TSTP Solution File: GRP001+6 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---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 : n029.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 01:20:15 EDT 2023
% Result : Theorem 0.21s 0.42s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 11 unt; 0 def)
% Number of atoms : 187 ( 0 equ)
% Maximal formula atoms : 32 ( 6 avg)
% Number of connectives : 227 ( 69 ~; 52 |; 86 &)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 263 (; 232 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f198,plain,
$false,
inference(unit_resulting_resolution,[],[f167,f103,f122,f24]) ).
fof(f24,plain,
! [X19,X16,X17,X15,X20] :
( ~ sP6(X15,X20,X16,X17)
| ~ product(X16,X17,X19)
| product(X15,X19,X20) ),
inference(general_splitting,[],[f12,f23_D]) ).
fof(f23,plain,
! [X18,X16,X17,X15,X20] :
( ~ product(X18,X17,X20)
| ~ product(X15,X16,X18)
| sP6(X15,X20,X16,X17) ),
inference(cnf_transformation,[],[f23_D]) ).
fof(f23_D,plain,
! [X17,X16,X20,X15] :
( ! [X18] :
( ~ product(X18,X17,X20)
| ~ product(X15,X16,X18) )
<=> ~ sP6(X15,X20,X16,X17) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP6])]) ).
fof(f12,plain,
! [X18,X19,X16,X17,X15,X20] :
( product(X15,X19,X20)
| ~ product(X18,X17,X20)
| ~ product(X16,X17,X19)
| ~ product(X15,X16,X18) ),
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/sandbox/tmp/tmp.wVGlKdxrBU/Vampire---4.8_8866',commutativity) ).
fof(f122,plain,
! [X0,X1] : sP6(X0,X1,X0,X1),
inference(unit_resulting_resolution,[],[f18,f15,f23]) ).
fof(f15,plain,
! [X7] : product(sK0,X7,X7),
inference(cnf_transformation,[],[f10]) ).
fof(f18,plain,
! [X4] : product(X4,X4,sK0),
inference(cnf_transformation,[],[f10]) ).
fof(f103,plain,
product(sK3,sK2,sK1),
inference(unit_resulting_resolution,[],[f14,f42,f22]) ).
fof(f22,plain,
! [X11,X9,X14,X12,X13] :
( ~ sP5(X11,X12,X9,X13)
| ~ product(X9,X13,X14)
| product(X12,X11,X14) ),
inference(general_splitting,[],[f13,f21_D]) ).
fof(f21,plain,
! [X10,X11,X9,X12,X13] :
( ~ product(X10,X11,X13)
| ~ product(X9,X10,X12)
| sP5(X11,X12,X9,X13) ),
inference(cnf_transformation,[],[f21_D]) ).
fof(f21_D,plain,
! [X13,X9,X12,X11] :
( ! [X10] :
( ~ product(X10,X11,X13)
| ~ product(X9,X10,X12) )
<=> ~ sP5(X11,X12,X9,X13) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP5])]) ).
fof(f13,plain,
! [X10,X11,X9,X14,X12,X13] :
( product(X12,X11,X14)
| ~ product(X9,X13,X14)
| ~ product(X10,X11,X13)
| ~ product(X9,X10,X12) ),
inference(cnf_transformation,[],[f10]) ).
fof(f42,plain,
sP5(sK2,sK3,sK1,sK0),
inference(unit_resulting_resolution,[],[f19,f18,f21]) ).
fof(f19,plain,
product(sK1,sK2,sK3),
inference(cnf_transformation,[],[f10]) ).
fof(f14,plain,
! [X8] : product(X8,sK0,X8),
inference(cnf_transformation,[],[f10]) ).
fof(f167,plain,
~ product(sK3,sK1,sK2),
inference(unit_resulting_resolution,[],[f18,f67,f21]) ).
fof(f67,plain,
~ sP5(sK1,sK2,sK3,sK0),
inference(unit_resulting_resolution,[],[f20,f14,f22]) ).
fof(f20,plain,
~ product(sK2,sK1,sK3),
inference(cnf_transformation,[],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP001+6 : TPTP v8.1.2. Released v3.1.0.
% 0.07/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 22:01:26 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a FOF_THM_RFO_NEQ problem
% 0.14/0.35 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.wVGlKdxrBU/Vampire---4.8_8866
% 0.14/0.35 % (8973)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.41 % (8975)dis-1002_1_av=off:bsr=on:cond=on:flr=on:fsr=off:gsp=on:nwc=2.0:sims=off_1218 on Vampire---4 for (1218ds/0Mi)
% 0.21/0.41 % (8978)ott-1010_5_add=off:amm=off:anc=none:bce=on:cond=fast:flr=on:lma=on:nm=2:nwc=1.1:sp=occurrence:tgt=ground_470 on Vampire---4 for (470ds/0Mi)
% 0.21/0.41 % (8977)dis-1_128_add=large:amm=sco:anc=all_dependent:bs=on:bsr=on:bce=on:cond=fast:fsr=off:gsp=on:gs=on:gsem=off:lcm=predicate:lma=on:nm=32:nwc=4.0:nicw=on:sac=on:sp=weighted_frequency_692 on Vampire---4 for (692ds/0Mi)
% 0.21/0.41 % (8979)ott+10_8_br=off:cond=on:fsr=off:gsp=on:nm=16:nwc=3.0:sims=off:sp=reverse_frequency:urr=on_415 on Vampire---4 for (415ds/0Mi)
% 0.21/0.41 % (8974)lrs-1_7_acc=on:amm=off:anc=all:bs=on:bsr=on:cond=fast:flr=on:fsr=off:gsp=on:lcm=reverse:lma=on:msp=off:nm=0:nwc=1.2:sp=frequency:stl=188_1354 on Vampire---4 for (1354ds/0Mi)
% 0.21/0.41 % (8980)dis+3_1024_av=off:fsr=off:gsp=on:lcm=predicate:nm=4:sos=all:sp=weighted_frequency_338 on Vampire---4 for (338ds/0Mi)
% 0.21/0.41 % (8976)lrs+11_4:3_aac=none:add=off:amm=off:anc=none:bd=preordered:bs=on:bce=on:flr=on:fsd=off:fsr=off:fde=none:nwc=2.5:sims=off:sp=reverse_arity:tgt=full:stl=188_1106 on Vampire---4 for (1106ds/0Mi)
% 0.21/0.42 % (8979)First to succeed.
% 0.21/0.42 % (8979)Refutation found. Thanks to Tanya!
% 0.21/0.42 % SZS status Theorem for Vampire---4
% 0.21/0.42 % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.42 % (8979)------------------------------
% 0.21/0.42 % (8979)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.42 % (8979)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.42 % (8979)Termination reason: Refutation
% 0.21/0.42
% 0.21/0.42 % (8979)Memory used [KB]: 5500
% 0.21/0.42 % (8979)Time elapsed: 0.007 s
% 0.21/0.42 % (8979)------------------------------
% 0.21/0.42 % (8979)------------------------------
% 0.21/0.42 % (8973)Success in time 0.064 s
% 0.21/0.42 % Vampire---4.8 exiting
%------------------------------------------------------------------------------