%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET974+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 : n005.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 12:45:06 PM UTC 2026
% Result : Theorem 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 12 unt; 2 def)
% Number of atoms : 83 ( 4 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 80 ( 38 ~; 24 |; 13 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-5 aty)
% Number of variables : 73 ( 0 sgn 64 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f9,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f10,axiom,
! [X0,X1,X2,X3,X4] :
~ ( in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)))
& ! [X5,X6] :
~ ( X0 = ordered_pair(X5,X6)
& in(X5,set_intersection2(X1,X3))
& in(X6,set_intersection2(X2,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t104_zfmisc_1) ).
fof(f11,conjecture,
! [X0,X1,X2,X3] :
( ( disjoint(X0,X1)
| disjoint(X2,X3) )
=> disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t127_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( disjoint(X0,X1)
| disjoint(X2,X3) )
=> disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,axiom,
! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ~ ( ? [X2] : in(X2,set_intersection2(X0,X1))
& disjoint(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f15,plain,
! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X0,X1))
& disjoint(X0,X1) ) ),
inference(rectify,[],[f13]) ).
fof(f17,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f18,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)))
| ? [X5,X6] :
( X0 = ordered_pair(X5,X6)
& in(X5,set_intersection2(X1,X3))
& in(X6,set_intersection2(X2,X4)) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f19,plain,
? [X0,X1,X2,X3] :
( ~ disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
& ( disjoint(X0,X1)
| disjoint(X2,X3) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f20,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ( ! [X3] : ~ in(X3,set_intersection2(X0,X1))
| ~ disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f23,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f29,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f30,plain,
! [X2,X3,X0,X1,X4] :
( in(sK3(X0,X1,X2,X3,X4),set_intersection2(X2,X4))
| ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
inference(cnf_transformation,[],[f18]) ).
fof(f31,plain,
! [X2,X3,X0,X1,X4] :
( in(sK2(X0,X1,X2,X3,X4),set_intersection2(X1,X3))
| ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
inference(cnf_transformation,[],[f18]) ).
fof(f33,plain,
( disjoint(sK6,sK7)
| disjoint(sK4,sK5) ),
inference(cnf_transformation,[],[f19]) ).
fof(f34,plain,
~ disjoint(cartesian_product2(sK4,sK6),cartesian_product2(sK5,sK7)),
inference(cnf_transformation,[],[f19]) ).
fof(f35,plain,
! [X0,X1] :
( disjoint(X0,X1)
| in(sK8(X0,X1),set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f36,plain,
! [X3,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X3,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f40,definition,
( spl9_1
<=> disjoint(sK4,sK5) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f42,plain,
( disjoint(sK4,sK5)
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f44,definition,
( spl9_2
<=> disjoint(sK6,sK7) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
fof(f46,plain,
( disjoint(sK6,sK7)
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f47,plain,
( spl9_1
| spl9_2 ),
inference(avatar_split_clause,[],[f33,f44,f40]) ).
fof(f58,plain,
( ! [X0] : ~ in(X0,set_intersection2(sK6,sK7))
| ~ spl9_2 ),
inference(resolution,[],[f36,f46]) ).
fof(f60,plain,
in(sK8(cartesian_product2(sK4,sK6),cartesian_product2(sK5,sK7)),set_intersection2(cartesian_product2(sK4,sK6),cartesian_product2(sK5,sK7))),
inference(resolution,[],[f35,f34]) ).
fof(f62,plain,
! [X0,X1] :
( disjoint(X1,X0)
| in(sK8(X0,X1),set_intersection2(X0,X1)) ),
inference(resolution,[],[f35,f29]) ).
fof(f65,plain,
( ! [X2,X0,X1] : ~ in(X0,set_intersection2(cartesian_product2(X1,sK6),cartesian_product2(X2,sK7)))
| ~ spl9_2 ),
inference(resolution,[],[f30,f58]) ).
fof(f71,plain,
( $false
| ~ spl9_2 ),
inference(resolution,[],[f65,f60]) ).
fof(f75,plain,
~ spl9_2,
inference(avatar_contradiction_clause,[],[f71]) ).
fof(f76,plain,
( ! [X0] : ~ in(X0,set_intersection2(sK4,sK5))
| ~ spl9_1 ),
inference(resolution,[],[f42,f36]) ).
fof(f84,plain,
( ! [X2,X0,X1] : ~ in(X0,set_intersection2(cartesian_product2(sK4,X1),cartesian_product2(sK5,X2)))
| ~ spl9_1 ),
inference(resolution,[],[f76,f31]) ).
fof(f109,plain,
in(sK8(cartesian_product2(sK5,sK7),cartesian_product2(sK4,sK6)),set_intersection2(cartesian_product2(sK5,sK7),cartesian_product2(sK4,sK6))),
inference(resolution,[],[f62,f34]) ).
fof(f115,plain,
in(sK8(cartesian_product2(sK5,sK7),cartesian_product2(sK4,sK6)),set_intersection2(cartesian_product2(sK4,sK6),cartesian_product2(sK5,sK7))),
inference(forward_demodulation,[],[f109,f23]) ).
fof(f116,plain,
( $false
| ~ spl9_1 ),
inference(forward_subsumption_resolution,[],[f115,f84]) ).
fof(f117,plain,
~ spl9_1,
inference(avatar_contradiction_clause,[],[f116]) ).
cnf(s1,plain,
( spl9_1
| spl9_2 ),
inference(sat_conversion,[],[f47]) ).
cnf(s2,plain,
~ spl9_2,
inference(sat_conversion,[],[f75]) ).
cnf(s3,plain,
~ spl9_1,
inference(sat_conversion,[],[f117]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f118,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET974+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n005.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 03:17:17 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.10/0.45 % (400783)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (400792)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2282708165:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.45 % (400789)% WARNING: option uhcvi not known.
% 0.10/0.45 % (400792) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-400783-400792"...
% 0.10/0.45 % (400792)...printing done.
% 0.10/0.45 % (400792)Refutation found. Thanks to Tanya!
% 0.10/0.45 % SZS status Theorem for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.45 % (400792)------------------------------
% 0.10/0.45 % (400792)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (400792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (400792)CaDiCaL version: 2.1.3
% 0.10/0.45 % (400792)Termination reason: Refutation
% 0.10/0.45 % (400792)Time elapsed: 0.003 s
% 0.10/0.45 % (400792)Peak memory usage: 12 MB
% 0.10/0.45 % (400792)Instructions burned: 5 (million)
% 0.10/0.45 % (400783)Success in time 0.035 s
% 0.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------