TSTP Solution File: KLE144+2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : KLE144+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 : n017.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 13:12:02 EDT 2024
% Result : Theorem 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 20
% Syntax : Number of formulae : 76 ( 32 unt; 0 def)
% Number of atoms : 124 ( 44 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 88 ( 40 ~; 34 |; 4 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 103 ( 101 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4846,plain,
$false,
inference(avatar_sat_refutation,[],[f157,f295,f558,f836,f4845]) ).
fof(f4845,plain,
spl1_2,
inference(avatar_contradiction_clause,[],[f4843]) ).
fof(f4843,plain,
( $false
| spl1_2 ),
inference(resolution,[],[f4624,f156]) ).
fof(f156,plain,
( ~ leq(strong_iteration(one),strong_iteration(star(sK0)))
| spl1_2 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f154,plain,
( spl1_2
<=> leq(strong_iteration(one),strong_iteration(star(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).
fof(f4624,plain,
! [X0,X1] : leq(X1,strong_iteration(star(X0))),
inference(superposition,[],[f4618,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/sandbox/benchmark/theBenchmark.p',star_unfold1) ).
fof(f4618,plain,
! [X0,X1] : leq(X1,strong_iteration(addition(one,X0))),
inference(superposition,[],[f4505,f33]) ).
fof(f33,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(f4505,plain,
! [X2,X0,X1] : leq(X1,multiplication(strong_iteration(addition(one,X0)),X2)),
inference(subsumption_resolution,[],[f4504,f356]) ).
fof(f356,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(trivial_inequality_removal,[],[f350]) ).
fof(f350,plain,
! [X0,X1] :
( addition(X0,X1) != addition(X0,X1)
| leq(X0,addition(X0,X1)) ),
inference(superposition,[],[f42,f180]) ).
fof(f180,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f43,f35]) ).
fof(f35,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,
! [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(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/sandbox/benchmark/theBenchmark.p',order) ).
fof(f4504,plain,
! [X2,X0,X1] :
( ~ leq(X1,addition(X1,addition(multiplication(X0,X1),X2)))
| leq(X1,multiplication(strong_iteration(addition(one,X0)),X2)) ),
inference(forward_demodulation,[],[f4404,f43]) ).
fof(f4404,plain,
! [X2,X0,X1] :
( ~ leq(X1,addition(addition(X1,multiplication(X0,X1)),X2))
| leq(X1,multiplication(strong_iteration(addition(one,X0)),X2)) ),
inference(superposition,[],[f47,f431]) ).
fof(f431,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/sandbox/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/sandbox/benchmark/theBenchmark.p',distributivity2) ).
fof(f47,plain,
! [X2,X0,X1] :
( ~ leq(X2,addition(multiplication(X0,X2),X1))
| leq(X2,multiplication(strong_iteration(X0),X1)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1,X2] :
( leq(X2,multiplication(strong_iteration(X0),X1))
| ~ leq(X2,addition(multiplication(X0,X2),X1)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1,X2] :
( leq(X2,addition(multiplication(X0,X2),X1))
=> leq(X2,multiplication(strong_iteration(X0),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infty_coinduction) ).
fof(f836,plain,
( ~ spl1_5
| spl1_6 ),
inference(avatar_split_clause,[],[f826,f834,f830]) ).
fof(f830,plain,
( spl1_5
<=> leq(one,zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).
fof(f834,plain,
( spl1_6
<=> ! [X0] : leq(star(X0),zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_6])]) ).
fof(f826,plain,
! [X0] :
( leq(star(X0),zero)
| ~ leq(one,zero) ),
inference(superposition,[],[f656,f34]) ).
fof(f656,plain,
! [X0,X1] :
( leq(multiplication(X1,star(X0)),zero)
| ~ leq(X1,zero) ),
inference(forward_demodulation,[],[f639,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/sandbox/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/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f639,plain,
! [X0,X1] :
( ~ leq(addition(zero,X1),zero)
| leq(multiplication(X1,star(X0)),zero) ),
inference(superposition,[],[f48,f31]) ).
fof(f31,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] : zero = multiplication(zero,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
fof(f48,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) ).
fof(f558,plain,
spl1_1,
inference(avatar_contradiction_clause,[],[f557]) ).
fof(f557,plain,
( $false
| spl1_1 ),
inference(resolution,[],[f555,f152]) ).
fof(f152,plain,
( ~ leq(strong_iteration(star(sK0)),strong_iteration(one))
| spl1_1 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f150,plain,
( spl1_1
<=> leq(strong_iteration(star(sK0)),strong_iteration(one)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).
fof(f555,plain,
! [X0] : leq(X0,strong_iteration(one)),
inference(superposition,[],[f551,f33]) ).
fof(f551,plain,
! [X0,X1] : leq(X0,multiplication(strong_iteration(one),X1)),
inference(subsumption_resolution,[],[f536,f356]) ).
fof(f536,plain,
! [X0,X1] :
( ~ leq(X0,addition(X0,X1))
| leq(X0,multiplication(strong_iteration(one),X1)) ),
inference(superposition,[],[f47,f34]) ).
fof(f295,plain,
( ~ spl1_3
| spl1_4 ),
inference(avatar_split_clause,[],[f285,f292,f288]) ).
fof(f288,plain,
( spl1_3
<=> zero = star(one) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).
fof(f292,plain,
( spl1_4
<=> zero = one ),
introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).
fof(f285,plain,
( zero = one
| zero != star(one) ),
inference(inner_rewriting,[],[f265]) ).
fof(f265,plain,
( one = star(one)
| zero != star(one) ),
inference(superposition,[],[f213,f67]) ).
fof(f67,plain,
star(one) = addition(one,star(one)),
inference(superposition,[],[f36,f34]) ).
fof(f213,plain,
! [X0,X1] :
( addition(X1,X0) = X1
| zero != X0 ),
inference(superposition,[],[f206,f40]) ).
fof(f206,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| zero != X0 ),
inference(forward_demodulation,[],[f178,f50]) ).
fof(f178,plain,
! [X0,X1] :
( addition(zero,X1) = addition(X0,addition(zero,X1))
| zero != X0 ),
inference(superposition,[],[f43,f74]) ).
fof(f74,plain,
! [X0] :
( zero = addition(X0,zero)
| zero != X0 ),
inference(resolution,[],[f58,f41]) ).
fof(f41,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f29]) ).
fof(f58,plain,
! [X0] :
( leq(X0,zero)
| zero != X0 ),
inference(superposition,[],[f42,f32]) ).
fof(f157,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f30,f154,f150]) ).
fof(f30,plain,
( ~ leq(strong_iteration(one),strong_iteration(star(sK0)))
| ~ leq(strong_iteration(star(sK0)),strong_iteration(one)) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
( ~ leq(strong_iteration(one),strong_iteration(star(sK0)))
| ~ leq(strong_iteration(star(sK0)),strong_iteration(one)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f23,f27]) ).
fof(f27,plain,
( ? [X0] :
( ~ leq(strong_iteration(one),strong_iteration(star(X0)))
| ~ leq(strong_iteration(star(X0)),strong_iteration(one)) )
=> ( ~ leq(strong_iteration(one),strong_iteration(star(sK0)))
| ~ leq(strong_iteration(star(sK0)),strong_iteration(one)) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
? [X0] :
( ~ leq(strong_iteration(one),strong_iteration(star(X0)))
| ~ leq(strong_iteration(star(X0)),strong_iteration(one)) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
~ ! [X0] :
( leq(strong_iteration(one),strong_iteration(star(X0)))
& leq(strong_iteration(star(X0)),strong_iteration(one)) ),
inference(rectify,[],[f20]) ).
fof(f20,negated_conjecture,
~ ! [X3] :
( leq(strong_iteration(one),strong_iteration(star(X3)))
& leq(strong_iteration(star(X3)),strong_iteration(one)) ),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
! [X3] :
( leq(strong_iteration(one),strong_iteration(star(X3)))
& leq(strong_iteration(star(X3)),strong_iteration(one)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE144+2 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n017.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 Apr 30 04:32:48 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % (1638)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36 % (1641)WARNING: value z3 for option sas not known
% 0.13/0.36 % (1641)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)
% 0.13/0.36 % (1640)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.36 % (1644)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)
% 0.13/0.36 % (1645)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)
% 0.13/0.36 % (1642)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.36 % (1643)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)
% 0.13/0.36 TRYING [1]
% 0.13/0.36 TRYING [2]
% 0.13/0.36 % (1639)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.36 TRYING [3]
% 0.13/0.37 TRYING [1]
% 0.13/0.37 TRYING [2]
% 0.13/0.37 TRYING [4]
% 0.13/0.39 TRYING [3]
% 0.19/0.41 TRYING [5]
% 0.19/0.42 TRYING [4]
% 0.19/0.46 % (1641)First to succeed.
% 0.19/0.47 % (1641)Refutation found. Thanks to Tanya!
% 0.19/0.47 % SZS status Theorem for theBenchmark
% 0.19/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.47 % (1641)------------------------------
% 0.19/0.47 % (1641)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.19/0.47 % (1641)Termination reason: Refutation
% 0.19/0.47
% 0.19/0.47 % (1641)Memory used [KB]: 2180
% 0.19/0.47 % (1641)Time elapsed: 0.106 s
% 0.19/0.47 % (1641)Instructions burned: 233 (million)
% 0.19/0.47 % (1641)------------------------------
% 0.19/0.47 % (1641)------------------------------
% 0.19/0.47 % (1638)Success in time 0.12 s
%------------------------------------------------------------------------------