%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET804+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 : n004.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 12:44:39 PM UTC 2026
% Result : Theorem 0.18s 0.47s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 11 unt; 0 def)
% Number of atoms : 97 ( 20 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 98 ( 35 ~; 26 |; 25 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 5 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/sandbox2/benchmark/Axioms/SET006+3.ax',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/sandbox2/benchmark/Axioms/SET006+3.ax',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/sandbox2/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(f19,plain,
! [X0,X1,X2] :
( ( member(X2,X1)
& ! [X3] :
( apply(X0,X2,X3)
| ~ member(X3,X1) ) )
| ~ least(X2,X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f20,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(f21,plain,
! [X0,X1,X2] :
( ( member(X2,X1)
& ! [X3] :
( X2 = X3
| ~ member(X3,X1)
| ~ apply(X0,X3,X2) ) )
| ~ min(X2,X0,X1) ),
inference(flattening,[],[f20]) ).
fof(f22,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(f23,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,[],[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)],[f23]) ).
fof(f28,plain,
! [X2,X3,X0,X1] :
( ~ least(X2,X0,X1)
| ~ member(X3,X1)
| apply(X0,X2,X3) ),
inference(cnf_transformation,[],[f19]) ).
fof(f29,plain,
! [X2,X0,X1] :
( ~ least(X2,X0,X1)
| member(X2,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f30,plain,
! [X2,X3,X0,X1] :
( ~ min(X2,X0,X1)
| ~ member(X3,X1)
| ~ apply(X0,X3,X2)
| X2 = X3 ),
inference(cnf_transformation,[],[f21]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ min(X2,X0,X1)
| member(X2,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f33,plain,
sK2 != sK3,
inference(cnf_transformation,[],[f24]) ).
fof(f34,plain,
min(sK3,sK0,sK1),
inference(cnf_transformation,[],[f24]) ).
fof(f35,plain,
min(sK2,sK0,sK1),
inference(cnf_transformation,[],[f24]) ).
fof(f36,plain,
least(sK4,sK0,sK1),
inference(cnf_transformation,[],[f24]) ).
fof(f43,plain,
member(sK4,sK1),
inference(resolution,[],[f29,f36]) ).
fof(f188,plain,
member(sK3,sK1),
inference(resolution,[],[f31,f34]) ).
fof(f189,plain,
member(sK2,sK1),
inference(resolution,[],[f31,f35]) ).
fof(f193,plain,
! [X0] :
( apply(sK0,sK4,X0)
| ~ member(X0,sK1) ),
inference(resolution,[],[f28,f36]) ).
fof(f220,plain,
! [X0] :
( ~ apply(sK0,X0,sK3)
| ~ member(X0,sK1)
| sK3 = X0 ),
inference(resolution,[],[f30,f34]) ).
fof(f221,plain,
! [X0] :
( ~ apply(sK0,X0,sK2)
| ~ member(X0,sK1)
| sK2 = X0 ),
inference(resolution,[],[f30,f35]) ).
fof(f223,plain,
( ~ member(sK4,sK1)
| sK3 = sK4
| ~ member(sK3,sK1) ),
inference(resolution,[],[f220,f193]) ).
fof(f225,plain,
( sK3 = sK4
| ~ member(sK3,sK1) ),
inference(forward_subsumption_resolution,[],[f223,f43]) ).
fof(f227,plain,
sK3 = sK4,
inference(forward_subsumption_resolution,[],[f225,f188]) ).
fof(f236,plain,
( ~ member(sK4,sK1)
| sK2 = sK4
| ~ member(sK2,sK1) ),
inference(resolution,[],[f221,f193]) ).
fof(f240,plain,
( sK2 = sK4
| ~ member(sK2,sK1) ),
inference(forward_subsumption_resolution,[],[f236,f43]) ).
fof(f244,plain,
sK2 = sK4,
inference(forward_subsumption_resolution,[],[f240,f189]) ).
fof(f249,plain,
sK2 = sK3,
inference(superposition,[],[f227,f244]) ).
fof(f253,plain,
$false,
inference(forward_subsumption_resolution,[],[f249,f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET804+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n004.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 02:50:37 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.18/0.47 % (4103664)Will run a generic schedule for satisfiability detection.
% 0.18/0.47 % (4103671)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3972639230:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.47 % (4103671) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4103664-4103671"...
% 0.18/0.47 % (4103670)% WARNING: option uhcvi not known.
% 0.18/0.47 % (4103671)...printing done.
% 0.18/0.47 % (4103671)Refutation found. Thanks to Tanya!
% 0.18/0.47 % SZS status Theorem for theBenchmark
% 0.18/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.47 % (4103671)------------------------------
% 0.18/0.47 % (4103671)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.47 % (4103671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.47 % (4103671)CaDiCaL version: 2.1.3
% 0.18/0.47 % (4103671)Termination reason: Refutation
% 0.18/0.47 % (4103671)Time elapsed: 0.003 s
% 0.18/0.47 % (4103671)Peak memory usage: 12 MB
% 0.18/0.47 % (4103671)Instructions burned: 6 (million)
% 0.18/0.47 % (4103664)Success in time 0.039 s
% 0.18/0.47 % Vampire exiting
%------------------------------------------------------------------------------