%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET002+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 12:39:26 PM UTC 2026
% Result : Theorem 2.67s 1.36s
% Output : Refutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 9 unt; 0 def)
% Number of atoms : 17 ( 9 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 9 ~; 3 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 11 ( 10 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
=> union(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_union) ).
fof(f6,axiom,
! [X0] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
fof(f8,conjecture,
! [X0] : union(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_idempotency_of_union) ).
fof(f9,negated_conjecture,
~ ! [X0] : union(X0,X0) = X0,
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,plain,
? [X0] : union(X0,X0) != X0,
inference(ennf_transformation,[],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( union(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f12,plain,
sK0 != union(sK0,sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f10]) ).
fof(f15,plain,
sK0 != union(sK0,sK0),
inference(cnf_transformation,[],[f12]) ).
fof(f17,plain,
! [X0,X1] :
( union(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f18,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f26,plain,
( sK0 != sK0
| ~ subset(sK0,sK0) ),
inference(superposition,[],[f15,f17]) ).
fof(f29,plain,
~ subset(sK0,sK0),
inference(trivial_inequality_removal,[],[f26]) ).
fof(f30,plain,
$false,
inference(forward_subsumption_resolution,[],[f29,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET002+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n015.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 00:06:01 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.67/1.36 % (2151541)Detected formulas, will run a generic FOF schedule.
% 2.67/1.36 % (2151550)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=853595801:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.67/1.36 % (2151550)First to succeed.
% 2.67/1.36 % (2151550)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2151541"
% 2.67/1.36 % (2151549)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3352024089:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.67/1.36 % (2151552)dis-21_1_sil=8000:lcm=predicate:random_seed=1929466804: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)
% 2.67/1.36 % (2151546)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=179117729:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.67/1.36 % (2151547)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=931083460:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.67/1.36 % (2151551)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1533745142:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.67/1.36 % (2151548)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=3345311564:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.67/1.36 % (2151549)Refutation not found, incomplete strategy
% 2.67/1.36 % (2151549)------------------------------
% 2.67/1.36 % (2151549)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.36 % (2151549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.36 % (2151549)CaDiCaL version: 2.1.3
% 2.67/1.36 % (2151549)Termination reason: Refutation not found, incomplete strategy
% 2.67/1.36 % (2151549)Time elapsed: 0.001 s
% 2.67/1.36 % (2151549)Peak memory usage: 88 MB
% 2.67/1.36 % (2151552)Also succeeded, but the first one will report.
% 2.67/1.36 % (2151551)Also succeeded, but the first one will report.
% 2.67/1.36 % (2151550)Refutation found. Thanks to Tanya!
% 2.67/1.36 % SZS status Theorem for theBenchmark
% 2.67/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 2.67/1.36 % (2151550)------------------------------
% 2.67/1.36 % (2151550)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.36 % (2151550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.36 % (2151550)CaDiCaL version: 2.1.3
% 2.67/1.36 % (2151550)Termination reason: Refutation
% 2.67/1.36 % (2151550)Time elapsed: 0.001 s
% 2.67/1.36 % (2151550)Peak memory usage: 88 MB
% 2.67/1.36 % (2151550)------------------------------
% 2.67/1.36 % (2151550)------------------------------
% 2.67/1.36 % (2151541)Success in time 0.29 s
% 2.67/1.36 % Vampire exiting
%------------------------------------------------------------------------------