%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET985+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 12:42:28 PM UTC 2026
% Result : Theorem 3.61s 1.47s
% Output : Refutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 58 ( 14 unt; 4 def)
% Number of atoms : 141 ( 44 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 137 ( 54 ~; 62 |; 11 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 42 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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(X1,X3)
| empty_set = cartesian_product2(X0,X1)
| ~ subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f27,plain,
! [X2,X3,X0,X1] :
( subset(X0,X2)
| empty_set = cartesian_product2(X0,X1)
| ~ subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) ),
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(f35,definition,
( spl6_1
<=> subset(cartesian_product2(sK3,sK2),cartesian_product2(sK5,sK4)) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f37,plain,
( subset(cartesian_product2(sK3,sK2),cartesian_product2(sK5,sK4))
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f39,definition,
( spl6_2
<=> subset(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5)) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f41,plain,
( subset(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5))
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f42,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f29,f39,f35]) ).
fof(f43,plain,
! [X0,X1] :
( ~ subset(cartesian_product2(X0,sK3),cartesian_product2(X1,sK5))
| empty_set = cartesian_product2(X0,sK3) ),
inference(resolution,[],[f26,f30]) ).
fof(f44,plain,
( empty_set = cartesian_product2(sK2,sK3)
| ~ spl6_2 ),
inference(resolution,[],[f43,f41]) ).
fof(f47,plain,
! [X0,X1] :
( ~ subset(cartesian_product2(sK3,X0),cartesian_product2(sK5,X1))
| empty_set = cartesian_product2(sK3,X0) ),
inference(resolution,[],[f27,f30]) ).
fof(f50,plain,
( empty_set != empty_set
| empty_set = sK3
| empty_set = sK2
| ~ spl6_2 ),
inference(superposition,[],[f23,f44]) ).
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,f39,f57,f53]) ).
fof(f66,plain,
( ~ empty(empty_set)
| ~ spl6_3 ),
inference(superposition,[],[f28,f55]) ).
fof(f67,plain,
( $false
| ~ spl6_3 ),
inference(forward_subsumption_resolution,[],[f66,f19]) ).
fof(f68,plain,
~ spl6_3,
inference(avatar_contradiction_clause,[],[f67]) ).
fof(f78,plain,
( ~ subset(empty_set,sK5)
| ~ spl6_4 ),
inference(superposition,[],[f30,f59]) ).
fof(f86,plain,
( $false
| ~ spl6_4 ),
inference(forward_subsumption_resolution,[],[f78,f31]) ).
fof(f87,plain,
~ spl6_4,
inference(avatar_contradiction_clause,[],[f86]) ).
fof(f88,plain,
( empty_set = cartesian_product2(sK3,sK2)
| ~ spl6_1 ),
inference(resolution,[],[f37,f47]) ).
fof(f92,plain,
( empty_set != empty_set
| empty_set = sK2
| empty_set = sK3
| ~ spl6_1 ),
inference(superposition,[],[f23,f88]) ).
fof(f93,plain,
( empty_set = sK2
| empty_set = sK3
| ~ spl6_1 ),
inference(trivial_inequality_removal,[],[f92]) ).
fof(f94,plain,
( empty_set = sK3
| ~ spl6_1
| spl6_3 ),
inference(forward_subsumption_resolution,[],[f93,f54]) ).
fof(f95,plain,
( $false
| ~ spl6_1
| spl6_3
| spl6_4 ),
inference(forward_subsumption_resolution,[],[f94,f58]) ).
fof(f96,plain,
( ~ spl6_1
| spl6_3
| spl6_4 ),
inference(avatar_contradiction_clause,[],[f95]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f42]) ).
cnf(s2,plain,
( ~ spl6_2
| spl6_3
| spl6_4 ),
inference(sat_conversion,[],[f60]) ).
cnf(s3,plain,
~ spl6_3,
inference(sat_conversion,[],[f68]) ).
cnf(s4,plain,
~ spl6_4,
inference(sat_conversion,[],[f87]) ).
cnf(s5,plain,
( ~ spl6_1
| spl6_3
| spl6_4 ),
inference(sat_conversion,[],[f96]) ).
cnf(s6,plain,
~ spl6_1,
inference(rat,[],[s5,s4,s3]) ).
cnf(s7,plain,
~ spl6_2,
inference(rat,[],[s2,s4,s3]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s7,s6]) ).
fof(f97,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET985+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n014.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
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 03:17:47 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.61/1.47 % (1405569)Detected formulas, will run a generic FOF schedule.
% 3.61/1.47 % (1405575)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2047383804:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.61/1.47 % (1405577)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3771020224:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.61/1.47 % (1405578)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3059486339:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.61/1.47 % (1405577)Refutation not found, incomplete strategy
% 3.61/1.47 % (1405577)------------------------------
% 3.61/1.47 % (1405577)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.47 % (1405577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.47 % (1405578)Refutation not found, incomplete strategy
% 3.61/1.47 % (1405578)------------------------------
% 3.61/1.47 % (1405578)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.47 % (1405577)CaDiCaL version: 2.1.3
% 3.61/1.47 % (1405577)Termination reason: Refutation not found, incomplete strategy
% 3.61/1.47 % (1405577)Time elapsed: 0.001 s
% 3.61/1.47 % (1405577)Peak memory usage: 87 MB
% 3.61/1.47 % (1405578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.47 % (1405578)CaDiCaL version: 2.1.3
% 3.61/1.47 % (1405578)Termination reason: Refutation not found, incomplete strategy
% 3.61/1.47 % (1405578)Time elapsed: 0.001 s
% 3.61/1.47 % (1405578)Peak memory usage: 88 MB
% 3.61/1.47 % (1405576)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2533241347:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.61/1.47 % (1405574)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3313821119:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.61/1.47 % (1405580)dis-21_1_sil=8000:lcm=predicate:random_seed=1407666569:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.61/1.47 % (1405579)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1869274543:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.61/1.47 % (1405579)First to succeed.
% 3.61/1.47 % (1405579)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1405569"
% 3.61/1.47 % (1405580)Instruction limit reached!
% 3.61/1.47 % (1405580)------------------------------
% 3.61/1.47 % (1405580)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.47 % (1405580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.47 % (1405580)CaDiCaL version: 2.1.3
% 3.61/1.47 % (1405580)Termination reason: Instruction limit
% 3.61/1.47 % (1405580)Termination phase: Saturation
% 3.61/1.47 % (1405580)Time elapsed: 0.043 s
% 3.61/1.47 % (1405580)Peak memory usage: 89 MB
% 3.61/1.47 % (1405580)Instructions burned: 132 (million)
% 3.61/1.47 % (1405588)lrs+10_1_sil=8000:sp=occurrence:random_seed=1786024984:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.61/1.47 % (1405588)Also succeeded, but the first one will report.
% 3.61/1.47 % (1405577)------------------------------
% 3.61/1.47 % (1405577)------------------------------
% 3.61/1.47 % (1405578)------------------------------
% 3.61/1.47 % (1405578)------------------------------
% 3.61/1.47 % (1405579)Refutation found. Thanks to Tanya!
% 3.61/1.47 % SZS status Theorem for theBenchmark
% 3.61/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.61/1.47 % (1405579)------------------------------
% 3.61/1.47 % (1405579)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.47 % (1405579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.47 % (1405579)CaDiCaL version: 2.1.3
% 3.61/1.47 % (1405579)Termination reason: Refutation
% 3.61/1.47 % (1405579)Time elapsed: 0.006 s
% 3.61/1.47 % (1405579)Peak memory usage: 89 MB
% 3.61/1.47 % (1405579)Instructions burned: 4 (million)
% 3.61/1.47 % (1405579)------------------------------
% 3.61/1.47 % (1405579)------------------------------
% 3.61/1.47 % (1405569)Success in time 0.432 s
% 3.61/1.47 % Vampire exiting
%------------------------------------------------------------------------------