TSTP Solution File: KLE041+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : KLE041+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 : n004.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 13:11:46 EDT 2024

% Result   : Theorem 6.90s 1.33s
% Output   : Refutation 6.90s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   87 (  68 unt;   0 def)
%            Number of atoms       :  110 (  50 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   42 (  19   ~;  12   |;   5   &)
%                                         (   1 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :  125 ( 121   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f46496,plain,
    $false,
    inference(resolution,[],[f46495,f28]) ).

fof(f28,plain,
    ~ leq(star(sK0),star(sK1)),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ( ~ leq(star(sK0),star(sK1))
    & leq(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f21,f24]) ).

fof(f24,plain,
    ( ? [X0,X1] :
        ( ~ leq(star(X0),star(X1))
        & leq(X0,X1) )
   => ( ~ leq(star(sK0),star(sK1))
      & leq(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f21,plain,
    ? [X0,X1] :
      ( ~ leq(star(X0),star(X1))
      & leq(X0,X1) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,plain,
    ~ ! [X0,X1] :
        ( leq(X0,X1)
       => leq(star(X0),star(X1)) ),
    inference(rectify,[],[f18]) ).

fof(f18,negated_conjecture,
    ~ ! [X3,X4] :
        ( leq(X3,X4)
       => leq(star(X3),star(X4)) ),
    inference(negated_conjecture,[],[f17]) ).

fof(f17,conjecture,
    ! [X3,X4] :
      ( leq(X3,X4)
     => leq(star(X3),star(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

fof(f46495,plain,
    leq(star(sK0),star(sK1)),
    inference(forward_demodulation,[],[f46491,f33]) ).

fof(f33,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(f46491,plain,
    leq(multiplication(one,star(sK0)),star(sK1)),
    inference(resolution,[],[f46473,f918]) ).

fof(f918,plain,
    ! [X2,X0,X1] :
      ( ~ leq(addition(X2,multiplication(X0,X1)),X0)
      | leq(multiplication(X2,star(X1)),X0) ),
    inference(superposition,[],[f44,f37]) ).

fof(f37,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(f44,plain,
    ! [X2,X0,X1] :
      ( ~ leq(addition(multiplication(X0,X1),X2),X0)
      | leq(multiplication(X2,star(X1)),X0) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1,X2] :
      ( leq(multiplication(X2,star(X1)),X0)
      | ~ leq(addition(multiplication(X0,X1),X2),X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0,X1,X2] :
      ( leq(addition(multiplication(X0,X1),X2),X0)
     => leq(multiplication(X2,star(X1)),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction_right) ).

fof(f46473,plain,
    leq(addition(one,multiplication(star(sK1),sK0)),star(sK1)),
    inference(forward_demodulation,[],[f46472,f35192]) ).

fof(f35192,plain,
    ! [X0] : star(X0) = addition(one,star(X0)),
    inference(superposition,[],[f103,f4911]) ).

fof(f4911,plain,
    ! [X0] : star(X0) = addition(one,multiplication(addition(one,X0),star(X0))),
    inference(forward_demodulation,[],[f4910,f763]) ).

fof(f763,plain,
    ! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
    inference(superposition,[],[f43,f33]) ).

fof(f43,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',left_distributivity) ).

fof(f4910,plain,
    ! [X0] : star(X0) = addition(one,addition(star(X0),multiplication(X0,star(X0)))),
    inference(forward_demodulation,[],[f4872,f37]) ).

fof(f4872,plain,
    ! [X0] : star(X0) = addition(one,addition(multiplication(X0,star(X0)),star(X0))),
    inference(superposition,[],[f76,f40]) ).

fof(f40,plain,
    ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,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(f76,plain,
    ! [X0] : star(X0) = addition(addition(one,multiplication(X0,star(X0))),star(X0)),
    inference(resolution,[],[f35,f38]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ~ leq(X0,X1)
      | addition(X0,X1) = X1 ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( leq(X0,X1)
        | addition(X0,X1) != X1 )
      & ( addition(X0,X1) = X1
        | ~ leq(X0,X1) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0,X1] :
      ( leq(X0,X1)
    <=> addition(X0,X1) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).

fof(f35,plain,
    ! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
    inference(cnf_transformation,[],[f13]) ).

fof(f13,axiom,
    ! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold_right) ).

fof(f103,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
    inference(superposition,[],[f40,f34]) ).

fof(f34,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(f46472,plain,
    leq(addition(one,multiplication(addition(one,star(sK1)),sK0)),star(sK1)),
    inference(forward_demodulation,[],[f46471,f763]) ).

fof(f46471,plain,
    leq(addition(one,addition(sK0,multiplication(star(sK1),sK0))),star(sK1)),
    inference(forward_demodulation,[],[f46470,f40]) ).

fof(f46470,plain,
    leq(addition(addition(one,sK0),multiplication(star(sK1),sK0)),star(sK1)),
    inference(forward_demodulation,[],[f46408,f37]) ).

fof(f46408,plain,
    leq(addition(multiplication(star(sK1),sK0),addition(one,sK0)),star(sK1)),
    inference(superposition,[],[f42947,f35555]) ).

fof(f35555,plain,
    star(sK1) = addition(multiplication(star(sK1),sK0),star(sK1)),
    inference(resolution,[],[f35453,f38]) ).

fof(f35453,plain,
    leq(multiplication(star(sK1),sK0),star(sK1)),
    inference(superposition,[],[f9161,f35261]) ).

fof(f35261,plain,
    ! [X0] : star(X0) = addition(multiplication(star(X0),X0),star(X0)),
    inference(backward_demodulation,[],[f5155,f35192]) ).

fof(f5155,plain,
    ! [X0] : star(X0) = addition(multiplication(star(X0),X0),addition(one,star(X0))),
    inference(superposition,[],[f81,f104]) ).

fof(f104,plain,
    ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
    inference(superposition,[],[f40,f37]) ).

fof(f81,plain,
    ! [X0] : star(X0) = addition(addition(one,multiplication(star(X0),X0)),star(X0)),
    inference(resolution,[],[f36,f38]) ).

fof(f36,plain,
    ! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
    inference(cnf_transformation,[],[f14]) ).

fof(f14,axiom,
    ! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold_left) ).

fof(f9161,plain,
    ! [X0,X1] : leq(multiplication(X1,sK0),addition(multiplication(X1,sK1),X0)),
    inference(superposition,[],[f9116,f37]) ).

fof(f9116,plain,
    ! [X0,X1] : leq(multiplication(X0,sK0),addition(X1,multiplication(X0,sK1))),
    inference(superposition,[],[f827,f8328]) ).

fof(f8328,plain,
    ! [X0] : multiplication(X0,sK1) = addition(multiplication(X0,sK0),multiplication(X0,sK1)),
    inference(resolution,[],[f8301,f38]) ).

fof(f8301,plain,
    ! [X0] : leq(multiplication(X0,sK0),multiplication(X0,sK1)),
    inference(trivial_inequality_removal,[],[f8282]) ).

fof(f8282,plain,
    ! [X0] :
      ( multiplication(X0,sK1) != multiplication(X0,sK1)
      | leq(multiplication(X0,sK0),multiplication(X0,sK1)) ),
    inference(superposition,[],[f359,f54]) ).

fof(f54,plain,
    sK1 = addition(sK0,sK1),
    inference(resolution,[],[f38,f27]) ).

fof(f27,plain,
    leq(sK0,sK1),
    inference(cnf_transformation,[],[f25]) ).

fof(f359,plain,
    ! [X2,X0,X1] :
      ( multiplication(X0,addition(X1,X2)) != multiplication(X0,X2)
      | leq(multiplication(X0,X1),multiplication(X0,X2)) ),
    inference(superposition,[],[f39,f42]) ).

fof(f42,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',right_distributivity) ).

fof(f39,plain,
    ! [X0,X1] :
      ( addition(X0,X1) != X1
      | leq(X0,X1) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f827,plain,
    ! [X2,X0,X1] : leq(X1,addition(X2,addition(X1,X0))),
    inference(superposition,[],[f814,f37]) ).

fof(f814,plain,
    ! [X2,X0,X1] : leq(X2,addition(X0,addition(X1,X2))),
    inference(superposition,[],[f793,f40]) ).

fof(f793,plain,
    ! [X0,X1] : leq(X0,addition(X1,X0)),
    inference(superposition,[],[f753,f37]) ).

fof(f753,plain,
    ! [X0,X1] : leq(X0,addition(X0,X1)),
    inference(trivial_inequality_removal,[],[f743]) ).

fof(f743,plain,
    ! [X0,X1] :
      ( addition(X0,X1) != addition(X0,X1)
      | leq(X0,addition(X0,X1)) ),
    inference(superposition,[],[f39,f103]) ).

fof(f42947,plain,
    ! [X0] : leq(addition(X0,addition(one,sK0)),addition(X0,star(sK1))),
    inference(superposition,[],[f797,f42852]) ).

fof(f42852,plain,
    star(sK1) = addition(addition(one,sK0),star(sK1)),
    inference(forward_demodulation,[],[f42851,f42639]) ).

fof(f42639,plain,
    star(sK1) = multiplication(addition(one,sK0),star(sK1)),
    inference(superposition,[],[f35859,f5748]) ).

fof(f5748,plain,
    ! [X0,X1] : multiplication(addition(one,X1),X0) = addition(multiplication(X1,X0),X0),
    inference(superposition,[],[f771,f33]) ).

fof(f771,plain,
    ! [X2,X0,X1] : multiplication(addition(X0,X2),X1) = addition(multiplication(X2,X1),multiplication(X0,X1)),
    inference(superposition,[],[f43,f37]) ).

fof(f35859,plain,
    star(sK1) = addition(multiplication(sK0,star(sK1)),star(sK1)),
    inference(resolution,[],[f35747,f38]) ).

fof(f35747,plain,
    leq(multiplication(sK0,star(sK1)),star(sK1)),
    inference(superposition,[],[f9711,f35262]) ).

fof(f35262,plain,
    ! [X0] : star(X0) = addition(multiplication(X0,star(X0)),star(X0)),
    inference(backward_demodulation,[],[f4871,f35192]) ).

fof(f4871,plain,
    ! [X0] : star(X0) = addition(multiplication(X0,star(X0)),addition(one,star(X0))),
    inference(superposition,[],[f76,f104]) ).

fof(f9711,plain,
    ! [X0,X1] : leq(multiplication(sK0,X1),addition(multiplication(sK1,X1),X0)),
    inference(superposition,[],[f9666,f37]) ).

fof(f9666,plain,
    ! [X0,X1] : leq(multiplication(sK0,X0),addition(X1,multiplication(sK1,X0))),
    inference(superposition,[],[f827,f9013]) ).

fof(f9013,plain,
    ! [X0] : multiplication(sK1,X0) = addition(multiplication(sK0,X0),multiplication(sK1,X0)),
    inference(resolution,[],[f8962,f38]) ).

fof(f8962,plain,
    ! [X0] : leq(multiplication(sK0,X0),multiplication(sK1,X0)),
    inference(trivial_inequality_removal,[],[f8944]) ).

fof(f8944,plain,
    ! [X0] :
      ( multiplication(sK1,X0) != multiplication(sK1,X0)
      | leq(multiplication(sK0,X0),multiplication(sK1,X0)) ),
    inference(superposition,[],[f778,f54]) ).

fof(f778,plain,
    ! [X2,X0,X1] :
      ( multiplication(X2,X1) != multiplication(addition(X0,X2),X1)
      | leq(multiplication(X0,X1),multiplication(X2,X1)) ),
    inference(superposition,[],[f39,f43]) ).

fof(f42851,plain,
    multiplication(addition(one,sK0),star(sK1)) = addition(addition(one,sK0),star(sK1)),
    inference(forward_demodulation,[],[f42797,f35192]) ).

fof(f42797,plain,
    addition(addition(one,sK0),star(sK1)) = multiplication(addition(one,sK0),addition(one,star(sK1))),
    inference(superposition,[],[f344,f42639]) ).

fof(f344,plain,
    ! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
    inference(superposition,[],[f42,f32]) ).

fof(f32,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(f797,plain,
    ! [X2,X0,X1] : leq(addition(X0,X1),addition(X0,addition(X1,X2))),
    inference(superposition,[],[f753,f40]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : KLE041+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n004.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Tue Apr 30 04:58:18 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.36  % (11409)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37  % (11412)WARNING: value z3 for option sas not known
% 0.15/0.37  % (11413)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.37  % (11410)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.37  % (11412)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)
% 0.15/0.37  % (11414)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)
% 0.15/0.37  % (11411)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.37  % (11416)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)
% 0.15/0.37  % (11415)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)
% 0.15/0.38  TRYING [1]
% 0.15/0.38  TRYING [2]
% 0.15/0.38  TRYING [3]
% 0.15/0.38  TRYING [1]
% 0.15/0.38  TRYING [2]
% 0.15/0.39  TRYING [4]
% 0.15/0.40  TRYING [3]
% 0.21/0.43  TRYING [5]
% 0.21/0.44  TRYING [4]
% 0.21/0.50  TRYING [6]
% 0.21/0.54  TRYING [5]
% 2.12/0.66  TRYING [7]
% 4.23/0.95  TRYING [6]
% 4.70/1.03  TRYING [8]
% 6.23/1.32  % (11415)First to succeed.
% 6.90/1.33  % (11415)Refutation found. Thanks to Tanya!
% 6.90/1.33  % SZS status Theorem for theBenchmark
% 6.90/1.33  % SZS output start Proof for theBenchmark
% See solution above
% 6.90/1.33  % (11415)------------------------------
% 6.90/1.33  % (11415)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 6.90/1.33  % (11415)Termination reason: Refutation
% 6.90/1.33  
% 6.90/1.33  % (11415)Memory used [KB]: 15081
% 6.90/1.33  % (11415)Time elapsed: 0.956 s
% 6.90/1.33  % (11415)Instructions burned: 2853 (million)
% 6.90/1.33  % (11415)------------------------------
% 6.90/1.33  % (11415)------------------------------
% 6.90/1.33  % (11409)Success in time 0.95 s
%------------------------------------------------------------------------------