TSTP Solution File: KLE007+2 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : KLE007+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 : n010.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 17:27:32 EDT 2022
% Result : Theorem 1.87s 0.60s
% Output : Refutation 1.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 66 ( 26 unt; 0 def)
% Number of atoms : 147 ( 49 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 129 ( 48 ~; 39 |; 27 &)
% ( 8 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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 : 69 ( 63 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f231,plain,
$false,
inference(avatar_sat_refutation,[],[f84,f213,f227]) ).
fof(f227,plain,
spl3_2,
inference(avatar_contradiction_clause,[],[f226]) ).
fof(f226,plain,
( $false
| spl3_2 ),
inference(subsumption_resolution,[],[f225,f166]) ).
fof(f166,plain,
! [X0] : leq(X0,X0),
inference(trivial_inequality_removal,[],[f153]) ).
fof(f153,plain,
! [X0] :
( X0 != X0
| leq(X0,X0) ),
inference(superposition,[],[f61,f66]) ).
fof(f66,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f61,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( addition(X0,X1) = X1
=> leq(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
fof(f225,plain,
( ~ leq(one,one)
| spl3_2 ),
inference(forward_demodulation,[],[f224,f132]) ).
fof(f132,plain,
one = addition(sK1,c(sK1)),
inference(superposition,[],[f55,f127]) ).
fof(f127,plain,
one = addition(c(sK1),sK1),
inference(unit_resulting_resolution,[],[f87,f52]) ).
fof(f52,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0,X1] :
( ( ( zero = multiplication(X0,X1)
& addition(X0,X1) = one
& zero = multiplication(X1,X0) )
| ~ complement(X1,X0) )
& ( complement(X1,X0)
| zero != multiplication(X0,X1)
| addition(X0,X1) != one
| zero != multiplication(X1,X0) ) ),
inference(flattening,[],[f35]) ).
fof(f35,plain,
! [X0,X1] :
( ( ( zero = multiplication(X0,X1)
& addition(X0,X1) = one
& zero = multiplication(X1,X0) )
| ~ complement(X1,X0) )
& ( complement(X1,X0)
| zero != multiplication(X0,X1)
| addition(X0,X1) != one
| zero != multiplication(X1,X0) ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( ( zero = multiplication(X0,X1)
& addition(X0,X1) = one
& zero = multiplication(X1,X0) )
<=> complement(X1,X0) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X3,X4] :
( ( zero = multiplication(X3,X4)
& one = addition(X3,X4)
& zero = multiplication(X4,X3) )
<=> complement(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_2) ).
fof(f87,plain,
complement(sK1,c(sK1)),
inference(unit_resulting_resolution,[],[f71,f73]) ).
fof(f73,plain,
! [X1] :
( complement(X1,c(X1))
| ~ test(X1) ),
inference(equality_resolution,[],[f63]) ).
fof(f63,plain,
! [X0,X1] :
( ~ test(X1)
| complement(X1,X0)
| c(X1) != X0 ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0,X1] :
( ~ test(X1)
| ( ( complement(X1,X0)
| c(X1) != X0 )
& ( c(X1) = X0
| ~ complement(X1,X0) ) ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1] :
( ~ test(X1)
| ( complement(X1,X0)
<=> c(X1) = X0 ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( test(X1)
=> ( complement(X1,X0)
<=> c(X1) = X0 ) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X4,X3] :
( test(X3)
=> ( c(X3) = X4
<=> complement(X3,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_3) ).
fof(f71,plain,
test(sK1),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
( test(sK2)
& test(sK1)
& ( ~ leq(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2))),one)
| ~ leq(one,addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2)))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f31,f47]) ).
fof(f47,plain,
( ? [X0,X1] :
( test(X1)
& test(X0)
& ( ~ leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one)
| ~ leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1)))) ) )
=> ( test(sK2)
& test(sK1)
& ( ~ leq(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2))),one)
| ~ leq(one,addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2)))) ) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
? [X0,X1] :
( test(X1)
& test(X0)
& ( ~ leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one)
| ~ leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1)))) ) ),
inference(flattening,[],[f30]) ).
fof(f30,plain,
? [X1,X0] :
( ( ~ leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one)
| ~ leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1)))) )
& test(X1)
& test(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,plain,
~ ! [X1,X0] :
( ( test(X1)
& test(X0) )
=> ( leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))))
& leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one) ) ),
inference(rectify,[],[f18]) ).
fof(f18,negated_conjecture,
~ ! [X3,X4] :
( ( test(X3)
& test(X4) )
=> ( leq(one,addition(multiplication(addition(X3,c(X3)),X4),multiplication(addition(X3,c(X3)),c(X4))))
& leq(addition(multiplication(addition(X3,c(X3)),X4),multiplication(addition(X3,c(X3)),c(X4))),one) ) ),
inference(negated_conjecture,[],[f17]) ).
fof(f17,conjecture,
! [X3,X4] :
( ( test(X3)
& test(X4) )
=> ( leq(one,addition(multiplication(addition(X3,c(X3)),X4),multiplication(addition(X3,c(X3)),c(X4))))
& leq(addition(multiplication(addition(X3,c(X3)),X4),multiplication(addition(X3,c(X3)),c(X4))),one) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f55,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(rectify,[],[f24]) ).
fof(f24,plain,
! [X1,X0] : addition(X0,X1) = addition(X1,X0),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X1,X0] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f224,plain,
( ~ leq(one,addition(sK1,c(sK1)))
| spl3_2 ),
inference(forward_demodulation,[],[f223,f59]) ).
fof(f59,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f223,plain,
( ~ leq(one,multiplication(addition(sK1,c(sK1)),one))
| spl3_2 ),
inference(forward_demodulation,[],[f83,f138]) ).
fof(f138,plain,
one = addition(sK2,c(sK2)),
inference(superposition,[],[f55,f128]) ).
fof(f128,plain,
one = addition(c(sK2),sK2),
inference(unit_resulting_resolution,[],[f88,f52]) ).
fof(f88,plain,
complement(sK2,c(sK2)),
inference(unit_resulting_resolution,[],[f72,f73]) ).
fof(f72,plain,
test(sK2),
inference(cnf_transformation,[],[f48]) ).
fof(f83,plain,
( ~ leq(one,multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2))))
| spl3_2 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f81,plain,
( spl3_2
<=> leq(one,multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
fof(f213,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f212]) ).
fof(f212,plain,
( $false
| spl3_1 ),
inference(subsumption_resolution,[],[f148,f66]) ).
fof(f148,plain,
( one != addition(one,one)
| spl3_1 ),
inference(unit_resulting_resolution,[],[f139,f61]) ).
fof(f139,plain,
( ~ leq(one,one)
| spl3_1 ),
inference(backward_demodulation,[],[f134,f138]) ).
fof(f134,plain,
( ~ leq(addition(sK2,c(sK2)),one)
| spl3_1 ),
inference(forward_demodulation,[],[f133,f56]) ).
fof(f56,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f133,plain,
( ~ leq(multiplication(one,addition(sK2,c(sK2))),one)
| spl3_1 ),
inference(backward_demodulation,[],[f79,f132]) ).
fof(f79,plain,
( ~ leq(multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2))),one)
| spl3_1 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f77,plain,
( spl3_1
<=> leq(multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2))),one) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f84,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f75,f81,f77]) ).
fof(f75,plain,
( ~ leq(one,multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2))))
| ~ leq(multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2))),one) ),
inference(forward_demodulation,[],[f74,f58]) ).
fof(f58,plain,
! [X2,X0,X1] : multiplication(X2,addition(X0,X1)) = addition(multiplication(X2,X0),multiplication(X2,X1)),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1,X2] : multiplication(X2,addition(X0,X1)) = addition(multiplication(X2,X0),multiplication(X2,X1)),
inference(rectify,[],[f22]) ).
fof(f22,plain,
! [X2,X1,X0] : multiplication(X0,addition(X2,X1)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X0,X2,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
fof(f74,plain,
( ~ leq(multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2))),one)
| ~ leq(one,addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2)))) ),
inference(forward_demodulation,[],[f70,f58]) ).
fof(f70,plain,
( ~ leq(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2))),one)
| ~ leq(one,addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2)))) ),
inference(cnf_transformation,[],[f48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE007+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 00:14:14 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.55 % (13441)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)
% 0.19/0.55 % (13433)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.57 % (13428)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.19/0.57 % (13433)Instruction limit reached!
% 0.19/0.57 % (13433)------------------------------
% 0.19/0.57 % (13433)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.57 % (13433)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.57 % (13433)Termination reason: Unknown
% 0.19/0.57 % (13433)Termination phase: Saturation
% 0.19/0.57
% 0.19/0.57 % (13433)Memory used [KB]: 6012
% 0.19/0.57 % (13433)Time elapsed: 0.083 s
% 0.19/0.57 % (13433)Instructions burned: 7 (million)
% 0.19/0.57 % (13433)------------------------------
% 0.19/0.57 % (13433)------------------------------
% 0.19/0.57 % (13428)Refutation not found, incomplete strategy% (13428)------------------------------
% 0.19/0.57 % (13428)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.57 % (13428)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.57 % (13428)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.57
% 0.19/0.57 % (13428)Memory used [KB]: 5884
% 0.19/0.57 % (13428)Time elapsed: 0.086 s
% 0.19/0.57 % (13428)Instructions burned: 3 (million)
% 0.19/0.57 % (13428)------------------------------
% 0.19/0.57 % (13428)------------------------------
% 0.19/0.57 % (13447)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.19/0.58 % (13439)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.58 % (13418)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 1.63/0.59 % (13431)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.63/0.59 % (13422)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 1.63/0.59 % (13423)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 1.63/0.59 % (13431)First to succeed.
% 1.63/0.59 % (13421)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.63/0.60 % (13424)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)
% 1.87/0.60 % (13431)Refutation found. Thanks to Tanya!
% 1.87/0.60 % SZS status Theorem for theBenchmark
% 1.87/0.60 % SZS output start Proof for theBenchmark
% See solution above
% 1.87/0.60 % (13431)------------------------------
% 1.87/0.60 % (13431)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.87/0.60 % (13431)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.87/0.60 % (13431)Termination reason: Refutation
% 1.87/0.60
% 1.87/0.60 % (13431)Memory used [KB]: 6012
% 1.87/0.60 % (13431)Time elapsed: 0.169 s
% 1.87/0.60 % (13431)Instructions burned: 7 (million)
% 1.87/0.60 % (13431)------------------------------
% 1.87/0.60 % (13431)------------------------------
% 1.87/0.60 % (13417)Success in time 0.25 s
%------------------------------------------------------------------------------