%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU152+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 12:47:27 PM UTC 2026
% Result : Theorem 0.16s 1.31s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 8 unt; 0 def)
% Number of atoms : 34 ( 12 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 29 ( 15 ~; 7 |; 3 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 22 ( 20 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f31,conjecture,
! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l23_zfmisc_1) ).
fof(f32,negated_conjecture,
~ ! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f33,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(f42,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f67,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f84,plain,
? [X0,X1] :
( set_union2(singleton(X0),X1) != X1
& in(X0,X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f88,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f42]) ).
fof(f115,plain,
( sK1 != set_union2(singleton(sK0),sK1)
& in(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f84]) ).
fof(f116,plain,
! [X0,X1] :
( ( subset(singleton(X0),X1)
| ~ in(X0,X1) )
& ( in(X0,X1)
| ~ subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f158,plain,
in(sK0,sK1),
inference(cnf_transformation,[],[f115]) ).
fof(f159,plain,
sK1 != set_union2(singleton(sK0),sK1),
inference(cnf_transformation,[],[f115]) ).
fof(f161,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
fof(f169,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f193,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f67]) ).
fof(f261,plain,
sK1 != set_union2(unordered_pair(sK0,sK0),sK1),
inference(definition_unfolding,[],[f159,f193]) ).
fof(f262,plain,
! [X0,X1] :
( subset(unordered_pair(X0,X0),X1)
| ~ in(X0,X1) ),
inference(definition_unfolding,[],[f161,f193]) ).
fof(f409,plain,
( sK1 != sK1
| ~ subset(unordered_pair(sK0,sK0),sK1) ),
inference(superposition,[],[f261,f169]) ).
fof(f411,plain,
~ subset(unordered_pair(sK0,sK0),sK1),
inference(trivial_inequality_removal,[],[f409]) ).
fof(f443,plain,
~ in(sK0,sK1),
inference(resolution,[],[f262,f411]) ).
fof(f447,plain,
$false,
inference(forward_subsumption_resolution,[],[f443,f158]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU152+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 03:46:22 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.16/1.31 % (4127577)Detected formulas, will run a generic FOF schedule.
% 0.16/1.31 % (4127586)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1207377235:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.16/1.31 % (4127586)First to succeed.
% 0.16/1.31 % (4127586)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4127577"
% 0.16/1.31 % (4127588)dis-21_1_sil=8000:lcm=predicate:random_seed=2900922124: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)
% 0.16/1.31 % (4127583)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=711033519:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.16/1.31 % (4127585)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3859768401:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.16/1.31 % (4127584)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=4047569433:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.16/1.31 % (4127582)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=2145819963:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.16/1.31 % (4127587)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3342928959:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.16/1.31 % (4127588)Also succeeded, but the first one will report.
% 0.16/1.31 % (4127585)Also succeeded, but the first one will report.
% 0.16/1.31 % (4127587)Also succeeded, but the first one will report.
% 0.16/1.31 % (4127586)Refutation found. Thanks to Tanya!
% 0.16/1.31 % SZS status Theorem for theBenchmark
% 0.16/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.31 % (4127586)------------------------------
% 0.16/1.31 % (4127586)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.31 % (4127586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.31 % (4127586)CaDiCaL version: 2.1.3
% 0.16/1.31 % (4127586)Termination reason: Refutation
% 0.16/1.31 % (4127586)Time elapsed: 0.004 s
% 0.16/1.31 % (4127586)Peak memory usage: 88 MB
% 0.16/1.31 % (4127586)Instructions burned: 8 (million)
% 0.16/1.31 % (4127586)------------------------------
% 0.16/1.31 % (4127586)------------------------------
% 0.16/1.31 % (4127577)Success in time 0.27 s
% 0.16/1.31 % Vampire exiting
%------------------------------------------------------------------------------