TSTP Solution File: KLE022+4 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : KLE022+4 : 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 : n013.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 17:28:49 EDT 2022
% Result : Theorem 0.20s 0.56s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 58 ( 17 unt; 0 def)
% Number of atoms : 140 ( 53 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 133 ( 51 ~; 45 |; 22 &)
% ( 8 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 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 : 71 ( 67 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f295,plain,
$false,
inference(avatar_sat_refutation,[],[f91,f286,f291]) ).
fof(f291,plain,
spl3_2,
inference(avatar_contradiction_clause,[],[f290]) ).
fof(f290,plain,
( $false
| spl3_2 ),
inference(subsumption_resolution,[],[f289,f116]) ).
fof(f116,plain,
! [X0] : leq(X0,X0),
inference(trivial_inequality_removal,[],[f110]) ).
fof(f110,plain,
! [X0] :
( leq(X0,X0)
| X0 != X0 ),
inference(superposition,[],[f81,f69]) ).
fof(f69,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(f81,plain,
! [X0,X1] :
( addition(X1,X0) != X0
| leq(X1,X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1] :
( addition(X1,X0) != X0
| leq(X1,X0) ),
inference(rectify,[],[f37]) ).
fof(f37,plain,
! [X1,X0] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1] :
( addition(X0,X1) = X1
=> leq(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( addition(X0,X1) = X1
<=> leq(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
fof(f289,plain,
( ~ leq(sK1,sK1)
| spl3_2 ),
inference(forward_demodulation,[],[f288,f68]) ).
fof(f68,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(f288,plain,
( ~ leq(multiplication(sK1,one),sK1)
| spl3_2 ),
inference(forward_demodulation,[],[f287,f282]) ).
fof(f282,plain,
one = addition(sK0,c(sK0)),
inference(resolution,[],[f105,f57]) ).
fof(f57,plain,
test(sK0),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
( ( ~ leq(addition(multiplication(sK1,sK0),multiplication(sK1,c(sK0))),sK1)
| ~ leq(sK1,addition(multiplication(sK1,sK0),multiplication(sK1,c(sK0)))) )
& test(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f34,f42]) ).
fof(f42,plain,
( ? [X0,X1] :
( ( ~ leq(addition(multiplication(X1,X0),multiplication(X1,c(X0))),X1)
| ~ leq(X1,addition(multiplication(X1,X0),multiplication(X1,c(X0)))) )
& test(X0) )
=> ( ( ~ leq(addition(multiplication(sK1,sK0),multiplication(sK1,c(sK0))),sK1)
| ~ leq(sK1,addition(multiplication(sK1,sK0),multiplication(sK1,c(sK0)))) )
& test(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
? [X0,X1] :
( ( ~ leq(addition(multiplication(X1,X0),multiplication(X1,c(X0))),X1)
| ~ leq(X1,addition(multiplication(X1,X0),multiplication(X1,c(X0)))) )
& test(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,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,[],[f20]) ).
fof(f20,negated_conjecture,
~ ! [X4,X3] :
( test(X4)
=> ( leq(X3,addition(multiplication(X3,X4),multiplication(X3,c(X4))))
& leq(addition(multiplication(X3,X4),multiplication(X3,c(X4))),X3) ) ),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
! [X4,X3] :
( test(X4)
=> ( leq(X3,addition(multiplication(X3,X4),multiplication(X3,c(X4))))
& leq(addition(multiplication(X3,X4),multiplication(X3,c(X4))),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f105,plain,
! [X1] :
( ~ test(X1)
| one = addition(X1,c(X1)) ),
inference(forward_demodulation,[],[f104,f78]) ).
fof(f78,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f25]) ).
fof(f25,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/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f104,plain,
! [X1] :
( ~ test(X1)
| one = addition(c(X1),X1) ),
inference(resolution,[],[f61,f82]) ).
fof(f82,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( ~ test(X0)
| complement(X0,X1)
| c(X0) != X1 ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1] :
( ~ test(X0)
| ( ( complement(X0,X1)
| c(X0) != X1 )
& ( c(X0) = X1
| ~ complement(X0,X1) ) ) ),
inference(rectify,[],[f54]) ).
fof(f54,plain,
! [X1,X0] :
( ~ test(X1)
| ( ( complement(X1,X0)
| c(X1) != X0 )
& ( c(X1) = X0
| ~ complement(X1,X0) ) ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X1,X0] :
( ~ test(X1)
| ( complement(X1,X0)
<=> c(X1) = X0 ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
! [X1,X0] :
( 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(f61,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| addition(X1,X0) = one ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X1] :
( ( ( zero = multiplication(X1,X0)
& zero = multiplication(X0,X1)
& addition(X1,X0) = one )
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| zero != multiplication(X1,X0)
| zero != multiplication(X0,X1)
| addition(X1,X0) != one ) ),
inference(rectify,[],[f45]) ).
fof(f45,plain,
! [X1,X0] :
( ( ( zero = multiplication(X0,X1)
& zero = multiplication(X1,X0)
& addition(X0,X1) = one )
| ~ complement(X1,X0) )
& ( complement(X1,X0)
| zero != multiplication(X0,X1)
| zero != multiplication(X1,X0)
| addition(X0,X1) != one ) ),
inference(flattening,[],[f44]) ).
fof(f44,plain,
! [X1,X0] :
( ( ( zero = multiplication(X0,X1)
& zero = multiplication(X1,X0)
& addition(X0,X1) = one )
| ~ complement(X1,X0) )
& ( complement(X1,X0)
| zero != multiplication(X0,X1)
| zero != multiplication(X1,X0)
| addition(X0,X1) != one ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X1,X0] :
( ( zero = multiplication(X0,X1)
& zero = multiplication(X1,X0)
& addition(X0,X1) = one )
<=> complement(X1,X0) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X3,X4] :
( ( zero = multiplication(X3,X4)
& zero = multiplication(X4,X3)
& one = addition(X3,X4) )
<=> complement(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_2) ).
fof(f287,plain,
( ~ leq(multiplication(sK1,addition(sK0,c(sK0))),sK1)
| spl3_2 ),
inference(forward_demodulation,[],[f90,f67]) ).
fof(f67,plain,
! [X2,X0,X1] : multiplication(X1,addition(X0,X2)) = addition(multiplication(X1,X0),multiplication(X1,X2)),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0,X1,X2] : multiplication(X1,addition(X0,X2)) = addition(multiplication(X1,X0),multiplication(X1,X2)),
inference(rectify,[],[f31]) ).
fof(f31,plain,
! [X0,X2,X1] : addition(multiplication(X2,X0),multiplication(X2,X1)) = multiplication(X2,addition(X0,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/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
fof(f90,plain,
( ~ leq(addition(multiplication(sK1,sK0),multiplication(sK1,c(sK0))),sK1)
| spl3_2 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f88,plain,
( spl3_2
<=> leq(addition(multiplication(sK1,sK0),multiplication(sK1,c(sK0))),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
fof(f286,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f285]) ).
fof(f285,plain,
( $false
| spl3_1 ),
inference(subsumption_resolution,[],[f284,f116]) ).
fof(f284,plain,
( ~ leq(sK1,sK1)
| spl3_1 ),
inference(forward_demodulation,[],[f283,f68]) ).
fof(f283,plain,
( ~ leq(sK1,multiplication(sK1,one))
| spl3_1 ),
inference(backward_demodulation,[],[f92,f282]) ).
fof(f92,plain,
( ~ leq(sK1,multiplication(sK1,addition(sK0,c(sK0))))
| spl3_1 ),
inference(forward_demodulation,[],[f86,f67]) ).
fof(f86,plain,
( ~ leq(sK1,addition(multiplication(sK1,sK0),multiplication(sK1,c(sK0))))
| spl3_1 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f84,plain,
( spl3_1
<=> leq(sK1,addition(multiplication(sK1,sK0),multiplication(sK1,c(sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f91,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f58,f88,f84]) ).
fof(f58,plain,
( ~ leq(addition(multiplication(sK1,sK0),multiplication(sK1,c(sK0))),sK1)
| ~ leq(sK1,addition(multiplication(sK1,sK0),multiplication(sK1,c(sK0)))) ),
inference(cnf_transformation,[],[f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : KLE022+4 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 30 02:19:31 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.51 % (12114)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.20/0.51 % (12106)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.52 % (12095)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.20/0.53 % (12101)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.53 % (12111)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.53 % (12092)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.20/0.53 % (12103)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.54 % (12111)First to succeed.
% 0.20/0.54 % (12118)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.54 % (12094)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.54 % (12112)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.20/0.54 % (12093)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.55 % (12104)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.55 % (12110)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)
% 0.20/0.55 % (12090)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.20/0.55 % (12107)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.20/0.55 % (12091)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.55 % (12099)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.55 TRYING [1]
% 0.20/0.55 TRYING [2]
% 0.20/0.55 % (12096)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.56 % (12111)Refutation found. Thanks to Tanya!
% 0.20/0.56 % SZS status Theorem for theBenchmark
% 0.20/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.56 % (12111)------------------------------
% 0.20/0.56 % (12111)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.56 % (12111)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.56 % (12111)Termination reason: Refutation
% 0.20/0.56
% 0.20/0.56 % (12111)Memory used [KB]: 5628
% 0.20/0.56 % (12111)Time elapsed: 0.125 s
% 0.20/0.56 % (12111)Instructions burned: 11 (million)
% 0.20/0.56 % (12111)------------------------------
% 0.20/0.56 % (12111)------------------------------
% 0.20/0.56 % (12089)Success in time 0.197 s
%------------------------------------------------------------------------------