%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET985+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 : 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 12:45:08 PM UTC 2026
% Result : Theorem 0.16s 0.48s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 63 ( 15 unt; 5 def)
% Number of atoms : 152 ( 46 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 147 ( 58 ~; 67 |; 11 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 38 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f5,axiom,
! [X0,X1] :
( cartesian_product2(X0,X1) = empty_set
<=> ( X0 = empty_set
| X1 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_zfmisc_1) ).
fof(f6,axiom,
! [X0,X1,X2,X3] :
( subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3))
=> ( cartesian_product2(X0,X1) = empty_set
| ( subset(X0,X2)
& subset(X1,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t138_zfmisc_1) ).
fof(f7,conjecture,
! [X0] :
( ~ empty(X0)
=> ! [X1,X2,X3] :
( ( subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3))
| subset(cartesian_product2(X1,X0),cartesian_product2(X3,X2)) )
=> subset(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t139_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0] :
( ~ empty(X0)
=> ! [X1,X2,X3] :
( ( subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3))
| subset(cartesian_product2(X1,X0),cartesian_product2(X3,X2)) )
=> subset(X1,X3) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f11,plain,
! [X0,X1,X2,X3] :
( cartesian_product2(X0,X1) = empty_set
| ( subset(X0,X2)
& subset(X1,X3) )
| ~ subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f12,plain,
! [X0,X1,X2,X3] :
( cartesian_product2(X0,X1) = empty_set
| ( subset(X0,X2)
& subset(X1,X3) )
| ~ subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
? [X0] :
( ? [X1,X2,X3] :
( ~ subset(X1,X3)
& ( subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3))
| subset(cartesian_product2(X1,X0),cartesian_product2(X3,X2)) ) )
& ~ empty(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f16,plain,
! [X0,X1] :
( ( cartesian_product2(X0,X1) = empty_set
| ( empty_set != X0
& empty_set != X1 ) )
& ( X0 = empty_set
| X1 = empty_set
| empty_set != cartesian_product2(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f17,plain,
! [X0,X1] :
( ( cartesian_product2(X0,X1) = empty_set
| ( empty_set != X0
& empty_set != X1 ) )
& ( X0 = empty_set
| X1 = empty_set
| empty_set != cartesian_product2(X0,X1) ) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
( ~ subset(sK3,sK5)
& ( subset(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5))
| subset(cartesian_product2(sK3,sK2),cartesian_product2(sK5,sK4)) )
& ~ empty(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5)],[f13]) ).
fof(f19,plain,
empty(empty_set),
inference(cnf_transformation,[],[f1]) ).
fof(f23,plain,
! [X0,X1] :
( empty_set != cartesian_product2(X0,X1)
| empty_set = X1
| empty_set = X0 ),
inference(cnf_transformation,[],[f17]) ).
fof(f26,plain,
! [X2,X3,X0,X1] :
( ~ subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3))
| subset(X1,X3)
| empty_set = cartesian_product2(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f27,plain,
! [X2,X3,X0,X1] :
( ~ subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3))
| subset(X0,X2)
| empty_set = cartesian_product2(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f28,plain,
~ empty(sK2),
inference(cnf_transformation,[],[f18]) ).
fof(f29,plain,
( subset(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5))
| subset(cartesian_product2(sK3,sK2),cartesian_product2(sK5,sK4)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f30,plain,
~ subset(sK3,sK5),
inference(cnf_transformation,[],[f18]) ).
fof(f31,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f33,definition,
( spl6_1
<=> subset(cartesian_product2(sK3,sK2),cartesian_product2(sK5,sK4)) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f35,plain,
( subset(cartesian_product2(sK3,sK2),cartesian_product2(sK5,sK4))
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f33]) ).
fof(f37,definition,
( spl6_2
<=> subset(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5)) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f39,plain,
( subset(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5))
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f40,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f29,f37,f33]) ).
fof(f43,plain,
( subset(sK3,sK5)
| empty_set = cartesian_product2(sK2,sK3)
| ~ spl6_2 ),
inference(resolution,[],[f26,f39]) ).
fof(f47,plain,
( empty_set = cartesian_product2(sK2,sK3)
| ~ spl6_2 ),
inference(forward_subsumption_resolution,[],[f43,f30]) ).
fof(f50,plain,
( empty_set != empty_set
| empty_set = sK3
| empty_set = sK2
| ~ spl6_2 ),
inference(superposition,[],[f23,f47]) ).
fof(f51,plain,
( empty_set = sK3
| empty_set = sK2
| ~ spl6_2 ),
inference(trivial_inequality_removal,[],[f50]) ).
fof(f53,definition,
( spl6_3
<=> empty_set = sK2 ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
fof(f54,plain,
( empty_set != sK2
| spl6_3 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f55,plain,
( empty_set = sK2
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f57,definition,
( spl6_4
<=> empty_set = sK3 ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
fof(f58,plain,
( empty_set != sK3
| spl6_4 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f59,plain,
( empty_set = sK3
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f60,plain,
( spl6_3
| spl6_4
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f51,f37,f57,f53]) ).
fof(f69,plain,
( ~ empty(empty_set)
| ~ spl6_3 ),
inference(superposition,[],[f28,f55]) ).
fof(f70,plain,
( $false
| ~ spl6_3 ),
inference(forward_subsumption_resolution,[],[f69,f19]) ).
fof(f71,plain,
~ spl6_3,
inference(avatar_contradiction_clause,[],[f70]) ).
fof(f75,plain,
( ~ subset(empty_set,sK5)
| ~ spl6_4 ),
inference(superposition,[],[f30,f59]) ).
fof(f76,plain,
( $false
| ~ spl6_4 ),
inference(forward_subsumption_resolution,[],[f75,f31]) ).
fof(f77,plain,
~ spl6_4,
inference(avatar_contradiction_clause,[],[f76]) ).
fof(f79,plain,
( subset(sK3,sK5)
| empty_set = cartesian_product2(sK3,sK2)
| ~ spl6_1 ),
inference(resolution,[],[f35,f27]) ).
fof(f82,definition,
( spl6_5
<=> empty_set = cartesian_product2(sK3,sK2) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
fof(f84,plain,
( empty_set = cartesian_product2(sK3,sK2)
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f90,plain,
( empty_set = cartesian_product2(sK3,sK2)
| ~ spl6_1 ),
inference(forward_subsumption_resolution,[],[f79,f30]) ).
fof(f91,plain,
( spl6_5
| ~ spl6_1 ),
inference(avatar_split_clause,[],[f90,f33,f82]) ).
fof(f95,plain,
( empty_set != empty_set
| empty_set = sK2
| empty_set = sK3
| ~ spl6_5 ),
inference(superposition,[],[f23,f84]) ).
fof(f96,plain,
( empty_set = sK2
| empty_set = sK3
| ~ spl6_5 ),
inference(trivial_inequality_removal,[],[f95]) ).
fof(f97,plain,
( empty_set = sK3
| spl6_3
| ~ spl6_5 ),
inference(forward_subsumption_resolution,[],[f96,f54]) ).
fof(f98,plain,
( $false
| spl6_3
| spl6_4
| ~ spl6_5 ),
inference(forward_subsumption_resolution,[],[f97,f58]) ).
fof(f99,plain,
( spl6_3
| spl6_4
| ~ spl6_5 ),
inference(avatar_contradiction_clause,[],[f98]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f40]) ).
cnf(s2,plain,
( ~ spl6_2
| spl6_3
| spl6_4 ),
inference(sat_conversion,[],[f60]) ).
cnf(s3,plain,
~ spl6_3,
inference(sat_conversion,[],[f71]) ).
cnf(s4,plain,
~ spl6_4,
inference(sat_conversion,[],[f77]) ).
cnf(s6,plain,
( ~ spl6_1
| spl6_5 ),
inference(sat_conversion,[],[f91]) ).
cnf(s7,plain,
( spl6_3
| spl6_4
| ~ spl6_5 ),
inference(sat_conversion,[],[f99]) ).
cnf(s8,plain,
~ spl6_5,
inference(rat,[],[s7,s4,s3]) ).
cnf(s9,plain,
~ spl6_1,
inference(rat,[],[s6,s8]) ).
cnf(s10,plain,
~ spl6_2,
inference(rat,[],[s2,s4,s3]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s1,s10,s9]) ).
fof(f100,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET985+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n016.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 03:24:18 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.16/0.48 % (3229699)Will run a generic schedule for satisfiability detection.
% 0.16/0.48 % (3229704)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1410097405_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.48 % TRYING [1]
% 0.16/0.48 % TRYING [2]
% 0.16/0.48 % TRYING [3]
% 0.16/0.48 % TRYING [4]
% 0.16/0.48 % (3229705)% WARNING: option uhcvi not known.
% 0.16/0.48 % (3229705)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1390992496:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.48 % (3229709)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2194988495:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.48 % (3229706)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3522536664:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.48 % (3229707)dis+10_1_sil=32000:sp=arity:random_seed=3729088574:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.48 % (3229708)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3963352176:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.48 % (3229710)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=584089567:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.48 % (3229709) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3229699-3229709"...
% 0.16/0.48 % (3229705) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3229699-3229705"...
% 0.16/0.48 % (3229707) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3229699-3229707"...
% 0.16/0.48 % (3229708) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3229699-3229708"...
% 0.16/0.48 % TRYING [5]
% 0.16/0.48 % (3229710) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3229699-3229710"...
% 0.16/0.48 % (3229706) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3229699-3229706"...
% 0.16/0.48 % (3229709)...printing done.
% 0.16/0.48 % (3229705)...printing done.
% 0.16/0.48 % (3229707)...printing done.
% 0.16/0.48 % (3229708)...printing done.
% 0.16/0.48 % (3229709)Refutation found. Thanks to Tanya!
% 0.16/0.48 % SZS status Theorem for theBenchmark
% 0.16/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.48 % (3229709)------------------------------
% 0.16/0.48 % (3229709)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.48 % (3229709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.48 % (3229709)CaDiCaL version: 2.1.3
% 0.16/0.48 % (3229709)Termination reason: Refutation
% 0.16/0.48 % (3229709)Time elapsed: 0.004 s
% 0.16/0.48 % (3229709)Peak memory usage: 12 MB
% 0.16/0.48 % (3229709)Instructions burned: 3 (million)
% 0.16/0.48 % (3229699)Success in time 0.046 s
% 0.16/0.48 % Vampire exiting
%------------------------------------------------------------------------------