%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU104+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 12:47:15 PM UTC 2026
% Result : Theorem 3.68s 1.41s
% Output : Refutation 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 61 ( 14 unt; 5 def)
% Number of atoms : 174 ( 2 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 190 ( 77 ~; 68 |; 27 &)
% ( 8 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 6 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 48 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f28,axiom,
! [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,conjecture,
! [X0] :
( ~ empty(X0)
=> ( ! [X1] :
( element(X1,X0)
=> ! [X2] :
( element(X2,X0)
=> ( in(symmetric_difference(X1,X2),X0)
& in(set_difference(X1,X2),X0) ) ) )
=> preboolean(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_finsub_1) ).
fof(f30,negated_conjecture,
~ ! [X0] :
( ~ empty(X0)
=> ( ! [X1] :
( element(X1,X0)
=> ! [X2] :
( element(X2,X0)
=> ( in(symmetric_difference(X1,X2),X0)
& in(set_difference(X1,X2),X0) ) ) )
=> preboolean(X0) ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f32,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f43,axiom,
! [X0,X1] : set_union2(X0,X1) = symmetric_difference(X0,set_difference(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t98_xboole_1) ).
fof(f71,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,[],[f28]) ).
fof(f72,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,[],[f71]) ).
fof(f73,plain,
? [X0] :
( ~ preboolean(X0)
& ! [X1] :
( ! [X2] :
( ( in(symmetric_difference(X1,X2),X0)
& in(set_difference(X1,X2),X0) )
| ~ element(X2,X0) )
| ~ element(X1,X0) )
& ~ empty(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f74,plain,
? [X0] :
( ~ preboolean(X0)
& ! [X1] :
( ! [X2] :
( ( in(symmetric_difference(X1,X2),X0)
& in(set_difference(X1,X2),X0) )
| ~ element(X2,X0) )
| ~ element(X1,X0) )
& ~ empty(X0) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f95,plain,
! [X0] :
( ( preboolean(X0)
| ? [X1,X2] :
( ( ~ in(set_union2(X1,X2),X0)
| ~ in(set_difference(X1,X2),X0) )
& in(X1,X0)
& in(X2,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,[],[f72]) ).
fof(f96,plain,
! [X0] :
( ( preboolean(X0)
| ? [X1,X2] :
( ( ~ in(set_union2(X1,X2),X0)
| ~ in(set_difference(X1,X2),X0) )
& in(X1,X0)
& in(X2,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,[],[f95]) ).
fof(f97,plain,
! [X0] :
( ( preboolean(X0)
| ( ( ~ in(set_union2(sK10(X0),sK11(X0)),X0)
| ~ in(set_difference(sK10(X0),sK11(X0)),X0) )
& in(sK10(X0),X0)
& in(sK11(X0),X0) ) )
& ( ! [X3,X4] :
( ( in(set_union2(X3,X4),X0)
& in(set_difference(X3,X4),X0) )
| ~ in(X3,X0)
| ~ in(X4,X0) )
| ~ preboolean(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X1,sK10(X0)),skolemize(X2,sK11(X0))],[f96]) ).
fof(f98,plain,
( ~ preboolean(sK12)
& ! [X1] :
( ! [X2] :
( ( in(symmetric_difference(X1,X2),sK12)
& in(set_difference(X1,X2),sK12) )
| ~ element(X2,sK12) )
| ~ element(X1,sK12) )
& ~ empty(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X0,sK12)],[f74]) ).
fof(f141,plain,
! [X0] :
( preboolean(X0)
| in(sK11(X0),X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f142,plain,
! [X0] :
( preboolean(X0)
| in(sK10(X0),X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f143,plain,
! [X0] :
( preboolean(X0)
| ~ in(set_union2(sK10(X0),sK11(X0)),X0)
| ~ in(set_difference(sK10(X0),sK11(X0)),X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f145,plain,
! [X2,X1] :
( in(set_difference(X1,X2),sK12)
| ~ element(X2,sK12)
| ~ element(X1,sK12) ),
inference(cnf_transformation,[],[f98]) ).
fof(f146,plain,
! [X2,X1] :
( in(symmetric_difference(X1,X2),sK12)
| ~ element(X2,sK12)
| ~ element(X1,sK12) ),
inference(cnf_transformation,[],[f98]) ).
fof(f147,plain,
~ preboolean(sK12),
inference(cnf_transformation,[],[f98]) ).
fof(f149,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f160,plain,
! [X0,X1] : set_union2(X0,X1) = symmetric_difference(X0,set_difference(X1,X0)),
inference(cnf_transformation,[],[f43]) ).
fof(f167,plain,
! [X0] :
( preboolean(X0)
| ~ in(symmetric_difference(sK10(X0),set_difference(sK11(X0),sK10(X0))),X0)
| ~ in(set_difference(sK10(X0),sK11(X0)),X0) ),
inference(definition_unfolding,[],[f143,f160]) ).
fof(f196,plain,
in(sK11(sK12),sK12),
inference(resolution,[],[f141,f147]) ).
fof(f200,plain,
in(sK10(sK12),sK12),
inference(resolution,[],[f142,f147]) ).
fof(f264,plain,
( ~ in(symmetric_difference(sK10(sK12),set_difference(sK11(sK12),sK10(sK12))),sK12)
| ~ in(set_difference(sK10(sK12),sK11(sK12)),sK12) ),
inference(resolution,[],[f167,f147]) ).
fof(f268,definition,
( spl14_1
<=> in(set_difference(sK10(sK12),sK11(sK12)),sK12) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
fof(f269,plain,
( ~ in(set_difference(sK10(sK12),sK11(sK12)),sK12)
| spl14_1 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f271,definition,
( spl14_2
<=> in(symmetric_difference(sK10(sK12),set_difference(sK11(sK12),sK10(sK12))),sK12) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
fof(f272,plain,
( ~ in(symmetric_difference(sK10(sK12),set_difference(sK11(sK12),sK10(sK12))),sK12)
| spl14_2 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f273,plain,
( ~ spl14_1
| ~ spl14_2 ),
inference(avatar_split_clause,[],[f264,f271,f268]) ).
fof(f274,plain,
( ~ element(sK11(sK12),sK12)
| ~ element(sK10(sK12),sK12)
| spl14_1 ),
inference(resolution,[],[f269,f145]) ).
fof(f276,definition,
( spl14_3
<=> element(sK10(sK12),sK12) ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
fof(f277,plain,
( ~ element(sK10(sK12),sK12)
| spl14_3 ),
inference(avatar_component_clause,[],[f276]) ).
fof(f279,definition,
( spl14_4
<=> element(sK11(sK12),sK12) ),
introduced(definition,[new_symbols(definition,[spl14_4])],[avatar_definition]) ).
fof(f280,plain,
( ~ element(sK11(sK12),sK12)
| spl14_4 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f281,plain,
( ~ spl14_3
| ~ spl14_4
| spl14_1 ),
inference(avatar_split_clause,[],[f274,f268,f279,f276]) ).
fof(f283,plain,
( ~ in(sK10(sK12),sK12)
| spl14_3 ),
inference(resolution,[],[f277,f149]) ).
fof(f284,plain,
( $false
| spl14_3 ),
inference(resolution,[],[f283,f200]) ).
fof(f285,plain,
spl14_3,
inference(avatar_contradiction_clause,[],[f284]) ).
fof(f287,plain,
( ~ in(sK11(sK12),sK12)
| spl14_4 ),
inference(resolution,[],[f280,f149]) ).
fof(f288,plain,
( $false
| spl14_4 ),
inference(resolution,[],[f287,f196]) ).
fof(f289,plain,
spl14_4,
inference(avatar_contradiction_clause,[],[f288]) ).
fof(f290,plain,
( ~ element(set_difference(sK11(sK12),sK10(sK12)),sK12)
| ~ element(sK10(sK12),sK12)
| spl14_2 ),
inference(resolution,[],[f272,f146]) ).
fof(f292,definition,
( spl14_5
<=> element(set_difference(sK11(sK12),sK10(sK12)),sK12) ),
introduced(definition,[new_symbols(definition,[spl14_5])],[avatar_definition]) ).
fof(f293,plain,
( ~ element(set_difference(sK11(sK12),sK10(sK12)),sK12)
| spl14_5 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f294,plain,
( ~ spl14_3
| ~ spl14_5
| spl14_2 ),
inference(avatar_split_clause,[],[f290,f271,f292,f276]) ).
fof(f296,plain,
( ~ in(set_difference(sK11(sK12),sK10(sK12)),sK12)
| spl14_5 ),
inference(resolution,[],[f293,f149]) ).
fof(f297,plain,
( ~ element(sK10(sK12),sK12)
| ~ element(sK11(sK12),sK12)
| spl14_5 ),
inference(resolution,[],[f296,f145]) ).
fof(f298,plain,
( ~ spl14_4
| ~ spl14_3
| spl14_5 ),
inference(avatar_split_clause,[],[f297,f292,f276,f279]) ).
cnf(s1,plain,
( ~ spl14_1
| ~ spl14_2 ),
inference(sat_conversion,[],[f273]) ).
cnf(s2,plain,
( spl14_1
| ~ spl14_3
| ~ spl14_4 ),
inference(sat_conversion,[],[f281]) ).
cnf(s3,plain,
spl14_3,
inference(sat_conversion,[],[f285]) ).
cnf(s4,plain,
spl14_4,
inference(sat_conversion,[],[f289]) ).
cnf(s5,plain,
( spl14_2
| ~ spl14_3
| ~ spl14_5 ),
inference(sat_conversion,[],[f294]) ).
cnf(s6,plain,
( ~ spl14_3
| ~ spl14_4
| spl14_5 ),
inference(sat_conversion,[],[f298]) ).
cnf(s7,plain,
spl14_5,
inference(rat,[],[s6,s4,s3]) ).
cnf(s8,plain,
spl14_2,
inference(rat,[],[s5,s7,s3]) ).
cnf(s9,plain,
spl14_1,
inference(rat,[],[s2,s4,s3]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s8,s9]) ).
fof(f299,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU104+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n001.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 28 03:40:02 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 3.68/1.41 % (4185678)Detected formulas, will run a generic FOF schedule.
% 3.68/1.41 % (4185683)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=3940328484:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.68/1.41 % (4185684)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=971719833:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.68/1.41 % (4185685)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=218861029:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.68/1.41 % (4185689)dis-21_1_sil=8000:lcm=predicate:random_seed=2112545943: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)
% 3.68/1.41 % (4185687)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1002197026:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.68/1.41 % (4185688)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2695683206:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.68/1.41 % (4185686)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2504425435:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.68/1.41 % (4185686)Refutation not found, incomplete strategy
% 3.68/1.41 % (4185686)------------------------------
% 3.68/1.41 % (4185686)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.41 % (4185686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.41 % (4185686)CaDiCaL version: 2.1.3
% 3.68/1.41 % (4185686)Termination reason: Refutation not found, incomplete strategy
% 3.68/1.41 % (4185686)Time elapsed: 0.003 s
% 3.68/1.41 % (4185686)Peak memory usage: 89 MB
% 3.68/1.41 % (4185686)Instructions burned: 3 (million)
% 3.68/1.41 % (4185689)First to succeed.
% 3.68/1.41 % (4185689)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4185678"
% 3.68/1.41 % (4185687)Also succeeded, but the first one will report.
% 3.68/1.41 % (4185688)Also succeeded, but the first one will report.
% 3.68/1.41 % (4185686)------------------------------
% 3.68/1.41 % (4185686)------------------------------
% 3.68/1.41 % (4185689)Refutation found. Thanks to Tanya!
% 3.68/1.41 % SZS status Theorem for theBenchmark
% 3.68/1.41 % SZS output start Proof for theBenchmark
% See solution above
% 3.68/1.41 % (4185689)------------------------------
% 3.68/1.41 % (4185689)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.41 % (4185689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.41 % (4185689)CaDiCaL version: 2.1.3
% 3.68/1.41 % (4185689)Termination reason: Refutation
% 3.68/1.41 % (4185689)Time elapsed: 0.006 s
% 3.68/1.41 % (4185689)Peak memory usage: 89 MB
% 3.68/1.41 % (4185689)Instructions burned: 6 (million)
% 3.68/1.41 % (4185689)------------------------------
% 3.68/1.41 % (4185689)------------------------------
% 3.68/1.41 % (4185678)Success in time 0.443 s
% 3.68/1.41 % Vampire exiting
%------------------------------------------------------------------------------