_1_sil=8000:lcm=predicate:random_seed=3176494459: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)
% 3.62/1.41 % (3215513)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3283215513:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.62/1.41 % (3215513)First to succeed.
% 3.62/1.41 % (3215514)Also succeeded, but the first one will report.
% 3.62/1.41 % (3215513)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3215505"
% 3.62/1.41 % (3215515)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=81505647:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.62/1.41 % (3215515)Also succeeded, but the first one will report.
% 3.62/1.41 % (3215516)Instruction limit reached!
% 3.62/1.41 % (3215516)------------------------------
% 3.62/1.41 % (3215516)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.41 % (3215516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.41 % (3215516)CaDiCaL version: 2.1.3
% 3.62/1.41 % (3215516)Termination reason: Instruction limit
% 3.62/1.41 % (3215516)Termination phase: Saturation
% 3.62/1.41 % (3215516)Time elapsed: 0.058 s
% 3.62/1.41 % (3215516)Peak memory usage: 88 MB
% 3.62/1.41 % (3215516)Instructions burned: 130 (million)
% 3.62/1.41 % (3215524)lrs+10_1_sil=8000:sp=occurrence:random_seed=1289004060:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.62/1.41 % (3215524)Also succeeded, but the first one will report.
% 3.62/1.41 % (3215513)Refutation found. Thanks to Tanya!
% 3.62/1.41 % SZS status Theorem for theBenchmark
% 3.62/1.41 % SZS output start Proof for theBenchmark
% See solution above
% 3.62/1.41 % (3215513)------------------------------
% 3.62/1.41 % (3215513)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.41 % (3215513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.41 % (3215513)CaDiCaL version: 2.1.3
% 3.62/1.41 % (3215513)Termination reason: Refutation
% 3.62/1.41 % (3215513)Time elapsed: 0.003 s
% 3.62/1.41 % (3215513)Peak memory usage: 88 MB
% 3.62/1.41 % (3215513)Instructions burned: 2 (million)
% 3.62/1.41 % (3215513)------------------------------
% 3.62/1.41 % (3215513)------------------------------
% 3.62/1.41 % (3215505)Success in time 0.434 s
% 3.62/1.41 % Vampire exiting
%------------------------------------------------------------------------------