TSTP Solution File: KLE148+2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : KLE148+2 : TPTP v8.1.2. Released v4.0.0.
% 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 : n014.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 05:37:03 EDT 2023
% Result : Theorem 0.23s 0.45s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 60 ( 25 unt; 0 def)
% Number of atoms : 107 ( 50 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 84 ( 37 ~; 31 |; 8 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 63 (; 59 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f338,plain,
$false,
inference(avatar_sat_refutation,[],[f57,f61,f245,f331]) ).
fof(f331,plain,
( spl2_1
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f330]) ).
fof(f330,plain,
( $false
| spl2_1
| ~ spl2_3 ),
inference(subsumption_resolution,[],[f329,f275]) ).
fof(f275,plain,
( sK0 != multiplication(sK0,strong_iteration(sK1))
| spl2_1 ),
inference(forward_demodulation,[],[f274,f124]) ).
fof(f124,plain,
! [X13] : strong_iteration(X13) = addition(one,strong_iteration(X13)),
inference(superposition,[],[f93,f62]) ).
fof(f62,plain,
! [X0] : strong_iteration(X0) = addition(one,multiplication(X0,strong_iteration(X0))),
inference(backward_demodulation,[],[f39,f41]) ).
fof(f41,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/tmp/tmp.nomDKvGdvZ/Vampire---4.8_680',additive_commutativity) ).
fof(f39,plain,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(cnf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
file('/export/starexec/sandbox2/tmp/tmp.nomDKvGdvZ/Vampire---4.8_680',infty_unfold1) ).
fof(f93,plain,
! [X2,X3] : addition(X2,X3) = addition(X2,addition(X2,X3)),
inference(superposition,[],[f44,f36]) ).
fof(f36,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/tmp/tmp.nomDKvGdvZ/Vampire---4.8_680',idempotence) ).
fof(f44,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X2,X1,X0] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
file('/export/starexec/sandbox2/tmp/tmp.nomDKvGdvZ/Vampire---4.8_680',additive_associativity) ).
fof(f274,plain,
( sK0 != multiplication(sK0,addition(one,strong_iteration(sK1)))
| spl2_1 ),
inference(forward_demodulation,[],[f273,f222]) ).
fof(f222,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[],[f46,f34]) ).
fof(f34,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/tmp/tmp.nomDKvGdvZ/Vampire---4.8_680',multiplicative_right_identity) ).
fof(f46,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox2/tmp/tmp.nomDKvGdvZ/Vampire---4.8_680',distributivity1) ).
fof(f273,plain,
( sK0 != addition(sK0,multiplication(sK0,strong_iteration(sK1)))
| spl2_1 ),
inference(forward_demodulation,[],[f272,f41]) ).
fof(f272,plain,
( sK0 != addition(multiplication(sK0,strong_iteration(sK1)),sK0)
| spl2_1 ),
inference(resolution,[],[f53,f43]) ).
fof(f43,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.nomDKvGdvZ/Vampire---4.8_680',order) ).
fof(f53,plain,
( ~ leq(multiplication(sK0,strong_iteration(sK1)),sK0)
| spl2_1 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f52,plain,
( spl2_1
<=> leq(multiplication(sK0,strong_iteration(sK1)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
fof(f329,plain,
( sK0 = multiplication(sK0,strong_iteration(sK1))
| ~ spl2_3 ),
inference(forward_demodulation,[],[f320,f34]) ).
fof(f320,plain,
( multiplication(sK0,strong_iteration(sK1)) = multiplication(sK0,one)
| ~ spl2_3 ),
inference(superposition,[],[f280,f62]) ).
fof(f280,plain,
( ! [X0,X1] : multiplication(sK0,X1) = multiplication(sK0,addition(X1,multiplication(sK1,X0)))
| ~ spl2_3 ),
inference(forward_demodulation,[],[f277,f33]) ).
fof(f33,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/tmp/tmp.nomDKvGdvZ/Vampire---4.8_680',additive_identity) ).
fof(f277,plain,
( ! [X0,X1] : addition(multiplication(sK0,X1),zero) = multiplication(sK0,addition(X1,multiplication(sK1,X0)))
| ~ spl2_3 ),
inference(superposition,[],[f46,f271]) ).
fof(f271,plain,
( ! [X2] : zero = multiplication(sK0,multiplication(sK1,X2))
| ~ spl2_3 ),
inference(forward_demodulation,[],[f268,f32]) ).
fof(f32,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] : zero = multiplication(zero,X0),
file('/export/starexec/sandbox2/tmp/tmp.nomDKvGdvZ/Vampire---4.8_680',left_annihilation) ).
fof(f268,plain,
( ! [X2] : multiplication(zero,X2) = multiplication(sK0,multiplication(sK1,X2))
| ~ spl2_3 ),
inference(superposition,[],[f45,f60]) ).
fof(f60,plain,
( zero = multiplication(sK0,sK1)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f59,plain,
( spl2_3
<=> zero = multiplication(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
fof(f45,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox2/tmp/tmp.nomDKvGdvZ/Vampire---4.8_680',multiplicative_associativity) ).
fof(f245,plain,
spl2_2,
inference(avatar_contradiction_clause,[],[f244]) ).
fof(f244,plain,
( $false
| spl2_2 ),
inference(trivial_inequality_removal,[],[f243]) ).
fof(f243,plain,
( multiplication(sK0,strong_iteration(sK1)) != multiplication(sK0,strong_iteration(sK1))
| spl2_2 ),
inference(forward_demodulation,[],[f241,f124]) ).
fof(f241,plain,
( multiplication(sK0,strong_iteration(sK1)) != multiplication(sK0,addition(one,strong_iteration(sK1)))
| spl2_2 ),
inference(backward_demodulation,[],[f71,f222]) ).
fof(f71,plain,
( multiplication(sK0,strong_iteration(sK1)) != addition(sK0,multiplication(sK0,strong_iteration(sK1)))
| spl2_2 ),
inference(resolution,[],[f43,f56]) ).
fof(f56,plain,
( ~ leq(sK0,multiplication(sK0,strong_iteration(sK1)))
| spl2_2 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f55,plain,
( spl2_2
<=> leq(sK0,multiplication(sK0,strong_iteration(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
fof(f61,plain,
( spl2_3
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f30,f55,f59]) ).
fof(f30,plain,
( ~ leq(sK0,multiplication(sK0,strong_iteration(sK1)))
| zero = multiplication(sK0,sK1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
( ~ leq(sK0,multiplication(sK0,strong_iteration(sK1)))
| ( ~ leq(multiplication(sK0,strong_iteration(sK1)),sK0)
& zero = multiplication(sK0,sK1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f23,f27]) ).
fof(f27,plain,
( ? [X0,X1] :
( ~ leq(X0,multiplication(X0,strong_iteration(X1)))
| ( ~ leq(multiplication(X0,strong_iteration(X1)),X0)
& zero = multiplication(X0,X1) ) )
=> ( ~ leq(sK0,multiplication(sK0,strong_iteration(sK1)))
| ( ~ leq(multiplication(sK0,strong_iteration(sK1)),sK0)
& zero = multiplication(sK0,sK1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
? [X0,X1] :
( ~ leq(X0,multiplication(X0,strong_iteration(X1)))
| ( ~ leq(multiplication(X0,strong_iteration(X1)),X0)
& zero = multiplication(X0,X1) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
~ ! [X0,X1] :
( leq(X0,multiplication(X0,strong_iteration(X1)))
& ( zero = multiplication(X0,X1)
=> leq(multiplication(X0,strong_iteration(X1)),X0) ) ),
inference(rectify,[],[f20]) ).
fof(f20,negated_conjecture,
~ ! [X3,X4] :
( leq(X3,multiplication(X3,strong_iteration(X4)))
& ( zero = multiplication(X3,X4)
=> leq(multiplication(X3,strong_iteration(X4)),X3) ) ),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
! [X3,X4] :
( leq(X3,multiplication(X3,strong_iteration(X4)))
& ( zero = multiplication(X3,X4)
=> leq(multiplication(X3,strong_iteration(X4)),X3) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nomDKvGdvZ/Vampire---4.8_680',goals) ).
fof(f57,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f31,f55,f52]) ).
fof(f31,plain,
( ~ leq(sK0,multiplication(sK0,strong_iteration(sK1)))
| ~ leq(multiplication(sK0,strong_iteration(sK1)),sK0) ),
inference(cnf_transformation,[],[f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : KLE148+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.16 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.37 % Computer : n014.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Tue Aug 29 12:01:45 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.16/0.37 This is a FOF_THM_RFO_SEQ problem
% 0.16/0.37 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.nomDKvGdvZ/Vampire---4.8_680
% 0.16/0.38 % (794)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.44 % (799)ott+1003_4:1_av=off:cond=on:drc=off:fsd=off:fsr=off:fde=none:gsp=on:nm=2:nwc=1.5:sos=all:sp=reverse_arity:tgt=full_871 on Vampire---4 for (871ds/0Mi)
% 0.23/0.44 % (796)lrs-11_28_aac=none:afr=on:anc=none:bs=on:drc=off:fde=unused:gs=on:nm=2:nwc=1.3:sp=frequency:stl=188_1092 on Vampire---4 for (1092ds/0Mi)
% 0.23/0.44 % (800)lrs-11_32_av=off:bd=off:bs=on:bsr=on:drc=off:flr=on:fsd=off:fsr=off:fde=none:gsp=on:irw=on:lcm=predicate:nm=4:sp=scramble:stl=125_825 on Vampire---4 for (825ds/0Mi)
% 0.23/0.44 % (798)lrs+3_20_av=off:bd=preordered:drc=off:fsd=off:fsr=off:fde=unused:irw=on:lcm=reverse:sos=theory:stl=315_961 on Vampire---4 for (961ds/0Mi)
% 0.23/0.44 % (795)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_1169 on Vampire---4 for (1169ds/0Mi)
% 0.23/0.44 % (801)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_501 on Vampire---4 for (501ds/0Mi)
% 0.23/0.44 % (799)Refutation not found, incomplete strategy% (799)------------------------------
% 0.23/0.44 % (799)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.44 % (799)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.44 % (799)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.44
% 0.23/0.44 % (799)Memory used [KB]: 895
% 0.23/0.44 % (799)Time elapsed: 0.005 s
% 0.23/0.44 % (799)------------------------------
% 0.23/0.44 % (799)------------------------------
% 0.23/0.44 % (797)ott-4_11_av=off:bd=preordered:bce=on:drc=off:flr=on:fsr=off:lma=on:nwc=2.0:sp=occurrence:tgt=ground:urr=ec_only_1010 on Vampire---4 for (1010ds/0Mi)
% 0.23/0.45 % (796)First to succeed.
% 0.23/0.45 % (796)Refutation found. Thanks to Tanya!
% 0.23/0.45 % SZS status Theorem for Vampire---4
% 0.23/0.45 % SZS output start Proof for Vampire---4
% See solution above
% 0.23/0.45 % (796)------------------------------
% 0.23/0.45 % (796)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.45 % (796)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.45 % (796)Termination reason: Refutation
% 0.23/0.45
% 0.23/0.45 % (796)Memory used [KB]: 10234
% 0.23/0.45 % (796)Time elapsed: 0.016 s
% 0.23/0.45 % (796)------------------------------
% 0.23/0.45 % (796)------------------------------
% 0.23/0.45 % (794)Success in time 0.073 s
% 0.23/0.45 % Vampire---4.8 exiting
%------------------------------------------------------------------------------