TSTP Solution File: KLE148+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : KLE148+1 : 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 : n006.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 17:29:17 EDT 2022

% Result   : Theorem 2.36s 0.68s
% Output   : Refutation 2.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   65 (  55 unt;   3 typ;   0 def)
%            Number of atoms       :   71 (  70 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   18 (   9   ~;   0   |;   5   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    4 (   0 usr;   3 ari)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   83 (  77   !;   6   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(pred_def_3,type,
    sQ3_eqProxy: ( $int * $int ) > $o ).

tff(pred_def_4,type,
    sQ4_eqProxy: ( $rat * $rat ) > $o ).

tff(pred_def_5,type,
    sQ5_eqProxy: ( $real * $real ) > $o ).

fof(f911,plain,
    $false,
    inference(subsumption_resolution,[],[f910,f78]) ).

fof(f78,plain,
    multiplication(sK1,strong_iteration(sK0)) != sK1,
    inference(literal_reordering,[],[f48]) ).

fof(f48,plain,
    multiplication(sK1,strong_iteration(sK0)) != sK1,
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ( zero = multiplication(sK1,sK0)
    & multiplication(sK1,strong_iteration(sK0)) != sK1 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f33,f34]) ).

fof(f34,plain,
    ( ? [X0,X1] :
        ( zero = multiplication(X1,X0)
        & multiplication(X1,strong_iteration(X0)) != X1 )
   => ( zero = multiplication(sK1,sK0)
      & multiplication(sK1,strong_iteration(sK0)) != sK1 ) ),
    introduced(choice_axiom,[]) ).

fof(f33,plain,
    ? [X0,X1] :
      ( zero = multiplication(X1,X0)
      & multiplication(X1,strong_iteration(X0)) != X1 ),
    inference(rectify,[],[f28]) ).

fof(f28,plain,
    ? [X1,X0] :
      ( zero = multiplication(X0,X1)
      & multiplication(X0,strong_iteration(X1)) != X0 ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,plain,
    ~ ! [X1,X0] :
        ( zero = multiplication(X0,X1)
       => multiplication(X0,strong_iteration(X1)) = X0 ),
    inference(rectify,[],[f20]) ).

fof(f20,negated_conjecture,
    ~ ! [X3,X4] :
        ( zero = multiplication(X3,X4)
       => multiplication(X3,strong_iteration(X4)) = X3 ),
    inference(negated_conjecture,[],[f19]) ).

fof(f19,conjecture,
    ! [X3,X4] :
      ( zero = multiplication(X3,X4)
     => multiplication(X3,strong_iteration(X4)) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

fof(f910,plain,
    multiplication(sK1,strong_iteration(sK0)) = sK1,
    inference(forward_demodulation,[],[f894,f411]) ).

fof(f411,plain,
    ! [X0] : multiplication(X0,star(zero)) = X0,
    inference(backward_demodulation,[],[f380,f408]) ).

fof(f408,plain,
    strong_iteration(zero) = star(zero),
    inference(forward_demodulation,[],[f398,f65]) ).

fof(f65,plain,
    ! [X0] : addition(X0,zero) = X0,
    inference(literal_reordering,[],[f44]) ).

fof(f44,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(f398,plain,
    strong_iteration(zero) = addition(star(zero),zero),
    inference(superposition,[],[f67,f381]) ).

fof(f381,plain,
    ! [X0] : multiplication(strong_iteration(zero),X0) = X0,
    inference(backward_demodulation,[],[f69,f373]) ).

fof(f373,plain,
    one = strong_iteration(zero),
    inference(superposition,[],[f150,f136]) ).

fof(f136,plain,
    ! [X0] : addition(zero,X0) = X0,
    inference(superposition,[],[f71,f65]) ).

fof(f71,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X1,X0),
    inference(literal_reordering,[],[f51]) ).

fof(f51,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X1,X0),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X1,X0),
    inference(rectify,[],[f25]) ).

fof(f25,plain,
    ! [X1,X0] : 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(f150,plain,
    addition(zero,one) = strong_iteration(zero),
    inference(superposition,[],[f79,f76]) ).

fof(f76,plain,
    ! [X0] : zero = multiplication(zero,X0),
    inference(literal_reordering,[],[f45]) ).

fof(f45,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(f79,plain,
    ! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
    inference(literal_reordering,[],[f55]) ).

fof(f55,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/sandbox/benchmark/theBenchmark.p',infty_unfold1) ).

fof(f69,plain,
    ! [X0] : multiplication(one,X0) = X0,
    inference(literal_reordering,[],[f47]) ).

fof(f47,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(f67,plain,
    ! [X0] : strong_iteration(X0) = addition(star(X0),multiplication(strong_iteration(X0),zero)),
    inference(literal_reordering,[],[f56]) ).

fof(f56,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/sandbox/benchmark/theBenchmark.p',isolation) ).

fof(f380,plain,
    ! [X0] : multiplication(X0,strong_iteration(zero)) = X0,
    inference(backward_demodulation,[],[f74,f373]) ).

fof(f74,plain,
    ! [X0] : multiplication(X0,one) = X0,
    inference(literal_reordering,[],[f53]) ).

fof(f53,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(f894,plain,
    multiplication(sK1,strong_iteration(sK0)) = multiplication(sK1,star(zero)),
    inference(superposition,[],[f250,f477]) ).

fof(f477,plain,
    ! [X1] : strong_iteration(X1) = addition(star(zero),multiplication(X1,strong_iteration(X1))),
    inference(superposition,[],[f460,f71]) ).

fof(f460,plain,
    ! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),star(zero)),
    inference(forward_demodulation,[],[f378,f408]) ).

fof(f378,plain,
    ! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),strong_iteration(zero)),
    inference(backward_demodulation,[],[f79,f373]) ).

fof(f250,plain,
    ! [X11,X12] : multiplication(sK1,addition(X12,multiplication(sK0,X11))) = multiplication(sK1,X12),
    inference(forward_demodulation,[],[f229,f65]) ).

fof(f229,plain,
    ! [X11,X12] : addition(multiplication(sK1,X12),zero) = multiplication(sK1,addition(X12,multiplication(sK0,X11))),
    inference(superposition,[],[f70,f176]) ).

fof(f176,plain,
    ! [X10] : zero = multiplication(sK1,multiplication(sK0,X10)),
    inference(forward_demodulation,[],[f169,f76]) ).

fof(f169,plain,
    ! [X10] : multiplication(zero,X10) = multiplication(sK1,multiplication(sK0,X10)),
    inference(superposition,[],[f66,f75]) ).

fof(f75,plain,
    zero = multiplication(sK1,sK0),
    inference(literal_reordering,[],[f49]) ).

fof(f49,plain,
    zero = multiplication(sK1,sK0),
    inference(cnf_transformation,[],[f35]) ).

fof(f66,plain,
    ! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
    inference(literal_reordering,[],[f52]) ).

fof(f52,plain,
    ! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
    inference(rectify,[],[f26]) ).

fof(f26,plain,
    ! [X1,X0,X2] : multiplication(multiplication(X1,X0),X2) = multiplication(X1,multiplication(X0,X2)),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X1,X0,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).

fof(f70,plain,
    ! [X2,X0,X1] : multiplication(X2,addition(X0,X1)) = addition(multiplication(X2,X0),multiplication(X2,X1)),
    inference(literal_reordering,[],[f57]) ).

fof(f57,plain,
    ! [X2,X0,X1] : multiplication(X2,addition(X0,X1)) = addition(multiplication(X2,X0),multiplication(X2,X1)),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0,X1,X2] : multiplication(X2,addition(X0,X1)) = addition(multiplication(X2,X0),multiplication(X2,X1)),
    inference(rectify,[],[f21]) ).

fof(f21,plain,
    ! [X2,X0,X1] : addition(multiplication(X1,X2),multiplication(X1,X0)) = multiplication(X1,addition(X2,X0)),
    inference(rectify,[],[f8]) ).

fof(f8,axiom,
    ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : KLE148+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.34  % Computer : n006.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Tue Aug 30 00:26:10 EDT 2022
% 0.14/0.34  % CPUTime    : 
% 0.20/0.54  % (30575)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)
% 0.20/0.56  % (30601)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)
% 0.20/0.56  % (30587)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.56  TRYING [1]
% 0.20/0.56  TRYING [2]
% 0.20/0.56  TRYING [3]
% 0.20/0.57  % (30583)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.57  % (30583)Instruction limit reached!
% 0.20/0.57  % (30583)------------------------------
% 0.20/0.57  % (30583)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.58  % (30583)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.58  % (30583)Termination reason: Unknown
% 0.20/0.58  % (30583)Termination phase: Saturation
% 0.20/0.58  
% 0.20/0.58  % (30583)Memory used [KB]: 5373
% 0.20/0.58  % (30583)Time elapsed: 0.146 s
% 0.20/0.58  % (30583)Instructions burned: 2 (million)
% 0.20/0.58  % (30583)------------------------------
% 0.20/0.58  % (30583)------------------------------
% 0.20/0.58  % (30579)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.59  % (30586)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)
% 0.20/0.59  % (30588)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.59  % (30591)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)
% 0.20/0.60  % (30589)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)
% 0.20/0.60  % (30577)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)
% 0.20/0.61  % (30578)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)
% 0.20/0.61  % (30603)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.61  % (30576)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)
% 0.20/0.61  % (30595)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)
% 0.20/0.61  % (30580)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)
% 0.20/0.61  % (30581)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)
% 0.20/0.61  TRYING [4]
% 0.20/0.61  TRYING [1]
% 0.20/0.61  TRYING [2]
% 0.20/0.62  % (30598)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.20/0.62  % (30585)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.62  % (30590)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.20/0.63  % (30605)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 2.10/0.63  % (30602)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 2.10/0.63  % (30592)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 2.10/0.64  % (30597)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)
% 2.10/0.64  % (30593)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 2.10/0.64  TRYING [3]
% 2.10/0.64  % (30596)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 2.10/0.64  % (30594)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 2.10/0.64  % (30600)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 2.30/0.65  % (30599)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 2.30/0.65  % (30584)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)
% 2.36/0.66  % (30582)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 2.36/0.66  TRYING [1]
% 2.36/0.66  TRYING [2]
% 2.36/0.66  TRYING [3]
% 2.36/0.66  % (30582)Instruction limit reached!
% 2.36/0.66  % (30582)------------------------------
% 2.36/0.66  % (30582)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.36/0.66  % (30582)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.36/0.66  % (30582)Termination reason: Unknown
% 2.36/0.66  % (30582)Termination phase: Saturation
% 2.36/0.66  
% 2.36/0.66  % (30582)Memory used [KB]: 5500
% 2.36/0.66  % (30582)Time elapsed: 0.188 s
% 2.36/0.66  % (30582)Instructions burned: 7 (million)
% 2.36/0.66  % (30582)------------------------------
% 2.36/0.66  % (30582)------------------------------
% 2.36/0.67  % (30601)First to succeed.
% 2.36/0.68  % (30601)Refutation found. Thanks to Tanya!
% 2.36/0.68  % SZS status Theorem for theBenchmark
% 2.36/0.68  % SZS output start Proof for theBenchmark
% See solution above
% 2.36/0.68  % (30601)------------------------------
% 2.36/0.68  % (30601)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.36/0.68  % (30601)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.36/0.68  % (30601)Termination reason: Refutation
% 2.36/0.68  
% 2.36/0.68  % (30601)Memory used [KB]: 6396
% 2.36/0.68  % (30601)Time elapsed: 0.057 s
% 2.36/0.68  % (30601)Instructions burned: 38 (million)
% 2.36/0.68  % (30601)------------------------------
% 2.36/0.68  % (30601)------------------------------
% 2.36/0.68  % (30574)Success in time 0.32 s
%------------------------------------------------------------------------------