%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU101+1 : 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 : n001.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 12:47:14 PM UTC 2026
% Result : Theorem 3.12s 1.33s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 57 ( 5 unt; 0 def)
% Number of atoms : 227 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 282 ( 112 ~; 112 |; 43 &)
% ( 9 <=>; 4 =>; 0 <=; 2 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 90 ( 74 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0] :
( cup_closed(X0)
<=> ! [X1,X2] :
( ( in(X1,X0)
& in(X2,X0) )
=> in(set_union2(X1,X2),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_finsub_1) ).
fof(f8,axiom,
! [X0] :
( diff_closed(X0)
<=> ! [X1,X2] :
( ( in(X1,X0)
& in(X2,X0) )
=> in(set_difference(X1,X2),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_finsub_1) ).
fof(f9,axiom,
! [X0] :
( preboolean(X0)
<=> ( cup_closed(X0)
& diff_closed(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_finsub_1) ).
fof(f28,conjecture,
! [X0] :
( preboolean(X0)
<=> ! [X1,X2] :
( ( in(X1,X0)
& in(X2,X0) )
=> ( in(set_union2(X1,X2),X0)
& in(set_difference(X1,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_finsub_1) ).
fof(f29,negated_conjecture,
~ ! [X0] :
( preboolean(X0)
<=> ! [X1,X2] :
( ( in(X1,X0)
& in(X2,X0) )
=> ( in(set_union2(X1,X2),X0)
& in(set_difference(X1,X2),X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f42,plain,
? [X0] :
( preboolean(X0)
<~> ! [X1,X2] :
( ( in(set_union2(X1,X2),X0)
& in(set_difference(X1,X2),X0) )
| ~ in(X1,X0)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f29]) ).
fof(f43,plain,
? [X0] :
( preboolean(X0)
<~> ! [X1,X2] :
( ( in(set_union2(X1,X2),X0)
& in(set_difference(X1,X2),X0) )
| ~ in(X1,X0)
| ~ in(X2,X0) ) ),
inference(flattening,[],[f42]) ).
fof(f57,plain,
! [X0] :
( diff_closed(X0)
<=> ! [X1,X2] :
( in(set_difference(X1,X2),X0)
| ~ in(X1,X0)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f58,plain,
! [X0] :
( diff_closed(X0)
<=> ! [X1,X2] :
( in(set_difference(X1,X2),X0)
| ~ in(X1,X0)
| ~ in(X2,X0) ) ),
inference(flattening,[],[f57]) ).
fof(f69,plain,
! [X0] :
( cup_closed(X0)
<=> ! [X1,X2] :
( in(set_union2(X1,X2),X0)
| ~ in(X1,X0)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f70,plain,
! [X0] :
( cup_closed(X0)
<=> ! [X1,X2] :
( in(set_union2(X1,X2),X0)
| ~ in(X1,X0)
| ~ in(X2,X0) ) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
? [X0] :
( ( ? [X1,X2] :
( ( ~ in(set_union2(X1,X2),X0)
| ~ in(set_difference(X1,X2),X0) )
& in(X1,X0)
& in(X2,X0) )
| ~ preboolean(X0) )
& ( ! [X1,X2] :
( ( in(set_union2(X1,X2),X0)
& in(set_difference(X1,X2),X0) )
| ~ in(X1,X0)
| ~ in(X2,X0) )
| preboolean(X0) ) ),
inference(nnf_transformation,[],[f43]) ).
fof(f72,plain,
? [X0] :
( ( ? [X1,X2] :
( ( ~ in(set_union2(X1,X2),X0)
| ~ in(set_difference(X1,X2),X0) )
& in(X1,X0)
& in(X2,X0) )
| ~ preboolean(X0) )
& ( ! [X3,X4] :
( ( in(set_union2(X3,X4),X0)
& in(set_difference(X3,X4),X0) )
| ~ in(X3,X0)
| ~ in(X4,X0) )
| preboolean(X0) ) ),
inference(rectify,[],[f71]) ).
fof(f73,plain,
( ( ( ( ~ in(set_union2(sK1,sK2),sK0)
| ~ in(set_difference(sK1,sK2),sK0) )
& in(sK1,sK0)
& in(sK2,sK0) )
| ~ preboolean(sK0) )
& ( ! [X3,X4] :
( ( in(set_union2(X3,X4),sK0)
& in(set_difference(X3,X4),sK0) )
| ~ in(X3,sK0)
| ~ in(X4,sK0) )
| preboolean(sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f72]) ).
fof(f74,plain,
! [X0] :
( ( diff_closed(X0)
| ? [X1,X2] :
( ~ in(set_difference(X1,X2),X0)
& in(X1,X0)
& in(X2,X0) ) )
& ( ! [X1,X2] :
( in(set_difference(X1,X2),X0)
| ~ in(X1,X0)
| ~ in(X2,X0) )
| ~ diff_closed(X0) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f75,plain,
! [X0] :
( ( diff_closed(X0)
| ? [X1,X2] :
( ~ in(set_difference(X1,X2),X0)
& in(X1,X0)
& in(X2,X0) ) )
& ( ! [X3,X4] :
( in(set_difference(X3,X4),X0)
| ~ in(X3,X0)
| ~ in(X4,X0) )
| ~ diff_closed(X0) ) ),
inference(rectify,[],[f74]) ).
fof(f76,plain,
! [X0] :
( ( diff_closed(X0)
| ( ~ in(set_difference(sK3(X0),sK4(X0)),X0)
& in(sK3(X0),X0)
& in(sK4(X0),X0) ) )
& ( ! [X3,X4] :
( in(set_difference(X3,X4),X0)
| ~ in(X3,X0)
| ~ in(X4,X0) )
| ~ diff_closed(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X1,sK3(X0)),skolemize(X2,sK4(X0))],[f75]) ).
fof(f77,plain,
! [X0] :
( ( preboolean(X0)
| ~ cup_closed(X0)
| ~ diff_closed(X0) )
& ( ( cup_closed(X0)
& diff_closed(X0) )
| ~ preboolean(X0) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f78,plain,
! [X0] :
( ( preboolean(X0)
| ~ cup_closed(X0)
| ~ diff_closed(X0) )
& ( ( cup_closed(X0)
& diff_closed(X0) )
| ~ preboolean(X0) ) ),
inference(flattening,[],[f77]) ).
fof(f87,plain,
! [X0] :
( ( cup_closed(X0)
| ? [X1,X2] :
( ~ in(set_union2(X1,X2),X0)
& in(X1,X0)
& in(X2,X0) ) )
& ( ! [X1,X2] :
( in(set_union2(X1,X2),X0)
| ~ in(X1,X0)
| ~ in(X2,X0) )
| ~ cup_closed(X0) ) ),
inference(nnf_transformation,[],[f70]) ).
fof(f88,plain,
! [X0] :
( ( cup_closed(X0)
| ? [X1,X2] :
( ~ in(set_union2(X1,X2),X0)
& in(X1,X0)
& in(X2,X0) ) )
& ( ! [X3,X4] :
( in(set_union2(X3,X4),X0)
| ~ in(X3,X0)
| ~ in(X4,X0) )
| ~ cup_closed(X0) ) ),
inference(rectify,[],[f87]) ).
fof(f89,plain,
! [X0] :
( ( cup_closed(X0)
| ( ~ in(set_union2(sK13(X0),sK14(X0)),X0)
& in(sK13(X0),X0)
& in(sK14(X0),X0) ) )
& ( ! [X3,X4] :
( in(set_union2(X3,X4),X0)
| ~ in(X3,X0)
| ~ in(X4,X0) )
| ~ cup_closed(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X1,sK13(X0)),skolemize(X2,sK14(X0))],[f88]) ).
fof(f90,plain,
! [X3,X4] :
( in(set_difference(X3,X4),sK0)
| ~ in(X3,sK0)
| ~ in(X4,sK0)
| preboolean(sK0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f91,plain,
! [X3,X4] :
( in(set_union2(X3,X4),sK0)
| ~ in(X3,sK0)
| ~ in(X4,sK0)
| preboolean(sK0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f92,plain,
( in(sK2,sK0)
| ~ preboolean(sK0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f93,plain,
( in(sK1,sK0)
| ~ preboolean(sK0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f94,plain,
( ~ in(set_difference(sK1,sK2),sK0)
| ~ in(set_union2(sK1,sK2),sK0)
| ~ preboolean(sK0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f107,plain,
! [X3,X0,X4] :
( in(set_difference(X3,X4),X0)
| ~ in(X3,X0)
| ~ in(X4,X0)
| ~ diff_closed(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f108,plain,
! [X0] :
( in(sK4(X0),X0)
| diff_closed(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f109,plain,
! [X0] :
( in(sK3(X0),X0)
| diff_closed(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f110,plain,
! [X0] :
( ~ in(set_difference(sK3(X0),sK4(X0)),X0)
| diff_closed(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f111,plain,
! [X0] :
( diff_closed(X0)
| ~ preboolean(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f112,plain,
! [X0] :
( cup_closed(X0)
| ~ preboolean(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f113,plain,
! [X0] :
( preboolean(X0)
| ~ cup_closed(X0)
| ~ diff_closed(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f141,plain,
! [X3,X0,X4] :
( in(set_union2(X3,X4),X0)
| ~ in(X3,X0)
| ~ in(X4,X0)
| ~ cup_closed(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f142,plain,
! [X0] :
( in(sK14(X0),X0)
| cup_closed(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f143,plain,
! [X0] :
( in(sK13(X0),X0)
| cup_closed(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f144,plain,
! [X0] :
( ~ in(set_union2(sK13(X0),sK14(X0)),X0)
| cup_closed(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f255,plain,
( diff_closed(sK0)
| ~ in(sK3(sK0),sK0)
| ~ in(sK4(sK0),sK0)
| preboolean(sK0) ),
inference(resolution,[],[f110,f90]) ).
fof(f258,plain,
( diff_closed(sK0)
| ~ in(sK4(sK0),sK0)
| preboolean(sK0) ),
inference(forward_subsumption_resolution,[],[f255,f109]) ).
fof(f259,plain,
( diff_closed(sK0)
| preboolean(sK0) ),
inference(forward_subsumption_resolution,[],[f258,f108]) ).
fof(f260,plain,
diff_closed(sK0),
inference(forward_subsumption_resolution,[],[f259,f111]) ).
fof(f261,plain,
( cup_closed(sK0)
| ~ in(sK13(sK0),sK0)
| ~ in(sK14(sK0),sK0)
| preboolean(sK0) ),
inference(resolution,[],[f144,f91]) ).
fof(f264,plain,
( cup_closed(sK0)
| ~ in(sK14(sK0),sK0)
| preboolean(sK0) ),
inference(forward_subsumption_resolution,[],[f261,f143]) ).
fof(f265,plain,
( cup_closed(sK0)
| preboolean(sK0) ),
inference(forward_subsumption_resolution,[],[f264,f142]) ).
fof(f266,plain,
cup_closed(sK0),
inference(forward_subsumption_resolution,[],[f265,f112]) ).
fof(f278,plain,
( ~ in(sK1,sK0)
| ~ in(sK2,sK0)
| ~ diff_closed(sK0)
| ~ in(set_union2(sK1,sK2),sK0)
| ~ preboolean(sK0) ),
inference(resolution,[],[f107,f94]) ).
fof(f289,plain,
( ~ in(sK2,sK0)
| ~ diff_closed(sK0)
| ~ in(set_union2(sK1,sK2),sK0)
| ~ preboolean(sK0) ),
inference(forward_subsumption_resolution,[],[f278,f93]) ).
fof(f290,plain,
( ~ diff_closed(sK0)
| ~ in(set_union2(sK1,sK2),sK0)
| ~ preboolean(sK0) ),
inference(forward_subsumption_resolution,[],[f289,f92]) ).
fof(f291,plain,
( ~ in(set_union2(sK1,sK2),sK0)
| ~ preboolean(sK0) ),
inference(forward_subsumption_resolution,[],[f290,f111]) ).
fof(f296,plain,
( ~ in(sK1,sK0)
| ~ in(sK2,sK0)
| ~ cup_closed(sK0)
| ~ preboolean(sK0) ),
inference(resolution,[],[f141,f291]) ).
fof(f310,plain,
( ~ in(sK2,sK0)
| ~ cup_closed(sK0)
| ~ preboolean(sK0) ),
inference(forward_subsumption_resolution,[],[f296,f93]) ).
fof(f311,plain,
( ~ cup_closed(sK0)
| ~ preboolean(sK0) ),
inference(forward_subsumption_resolution,[],[f310,f92]) ).
fof(f312,plain,
~ preboolean(sK0),
inference(forward_subsumption_resolution,[],[f311,f112]) ).
fof(f313,plain,
( ~ cup_closed(sK0)
| ~ diff_closed(sK0) ),
inference(resolution,[],[f312,f113]) ).
fof(f314,plain,
~ diff_closed(sK0),
inference(forward_subsumption_resolution,[],[f313,f266]) ).
fof(f315,plain,
$false,
inference(forward_subsumption_resolution,[],[f314,f260]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU101+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n001.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 03:39:47 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 3.12/1.33 % (4184828)Detected formulas, will run a generic FOF schedule.
% 3.12/1.33 % (4184856)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3289231478:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.12/1.33 % (4184851)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=1480219938:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.12/1.33 % (4184856)First to succeed.
% 3.12/1.33 % (4184856)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4184828"
% 3.12/1.33 % (4184857)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2313764838:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.12/1.33 % (4184857)Also succeeded, but the first one will report.
% 3.12/1.33 % (4184853)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=3482545651:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.12/1.33 % (4184854)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=2771504362:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.12/1.33 % (4184855)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2114210859:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.12/1.33 % (4184855)Refutation not found, incomplete strategy
% 3.12/1.33 % (4184855)------------------------------
% 3.12/1.33 % (4184855)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.33 % (4184855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.33 % (4184855)CaDiCaL version: 2.1.3
% 3.12/1.33 % (4184855)Termination reason: Refutation not found, incomplete strategy
% 3.12/1.33 % (4184855)Time elapsed: 0.004 s
% 3.12/1.33 % (4184855)Peak memory usage: 88 MB
% 3.12/1.33 % (4184855)Instructions burned: 2 (million)
% 3.12/1.33 % (4184858)dis-21_1_sil=8000:lcm=predicate:random_seed=162301790: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)
% 3.12/1.33 % (4184858)Instruction limit reached!
% 3.12/1.33 % (4184858)------------------------------
% 3.12/1.33 % (4184858)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.33 % (4184858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.33 % (4184858)CaDiCaL version: 2.1.3
% 3.12/1.33 % (4184858)Termination reason: Instruction limit
% 3.12/1.33 % (4184858)Termination phase: Saturation
% 3.12/1.33 % (4184858)Time elapsed: 0.124 s
% 3.12/1.33 % (4184858)Peak memory usage: 89 MB
% 3.12/1.33 % (4184858)Instructions burned: 129 (million)
% 3.12/1.33 % (4184856)Refutation found. Thanks to Tanya!
% 3.12/1.33 % SZS status Theorem for theBenchmark
% 3.12/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.49/1.57 % (4184856)------------------------------
% 3.49/1.57 % (4184856)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.57 % (4184856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.57 % (4184856)CaDiCaL version: 2.1.3
% 3.49/1.57 % (4184856)Termination reason: Refutation
% 3.49/1.57 % (4184856)Time elapsed: 0.007 s
% 3.49/1.57 % (4184856)Peak memory usage: 88 MB
% 3.49/1.57 % (4184856)Instructions burned: 9 (million)
% 3.49/1.57 % (4184856)------------------------------
% 3.49/1.57 % (4184856)------------------------------
% 3.49/1.57 % (4184828)Success in time 0.407 s
% 3.49/1.57 % Vampire exiting
%------------------------------------------------------------------------------