%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU167+3 : 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 : n026.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 12:47:32 PM UTC 2026
% Result : Theorem 3.47s 1.47s
% Output : Refutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 5 unt; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 48 ( 21 ~; 12 |; 11 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 42 ( 34 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
& subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
fof(f5,conjecture,
! [X0,X1,X2,X3] :
( ( subset(X0,X1)
& subset(X2,X3) )
=> subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
fof(f6,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( subset(X0,X1)
& subset(X2,X3) )
=> subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,axiom,
! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X1,X2) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f9,plain,
! [X0,X1,X2] :
( ( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
& subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1)) )
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f10,plain,
? [X0,X1,X2,X3] :
( ~ subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
& subset(X0,X1)
& subset(X2,X3) ),
inference(ennf_transformation,[],[f6]) ).
fof(f11,plain,
? [X0,X1,X2,X3] :
( ~ subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
& subset(X0,X1)
& subset(X2,X3) ),
inference(flattening,[],[f10]) ).
fof(f12,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(ennf_transformation,[],[f7]) ).
fof(f13,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(flattening,[],[f12]) ).
fof(f16,plain,
( ~ subset(cartesian_product2(sK2,sK4),cartesian_product2(sK3,sK5))
& subset(sK2,sK3)
& subset(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)],[f11]) ).
fof(f20,plain,
! [X2,X0,X1] :
( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f9]) ).
fof(f21,plain,
! [X2,X0,X1] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f9]) ).
fof(f22,plain,
subset(sK4,sK5),
inference(cnf_transformation,[],[f16]) ).
fof(f23,plain,
subset(sK2,sK3),
inference(cnf_transformation,[],[f16]) ).
fof(f24,plain,
~ subset(cartesian_product2(sK2,sK4),cartesian_product2(sK3,sK5)),
inference(cnf_transformation,[],[f16]) ).
fof(f25,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(cnf_transformation,[],[f13]) ).
fof(f26,plain,
! [X0] :
( ~ subset(cartesian_product2(sK2,sK4),X0)
| ~ subset(X0,cartesian_product2(sK3,sK5)) ),
inference(resolution,[],[f25,f24]) ).
fof(f29,plain,
! [X0] :
( ~ subset(cartesian_product2(sK2,X0),cartesian_product2(sK3,sK5))
| ~ subset(sK4,X0) ),
inference(resolution,[],[f20,f26]) ).
fof(f32,plain,
( ~ subset(sK2,sK3)
| ~ subset(sK4,sK5) ),
inference(resolution,[],[f21,f29]) ).
fof(f33,plain,
~ subset(sK4,sK5),
inference(forward_subsumption_resolution,[],[f32,f23]) ).
fof(f34,plain,
$false,
inference(forward_subsumption_resolution,[],[f33,f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU167+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n026.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Mon Sep 28 03:54:27 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 3.47/1.47 % (3444738)Detected formulas, will run a generic FOF schedule.
% 3.47/1.47 % (3444746)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3923356900:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.47/1.47 % (3444746)Refutation not found, incomplete strategy
% 3.47/1.47 % (3444746)------------------------------
% 3.47/1.47 % (3444746)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.47 % (3444746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.47 % (3444746)CaDiCaL version: 2.1.3
% 3.47/1.47 % (3444746)Termination reason: Refutation not found, incomplete strategy
% 3.47/1.47 % (3444746)Time elapsed: 0.001 s
% 3.47/1.47 % (3444746)Peak memory usage: 88 MB
% 3.47/1.47 % (3444744)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=1697848007:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.47/1.47 % (3444745)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=1874641480:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.47/1.47 % (3444743)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=1192995030:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.47/1.47 % (3444748)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1252683485:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.47/1.47 % (3444748)First to succeed.
% 3.47/1.47 % (3444748)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3444738"
% 3.47/1.47 % (3444749)dis-21_1_sil=8000:lcm=predicate:random_seed=1964500733: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)
% 3.47/1.47 % (3444747)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3777976672:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.47/1.47 % (3444747)Also succeeded, but the first one will report.
% 3.47/1.47 % (3444749)Also succeeded, but the first one will report.
% 3.47/1.47 % (3444746)------------------------------
% 3.47/1.47 % (3444746)------------------------------
% 3.47/1.47 % (3444757)lrs+10_1_sil=8000:sp=occurrence:random_seed=2391417610:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.47/1.47 % (3444757)Also succeeded, but the first one will report.
% 3.47/1.47 % (3444748)Refutation found. Thanks to Tanya!
% 3.47/1.47 % SZS status Theorem for theBenchmark
% 3.47/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.47/1.47 % (3444748)------------------------------
% 3.47/1.47 % (3444748)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.47 % (3444748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.47 % (3444748)CaDiCaL version: 2.1.3
% 3.47/1.47 % (3444748)Termination reason: Refutation
% 3.47/1.47 % (3444748)Time elapsed: 0.002 s
% 3.47/1.47 % (3444748)Peak memory usage: 88 MB
% 3.47/1.47 % (3444748)Instructions burned: 1 (million)
% 3.47/1.47 % (3444748)------------------------------
% 3.47/1.47 % (3444748)------------------------------
% 3.47/1.47 % (3444738)Success in time 0.406 s
% 3.47/1.47 % Vampire exiting
%------------------------------------------------------------------------------