%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU161+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 12:47:30 PM UTC 2026
% Result : Theorem 2.71s 1.35s
% Output : Refutation 2.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 11 ( 4 unt; 0 def)
% Number of atoms : 18 ( 9 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 6 ~; 2 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 12 ( 10 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f38,axiom,
! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l23_zfmisc_1) ).
fof(f76,conjecture,
! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_zfmisc_1) ).
fof(f77,negated_conjecture,
~ ! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
inference(negated_conjecture,[status(cth)],[f76]) ).
fof(f107,plain,
! [X0,X1] :
( set_union2(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f128,plain,
? [X0,X1] :
( set_union2(singleton(X0),X1) != X1
& in(X0,X1) ),
inference(ennf_transformation,[],[f77]) ).
fof(f195,plain,
( sK21 != set_union2(singleton(sK20),sK21)
& in(sK20,sK21) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21]),skolemize(X0,sK20),skolemize(X1,sK21)],[f128]) ).
fof(f269,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_union2(singleton(X0),X1) = X1 ),
inference(cnf_transformation,[],[f107]) ).
fof(f323,plain,
in(sK20,sK21),
inference(cnf_transformation,[],[f195]) ).
fof(f324,plain,
sK21 != set_union2(singleton(sK20),sK21),
inference(cnf_transformation,[],[f195]) ).
fof(f668,plain,
sK21 = set_union2(singleton(sK20),sK21),
inference(resolution,[],[f269,f323]) ).
fof(f671,plain,
$false,
inference(forward_subsumption_resolution,[],[f668,f324]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU161+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n004.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % 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 03:49:07 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.71/1.35 % (4132041)Detected formulas, will run a generic FOF schedule.
% 2.71/1.35 % (4132051)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3113108241:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.71/1.35 % (4132051)First to succeed.
% 2.71/1.35 % (4132051)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4132041"
% 2.71/1.35 % (4132046)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=563413276:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.71/1.35 % (4132047)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=4233178624:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.71/1.35 % (4132048)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=1536673058:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.71/1.35 % (4132049)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3495474421:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.71/1.35 % (4132049)Also succeeded, but the first one will report.
% 2.71/1.35 % (4132052)dis-21_1_sil=8000:lcm=predicate:random_seed=597232096: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)
% 2.71/1.35 % (4132050)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=470398723:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.71/1.35 % (4132052)Also succeeded, but the first one will report.
% 2.71/1.35 % (4132050)Also succeeded, but the first one will report.
% 2.71/1.35 % (4132051)Refutation found. Thanks to Tanya!
% 2.71/1.35 % SZS status Theorem for theBenchmark
% 2.71/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.71/1.35 % (4132051)------------------------------
% 2.71/1.35 % (4132051)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.35 % (4132051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.35 % (4132051)CaDiCaL version: 2.1.3
% 2.71/1.35 % (4132051)Termination reason: Refutation
% 2.71/1.35 % (4132051)Time elapsed: 0.007 s
% 2.71/1.35 % (4132051)Peak memory usage: 89 MB
% 2.71/1.35 % (4132051)Instructions burned: 16 (million)
% 2.71/1.35 % (4132051)------------------------------
% 2.71/1.35 % (4132051)------------------------------
% 2.71/1.35 % (4132041)Success in time 0.299 s
% 2.71/1.35 % Vampire exiting
%------------------------------------------------------------------------------