%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU056+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 12:51:52 PM UTC 2026
% Result : Theorem 0.11s 0.45s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 10 unt; 0 def)
% Number of atoms : 76 ( 19 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 71 ( 25 ~; 20 |; 18 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 43 ( 37 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f26,axiom,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( one_to_one(X2)
=> relation_image(X2,set_intersection2(X0,X1)) = set_intersection2(relation_image(X2,X0),relation_image(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_funct_1) ).
fof(f27,conjecture,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( disjoint(X0,X1)
& one_to_one(X2) )
=> disjoint(relation_image(X2,X0),relation_image(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t125_funct_1) ).
fof(f28,negated_conjecture,
~ ! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( disjoint(X0,X1)
& one_to_one(X2) )
=> disjoint(relation_image(X2,X0),relation_image(X2,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,axiom,
! [X0] :
( relation(X0)
=> relation_image(X0,empty_set) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t149_relat_1) ).
fof(f53,plain,
! [X0,X1,X2] :
( relation_image(X2,set_intersection2(X0,X1)) = set_intersection2(relation_image(X2,X0),relation_image(X2,X1))
| ~ one_to_one(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(ennf_transformation,[],[f26]) ).
fof(f54,plain,
! [X0,X1,X2] :
( relation_image(X2,set_intersection2(X0,X1)) = set_intersection2(relation_image(X2,X0),relation_image(X2,X1))
| ~ one_to_one(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(flattening,[],[f53]) ).
fof(f55,plain,
? [X0,X1,X2] :
( ~ disjoint(relation_image(X2,X0),relation_image(X2,X1))
& disjoint(X0,X1)
& one_to_one(X2)
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f28]) ).
fof(f56,plain,
? [X0,X1,X2] :
( ~ disjoint(relation_image(X2,X0),relation_image(X2,X1))
& disjoint(X0,X1)
& one_to_one(X2)
& relation(X2)
& function(X2) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0] :
( relation_image(X0,empty_set) = empty_set
| ~ relation(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f68,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set )
& ( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f80,plain,
( ~ disjoint(relation_image(sK13,sK11),relation_image(sK13,sK12))
& disjoint(sK11,sK12)
& one_to_one(sK13)
& relation(sK13)
& function(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13)],[f56]) ).
fof(f88,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = empty_set ),
inference(cnf_transformation,[],[f68]) ).
fof(f89,plain,
! [X0,X1] :
( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f120,plain,
! [X2,X0,X1] :
( ~ one_to_one(X2)
| relation_image(X2,set_intersection2(X0,X1)) = set_intersection2(relation_image(X2,X0),relation_image(X2,X1))
| ~ relation(X2)
| ~ function(X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f121,plain,
function(sK13),
inference(cnf_transformation,[],[f80]) ).
fof(f122,plain,
relation(sK13),
inference(cnf_transformation,[],[f80]) ).
fof(f123,plain,
one_to_one(sK13),
inference(cnf_transformation,[],[f80]) ).
fof(f124,plain,
disjoint(sK11,sK12),
inference(cnf_transformation,[],[f80]) ).
fof(f125,plain,
~ disjoint(relation_image(sK13,sK11),relation_image(sK13,sK12)),
inference(cnf_transformation,[],[f80]) ).
fof(f126,plain,
! [X0] :
( ~ relation(X0)
| empty_set = relation_image(X0,empty_set) ),
inference(cnf_transformation,[],[f57]) ).
fof(f183,plain,
empty_set = relation_image(sK13,empty_set),
inference(resolution,[],[f126,f122]) ).
fof(f208,plain,
empty_set = set_intersection2(sK11,sK12),
inference(resolution,[],[f88,f124]) ).
fof(f258,plain,
! [X0,X1] :
( relation_image(sK13,set_intersection2(X0,X1)) = set_intersection2(relation_image(sK13,X0),relation_image(sK13,X1))
| ~ relation(sK13)
| ~ function(sK13) ),
inference(resolution,[],[f120,f123]) ).
fof(f263,plain,
! [X0,X1] :
( relation_image(sK13,set_intersection2(X0,X1)) = set_intersection2(relation_image(sK13,X0),relation_image(sK13,X1))
| ~ function(sK13) ),
inference(forward_subsumption_resolution,[],[f258,f122]) ).
fof(f266,plain,
! [X0,X1] : relation_image(sK13,set_intersection2(X0,X1)) = set_intersection2(relation_image(sK13,X0),relation_image(sK13,X1)),
inference(forward_subsumption_resolution,[],[f263,f121]) ).
fof(f274,plain,
! [X0,X1] :
( empty_set != relation_image(sK13,set_intersection2(X0,X1))
| disjoint(relation_image(sK13,X0),relation_image(sK13,X1)) ),
inference(superposition,[],[f89,f266]) ).
fof(f302,plain,
( empty_set != relation_image(sK13,empty_set)
| disjoint(relation_image(sK13,sK11),relation_image(sK13,sK12)) ),
inference(superposition,[],[f274,f208]) ).
fof(f303,plain,
disjoint(relation_image(sK13,sK11),relation_image(sK13,sK12)),
inference(forward_subsumption_resolution,[],[f302,f183]) ).
fof(f306,plain,
$false,
inference(forward_subsumption_resolution,[],[f303,f125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU056+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n019.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 03:28:18 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.45 % (3634268)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (3634282)dis+10_1_sil=32000:sp=arity:random_seed=497914817:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.45 % (3634280)% WARNING: option uhcvi not known.
% 0.11/0.45 % (3634282) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3634268-3634282"...
% 0.11/0.45 % (3634282)...printing done.
% 0.11/0.45 % (3634282)Refutation found. Thanks to Tanya!
% 0.11/0.45 % SZS status Theorem for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (3634282)------------------------------
% 0.11/0.45 % (3634282)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (3634282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (3634282)CaDiCaL version: 2.1.3
% 0.11/0.45 % (3634282)Termination reason: Refutation
% 0.11/0.45 % (3634282)Time elapsed: 0.004 s
% 0.11/0.45 % (3634282)Peak memory usage: 12 MB
% 0.11/0.45 % (3634282)Instructions burned: 8 (million)
% 0.11/0.45 % (3634268)Success in time 0.034 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------