%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET799+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 12:44:38 PM UTC 2026
% Result : Theorem 0.17s 0.46s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 9 unt; 0 def)
% Number of atoms : 130 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 136 ( 40 ~; 34 |; 46 &)
% ( 5 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-3 aty)
% Number of variables : 100 ( 84 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f14,axiom,
! [X0,X1,X2] :
( upper_bound(X2,X0,X1)
<=> ! [X3] :
( member(X3,X1)
=> apply(X0,X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',upper_bound) ).
fof(f20,axiom,
! [X0,X1,X2,X3] :
( least_upper_bound(X0,X1,X2,X3)
<=> ( member(X0,X1)
& upper_bound(X0,X2,X1)
& ! [X4] :
( ( member(X4,X3)
& upper_bound(X4,X2,X1) )
=> apply(X2,X0,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',least_upper_bound) ).
fof(f22,conjecture,
! [X0,X1] :
( order(X0,X1)
=> ! [X2,X3] :
( ( subset(X2,X1)
& subset(X3,X1)
& subset(X2,X3) )
=> ! [X4,X5] :
( ( least_upper_bound(X4,X2,X0,X1)
& least_upper_bound(X5,X3,X0,X1) )
=> apply(X0,X4,X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV11) ).
fof(f23,negated_conjecture,
~ ! [X0,X1] :
( order(X0,X1)
=> ! [X2,X3] :
( ( subset(X2,X1)
& subset(X3,X1)
& subset(X2,X3) )
=> ! [X4,X5] :
( ( least_upper_bound(X4,X2,X0,X1)
& least_upper_bound(X5,X3,X0,X1) )
=> apply(X0,X4,X5) ) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( least_upper_bound(X0,X1,X2,X3)
=> ( member(X0,X1)
& upper_bound(X0,X2,X1)
& ! [X4] :
( ( member(X4,X3)
& upper_bound(X4,X2,X1) )
=> apply(X2,X0,X4) ) ) ),
inference(unused_predicate_definition_removal,[],[f20]) ).
fof(f27,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f31,plain,
! [X0,X1,X2] :
( upper_bound(X2,X0,X1)
<=> ! [X3] :
( apply(X0,X3,X2)
| ~ member(X3,X1) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( ( member(X0,X1)
& upper_bound(X0,X2,X1)
& ! [X4] :
( apply(X2,X0,X4)
| ~ member(X4,X3)
| ~ upper_bound(X4,X2,X1) ) )
| ~ least_upper_bound(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f25]) ).
fof(f33,plain,
! [X0,X1,X2,X3] :
( ( member(X0,X1)
& upper_bound(X0,X2,X1)
& ! [X4] :
( apply(X2,X0,X4)
| ~ member(X4,X3)
| ~ upper_bound(X4,X2,X1) ) )
| ~ least_upper_bound(X0,X1,X2,X3) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
? [X0,X1] :
( ? [X2,X3] :
( ? [X4,X5] :
( ~ apply(X0,X4,X5)
& least_upper_bound(X4,X2,X0,X1)
& least_upper_bound(X5,X3,X0,X1) )
& subset(X2,X1)
& subset(X3,X1)
& subset(X2,X3) )
& order(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f35,plain,
? [X0,X1] :
( ? [X2,X3] :
( ? [X4,X5] :
( ~ apply(X0,X4,X5)
& least_upper_bound(X4,X2,X0,X1)
& least_upper_bound(X5,X3,X0,X1) )
& subset(X2,X1)
& subset(X3,X1)
& subset(X2,X3) )
& order(X0,X1) ),
inference(flattening,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f27]) ).
fof(f37,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f37]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ( upper_bound(X2,X0,X1)
| ? [X3] :
( ~ apply(X0,X3,X2)
& member(X3,X1) ) )
& ( ! [X3] :
( apply(X0,X3,X2)
| ~ member(X3,X1) )
| ~ upper_bound(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ( upper_bound(X2,X0,X1)
| ? [X3] :
( ~ apply(X0,X3,X2)
& member(X3,X1) ) )
& ( ! [X4] :
( apply(X0,X4,X2)
| ~ member(X4,X1) )
| ~ upper_bound(X2,X0,X1) ) ),
inference(rectify,[],[f55]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ( upper_bound(X2,X0,X1)
| ( ~ apply(X0,sK3(X0,X1,X2),X2)
& member(sK3(X0,X1,X2),X1) ) )
& ( ! [X4] :
( apply(X0,X4,X2)
| ~ member(X4,X1) )
| ~ upper_bound(X2,X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f56]) ).
fof(f58,plain,
( ~ apply(sK4,sK8,sK9)
& least_upper_bound(sK8,sK6,sK4,sK5)
& least_upper_bound(sK9,sK7,sK4,sK5)
& subset(sK6,sK5)
& subset(sK7,sK5)
& subset(sK6,sK7)
& order(sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8,sK9]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7),skolemize(X4,sK8),skolemize(X5,sK9)],[f35]) ).
fof(f59,plain,
! [X3,X0,X1] :
( ~ member(X3,X0)
| member(X3,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f88,plain,
! [X2,X0,X1,X4] :
( ~ upper_bound(X2,X0,X1)
| ~ member(X4,X1)
| apply(X0,X4,X2) ),
inference(cnf_transformation,[],[f57]) ).
fof(f92,plain,
! [X2,X3,X0,X1] :
( ~ least_upper_bound(X0,X1,X2,X3)
| upper_bound(X0,X2,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f93,plain,
! [X2,X3,X0,X1] :
( ~ least_upper_bound(X0,X1,X2,X3)
| member(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f95,plain,
subset(sK6,sK7),
inference(cnf_transformation,[],[f58]) ).
fof(f98,plain,
least_upper_bound(sK9,sK7,sK4,sK5),
inference(cnf_transformation,[],[f58]) ).
fof(f99,plain,
least_upper_bound(sK8,sK6,sK4,sK5),
inference(cnf_transformation,[],[f58]) ).
fof(f100,plain,
~ apply(sK4,sK8,sK9),
inference(cnf_transformation,[],[f58]) ).
fof(f119,plain,
member(sK8,sK6),
inference(resolution,[],[f93,f99]) ).
fof(f129,plain,
! [X0] :
( ~ subset(sK6,X0)
| member(sK8,X0) ),
inference(resolution,[],[f119,f59]) ).
fof(f149,plain,
member(sK8,sK7),
inference(resolution,[],[f129,f95]) ).
fof(f152,plain,
upper_bound(sK9,sK4,sK7),
inference(resolution,[],[f92,f98]) ).
fof(f214,plain,
! [X0] :
( apply(sK4,X0,sK9)
| ~ member(X0,sK7) ),
inference(resolution,[],[f88,f152]) ).
fof(f219,plain,
~ member(sK8,sK7),
inference(resolution,[],[f214,f100]) ).
fof(f221,plain,
$false,
inference(forward_subsumption_resolution,[],[f219,f149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET799+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 % Computer : n004.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 28 02:50:22 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 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
% 0.17/0.46 % (4103251)Will run a generic schedule for satisfiability detection.
% 0.17/0.46 % (4103259)dis+10_1_sil=32000:sp=arity:random_seed=2893715669:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.46 % (4103259) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4103251-4103259"...
% 0.17/0.46 % (4103257)% WARNING: option uhcvi not known.
% 0.17/0.46 % (4103259)...printing done.
% 0.17/0.46 % (4103259)Refutation found. Thanks to Tanya!
% 0.17/0.46 % SZS status Theorem for theBenchmark
% 0.17/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.46 % (4103259)------------------------------
% 0.17/0.46 % (4103259)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.46 % (4103259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.46 % (4103259)CaDiCaL version: 2.1.3
% 0.17/0.46 % (4103259)Termination reason: Refutation
% 0.17/0.46 % (4103259)Time elapsed: 0.003 s
% 0.17/0.46 % (4103259)Peak memory usage: 11 MB
% 0.17/0.46 % (4103259)Instructions burned: 7 (million)
% 0.17/0.46 % (4103251)Success in time 0.037 s
% 0.17/0.46 % Vampire exiting
%------------------------------------------------------------------------------