TSTP Solution File: KLE022+2 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : KLE022+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n020.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 : Wed Aug 31 17:27:40 EDT 2022
% Result : Theorem 1.48s 0.56s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 61 ( 16 unt; 0 def)
% Number of atoms : 148 ( 55 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 144 ( 57 ~; 49 |; 22 &)
% ( 9 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 67 ( 63 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f184,plain,
$false,
inference(avatar_sat_refutation,[],[f82,f177,f183]) ).
fof(f183,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_contradiction_clause,[],[f182]) ).
fof(f182,plain,
( $false
| ~ spl3_1
| spl3_2 ),
inference(subsumption_resolution,[],[f181,f179]) ).
fof(f179,plain,
( ~ leq(sK1,sK1)
| spl3_2 ),
inference(forward_demodulation,[],[f178,f57]) ).
fof(f57,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f178,plain,
( ~ leq(sK1,multiplication(sK1,one))
| spl3_2 ),
inference(forward_demodulation,[],[f81,f161]) ).
fof(f161,plain,
one = addition(sK0,c(sK0)),
inference(superposition,[],[f97,f63]) ).
fof(f63,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/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f97,plain,
one = addition(c(sK0),sK0),
inference(unit_resulting_resolution,[],[f86,f50]) ).
fof(f50,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0,X1] :
( ( complement(X1,X0)
| zero != multiplication(X0,X1)
| addition(X0,X1) != one
| zero != multiplication(X1,X0) )
& ( ( zero = multiplication(X0,X1)
& addition(X0,X1) = one
& zero = multiplication(X1,X0) )
| ~ complement(X1,X0) ) ),
inference(rectify,[],[f35]) ).
fof(f35,plain,
! [X1,X0] :
( ( complement(X0,X1)
| zero != multiplication(X1,X0)
| addition(X1,X0) != one
| zero != multiplication(X0,X1) )
& ( ( zero = multiplication(X1,X0)
& addition(X1,X0) = one
& zero = multiplication(X0,X1) )
| ~ complement(X0,X1) ) ),
inference(flattening,[],[f34]) ).
fof(f34,plain,
! [X1,X0] :
( ( complement(X0,X1)
| zero != multiplication(X1,X0)
| addition(X1,X0) != one
| zero != multiplication(X0,X1) )
& ( ( zero = multiplication(X1,X0)
& addition(X1,X0) = one
& zero = multiplication(X0,X1) )
| ~ complement(X0,X1) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X1,X0] :
( complement(X0,X1)
<=> ( zero = multiplication(X1,X0)
& addition(X1,X0) = one
& zero = multiplication(X0,X1) ) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X4,X3] :
( ( zero = multiplication(X3,X4)
& one = addition(X3,X4)
& zero = multiplication(X4,X3) )
<=> complement(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_2) ).
fof(f86,plain,
complement(sK0,c(sK0)),
inference(resolution,[],[f55,f71]) ).
fof(f71,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( ~ test(X0)
| complement(X0,X1)
| c(X0) != X1 ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X1] :
( ~ test(X0)
| ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) ) ),
inference(rectify,[],[f45]) ).
fof(f45,plain,
! [X1,X0] :
( ~ test(X1)
| ( ( c(X1) = X0
| ~ complement(X1,X0) )
& ( complement(X1,X0)
| c(X1) != X0 ) ) ),
inference(nnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X1,X0] :
( ~ test(X1)
| ( c(X1) = X0
<=> complement(X1,X0) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( test(X1)
=> ( c(X1) = X0
<=> complement(X1,X0) ) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X4,X3] :
( test(X3)
=> ( c(X3) = X4
<=> complement(X3,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_3) ).
fof(f55,plain,
test(sK0),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
( test(sK0)
& ( ~ leq(sK1,addition(multiplication(sK1,sK0),multiplication(sK1,c(sK0))))
| ~ leq(addition(multiplication(sK1,sK0),multiplication(sK1,c(sK0))),sK1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f29,f37]) ).
fof(f37,plain,
( ? [X0,X1] :
( test(X0)
& ( ~ leq(X1,addition(multiplication(X1,X0),multiplication(X1,c(X0))))
| ~ leq(addition(multiplication(X1,X0),multiplication(X1,c(X0))),X1) ) )
=> ( test(sK0)
& ( ~ leq(sK1,addition(multiplication(sK1,sK0),multiplication(sK1,c(sK0))))
| ~ leq(addition(multiplication(sK1,sK0),multiplication(sK1,c(sK0))),sK1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
? [X0,X1] :
( test(X0)
& ( ~ leq(X1,addition(multiplication(X1,X0),multiplication(X1,c(X0))))
| ~ leq(addition(multiplication(X1,X0),multiplication(X1,c(X0))),X1) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,plain,
~ ! [X0,X1] :
( test(X0)
=> ( leq(X1,addition(multiplication(X1,X0),multiplication(X1,c(X0))))
& leq(addition(multiplication(X1,X0),multiplication(X1,c(X0))),X1) ) ),
inference(rectify,[],[f18]) ).
fof(f18,negated_conjecture,
~ ! [X4,X3] :
( test(X4)
=> ( leq(addition(multiplication(X3,X4),multiplication(X3,c(X4))),X3)
& leq(X3,addition(multiplication(X3,X4),multiplication(X3,c(X4)))) ) ),
inference(negated_conjecture,[],[f17]) ).
fof(f17,conjecture,
! [X4,X3] :
( test(X4)
=> ( leq(addition(multiplication(X3,X4),multiplication(X3,c(X4))),X3)
& leq(X3,addition(multiplication(X3,X4),multiplication(X3,c(X4)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f81,plain,
( ~ leq(sK1,multiplication(sK1,addition(sK0,c(sK0))))
| spl3_2 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f79,plain,
( spl3_2
<=> leq(sK1,multiplication(sK1,addition(sK0,c(sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
fof(f181,plain,
( leq(sK1,sK1)
| ~ spl3_1 ),
inference(forward_demodulation,[],[f180,f57]) ).
fof(f180,plain,
( leq(multiplication(sK1,one),sK1)
| ~ spl3_1 ),
inference(forward_demodulation,[],[f76,f161]) ).
fof(f76,plain,
( leq(multiplication(sK1,addition(sK0,c(sK0))),sK1)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f75,plain,
( spl3_1
<=> leq(multiplication(sK1,addition(sK0,c(sK0))),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f177,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f176]) ).
fof(f176,plain,
( $false
| spl3_1 ),
inference(subsumption_resolution,[],[f175,f61]) ).
fof(f61,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f175,plain,
( sK1 != addition(sK1,sK1)
| spl3_1 ),
inference(forward_demodulation,[],[f168,f57]) ).
fof(f168,plain,
( addition(sK1,multiplication(sK1,one)) != sK1
| spl3_1 ),
inference(backward_demodulation,[],[f143,f161]) ).
fof(f143,plain,
( sK1 != addition(sK1,multiplication(sK1,addition(sK0,c(sK0))))
| spl3_1 ),
inference(superposition,[],[f116,f63]) ).
fof(f116,plain,
( addition(multiplication(sK1,addition(sK0,c(sK0))),sK1) != sK1
| spl3_1 ),
inference(unit_resulting_resolution,[],[f77,f66]) ).
fof(f66,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(rectify,[],[f32]) ).
fof(f32,plain,
! [X1,X0] :
( addition(X1,X0) != X0
| leq(X1,X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( addition(X1,X0) = X0
=> leq(X1,X0) ),
inference(unused_predicate_definition_removal,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( leq(X1,X0)
<=> addition(X1,X0) = X0 ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X1,X0] :
( addition(X0,X1) = X1
<=> leq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
fof(f77,plain,
( ~ leq(multiplication(sK1,addition(sK0,c(sK0))),sK1)
| spl3_1 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f82,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f73,f79,f75]) ).
fof(f73,plain,
( ~ leq(sK1,multiplication(sK1,addition(sK0,c(sK0))))
| ~ leq(multiplication(sK1,addition(sK0,c(sK0))),sK1) ),
inference(forward_demodulation,[],[f72,f48]) ).
fof(f48,plain,
! [X2,X0,X1] : multiplication(X0,addition(X2,X1)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1,X2] : multiplication(X0,addition(X2,X1)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(rectify,[],[f21]) ).
fof(f21,plain,
! [X2,X1,X0] : multiplication(X2,addition(X0,X1)) = addition(multiplication(X2,X0),multiplication(X2,X1)),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X1,X2,X0] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
fof(f72,plain,
( ~ leq(addition(multiplication(sK1,sK0),multiplication(sK1,c(sK0))),sK1)
| ~ leq(sK1,multiplication(sK1,addition(sK0,c(sK0)))) ),
inference(forward_demodulation,[],[f54,f48]) ).
fof(f54,plain,
( ~ leq(sK1,addition(multiplication(sK1,sK0),multiplication(sK1,c(sK0))))
| ~ leq(addition(multiplication(sK1,sK0),multiplication(sK1,c(sK0))),sK1) ),
inference(cnf_transformation,[],[f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : KLE022+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.35 % Computer : n020.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 : Tue Aug 30 00:32:30 EDT 2022
% 0.14/0.35 % CPUTime :
% 1.33/0.55 % (29622)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 1.33/0.55 % (29640)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.33/0.55 % (29623)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 1.33/0.55 % (29621)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 1.48/0.55 % (29622)First to succeed.
% 1.48/0.56 % (29626)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.48/0.56 % (29639)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 1.48/0.56 % (29632)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.48/0.56 % (29622)Refutation found. Thanks to Tanya!
% 1.48/0.56 % SZS status Theorem for theBenchmark
% 1.48/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 1.48/0.56 % (29622)------------------------------
% 1.48/0.56 % (29622)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.48/0.56 % (29622)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.48/0.56 % (29622)Termination reason: Refutation
% 1.48/0.56
% 1.48/0.56 % (29622)Memory used [KB]: 6012
% 1.48/0.56 % (29622)Time elapsed: 0.121 s
% 1.48/0.56 % (29622)Instructions burned: 4 (million)
% 1.48/0.56 % (29622)------------------------------
% 1.48/0.56 % (29622)------------------------------
% 1.48/0.56 % (29614)Success in time 0.198 s
%------------------------------------------------------------------------------