TSTP Solution File: SWC398+1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SWC398+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 20:59:11 EDT 2023
% Result : Theorem 0.18s 0.41s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 11 unt; 0 def)
% Number of atoms : 348 ( 107 equ)
% Maximal formula atoms : 38 ( 9 avg)
% Number of connectives : 462 ( 149 ~; 124 |; 160 &)
% ( 2 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 133 (; 78 !; 55 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f797,plain,
$false,
inference(subsumption_resolution,[],[f796,f349]) ).
fof(f349,plain,
ssItem(sK4),
inference(cnf_transformation,[],[f230]) ).
fof(f230,plain,
( ( nil != sK2
| nil = sK3 )
& ~ memberP(sK1,sK4)
& memberP(sK0,sK4)
& ssItem(sK4)
& ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != sK2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != sK5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& equalelemsP(sK2)
& sK3 = app(sK2,sK5)
& ssList(sK5)
& sK0 = sK2
& sK1 = sK3
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f100,f229,f228,f227,f226,f225,f224]) ).
fof(f224,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ? [X4] :
( ~ memberP(X1,X4)
& memberP(X0,X4)
& ssItem(X4) )
& ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != X2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& equalelemsP(X2)
& app(X2,X5) = X3
& ssList(X5) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ? [X4] :
( ~ memberP(X1,X4)
& memberP(sK0,X4)
& ssItem(X4) )
& ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != X2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& equalelemsP(X2)
& app(X2,X5) = X3
& ssList(X5) )
& sK0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f225,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ? [X4] :
( ~ memberP(X1,X4)
& memberP(sK0,X4)
& ssItem(X4) )
& ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != X2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& equalelemsP(X2)
& app(X2,X5) = X3
& ssList(X5) )
& sK0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ? [X4] :
( ~ memberP(sK1,X4)
& memberP(sK0,X4)
& ssItem(X4) )
& ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != X2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& equalelemsP(X2)
& app(X2,X5) = X3
& ssList(X5) )
& sK0 = X2
& sK1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f226,plain,
( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ? [X4] :
( ~ memberP(sK1,X4)
& memberP(sK0,X4)
& ssItem(X4) )
& ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != X2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& equalelemsP(X2)
& app(X2,X5) = X3
& ssList(X5) )
& sK0 = X2
& sK1 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( nil != sK2
| nil = X3 )
& ? [X4] :
( ~ memberP(sK1,X4)
& memberP(sK0,X4)
& ssItem(X4) )
& ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != sK2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& equalelemsP(sK2)
& app(sK2,X5) = X3
& ssList(X5) )
& sK0 = sK2
& sK1 = X3
& ssList(X3) )
& ssList(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f227,plain,
( ? [X3] :
( ( nil != sK2
| nil = X3 )
& ? [X4] :
( ~ memberP(sK1,X4)
& memberP(sK0,X4)
& ssItem(X4) )
& ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != sK2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& equalelemsP(sK2)
& app(sK2,X5) = X3
& ssList(X5) )
& sK0 = sK2
& sK1 = X3
& ssList(X3) )
=> ( ( nil != sK2
| nil = sK3 )
& ? [X4] :
( ~ memberP(sK1,X4)
& memberP(sK0,X4)
& ssItem(X4) )
& ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != sK2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& equalelemsP(sK2)
& app(sK2,X5) = sK3
& ssList(X5) )
& sK0 = sK2
& sK1 = sK3
& ssList(sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f228,plain,
( ? [X4] :
( ~ memberP(sK1,X4)
& memberP(sK0,X4)
& ssItem(X4) )
=> ( ~ memberP(sK1,sK4)
& memberP(sK0,sK4)
& ssItem(sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f229,plain,
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != sK2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& equalelemsP(sK2)
& app(sK2,X5) = sK3
& ssList(X5) )
=> ( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != sK2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != sK5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& equalelemsP(sK2)
& sK3 = app(sK2,sK5)
& ssList(sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ? [X4] :
( ~ memberP(X1,X4)
& memberP(X0,X4)
& ssItem(X4) )
& ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != X2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& equalelemsP(X2)
& app(X2,X5) = X3
& ssList(X5) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f99]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ? [X4] :
( ~ memberP(X1,X4)
& memberP(X0,X4)
& ssItem(X4) )
& ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != X2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& equalelemsP(X2)
& app(X2,X5) = X3
& ssList(X5) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X2
& nil != X3 )
| ! [X4] :
( ssItem(X4)
=> ( memberP(X1,X4)
| ~ memberP(X0,X4) ) )
| ! [X5] :
( ssList(X5)
=> ( ? [X6] :
( ? [X7] :
( ? [X8] :
( app(X8,cons(X6,nil)) = X2
& ssList(X8) )
& app(cons(X6,nil),X7) = X5
& ssList(X7) )
& ssItem(X6) )
| ~ equalelemsP(X2)
| app(X2,X5) != X3 ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X2
& nil != X3 )
| ! [X8] :
( ssItem(X8)
=> ( memberP(X1,X8)
| ~ memberP(X0,X8) ) )
| ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(X7,cons(X5,nil)) = X2
& ssList(X7) )
& app(cons(X5,nil),X6) = X4
& ssList(X6) )
& ssItem(X5) )
| ~ equalelemsP(X2)
| app(X2,X4) != X3 ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X2
& nil != X3 )
| ! [X8] :
( ssItem(X8)
=> ( memberP(X1,X8)
| ~ memberP(X0,X8) ) )
| ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(X7,cons(X5,nil)) = X2
& ssList(X7) )
& app(cons(X5,nil),X6) = X4
& ssList(X6) )
& ssItem(X5) )
| ~ equalelemsP(X2)
| app(X2,X4) != X3 ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cX8xXt9gCt/Vampire---4.8_2379',co1) ).
fof(f796,plain,
~ ssItem(sK4),
inference(subsumption_resolution,[],[f795,f351]) ).
fof(f351,plain,
~ memberP(sK1,sK4),
inference(cnf_transformation,[],[f230]) ).
fof(f795,plain,
( memberP(sK1,sK4)
| ~ ssItem(sK4) ),
inference(resolution,[],[f619,f350]) ).
fof(f350,plain,
memberP(sK0,sK4),
inference(cnf_transformation,[],[f230]) ).
fof(f619,plain,
! [X1] :
( ~ memberP(sK0,X1)
| memberP(sK1,X1)
| ~ ssItem(X1) ),
inference(subsumption_resolution,[],[f618,f587]) ).
fof(f587,plain,
ssList(sK0),
inference(forward_demodulation,[],[f341,f344]) ).
fof(f344,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f230]) ).
fof(f341,plain,
ssList(sK2),
inference(cnf_transformation,[],[f230]) ).
fof(f618,plain,
! [X1] :
( ~ ssList(sK0)
| ~ memberP(sK0,X1)
| memberP(sK1,X1)
| ~ ssItem(X1) ),
inference(forward_demodulation,[],[f617,f344]) ).
fof(f617,plain,
! [X1] :
( ~ memberP(sK0,X1)
| memberP(sK1,X1)
| ~ ssList(sK2)
| ~ ssItem(X1) ),
inference(forward_demodulation,[],[f616,f344]) ).
fof(f616,plain,
! [X1] :
( memberP(sK1,X1)
| ~ memberP(sK2,X1)
| ~ ssList(sK2)
| ~ ssItem(X1) ),
inference(forward_demodulation,[],[f615,f343]) ).
fof(f343,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f230]) ).
fof(f615,plain,
! [X1] :
( memberP(sK3,X1)
| ~ memberP(sK2,X1)
| ~ ssList(sK2)
| ~ ssItem(X1) ),
inference(subsumption_resolution,[],[f592,f345]) ).
fof(f345,plain,
ssList(sK5),
inference(cnf_transformation,[],[f230]) ).
fof(f592,plain,
! [X1] :
( memberP(sK3,X1)
| ~ memberP(sK2,X1)
| ~ ssList(sK5)
| ~ ssList(sK2)
| ~ ssItem(X1) ),
inference(superposition,[],[f409,f346]) ).
fof(f346,plain,
sK3 = app(sK2,sK5),
inference(cnf_transformation,[],[f230]) ).
fof(f409,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f245]) ).
fof(f245,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) ) )
& ( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f244]) ).
fof(f244,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) ) )
& ( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f140]) ).
fof(f140,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cX8xXt9gCt/Vampire---4.8_2379',ax36) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11 % Problem : SWC398+1 : TPTP v8.1.2. Released v2.4.0.
% 0.05/0.12 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.11/0.33 % Computer : n021.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.33 % CPULimit : 300
% 0.18/0.33 % WCLimit : 300
% 0.18/0.33 % DateTime : Mon Aug 28 14:59:58 EDT 2023
% 0.18/0.33 % CPUTime :
% 0.18/0.33 This is a FOF_THM_RFO_SEQ problem
% 0.18/0.33 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.cX8xXt9gCt/Vampire---4.8_2379
% 0.18/0.34 % (2486)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.40 % (2488)lrs-1004_3_av=off:ep=RSTC:fsd=off:fsr=off:urr=ec_only:stl=62_525 on Vampire---4 for (525ds/0Mi)
% 0.18/0.40 % (2489)lrs+10_4:5_amm=off:bsr=on:bce=on:flr=on:fsd=off:fde=unused:gs=on:gsem=on:lcm=predicate:sos=all:tgt=ground:stl=62_514 on Vampire---4 for (514ds/0Mi)
% 0.18/0.40 % (2487)lrs+1011_1_bd=preordered:flr=on:fsd=off:fsr=off:irw=on:lcm=reverse:msp=off:nm=2:nwc=10.0:sos=on:sp=reverse_weighted_frequency:tgt=full:stl=62_562 on Vampire---4 for (562ds/0Mi)
% 0.18/0.40 % (2493)ott+1010_2:5_bd=off:fsd=off:fde=none:nm=16:sos=on_419 on Vampire---4 for (419ds/0Mi)
% 0.18/0.40 % (2490)ott+1011_4_er=known:fsd=off:nm=4:tgt=ground_499 on Vampire---4 for (499ds/0Mi)
% 0.18/0.40 % (2491)ott+11_8:1_aac=none:amm=sco:anc=none:er=known:flr=on:fde=unused:irw=on:nm=0:nwc=1.2:nicw=on:sims=off:sos=all:sac=on_470 on Vampire---4 for (470ds/0Mi)
% 0.18/0.40 % (2492)lrs+10_1024_av=off:bsr=on:br=off:ep=RSTC:fsd=off:irw=on:nm=4:nwc=1.1:sims=off:urr=on:stl=125_440 on Vampire---4 for (440ds/0Mi)
% 0.18/0.41 % (2493)First to succeed.
% 0.18/0.41 % (2493)Refutation found. Thanks to Tanya!
% 0.18/0.41 % SZS status Theorem for Vampire---4
% 0.18/0.41 % SZS output start Proof for Vampire---4
% See solution above
% 0.18/0.41 % (2493)------------------------------
% 0.18/0.41 % (2493)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.18/0.41 % (2493)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.18/0.41 % (2493)Termination reason: Refutation
% 0.18/0.41
% 0.18/0.41 % (2493)Memory used [KB]: 6012
% 0.18/0.41 % (2493)Time elapsed: 0.012 s
% 0.18/0.41 % (2493)------------------------------
% 0.18/0.41 % (2493)------------------------------
% 0.18/0.41 % (2486)Success in time 0.071 s
% 0.18/0.41 % Vampire---4.8 exiting
%------------------------------------------------------------------------------