%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU161+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 2.32s 0.93s
% Output : Refutation 2.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 6 unt; 1 def)
% Number of atoms : 26 ( 9 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 11 ~; 4 |; 2 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 18 ( 16 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,conjecture,
! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,axiom,
! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l23_zfmisc_1) ).
fof(f15,plain,
? [X0,X1] :
( set_union2(singleton(X0),X1) != X1
& in(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f16,plain,
! [X0,X1] :
( set_union2(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f19,plain,
( sK3 != set_union2(singleton(sK2),sK3)
& in(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f15]) ).
fof(f27,plain,
in(sK2,sK3),
inference(cnf_transformation,[],[f19]) ).
fof(f28,plain,
sK3 != set_union2(singleton(sK2),sK3),
inference(cnf_transformation,[],[f19]) ).
fof(f29,plain,
! [X0,X1] :
( set_union2(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f30,definition,
! [X0,X1] :
( sQ4_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ4_eqProxy])],[equality_proxy_definition]) ).
fof(f33,plain,
~ sQ4_eqProxy(sK3,set_union2(singleton(sK2),sK3)),
inference(equality_proxy_replacement,[],[f28,f30]) ).
fof(f34,plain,
! [X0,X1] :
( sQ4_eqProxy(set_union2(singleton(X0),X1),X1)
| ~ in(X0,X1) ),
inference(equality_proxy_replacement,[],[f29,f30]) ).
fof(f36,plain,
! [X0,X1] :
( sQ4_eqProxy(X1,X0)
| ~ sQ4_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f30]) ).
fof(f40,plain,
~ sQ4_eqProxy(set_union2(singleton(sK2),sK3),sK3),
inference(resolution,[],[f36,f33]) ).
fof(f41,plain,
~ in(sK2,sK3),
inference(resolution,[],[f40,f34]) ).
fof(f43,plain,
$false,
inference(resolution,[],[f41,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU161+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Mon Sep 28 03:48:49 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.33 Running first-order theorem proving
% 0.08/0.33 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
% 2.32/0.93 % (2998116)Detected formulas, will run a generic FOF schedule.
% 2.32/0.93 % (2998124)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3584002482:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.32/0.93 % (2998121)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=2935016579:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.32/0.93 % (2998127)dis-21_1_sil=8000:lcm=predicate:random_seed=710305700: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)
% 2.32/0.93 % (2998126)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1931546128:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.32/0.93 % (2998122)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=2631940715:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.32/0.93 % (2998123)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=2589973950:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.32/0.93 % (2998125)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2942734421:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.32/0.93 % (2998124)Refutation not found, incomplete strategy
% 2.32/0.93 % (2998124)------------------------------
% 2.32/0.93 % (2998124)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.32/0.93 % (2998124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/0.93 % (2998127)First to succeed.
% 2.32/0.93 % (2998124)CaDiCaL version: 2.1.3
% 2.32/0.93 % (2998124)Termination reason: Refutation not found, incomplete strategy
% 2.32/0.93 % (2998124)Time elapsed: 0.001 s
% 2.32/0.93 % (2998124)Peak memory usage: 88 MB
% 2.32/0.93 % (2998125)Also succeeded, but the first one will report.
% 2.32/0.93 % (2998126)Also succeeded, but the first one will report.
% 2.32/0.93 % (2998127)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2998116"
% 2.32/0.93 % (2998124)------------------------------
% 2.32/0.93 % (2998124)------------------------------
% 2.32/0.93 % (2998127)Refutation found. Thanks to Tanya!
% 2.32/0.93 % SZS status Theorem for theBenchmark
% 2.32/0.93 % SZS output start Proof for theBenchmark
% See solution above
% 2.32/0.93 % (2998127)------------------------------
% 2.32/0.93 % (2998127)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.32/0.93 % (2998127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/0.93 % (2998127)CaDiCaL version: 2.1.3
% 2.32/0.93 % (2998127)Termination reason: Refutation
% 2.32/0.93 % (2998127)Time elapsed: 0.001 s
% 2.32/0.93 % (2998127)Peak memory usage: 88 MB
% 2.32/0.93 % (2998127)Instructions burned: 1 (million)
% 2.32/0.93 % (2998127)------------------------------
% 2.32/0.93 % (2998127)------------------------------
% 2.32/0.93 % (2998116)Success in time 0.295 s
% 2.32/0.93 % Vampire exiting
%------------------------------------------------------------------------------