TSTP Solution File: GRP001+6 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GRP001+6 : TPTP v8.1.2. Released v3.1.0.
% 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 : n017.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 : Fri Sep 1 15:37:59 EDT 2023
% Result : Theorem 0.16s 0.40s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 9 unt; 0 def)
% Number of atoms : 177 ( 0 equ)
% Maximal formula atoms : 32 ( 7 avg)
% Number of connectives : 211 ( 59 ~; 48 |; 86 &)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 245 (; 214 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f364,plain,
$false,
inference(subsumption_resolution,[],[f362,f20]) ).
fof(f20,plain,
~ product(sK2,sK1,sK3),
inference(cnf_transformation,[],[f10]) ).
fof(f10,plain,
( ~ product(sK2,sK1,sK3)
& product(sK1,sK2,sK3)
& ! [X4] : product(X4,X4,sK0)
& ! [X5] : product(inverse(X5),X5,sK0)
& ! [X6] : product(X6,inverse(X6),sK0)
& ! [X7] : product(sK0,X7,X7)
& ! [X8] : product(X8,sK0,X8)
& ! [X9,X10,X11,X12,X13,X14] :
( product(X12,X11,X14)
| ~ product(X9,X13,X14)
| ~ product(X10,X11,X13)
| ~ product(X9,X10,X12) )
& ! [X15,X16,X17,X18,X19,X20] :
( product(X15,X19,X20)
| ~ product(X18,X17,X20)
| ~ product(X16,X17,X19)
| ~ product(X15,X16,X18) )
& ! [X21,X22] : product(X21,X22,sK4(X21,X22)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f6,f9,f8,f7]) ).
fof(f7,plain,
( ? [X0] :
( ? [X1,X2,X3] :
( ~ product(X2,X1,X3)
& product(X1,X2,X3) )
& ! [X4] : product(X4,X4,X0)
& ! [X5] : product(inverse(X5),X5,X0)
& ! [X6] : product(X6,inverse(X6),X0)
& ! [X7] : product(X0,X7,X7)
& ! [X8] : product(X8,X0,X8)
& ! [X9,X10,X11,X12,X13,X14] :
( product(X12,X11,X14)
| ~ product(X9,X13,X14)
| ~ product(X10,X11,X13)
| ~ product(X9,X10,X12) )
& ! [X15,X16,X17,X18,X19,X20] :
( product(X15,X19,X20)
| ~ product(X18,X17,X20)
| ~ product(X16,X17,X19)
| ~ product(X15,X16,X18) )
& ! [X21,X22] :
? [X23] : product(X21,X22,X23) )
=> ( ? [X1,X2,X3] :
( ~ product(X2,X1,X3)
& product(X1,X2,X3) )
& ! [X4] : product(X4,X4,sK0)
& ! [X5] : product(inverse(X5),X5,sK0)
& ! [X6] : product(X6,inverse(X6),sK0)
& ! [X7] : product(sK0,X7,X7)
& ! [X8] : product(X8,sK0,X8)
& ! [X9,X10,X11,X12,X13,X14] :
( product(X12,X11,X14)
| ~ product(X9,X13,X14)
| ~ product(X10,X11,X13)
| ~ product(X9,X10,X12) )
& ! [X15,X16,X17,X18,X19,X20] :
( product(X15,X19,X20)
| ~ product(X18,X17,X20)
| ~ product(X16,X17,X19)
| ~ product(X15,X16,X18) )
& ! [X21,X22] :
? [X23] : product(X21,X22,X23) ) ),
introduced(choice_axiom,[]) ).
fof(f8,plain,
( ? [X1,X2,X3] :
( ~ product(X2,X1,X3)
& product(X1,X2,X3) )
=> ( ~ product(sK2,sK1,sK3)
& product(sK1,sK2,sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f9,plain,
! [X21,X22] :
( ? [X23] : product(X21,X22,X23)
=> product(X21,X22,sK4(X21,X22)) ),
introduced(choice_axiom,[]) ).
fof(f6,plain,
? [X0] :
( ? [X1,X2,X3] :
( ~ product(X2,X1,X3)
& product(X1,X2,X3) )
& ! [X4] : product(X4,X4,X0)
& ! [X5] : product(inverse(X5),X5,X0)
& ! [X6] : product(X6,inverse(X6),X0)
& ! [X7] : product(X0,X7,X7)
& ! [X8] : product(X8,X0,X8)
& ! [X9,X10,X11,X12,X13,X14] :
( product(X12,X11,X14)
| ~ product(X9,X13,X14)
| ~ product(X10,X11,X13)
| ~ product(X9,X10,X12) )
& ! [X15,X16,X17,X18,X19,X20] :
( product(X15,X19,X20)
| ~ product(X18,X17,X20)
| ~ product(X16,X17,X19)
| ~ product(X15,X16,X18) )
& ! [X21,X22] :
? [X23] : product(X21,X22,X23) ),
inference(rectify,[],[f5]) ).
fof(f5,plain,
? [X0] :
( ? [X21,X22,X23] :
( ~ product(X22,X21,X23)
& product(X21,X22,X23) )
& ! [X20] : product(X20,X20,X0)
& ! [X1] : product(inverse(X1),X1,X0)
& ! [X2] : product(X2,inverse(X2),X0)
& ! [X3] : product(X0,X3,X3)
& ! [X4] : product(X4,X0,X4)
& ! [X5,X6,X7,X8,X9,X10] :
( product(X8,X7,X10)
| ~ product(X5,X9,X10)
| ~ product(X6,X7,X9)
| ~ product(X5,X6,X8) )
& ! [X11,X12,X13,X14,X15,X16] :
( product(X11,X15,X16)
| ~ product(X14,X13,X16)
| ~ product(X12,X13,X15)
| ~ product(X11,X12,X14) )
& ! [X17,X18] :
? [X19] : product(X17,X18,X19) ),
inference(flattening,[],[f4]) ).
fof(f4,plain,
? [X0] :
( ? [X21,X22,X23] :
( ~ product(X22,X21,X23)
& product(X21,X22,X23) )
& ! [X20] : product(X20,X20,X0)
& ! [X1] : product(inverse(X1),X1,X0)
& ! [X2] : product(X2,inverse(X2),X0)
& ! [X3] : product(X0,X3,X3)
& ! [X4] : product(X4,X0,X4)
& ! [X5,X6,X7,X8,X9,X10] :
( product(X8,X7,X10)
| ~ product(X5,X9,X10)
| ~ product(X6,X7,X9)
| ~ product(X5,X6,X8) )
& ! [X11,X12,X13,X14,X15,X16] :
( product(X11,X15,X16)
| ~ product(X14,X13,X16)
| ~ product(X12,X13,X15)
| ~ product(X11,X12,X14) )
& ! [X17,X18] :
? [X19] : product(X17,X18,X19) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,plain,
~ ! [X0] :
( ( ! [X1] : product(inverse(X1),X1,X0)
& ! [X2] : product(X2,inverse(X2),X0)
& ! [X3] : product(X0,X3,X3)
& ! [X4] : product(X4,X0,X4)
& ! [X5,X6,X7,X8,X9,X10] :
( ( product(X5,X9,X10)
& product(X6,X7,X9)
& product(X5,X6,X8) )
=> product(X8,X7,X10) )
& ! [X11,X12,X13,X14,X15,X16] :
( ( product(X14,X13,X16)
& product(X12,X13,X15)
& product(X11,X12,X14) )
=> product(X11,X15,X16) )
& ! [X17,X18] :
? [X19] : product(X17,X18,X19) )
=> ( ! [X20] : product(X20,X20,X0)
=> ! [X21,X22,X23] :
( product(X21,X22,X23)
=> product(X22,X21,X23) ) ) ),
inference(rectify,[],[f2]) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( ! [X1] : product(inverse(X1),X1,X0)
& ! [X1] : product(X1,inverse(X1),X0)
& ! [X1] : product(X0,X1,X1)
& ! [X1] : product(X1,X0,X1)
& ! [X1,X2,X3,X4,X5,X6] :
( ( product(X1,X5,X6)
& product(X2,X3,X5)
& product(X1,X2,X4) )
=> product(X4,X3,X6) )
& ! [X1,X2,X3,X4,X5,X6] :
( ( product(X4,X3,X6)
& product(X2,X3,X5)
& product(X1,X2,X4) )
=> product(X1,X5,X6) )
& ! [X1,X2] :
? [X3] : product(X1,X2,X3) )
=> ( ! [X1] : product(X1,X1,X0)
=> ! [X4,X5,X6] :
( product(X4,X5,X6)
=> product(X5,X4,X6) ) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
! [X0] :
( ( ! [X1] : product(inverse(X1),X1,X0)
& ! [X1] : product(X1,inverse(X1),X0)
& ! [X1] : product(X0,X1,X1)
& ! [X1] : product(X1,X0,X1)
& ! [X1,X2,X3,X4,X5,X6] :
( ( product(X1,X5,X6)
& product(X2,X3,X5)
& product(X1,X2,X4) )
=> product(X4,X3,X6) )
& ! [X1,X2,X3,X4,X5,X6] :
( ( product(X4,X3,X6)
& product(X2,X3,X5)
& product(X1,X2,X4) )
=> product(X1,X5,X6) )
& ! [X1,X2] :
? [X3] : product(X1,X2,X3) )
=> ( ! [X1] : product(X1,X1,X0)
=> ! [X4,X5,X6] :
( product(X4,X5,X6)
=> product(X5,X4,X6) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.3uKzVx9AtG/Vampire---4.8_28282',commutativity) ).
fof(f362,plain,
product(sK2,sK1,sK3),
inference(resolution,[],[f337,f45]) ).
fof(f45,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| product(X0,X2,X1) ),
inference(resolution,[],[f22,f18]) ).
fof(f18,plain,
! [X4] : product(X4,X4,sK0),
inference(cnf_transformation,[],[f10]) ).
fof(f22,plain,
! [X6,X7,X4,X5] :
( ~ product(X4,X7,sK0)
| ~ product(X7,X6,X5)
| product(X4,X5,X6) ),
inference(resolution,[],[f12,f15]) ).
fof(f15,plain,
! [X7] : product(sK0,X7,X7),
inference(cnf_transformation,[],[f10]) ).
fof(f12,plain,
! [X18,X19,X16,X17,X15,X20] :
( ~ product(X18,X17,X20)
| product(X15,X19,X20)
| ~ product(X16,X17,X19)
| ~ product(X15,X16,X18) ),
inference(cnf_transformation,[],[f10]) ).
fof(f337,plain,
product(sK2,sK3,sK1),
inference(resolution,[],[f82,f79]) ).
fof(f79,plain,
product(sK1,sK3,sK2),
inference(resolution,[],[f45,f19]) ).
fof(f19,plain,
product(sK1,sK2,sK3),
inference(cnf_transformation,[],[f10]) ).
fof(f82,plain,
! [X2,X0,X1] :
( ~ product(X2,X1,X0)
| product(X0,X1,X2) ),
inference(resolution,[],[f33,f18]) ).
fof(f33,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,X1,sK0)
| product(X0,X1,X2)
| ~ product(X2,X3,X0) ),
inference(resolution,[],[f13,f14]) ).
fof(f14,plain,
! [X8] : product(X8,sK0,X8),
inference(cnf_transformation,[],[f10]) ).
fof(f13,plain,
! [X10,X11,X9,X14,X12,X13] :
( ~ product(X9,X13,X14)
| product(X12,X11,X14)
| ~ product(X10,X11,X13)
| ~ product(X9,X10,X12) ),
inference(cnf_transformation,[],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : GRP001+6 : TPTP v8.1.2. Released v3.1.0.
% 0.09/0.12 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.11/0.32 % Computer : n017.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Aug 30 16:52:59 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.16/0.38 % (28389)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.38 % (28391)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on Vampire---4 for (569ds/0Mi)
% 0.16/0.38 % (28395)dis+11_4:5_nm=4_216 on Vampire---4 for (216ds/0Mi)
% 0.16/0.38 % (28390)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on Vampire---4 for (1451ds/0Mi)
% 0.16/0.38 % (28396)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on Vampire---4 for (1451ds/0Mi)
% 0.16/0.38 % (28394)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on Vampire---4 for (396ds/0Mi)
% 0.16/0.38 % (28393)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on Vampire---4 for (470ds/0Mi)
% 0.16/0.38 TRYING [1]
% 0.16/0.38 TRYING [1]
% 0.16/0.38 TRYING [1]
% 0.16/0.38 TRYING [1]
% 0.16/0.38 % (28392)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on Vampire---4 for (476ds/0Mi)
% 0.16/0.38 TRYING [2]
% 0.16/0.38 TRYING [2]
% 0.16/0.38 TRYING [2]
% 0.16/0.39 TRYING [3]
% 0.16/0.39 TRYING [3]
% 0.16/0.39 TRYING [3]
% 0.16/0.39 TRYING [2]
% 0.16/0.39 TRYING [3]
% 0.16/0.39 TRYING [4]
% 0.16/0.39 TRYING [4]
% 0.16/0.39 TRYING [4]
% 0.16/0.39 TRYING [4]
% 0.16/0.39 % (28395)First to succeed.
% 0.16/0.40 % (28390)Also succeeded, but the first one will report.
% 0.16/0.40 % (28395)Refutation found. Thanks to Tanya!
% 0.16/0.40 % SZS status Theorem for Vampire---4
% 0.16/0.40 % SZS output start Proof for Vampire---4
% See solution above
% 0.16/0.40 % (28395)------------------------------
% 0.16/0.40 % (28395)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.16/0.40 % (28395)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.16/0.40 % (28395)Termination reason: Refutation
% 0.16/0.40
% 0.16/0.40 % (28395)Memory used [KB]: 5500
% 0.16/0.40 % (28395)Time elapsed: 0.015 s
% 0.16/0.40 % (28395)------------------------------
% 0.16/0.40 % (28395)------------------------------
% 0.16/0.40 % (28389)Success in time 0.067 s
% 0.16/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------