TSTP Solution File: KLE167+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : KLE167+1 : 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 : n014.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 13:12:05 EDT 2024
% Result : Theorem 0.21s 0.43s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 44 ( 25 unt; 0 def)
% Number of atoms : 74 ( 32 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 55 ( 25 ~; 16 |; 8 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 70 ( 66 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1544,plain,
$false,
inference(resolution,[],[f1338,f65]) ).
fof(f65,plain,
! [X0] : leq(X0,X0),
inference(trivial_inequality_removal,[],[f60]) ).
fof(f60,plain,
! [X0] :
( X0 != X0
| leq(X0,X0) ),
inference(superposition,[],[f43,f36]) ).
fof(f36,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',idempotence) ).
fof(f43,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/sandbox/benchmark/theBenchmark.p',order) ).
fof(f1338,plain,
~ leq(sK0,sK0),
inference(resolution,[],[f1325,f1083]) ).
fof(f1083,plain,
! [X0,X1] : leq(X1,multiplication(X1,star(X0))),
inference(forward_demodulation,[],[f1070,f34]) ).
fof(f34,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(f1070,plain,
! [X0,X1] : leq(multiplication(X1,one),multiplication(X1,star(X0))),
inference(superposition,[],[f345,f38]) ).
fof(f38,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/sandbox/benchmark/theBenchmark.p',star_unfold1) ).
fof(f345,plain,
! [X2,X0,X1] : leq(multiplication(X0,X1),multiplication(X0,addition(X1,X2))),
inference(superposition,[],[f196,f46]) ).
fof(f46,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/sandbox/benchmark/theBenchmark.p',distributivity1) ).
fof(f196,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(trivial_inequality_removal,[],[f194]) ).
fof(f194,plain,
! [X0,X1] :
( addition(X0,X1) != addition(X0,X1)
| leq(X0,addition(X0,X1)) ),
inference(superposition,[],[f43,f151]) ).
fof(f151,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f44,f36]) ).
fof(f44,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/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
fof(f1325,plain,
( ~ leq(sK0,multiplication(sK0,star(sK1)))
| ~ leq(sK0,sK0) ),
inference(resolution,[],[f1113,f31]) ).
fof(f31,plain,
( ~ leq(multiplication(sK0,star(sK1)),sK0)
| ~ leq(sK0,multiplication(sK0,star(sK1))) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
( ~ leq(sK0,multiplication(sK0,star(sK1)))
| ( ~ leq(multiplication(sK0,star(sK1)),sK0)
& zero = multiplication(sK0,sK1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f23,f27]) ).
fof(f27,plain,
( ? [X0,X1] :
( ~ leq(X0,multiplication(X0,star(X1)))
| ( ~ leq(multiplication(X0,star(X1)),X0)
& zero = multiplication(X0,X1) ) )
=> ( ~ leq(sK0,multiplication(sK0,star(sK1)))
| ( ~ leq(multiplication(sK0,star(sK1)),sK0)
& zero = multiplication(sK0,sK1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
? [X0,X1] :
( ~ leq(X0,multiplication(X0,star(X1)))
| ( ~ leq(multiplication(X0,star(X1)),X0)
& zero = multiplication(X0,X1) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
~ ! [X0,X1] :
( leq(X0,multiplication(X0,star(X1)))
& ( zero = multiplication(X0,X1)
=> leq(multiplication(X0,star(X1)),X0) ) ),
inference(rectify,[],[f20]) ).
fof(f20,negated_conjecture,
~ ! [X3,X4] :
( leq(X3,multiplication(X3,star(X4)))
& ( zero = multiplication(X3,X4)
=> leq(multiplication(X3,star(X4)),X3) ) ),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
! [X3,X4] :
( leq(X3,multiplication(X3,star(X4)))
& ( zero = multiplication(X3,X4)
=> leq(multiplication(X3,star(X4)),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f1113,plain,
! [X0] :
( leq(multiplication(X0,star(sK1)),sK0)
| ~ leq(X0,sK0) ),
inference(forward_demodulation,[],[f1104,f51]) ).
fof(f51,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f41,f33]) ).
fof(f33,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
fof(f41,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/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f1104,plain,
! [X0] :
( ~ leq(addition(zero,X0),sK0)
| leq(multiplication(X0,star(sK1)),sK0) ),
inference(superposition,[],[f49,f1092]) ).
fof(f1092,plain,
zero = multiplication(sK0,sK1),
inference(resolution,[],[f1083,f30]) ).
fof(f30,plain,
( ~ leq(sK0,multiplication(sK0,star(sK1)))
| zero = multiplication(sK0,sK1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ~ leq(addition(multiplication(X2,X0),X1),X2)
| leq(multiplication(X1,star(X0)),X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,star(X0)),X2)
| ~ leq(addition(multiplication(X2,X0),X1),X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1,X2] :
( leq(addition(multiplication(X2,X0),X1),X2)
=> leq(multiplication(X1,star(X0)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : KLE167+1 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n014.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 04:56:19 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (15775)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (15778)WARNING: value z3 for option sas not known
% 0.14/0.38 % (15776)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (15777)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 % (15779)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (15778)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 % (15780)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 % (15781)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 % (15782)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 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.39 TRYING [3]
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [2]
% 0.21/0.40 TRYING [4]
% 0.21/0.41 TRYING [3]
% 0.21/0.43 % (15781)First to succeed.
% 0.21/0.43 % (15781)Refutation found. Thanks to Tanya!
% 0.21/0.43 % SZS status Theorem for theBenchmark
% 0.21/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.43 % (15781)------------------------------
% 0.21/0.43 % (15781)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.43 % (15781)Termination reason: Refutation
% 0.21/0.43
% 0.21/0.43 % (15781)Memory used [KB]: 1476
% 0.21/0.43 % (15781)Time elapsed: 0.052 s
% 0.21/0.43 % (15781)Instructions burned: 83 (million)
% 0.21/0.43 % (15781)------------------------------
% 0.21/0.43 % (15781)------------------------------
% 0.21/0.43 % (15775)Success in time 0.069 s
%------------------------------------------------------------------------------