%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET813+4 : TPTP v9.3.1. Released v3.2.0.
% 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 12:41:59 PM UTC 2026
% Result : Theorem 2.40s 1.26s
% Output : Refutation 2.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 4 unt; 0 def)
% Number of atoms : 47 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 47 ( 19 ~; 15 |; 8 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 30 ( 29 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
<=> ( member(X0,X1)
| member(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
fof(f8,axiom,
! [X0,X1] :
( member(X0,singleton(X1))
<=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
fof(f19,axiom,
! [X0,X1] :
( member(X1,suc(X0))
<=> member(X1,union(X0,singleton(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor) ).
fof(f20,conjecture,
! [X0] :
( member(X0,on)
=> member(X0,suc(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thV12) ).
fof(f21,negated_conjecture,
~ ! [X0] :
( member(X0,on)
=> member(X0,suc(X0)) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f23,plain,
? [X0] :
( ~ member(X0,suc(X0))
& member(X0,on) ),
inference(ennf_transformation,[],[f21]) ).
fof(f35,plain,
( ~ member(sK1,suc(sK1))
& member(sK1,on) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f23]) ).
fof(f40,plain,
! [X0,X1] :
( ( member(X1,suc(X0))
| ~ member(X1,union(X0,singleton(X0))) )
& ( member(X1,union(X0,singleton(X0)))
| ~ member(X1,suc(X0)) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X1)
& ~ member(X0,X2) ) )
& ( member(X0,X1)
| member(X0,X2)
| ~ member(X0,union(X1,X2)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X1)
& ~ member(X0,X2) ) )
& ( member(X0,X1)
| member(X0,X2)
| ~ member(X0,union(X1,X2)) ) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( ( member(X0,singleton(X1))
| X0 != X1 )
& ( X0 = X1
| ~ member(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f64,plain,
~ member(sK1,suc(sK1)),
inference(cnf_transformation,[],[f35]) ).
fof(f71,plain,
! [X0,X1] :
( ~ member(X1,union(X0,singleton(X0)))
| member(X1,suc(X0)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f84,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f87,plain,
! [X0,X1] :
( member(X0,singleton(X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f51]) ).
fof(f106,plain,
! [X1] : member(X1,singleton(X1)),
inference(equality_resolution,[],[f87]) ).
fof(f142,plain,
! [X0,X1] :
( member(X0,suc(X1))
| ~ member(X0,singleton(X1)) ),
inference(resolution,[],[f71,f84]) ).
fof(f338,plain,
~ member(sK1,singleton(sK1)),
inference(resolution,[],[f142,f64]) ).
fof(f341,plain,
$false,
inference(forward_subsumption_resolution,[],[f338,f106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET813+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 % Computer : n004.cluster.edu
% 0.10/0.42 % Model : x86_64 x86_64
% 0.10/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.42 % Memory : 8046.5625MB
% 0.10/0.42 % OS : Linux 6.8.0-71-generic
% 0.10/0.42 % CPULimit : 300
% 0.10/0.42 % WCLimit : 300
% 0.10/0.42 % DateTime : Mon Sep 28 02:52:44 UTC 2026
% 0.10/0.42 % CPUTime :
% 0.10/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.46 Running first-order theorem proving
% 0.15/0.46 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
% 2.40/1.26 % (4104590)Detected formulas, will run a generic FOF schedule.
% 2.40/1.26 % (4104599)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1492919820:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.40/1.26 % (4104599)First to succeed.
% 2.40/1.26 % (4104599)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4104590"
% 2.40/1.26 % (4104600)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3810498763:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.40/1.26 % (4104595)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=2048608694:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.40/1.26 % (4104598)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2589442980:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.40/1.26 % (4104597)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=617130630:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.40/1.26 % (4104596)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=2212542826:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.40/1.26 % (4104601)dis-21_1_sil=8000:lcm=predicate:random_seed=2047253035: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)
% 2.40/1.26 % (4104598)Refutation not found, incomplete strategy
% 2.40/1.26 % (4104598)------------------------------
% 2.40/1.26 % (4104598)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.40/1.26 % (4104598)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.40/1.26 % (4104598)CaDiCaL version: 2.1.3
% 2.40/1.26 % (4104598)Termination reason: Refutation not found, incomplete strategy
% 2.40/1.26 % (4104598)Time elapsed: 0.001 s
% 2.40/1.26 % (4104598)Peak memory usage: 87 MB
% 2.40/1.26 % (4104601)Also succeeded, but the first one will report.
% 2.40/1.26 % (4104600)Also succeeded, but the first one will report.
% 2.40/1.26 % (4104599)Refutation found. Thanks to Tanya!
% 2.40/1.26 % SZS status Theorem for theBenchmark
% 2.40/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 2.40/1.26 % (4104599)------------------------------
% 2.40/1.26 % (4104599)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.40/1.26 % (4104599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.40/1.26 % (4104599)CaDiCaL version: 2.1.3
% 2.40/1.26 % (4104599)Termination reason: Refutation
% 2.40/1.26 % (4104599)Time elapsed: 0.005 s
% 2.40/1.26 % (4104599)Peak memory usage: 88 MB
% 2.40/1.26 % (4104599)Instructions burned: 13 (million)
% 2.40/1.26 % (4104599)------------------------------
% 2.40/1.26 % (4104599)------------------------------
% 2.40/1.26 % (4104590)Success in time 0.276 s
% 2.40/1.26 % Vampire exiting
%------------------------------------------------------------------------------