TSTP Solution File: KLE150+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : KLE150+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n011.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 : Tue Apr 30 13:12:03 EDT 2024
% Result : Theorem 2.02s 0.66s
% Output : Refutation 2.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 16
% Syntax : Number of formulae : 96 ( 83 unt; 0 def)
% Number of atoms : 113 ( 75 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 38 ( 21 ~; 11 |; 4 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 140 ( 138 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11782,plain,
$false,
inference(resolution,[],[f11765,f64]) ).
fof(f64,plain,
! [X0] : leq(X0,X0),
inference(trivial_inequality_removal,[],[f59]) ).
fof(f59,plain,
! [X0] :
( X0 != X0
| leq(X0,X0) ),
inference(superposition,[],[f42,f35]) ).
fof(f35,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',idempotence) ).
fof(f42,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,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/benchmark/theBenchmark.p',order) ).
fof(f11765,plain,
~ leq(star(multiplication(sK0,zero)),star(multiplication(sK0,zero))),
inference(backward_demodulation,[],[f11179,f11757]) ).
fof(f11757,plain,
! [X0] : strong_iteration(multiplication(X0,zero)) = star(multiplication(X0,zero)),
inference(backward_demodulation,[],[f11548,f11687]) ).
fof(f11687,plain,
! [X0] : star(multiplication(X0,zero)) = addition(multiplication(X0,zero),one),
inference(superposition,[],[f1835,f9126]) ).
fof(f9126,plain,
! [X0,X1] : multiplication(X0,zero) = multiplication(multiplication(X0,zero),X1),
inference(forward_demodulation,[],[f9125,f3382]) ).
fof(f3382,plain,
! [X0] : multiplication(X0,zero) = multiplication(addition(one,X0),zero),
inference(superposition,[],[f487,f50]) ).
fof(f50,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f40,f32]) ).
fof(f32,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
fof(f40,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(f487,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[],[f46,f34]) ).
fof(f34,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(f46,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
fof(f9125,plain,
! [X0,X1] : multiplication(multiplication(X0,zero),X1) = multiplication(addition(one,X0),zero),
inference(forward_demodulation,[],[f9082,f31]) ).
fof(f31,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] : zero = multiplication(zero,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
fof(f9082,plain,
! [X0,X1] : multiplication(multiplication(X0,zero),X1) = multiplication(addition(one,X0),multiplication(zero,X1)),
inference(superposition,[],[f44,f3382]) ).
fof(f44,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/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f1835,plain,
! [X0] : star(X0) = addition(multiplication(X0,star(X0)),one),
inference(forward_demodulation,[],[f1778,f50]) ).
fof(f1778,plain,
! [X0] : addition(multiplication(X0,star(X0)),one) = addition(zero,star(X0)),
inference(superposition,[],[f1586,f36]) ).
fof(f36,plain,
! [X0] : star(X0) = addition(one,multiplication(X0,star(X0))),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] : star(X0) = addition(one,multiplication(X0,star(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold1) ).
fof(f1586,plain,
! [X0,X1] : addition(X1,X0) = addition(zero,addition(X0,X1)),
inference(superposition,[],[f165,f50]) ).
fof(f165,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(superposition,[],[f43,f40]) ).
fof(f43,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/benchmark/theBenchmark.p',additive_associativity) ).
fof(f11548,plain,
! [X0] : strong_iteration(multiplication(X0,zero)) = addition(multiplication(X0,zero),one),
inference(forward_demodulation,[],[f11547,f3382]) ).
fof(f11547,plain,
! [X0] : strong_iteration(multiplication(X0,zero)) = addition(multiplication(addition(one,X0),zero),one),
inference(forward_demodulation,[],[f11431,f31]) ).
fof(f11431,plain,
! [X0] : strong_iteration(multiplication(X0,zero)) = addition(multiplication(addition(one,X0),multiplication(zero,strong_iteration(multiplication(X0,zero)))),one),
inference(superposition,[],[f183,f3382]) ).
fof(f183,plain,
! [X0,X1] : strong_iteration(multiplication(X0,X1)) = addition(multiplication(X0,multiplication(X1,strong_iteration(multiplication(X0,X1)))),one),
inference(superposition,[],[f38,f44]) ).
fof(f38,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/benchmark/theBenchmark.p',infty_unfold1) ).
fof(f11179,plain,
~ leq(strong_iteration(multiplication(sK0,zero)),star(multiplication(sK0,zero))),
inference(backward_demodulation,[],[f3904,f11176]) ).
fof(f11176,plain,
! [X0] : addition(one,multiplication(X0,zero)) = star(multiplication(X0,zero)),
inference(forward_demodulation,[],[f11175,f3382]) ).
fof(f11175,plain,
! [X0] : star(multiplication(X0,zero)) = addition(one,multiplication(addition(one,X0),zero)),
inference(forward_demodulation,[],[f11065,f31]) ).
fof(f11065,plain,
! [X0] : star(multiplication(X0,zero)) = addition(one,multiplication(addition(one,X0),multiplication(zero,star(multiplication(X0,zero))))),
inference(superposition,[],[f181,f3382]) ).
fof(f181,plain,
! [X0,X1] : star(multiplication(X0,X1)) = addition(one,multiplication(X0,multiplication(X1,star(multiplication(X0,X1))))),
inference(superposition,[],[f36,f44]) ).
fof(f3904,plain,
~ leq(strong_iteration(multiplication(sK0,zero)),addition(one,multiplication(sK0,zero))),
inference(resolution,[],[f3824,f30]) ).
fof(f30,plain,
( ~ leq(addition(one,multiplication(sK0,zero)),strong_iteration(multiplication(sK0,zero)))
| ~ leq(strong_iteration(multiplication(sK0,zero)),addition(one,multiplication(sK0,zero))) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
( ~ leq(addition(one,multiplication(sK0,zero)),strong_iteration(multiplication(sK0,zero)))
| ~ leq(strong_iteration(multiplication(sK0,zero)),addition(one,multiplication(sK0,zero))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f23,f27]) ).
fof(f27,plain,
( ? [X0] :
( ~ leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero)))
| ~ leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero))) )
=> ( ~ leq(addition(one,multiplication(sK0,zero)),strong_iteration(multiplication(sK0,zero)))
| ~ leq(strong_iteration(multiplication(sK0,zero)),addition(one,multiplication(sK0,zero))) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
? [X0] :
( ~ leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero)))
| ~ leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero))) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
~ ! [X0] :
( leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero)))
& leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero))) ),
inference(rectify,[],[f20]) ).
fof(f20,negated_conjecture,
~ ! [X3] :
( leq(addition(one,multiplication(X3,zero)),strong_iteration(multiplication(X3,zero)))
& leq(strong_iteration(multiplication(X3,zero)),addition(one,multiplication(X3,zero))) ),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
! [X3] :
( leq(addition(one,multiplication(X3,zero)),strong_iteration(multiplication(X3,zero)))
& leq(strong_iteration(multiplication(X3,zero)),addition(one,multiplication(X3,zero))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f3824,plain,
! [X0] : leq(addition(one,X0),strong_iteration(X0)),
inference(superposition,[],[f735,f3482]) ).
fof(f3482,plain,
! [X0] : strong_iteration(X0) = addition(X0,strong_iteration(X0)),
inference(resolution,[],[f3372,f41]) ).
fof(f41,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f29]) ).
fof(f3372,plain,
! [X0] : leq(X0,strong_iteration(X0)),
inference(superposition,[],[f3300,f1841]) ).
fof(f1841,plain,
! [X0] : strong_iteration(X0) = addition(strong_iteration(X0),star(X0)),
inference(forward_demodulation,[],[f1784,f50]) ).
fof(f1784,plain,
! [X0] : addition(strong_iteration(X0),star(X0)) = addition(zero,strong_iteration(X0)),
inference(superposition,[],[f1586,f200]) ).
fof(f200,plain,
! [X0] : strong_iteration(X0) = addition(star(X0),strong_iteration(X0)),
inference(superposition,[],[f150,f39]) ).
fof(f39,plain,
! [X0] : strong_iteration(X0) = addition(star(X0),multiplication(strong_iteration(X0),zero)),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] : strong_iteration(X0) = addition(star(X0),multiplication(strong_iteration(X0),zero)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isolation) ).
fof(f150,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f43,f35]) ).
fof(f3300,plain,
! [X0,X1] : leq(X0,addition(X1,star(X0))),
inference(superposition,[],[f275,f3225]) ).
fof(f3225,plain,
! [X0] : star(X0) = addition(X0,star(X0)),
inference(forward_demodulation,[],[f3224,f2094]) ).
fof(f2094,plain,
! [X0] : star(X0) = multiplication(addition(X0,one),star(X0)),
inference(forward_demodulation,[],[f2093,f1835]) ).
fof(f2093,plain,
! [X0] : addition(multiplication(X0,star(X0)),one) = multiplication(addition(X0,one),star(X0)),
inference(forward_demodulation,[],[f2015,f491]) ).
fof(f491,plain,
! [X0,X1] : multiplication(addition(X1,one),X0) = addition(multiplication(X1,X0),X0),
inference(superposition,[],[f46,f34]) ).
fof(f2015,plain,
! [X0] : addition(multiplication(X0,star(X0)),one) = addition(multiplication(X0,star(X0)),star(X0)),
inference(superposition,[],[f1599,f36]) ).
fof(f1599,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X1,X0)),
inference(superposition,[],[f165,f150]) ).
fof(f3224,plain,
! [X0] : multiplication(addition(X0,one),star(X0)) = addition(X0,star(X0)),
inference(forward_demodulation,[],[f3223,f195]) ).
fof(f195,plain,
! [X0] : star(X0) = addition(one,star(X0)),
inference(superposition,[],[f150,f36]) ).
fof(f3223,plain,
! [X0] : multiplication(addition(X0,one),addition(one,star(X0))) = addition(X0,star(X0)),
inference(forward_demodulation,[],[f3222,f40]) ).
fof(f3222,plain,
! [X0] : multiplication(addition(X0,one),addition(one,star(X0))) = addition(star(X0),X0),
inference(forward_demodulation,[],[f3221,f251]) ).
fof(f251,plain,
! [X0,X1] : addition(star(X0),X1) = addition(one,addition(star(X0),X1)),
inference(superposition,[],[f43,f195]) ).
fof(f3221,plain,
! [X0] : multiplication(addition(X0,one),addition(one,star(X0))) = addition(one,addition(star(X0),X0)),
inference(forward_demodulation,[],[f3220,f165]) ).
fof(f3220,plain,
! [X0] : multiplication(addition(X0,one),addition(one,star(X0))) = addition(star(X0),addition(X0,one)),
inference(forward_demodulation,[],[f3208,f40]) ).
fof(f3208,plain,
! [X0] : multiplication(addition(X0,one),addition(one,star(X0))) = addition(addition(X0,one),star(X0)),
inference(superposition,[],[f351,f2094]) ).
fof(f351,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[],[f45,f33]) ).
fof(f33,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(f45,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/benchmark/theBenchmark.p',distributivity1) ).
fof(f275,plain,
! [X2,X0,X1] : leq(X1,addition(X2,addition(X1,X0))),
inference(superposition,[],[f237,f40]) ).
fof(f237,plain,
! [X2,X0,X1] : leq(X2,addition(X0,addition(X1,X2))),
inference(superposition,[],[f215,f43]) ).
fof(f215,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(superposition,[],[f207,f40]) ).
fof(f207,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(trivial_inequality_removal,[],[f205]) ).
fof(f205,plain,
! [X0,X1] :
( addition(X0,X1) != addition(X0,X1)
| leq(X0,addition(X0,X1)) ),
inference(superposition,[],[f42,f150]) ).
fof(f735,plain,
! [X0,X1] : leq(addition(one,X0),addition(X0,strong_iteration(X1))),
inference(superposition,[],[f608,f40]) ).
fof(f608,plain,
! [X0,X1] : leq(addition(X1,one),addition(X1,strong_iteration(X0))),
inference(superposition,[],[f219,f102]) ).
fof(f102,plain,
! [X0] : strong_iteration(X0) = addition(one,multiplication(X0,strong_iteration(X0))),
inference(superposition,[],[f38,f40]) ).
fof(f219,plain,
! [X2,X0,X1] : leq(addition(X0,X1),addition(X0,addition(X1,X2))),
inference(superposition,[],[f207,f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KLE150+2 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Apr 30 05:05:16 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (15025)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (15028)WARNING: value z3 for option sas not known
% 0.14/0.38 % (15032)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.38 % (15027)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (15031)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.38 % (15029)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (15028)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38 % (15030)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 % (15026)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [3]
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [2]
% 0.14/0.39 TRYING [4]
% 0.14/0.41 TRYING [3]
% 0.20/0.43 TRYING [5]
% 0.20/0.46 TRYING [4]
% 0.20/0.53 TRYING [6]
% 0.20/0.57 TRYING [1]
% 0.20/0.57 TRYING [2]
% 0.20/0.58 TRYING [3]
% 0.20/0.59 TRYING [5]
% 0.20/0.59 TRYING [4]
% 2.02/0.65 % (15031)First to succeed.
% 2.02/0.66 % (15031)Refutation found. Thanks to Tanya!
% 2.02/0.66 % SZS status Theorem for theBenchmark
% 2.02/0.66 % SZS output start Proof for theBenchmark
% See solution above
% 2.02/0.66 % (15031)------------------------------
% 2.02/0.66 % (15031)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 2.02/0.66 % (15031)Termination reason: Refutation
% 2.02/0.66
% 2.02/0.66 % (15031)Memory used [KB]: 4535
% 2.02/0.66 % (15031)Time elapsed: 0.280 s
% 2.02/0.66 % (15031)Instructions burned: 525 (million)
% 2.02/0.66 % (15031)------------------------------
% 2.02/0.66 % (15031)------------------------------
% 2.02/0.66 % (15025)Success in time 0.287 s
%------------------------------------------------------------------------------