%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET589+3 : TPTP v9.3.1. Released v2.2.0.
% 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 12:41:14 PM UTC 2026
% Result : Theorem 3.31s 1.35s
% Output : Refutation 3.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 5 unt; 0 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 49 ( 22 ~; 13 |; 9 &)
% ( 0 <=>; 5 =>; 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 : 48 ( 40 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X1,X2) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_subset) ).
fof(f2,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(difference(X0,X2),difference(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_subset1) ).
fof(f3,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(difference(X2,X1),difference(X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_subset2) ).
fof(f7,conjecture,
! [X0,X1,X2,X3] :
( ( subset(X0,X1)
& subset(X2,X3) )
=> subset(difference(X0,X3),difference(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th48) ).
fof(f8,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( subset(X0,X1)
& subset(X2,X3) )
=> subset(difference(X0,X3),difference(X1,X2)) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(ennf_transformation,[],[f1]) ).
fof(f10,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
! [X0,X1,X2] :
( subset(difference(X0,X2),difference(X1,X2))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f12,plain,
! [X0,X1,X2] :
( subset(difference(X2,X1),difference(X2,X0))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f14,plain,
? [X0,X1,X2,X3] :
( ~ subset(difference(X0,X3),difference(X1,X2))
& subset(X0,X1)
& subset(X2,X3) ),
inference(ennf_transformation,[],[f8]) ).
fof(f15,plain,
? [X0,X1,X2,X3] :
( ~ subset(difference(X0,X3),difference(X1,X2))
& subset(X0,X1)
& subset(X2,X3) ),
inference(flattening,[],[f14]) ).
fof(f21,plain,
( ~ subset(difference(sK1,sK4),difference(sK2,sK3))
& subset(sK1,sK2)
& subset(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X3,sK4)],[f15]) ).
fof(f22,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(cnf_transformation,[],[f10]) ).
fof(f23,plain,
! [X2,X0,X1] :
( subset(difference(X0,X2),difference(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f24,plain,
! [X2,X0,X1] :
( subset(difference(X2,X1),difference(X2,X0))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f32,plain,
subset(sK3,sK4),
inference(cnf_transformation,[],[f21]) ).
fof(f33,plain,
subset(sK1,sK2),
inference(cnf_transformation,[],[f21]) ).
fof(f34,plain,
~ subset(difference(sK1,sK4),difference(sK2,sK3)),
inference(cnf_transformation,[],[f21]) ).
fof(f38,plain,
! [X0] :
( ~ subset(difference(sK1,sK4),X0)
| ~ subset(X0,difference(sK2,sK3)) ),
inference(resolution,[],[f22,f34]) ).
fof(f41,plain,
! [X0] :
( ~ subset(difference(X0,sK4),difference(sK2,sK3))
| ~ subset(sK1,X0) ),
inference(resolution,[],[f38,f23]) ).
fof(f46,plain,
( ~ subset(sK1,sK2)
| ~ subset(sK3,sK4) ),
inference(resolution,[],[f41,f24]) ).
fof(f49,plain,
~ subset(sK3,sK4),
inference(forward_subsumption_resolution,[],[f46,f33]) ).
fof(f50,plain,
$false,
inference(forward_subsumption_resolution,[],[f49,f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET589+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n026.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 02:19:26 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 3.31/1.35 % (3408030)Detected formulas, will run a generic FOF schedule.
% 3.31/1.35 % (3408037)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=1837362459:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.31/1.35 % (3408040)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1026414160:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.31/1.35 % (3408038)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2164903324:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.31/1.35 % (3408038)Refutation not found, incomplete strategy
% 3.31/1.35 % (3408038)------------------------------
% 3.31/1.35 % (3408038)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.31/1.35 % (3408038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.35 % (3408038)CaDiCaL version: 2.1.3
% 3.31/1.35 % (3408038)Termination reason: Refutation not found, incomplete strategy
% 3.31/1.35 % (3408038)Time elapsed: 0.001 s
% 3.31/1.35 % (3408038)Peak memory usage: 88 MB
% 3.31/1.35 % (3408040)First to succeed.
% 3.31/1.35 % (3408040)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3408030"
% 3.31/1.35 % (3408036)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=1918633558:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.31/1.35 % (3408035)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=3945334823:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.31/1.35 % (3408039)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3298311869:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.31/1.35 % (3408039)Also succeeded, but the first one will report.
% 3.31/1.35 % (3408041)dis-21_1_sil=8000:lcm=predicate:random_seed=2939134333: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)
% 3.31/1.35 % (3408041)Also succeeded, but the first one will report.
% 3.31/1.35 % (3408038)------------------------------
% 3.31/1.35 % (3408038)------------------------------
% 3.31/1.35 % (3408040)Refutation found. Thanks to Tanya!
% 3.31/1.35 % SZS status Theorem for theBenchmark
% 3.31/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.31/1.35 % (3408040)------------------------------
% 3.31/1.35 % (3408040)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.31/1.35 % (3408040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.35 % (3408040)CaDiCaL version: 2.1.3
% 3.31/1.35 % (3408040)Termination reason: Refutation
% 3.31/1.35 % (3408040)Time elapsed: 0.002 s
% 3.31/1.35 % (3408040)Peak memory usage: 88 MB
% 3.31/1.35 % (3408040)Instructions burned: 1 (million)
% 3.31/1.35 % (3408040)------------------------------
% 3.31/1.35 % (3408040)------------------------------
% 3.31/1.35 % (3408030)Success in time 0.399 s
% 3.31/1.35 % Vampire exiting
%------------------------------------------------------------------------------