%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET984+1 : 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 : 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 12:45:07 PM UTC 2026
% Result : Theorem 0.40s 0.47s
% Output : Refutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 78 ( 22 unt; 6 def)
% Number of atoms : 182 ( 93 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 162 ( 58 ~; 78 |; 15 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn 80 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f7,axiom,
! [X0,X1] :
( cartesian_product2(X0,X1) = empty_set
<=> ( X0 = empty_set
| X1 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
fof(f8,axiom,
! [X0,X1,X2,X3] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_zfmisc_1) ).
fof(f9,axiom,
! [X0,X1,X2,X3] :
( cartesian_product2(X0,X1) = cartesian_product2(X2,X3)
=> ( X0 = empty_set
| X1 = empty_set
| ( X0 = X2
& X1 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_zfmisc_1) ).
fof(f10,conjecture,
! [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/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [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) ) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f12,axiom,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(f13,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f16,plain,
! [X0,X1,X2,X3] :
( X0 = empty_set
| X1 = empty_set
| ( X0 = X2
& X1 = X3 )
| cartesian_product2(X0,X1) != cartesian_product2(X2,X3) ),
inference(ennf_transformation,[],[f9]) ).
fof(f17,plain,
! [X0,X1,X2,X3] :
( X0 = empty_set
| X1 = empty_set
| ( X0 = X2
& X1 = X3 )
| cartesian_product2(X0,X1) != cartesian_product2(X2,X3) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
? [X0,X1,X2,X3] :
( empty_set != cartesian_product2(X0,X1)
& ( ~ subset(X0,X2)
| ~ subset(X1,X3) )
& subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) ),
inference(ennf_transformation,[],[f11]) ).
fof(f19,plain,
? [X0,X1,X2,X3] :
( empty_set != cartesian_product2(X0,X1)
& ( ~ subset(X0,X2)
| ~ subset(X1,X3) )
& subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f23,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,[],[f7]) ).
fof(f24,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,[],[f23]) ).
fof(f25,plain,
( empty_set != cartesian_product2(sK2,sK3)
& ( ~ subset(sK2,sK4)
| ~ subset(sK3,sK5) )
& subset(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5)],[f19]) ).
fof(f26,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f33,plain,
! [X0,X1] :
( empty_set = cartesian_product2(X0,X1)
| empty_set != X1 ),
inference(cnf_transformation,[],[f24]) ).
fof(f34,plain,
! [X0,X1] :
( empty_set = cartesian_product2(X0,X1)
| empty_set != X0 ),
inference(cnf_transformation,[],[f24]) ).
fof(f35,plain,
! [X2,X3,X0,X1] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
inference(cnf_transformation,[],[f8]) ).
fof(f36,plain,
! [X2,X3,X0,X1] :
( cartesian_product2(X0,X1) != cartesian_product2(X2,X3)
| empty_set = X1
| X1 = X3
| empty_set = X0 ),
inference(cnf_transformation,[],[f17]) ).
fof(f37,plain,
! [X2,X3,X0,X1] :
( cartesian_product2(X0,X1) != cartesian_product2(X2,X3)
| empty_set = X1
| X0 = X2
| empty_set = X0 ),
inference(cnf_transformation,[],[f17]) ).
fof(f38,plain,
subset(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5)),
inference(cnf_transformation,[],[f25]) ).
fof(f39,plain,
( ~ subset(sK2,sK4)
| ~ subset(sK3,sK5) ),
inference(cnf_transformation,[],[f25]) ).
fof(f40,plain,
empty_set != cartesian_product2(sK2,sK3),
inference(cnf_transformation,[],[f25]) ).
fof(f41,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[],[f12]) ).
fof(f42,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,X1) = X0 ),
inference(cnf_transformation,[],[f20]) ).
fof(f43,plain,
! [X1] : empty_set = cartesian_product2(empty_set,X1),
inference(equality_resolution,[],[f34]) ).
fof(f44,plain,
! [X0] : empty_set = cartesian_product2(X0,empty_set),
inference(equality_resolution,[],[f33]) ).
fof(f46,definition,
( spl6_1
<=> subset(sK3,sK5) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f50,definition,
( spl6_2
<=> subset(sK2,sK4) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f52,plain,
( ~ subset(sK2,sK4)
| spl6_2 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f53,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f39,f50,f46]) ).
fof(f55,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X1),
inference(superposition,[],[f41,f26]) ).
fof(f60,plain,
cartesian_product2(sK2,sK3) = set_intersection2(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5)),
inference(resolution,[],[f42,f38]) ).
fof(f91,plain,
! [X2,X3,X0,X1,X4,X5] :
( set_intersection2(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) != cartesian_product2(X4,X5)
| empty_set = X5
| set_intersection2(X1,X3) = X5
| empty_set = X4 ),
inference(superposition,[],[f36,f35]) ).
fof(f105,plain,
! [X2,X3,X0,X1,X4,X5] :
( set_intersection2(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) != cartesian_product2(X4,X5)
| empty_set = X5
| set_intersection2(X0,X2) = X4
| empty_set = X4 ),
inference(superposition,[],[f37,f35]) ).
fof(f339,plain,
! [X0,X1] :
( cartesian_product2(X0,X1) != cartesian_product2(sK2,sK3)
| empty_set = X1
| set_intersection2(sK3,sK5) = X1
| empty_set = X0 ),
inference(superposition,[],[f91,f60]) ).
fof(f406,plain,
! [X0,X1] :
( cartesian_product2(X0,X1) != cartesian_product2(sK2,sK3)
| empty_set = X1
| set_intersection2(sK2,sK4) = X0
| empty_set = X0 ),
inference(superposition,[],[f105,f60]) ).
fof(f541,plain,
( empty_set = sK3
| sK3 = set_intersection2(sK3,sK5)
| empty_set = sK2 ),
inference(equality_resolution,[],[f339]) ).
fof(f543,definition,
( spl6_6
<=> empty_set = sK2 ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
fof(f544,plain,
( empty_set != sK2
| spl6_6 ),
inference(avatar_component_clause,[],[f543]) ).
fof(f545,plain,
( empty_set = sK2
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f543]) ).
fof(f547,definition,
( spl6_7
<=> sK3 = set_intersection2(sK3,sK5) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
fof(f549,plain,
( sK3 = set_intersection2(sK3,sK5)
| ~ spl6_7 ),
inference(avatar_component_clause,[],[f547]) ).
fof(f551,definition,
( spl6_8
<=> empty_set = sK3 ),
introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition]) ).
fof(f553,plain,
( empty_set = sK3
| ~ spl6_8 ),
inference(avatar_component_clause,[],[f551]) ).
fof(f554,plain,
( spl6_6
| spl6_7
| spl6_8 ),
inference(avatar_split_clause,[],[f541,f551,f547,f543]) ).
fof(f560,plain,
( empty_set != cartesian_product2(empty_set,sK3)
| ~ spl6_6 ),
inference(superposition,[],[f40,f545]) ).
fof(f587,plain,
( $false
| ~ spl6_6 ),
inference(forward_subsumption_resolution,[],[f560,f43]) ).
fof(f588,plain,
~ spl6_6,
inference(avatar_contradiction_clause,[],[f587]) ).
fof(f642,plain,
( empty_set = sK3
| sK2 = set_intersection2(sK2,sK4)
| empty_set = sK2 ),
inference(equality_resolution,[],[f406]) ).
fof(f643,plain,
( empty_set = sK3
| sK2 = set_intersection2(sK2,sK4)
| spl6_6 ),
inference(forward_subsumption_resolution,[],[f642,f544]) ).
fof(f646,definition,
( spl6_10
<=> sK2 = set_intersection2(sK2,sK4) ),
introduced(definition,[new_symbols(definition,[spl6_10])],[avatar_definition]) ).
fof(f648,plain,
( sK2 = set_intersection2(sK2,sK4)
| ~ spl6_10 ),
inference(avatar_component_clause,[],[f646]) ).
fof(f649,plain,
( spl6_10
| spl6_8
| spl6_6 ),
inference(avatar_split_clause,[],[f643,f543,f551,f646]) ).
fof(f659,plain,
( empty_set != cartesian_product2(sK2,empty_set)
| ~ spl6_8 ),
inference(superposition,[],[f40,f553]) ).
fof(f688,plain,
( $false
| ~ spl6_8 ),
inference(forward_subsumption_resolution,[],[f659,f44]) ).
fof(f689,plain,
~ spl6_8,
inference(avatar_contradiction_clause,[],[f688]) ).
fof(f798,plain,
( subset(sK3,sK5)
| ~ spl6_7 ),
inference(superposition,[],[f55,f549]) ).
fof(f810,plain,
( spl6_1
| ~ spl6_7 ),
inference(avatar_split_clause,[],[f798,f547,f46]) ).
fof(f817,plain,
( subset(sK2,sK4)
| ~ spl6_10 ),
inference(superposition,[],[f55,f648]) ).
fof(f827,plain,
( $false
| spl6_2
| ~ spl6_10 ),
inference(forward_subsumption_resolution,[],[f817,f52]) ).
fof(f828,plain,
( spl6_2
| ~ spl6_10 ),
inference(avatar_contradiction_clause,[],[f827]) ).
cnf(s1,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(sat_conversion,[],[f53]) ).
cnf(s3,plain,
( spl6_6
| spl6_7
| spl6_8 ),
inference(sat_conversion,[],[f554]) ).
cnf(s4,plain,
~ spl6_6,
inference(sat_conversion,[],[f588]) ).
cnf(s7,plain,
( spl6_6
| spl6_8
| spl6_10 ),
inference(sat_conversion,[],[f649]) ).
cnf(s9,plain,
~ spl6_8,
inference(sat_conversion,[],[f689]) ).
cnf(s12,plain,
( spl6_1
| ~ spl6_7 ),
inference(sat_conversion,[],[f810]) ).
cnf(s13,plain,
( spl6_2
| ~ spl6_10 ),
inference(sat_conversion,[],[f828]) ).
cnf(s14,plain,
( spl6_6
| spl6_10 ),
inference(rat,[],[s7,s9]) ).
cnf(s16,plain,
spl6_10,
inference(rat,[],[s14,s4]) ).
cnf(s18,plain,
spl6_2,
inference(rat,[],[s13,s16]) ).
cnf(s19,plain,
spl6_7,
inference(rat,[],[s3,s9,s4]) ).
cnf(s20,plain,
spl6_1,
inference(rat,[],[s12,s19]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s1,s18,s20]) ).
fof(f829,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET984+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 03:17:47 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 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
% 0.40/0.47 % (401433)Will run a generic schedule for satisfiability detection.
% 0.40/0.47 % (401438)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=542348905_2999 on theBenchmark for (2999ds/0Mi)
% 0.40/0.47 % TRYING [1]
% 0.40/0.47 % TRYING [2]
% 0.40/0.47 % TRYING [3]
% 0.40/0.47 % TRYING [4]
% 0.40/0.47 % (401444)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1673385993:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.40/0.47 % (401441)dis+10_1_sil=32000:sp=arity:random_seed=2989867740:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.40/0.47 % (401440)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3873343823:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.40/0.47 % (401442)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4018129776:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.40/0.47 % (401443)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3371131052:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.40/0.47 % TRYING [5]
% 0.40/0.47 % (401439)% WARNING: option uhcvi not known.
% 0.40/0.47 % (401439)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1680033883:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.40/0.47 % TRYING [6]
% 0.40/0.47 % (401441) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-401433-401441"...
% 0.40/0.47 % (401442) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-401433-401442"...
% 0.40/0.47 % (401441)...printing done.
% 0.40/0.47 % (401441)Refutation found. Thanks to Tanya!
% 0.40/0.47 % SZS status Theorem for theBenchmark
% 0.40/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.40/0.47 % (401441)------------------------------
% 0.40/0.47 % (401441)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.47 % (401441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.47 % (401441)CaDiCaL version: 2.1.3
% 0.40/0.47 % (401441)Termination reason: Refutation
% 0.40/0.47 % (401441)Time elapsed: 0.025 s
% 0.40/0.47 % (401441)Peak memory usage: 12 MB
% 0.40/0.47 % (401441)Instructions burned: 42 (million)
% 0.40/0.47 % (401433)Success in time 0.06 s
% 0.40/0.47 % Vampire exiting
%------------------------------------------------------------------------------