TSTP Solution File: KLE007+2 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---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_sat --cores 0 -t %d %s
% Computer : n006.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 17:28:43 EDT 2022
% Result : Theorem 0.20s 0.49s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 64 ( 24 unt; 0 def)
% Number of atoms : 145 ( 47 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 128 ( 47 ~; 38 |; 27 &)
% ( 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 : 66 ( 60 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f195,plain,
$false,
inference(avatar_sat_refutation,[],[f82,f177,f194]) ).
fof(f194,plain,
spl3_2,
inference(avatar_contradiction_clause,[],[f193]) ).
fof(f193,plain,
( $false
| spl3_2 ),
inference(subsumption_resolution,[],[f192,f125]) ).
fof(f125,plain,
! [X0] : leq(X0,X0),
inference(trivial_inequality_removal,[],[f121]) ).
fof(f121,plain,
! [X0] :
( X0 != X0
| leq(X0,X0) ),
inference(superposition,[],[f49,f53]) ).
fof(f53,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(f49,plain,
! [X0,X1] :
( addition(X1,X0) != X0
| leq(X1,X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( leq(X1,X0)
| addition(X1,X0) != X0 ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( addition(X1,X0) = X0
=> leq(X1,X0) ),
inference(unused_predicate_definition_removal,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( addition(X1,X0) = X0
<=> leq(X1,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(f192,plain,
( ~ leq(one,one)
| spl3_2 ),
inference(forward_demodulation,[],[f191,f158]) ).
fof(f158,plain,
one = addition(sK0,c(sK0)),
inference(superposition,[],[f52,f143]) ).
fof(f143,plain,
one = addition(c(sK0),sK0),
inference(resolution,[],[f57,f89]) ).
fof(f89,plain,
complement(sK0,c(sK0)),
inference(resolution,[],[f71,f63]) ).
fof(f63,plain,
test(sK0),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
( test(sK0)
& ( ~ leq(addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK0,c(sK0)),c(sK1))),one)
| ~ leq(one,addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK0,c(sK0)),c(sK1)))) )
& test(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f33,f39]) ).
fof(f39,plain,
( ? [X0,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(X1) )
=> ( test(sK0)
& ( ~ leq(addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK0,c(sK0)),c(sK1))),one)
| ~ leq(one,addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK0,c(sK0)),c(sK1)))) )
& test(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
? [X0,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(X1) ),
inference(flattening,[],[f32]) ).
fof(f32,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,[],[f26]) ).
fof(f26,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/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f71,plain,
! [X1] :
( ~ test(X1)
| complement(X1,c(X1)) ),
inference(equality_resolution,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( complement(X1,X0)
| c(X1) != X0
| ~ test(X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0,X1] :
( ( ( complement(X1,X0)
| c(X1) != X0 )
& ( c(X1) = X0
| ~ complement(X1,X0) ) )
| ~ test(X1) ),
inference(nnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1] :
( ( complement(X1,X0)
<=> c(X1) = X0 )
| ~ test(X1) ),
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/sandbox2/benchmark/theBenchmark.p',test_3) ).
fof(f57,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| addition(X1,X0) = one ),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0,X1] :
( ( ( zero = multiplication(X0,X1)
& zero = multiplication(X1,X0)
& addition(X1,X0) = one )
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| zero != multiplication(X0,X1)
| zero != multiplication(X1,X0)
| addition(X1,X0) != one ) ),
inference(flattening,[],[f37]) ).
fof(f37,plain,
! [X0,X1] :
( ( ( zero = multiplication(X0,X1)
& zero = multiplication(X1,X0)
& addition(X1,X0) = one )
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| zero != multiplication(X0,X1)
| zero != multiplication(X1,X0)
| addition(X1,X0) != one ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1] :
( ( zero = multiplication(X0,X1)
& zero = multiplication(X1,X0)
& addition(X1,X0) = one )
<=> complement(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(f52,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X1,X0] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f191,plain,
( ~ leq(one,addition(sK0,c(sK0)))
| spl3_2 ),
inference(forward_demodulation,[],[f190,f47]) ).
fof(f47,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(f190,plain,
( ~ leq(one,multiplication(addition(sK0,c(sK0)),one))
| spl3_2 ),
inference(forward_demodulation,[],[f81,f171]) ).
fof(f171,plain,
one = addition(sK1,c(sK1)),
inference(superposition,[],[f144,f52]) ).
fof(f144,plain,
one = addition(c(sK1),sK1),
inference(resolution,[],[f57,f88]) ).
fof(f88,plain,
complement(sK1,c(sK1)),
inference(resolution,[],[f71,f61]) ).
fof(f61,plain,
test(sK1),
inference(cnf_transformation,[],[f40]) ).
fof(f81,plain,
( ~ leq(one,multiplication(addition(sK0,c(sK0)),addition(sK1,c(sK1))))
| spl3_2 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f79,plain,
( spl3_2
<=> leq(one,multiplication(addition(sK0,c(sK0)),addition(sK1,c(sK1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
fof(f177,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f176]) ).
fof(f176,plain,
( $false
| spl3_1 ),
inference(subsumption_resolution,[],[f175,f125]) ).
fof(f175,plain,
( ~ leq(one,one)
| spl3_1 ),
inference(backward_demodulation,[],[f160,f171]) ).
fof(f160,plain,
( ~ leq(addition(sK1,c(sK1)),one)
| spl3_1 ),
inference(forward_demodulation,[],[f159,f60]) ).
fof(f60,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f159,plain,
( ~ leq(multiplication(one,addition(sK1,c(sK1))),one)
| spl3_1 ),
inference(backward_demodulation,[],[f77,f158]) ).
fof(f77,plain,
( ~ leq(multiplication(addition(sK0,c(sK0)),addition(sK1,c(sK1))),one)
| spl3_1 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f75,plain,
( spl3_1
<=> leq(multiplication(addition(sK0,c(sK0)),addition(sK1,c(sK1))),one) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f82,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f73,f79,f75]) ).
fof(f73,plain,
( ~ leq(one,multiplication(addition(sK0,c(sK0)),addition(sK1,c(sK1))))
| ~ leq(multiplication(addition(sK0,c(sK0)),addition(sK1,c(sK1))),one) ),
inference(forward_demodulation,[],[f72,f69]) ).
fof(f69,plain,
! [X2,X0,X1] : multiplication(X0,addition(X2,X1)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1,X2] : 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/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
fof(f72,plain,
( ~ leq(addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK0,c(sK0)),c(sK1))),one)
| ~ leq(one,multiplication(addition(sK0,c(sK0)),addition(sK1,c(sK1)))) ),
inference(forward_demodulation,[],[f62,f69]) ).
fof(f62,plain,
( ~ leq(one,addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK0,c(sK0)),c(sK1))))
| ~ leq(addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK0,c(sK0)),c(sK1))),one) ),
inference(cnf_transformation,[],[f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE007+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34 % Computer : n006.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 00:20:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.47 % (7260)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.20/0.47 % (7253)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.48 % (7268)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.49 % (7260)First to succeed.
% 0.20/0.49 % (7260)Refutation found. Thanks to Tanya!
% 0.20/0.49 % SZS status Theorem for theBenchmark
% 0.20/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.49 % (7260)------------------------------
% 0.20/0.49 % (7260)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49 % (7260)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49 % (7260)Termination reason: Refutation
% 0.20/0.49
% 0.20/0.49 % (7260)Memory used [KB]: 5628
% 0.20/0.49 % (7260)Time elapsed: 0.113 s
% 0.20/0.49 % (7260)Instructions burned: 7 (million)
% 0.20/0.49 % (7260)------------------------------
% 0.20/0.49 % (7260)------------------------------
% 0.20/0.49 % (7239)Success in time 0.146 s
%------------------------------------------------------------------------------