TSTP Solution File: ANA133-1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ANA133-1 : TPTP v8.2.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n005.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 : Mon May 20 18:41:54 EDT 2024

% Result   : Unsatisfiable 26.53s 4.15s
% Output   : Refutation 26.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   65 (  65 unt;   0 def)
%            Number of atoms       :   65 (  64 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    1 (   1   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-2 aty)
%            Number of variables   :   59 (  59   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f260142,plain,
    $false,
    inference(subsumption_resolution,[],[f260141,f17]) ).

fof(f17,axiom,
    ! [X3] : d(X3) != times(x,cos(x)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).

fof(f260141,plain,
    times(x,cos(x)) = d('+'(cos(x),times(x,sin(x)))),
    inference(forward_demodulation,[],[f260140,f54]) ).

fof(f54,plain,
    cos(x) = d(sin(x)),
    inference(forward_demodulation,[],[f47,f30]) ).

fof(f30,plain,
    ! [X0] : times(X0,one) = X0,
    inference(superposition,[],[f3,f7]) ).

fof(f7,axiom,
    ! [X0] : times(one,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times_one) ).

fof(f3,axiom,
    ! [X0,X1] : times(X0,X1) = times(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_times) ).

fof(f47,plain,
    d(sin(x)) = times(cos(x),one),
    inference(superposition,[],[f15,f12]) ).

fof(f12,axiom,
    one = d(x),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',derivative_of_x) ).

fof(f15,axiom,
    ! [X3] : d(sin(X3)) = times(cos(X3),d(X3)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',derivative_of_sin) ).

fof(f260140,plain,
    times(x,d(sin(x))) = d('+'(cos(x),times(x,sin(x)))),
    inference(forward_demodulation,[],[f260139,f691]) ).

fof(f691,plain,
    ! [X0] : minus(minus(X0)) = X0,
    inference(forward_demodulation,[],[f681,f21]) ).

fof(f21,plain,
    ! [X0] : '+'(X0,zero) = X0,
    inference(superposition,[],[f1,f5]) ).

fof(f5,axiom,
    ! [X0] : '+'(zero,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_zero) ).

fof(f1,axiom,
    ! [X0,X1] : '+'(X0,X1) = '+'(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_plus) ).

fof(f681,plain,
    ! [X0] : '+'(X0,zero) = minus(minus(X0)),
    inference(superposition,[],[f441,f9]) ).

fof(f9,axiom,
    ! [X0] : zero = '+'(X0,minus(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minus) ).

fof(f441,plain,
    ! [X0,X1] : '+'(X0,'+'(minus(X0),X1)) = X1,
    inference(forward_demodulation,[],[f423,f5]) ).

fof(f423,plain,
    ! [X0,X1] : '+'(X0,'+'(minus(X0),X1)) = '+'(zero,X1),
    inference(superposition,[],[f2,f9]) ).

fof(f2,axiom,
    ! [X2,X0,X1] : '+'(X0,'+'(X1,X2)) = '+'('+'(X0,X1),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associtivity_of_plus) ).

fof(f260139,plain,
    times(x,d(sin(x))) = d('+'(cos(x),times(x,minus(minus(sin(x)))))),
    inference(forward_demodulation,[],[f260138,f1]) ).

fof(f260138,plain,
    times(x,d(sin(x))) = d('+'(times(x,minus(minus(sin(x)))),cos(x))),
    inference(forward_demodulation,[],[f260137,f691]) ).

fof(f260137,plain,
    d('+'(times(x,minus(minus(sin(x)))),cos(x))) = times(x,minus(minus(d(sin(x))))),
    inference(forward_demodulation,[],[f259996,f38135]) ).

fof(f38135,plain,
    ! [X0] : minus(d(X0)) = d(minus(X0)),
    inference(forward_demodulation,[],[f38134,f37972]) ).

fof(f37972,plain,
    ! [X0] : minus(X0) = times(X0,minus(one)),
    inference(forward_demodulation,[],[f37971,f5]) ).

fof(f37971,plain,
    ! [X0] : '+'(zero,minus(X0)) = times(X0,minus(one)),
    inference(forward_demodulation,[],[f37910,f1]) ).

fof(f37910,plain,
    ! [X0] : '+'(minus(X0),zero) = times(X0,minus(one)),
    inference(superposition,[],[f697,f29868]) ).

fof(f29868,plain,
    ! [X0] : zero = '+'(X0,times(X0,minus(one))),
    inference(forward_demodulation,[],[f29867,f29]) ).

fof(f29,plain,
    ! [X0] : zero = times(X0,zero),
    inference(superposition,[],[f3,f6]) ).

fof(f6,axiom,
    ! [X0] : zero = times(zero,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times_zero) ).

fof(f29867,plain,
    ! [X0] : times(X0,zero) = '+'(X0,times(X0,minus(one))),
    inference(forward_demodulation,[],[f29750,f3109]) ).

fof(f3109,plain,
    minus(one) = d(minus(x)),
    inference(forward_demodulation,[],[f3103,f21]) ).

fof(f3103,plain,
    '+'(minus(one),zero) = d(minus(x)),
    inference(superposition,[],[f697,f2209]) ).

fof(f2209,plain,
    zero = '+'(one,d(minus(x))),
    inference(forward_demodulation,[],[f2186,f10]) ).

fof(f10,axiom,
    zero = d(zero),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',derivative_of_zero) ).

fof(f2186,plain,
    d(zero) = '+'(one,d(minus(x))),
    inference(superposition,[],[f57,f9]) ).

fof(f57,plain,
    ! [X0] : d('+'(x,X0)) = '+'(one,d(X0)),
    inference(superposition,[],[f13,f12]) ).

fof(f13,axiom,
    ! [X3,X4] : d('+'(X3,X4)) = '+'(d(X3),d(X4)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',derivative_of_plus) ).

fof(f29750,plain,
    ! [X0] : times(X0,zero) = '+'(X0,times(X0,d(minus(x)))),
    inference(superposition,[],[f723,f2209]) ).

fof(f723,plain,
    ! [X0,X1] : times(X0,'+'(one,X1)) = '+'(X0,times(X0,X1)),
    inference(superposition,[],[f8,f30]) ).

fof(f8,axiom,
    ! [X2,X0,X1] : times(X0,'+'(X1,X2)) = '+'(times(X0,X1),times(X0,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity) ).

fof(f697,plain,
    ! [X0,X1] : '+'(minus(X0),'+'(X0,X1)) = X1,
    inference(superposition,[],[f441,f691]) ).

fof(f38134,plain,
    ! [X0] : d(times(X0,minus(one))) = minus(d(X0)),
    inference(forward_demodulation,[],[f38133,f5]) ).

fof(f38133,plain,
    ! [X0] : d(times(X0,minus(one))) = '+'(zero,minus(d(X0))),
    inference(forward_demodulation,[],[f38132,f29]) ).

fof(f38132,plain,
    ! [X0] : d(times(X0,minus(one))) = '+'(times(X0,zero),minus(d(X0))),
    inference(forward_demodulation,[],[f38102,f113]) ).

fof(f113,plain,
    zero = d(minus(one)),
    inference(forward_demodulation,[],[f105,f10]) ).

fof(f105,plain,
    d(zero) = d(minus(one)),
    inference(superposition,[],[f66,f9]) ).

fof(f66,plain,
    ! [X0] : d(X0) = d('+'(one,X0)),
    inference(forward_demodulation,[],[f56,f5]) ).

fof(f56,plain,
    ! [X0] : '+'(zero,d(X0)) = d('+'(one,X0)),
    inference(superposition,[],[f13,f11]) ).

fof(f11,axiom,
    zero = d(one),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',derivative_of_one) ).

fof(f38102,plain,
    ! [X0] : d(times(X0,minus(one))) = '+'(times(X0,d(minus(one))),minus(d(X0))),
    inference(superposition,[],[f1093,f37972]) ).

fof(f1093,plain,
    ! [X0,X1] : d(times(X1,X0)) = '+'(times(X1,d(X0)),times(d(X1),X0)),
    inference(superposition,[],[f14,f3]) ).

fof(f14,axiom,
    ! [X3,X4] : d(times(X3,X4)) = '+'(times(X3,d(X4)),times(X4,d(X3))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',derivative_of_times) ).

fof(f259996,plain,
    d('+'(times(x,minus(minus(sin(x)))),cos(x))) = times(x,minus(d(minus(sin(x))))),
    inference(superposition,[],[f228751,f2609]) ).

fof(f2609,plain,
    ! [X0] : d('+'(X0,cos(x))) = '+'(minus(sin(x)),d(X0)),
    inference(superposition,[],[f61,f292]) ).

fof(f292,plain,
    d(cos(x)) = minus(sin(x)),
    inference(forward_demodulation,[],[f270,f7]) ).

fof(f270,plain,
    d(cos(x)) = minus(times(one,sin(x))),
    inference(superposition,[],[f142,f12]) ).

fof(f142,plain,
    ! [X3] : d(cos(X3)) = minus(times(d(X3),sin(X3))),
    inference(forward_demodulation,[],[f16,f3]) ).

fof(f16,axiom,
    ! [X3] : d(cos(X3)) = minus(times(sin(X3),d(X3))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',derivative_of_cos) ).

fof(f61,plain,
    ! [X0,X1] : d('+'(X0,X1)) = '+'(d(X1),d(X0)),
    inference(superposition,[],[f13,f1]) ).

fof(f228751,plain,
    ! [X0] : '+'(X0,d(times(x,minus(X0)))) = times(x,minus(d(X0))),
    inference(forward_demodulation,[],[f5638,f38135]) ).

fof(f5638,plain,
    ! [X0] : times(x,d(minus(X0))) = '+'(X0,d(times(x,minus(X0)))),
    inference(forward_demodulation,[],[f5067,f3]) ).

fof(f5067,plain,
    ! [X0] : times(x,d(minus(X0))) = '+'(X0,d(times(minus(X0),x))),
    inference(superposition,[],[f441,f1119]) ).

fof(f1119,plain,
    ! [X0] : d(times(X0,x)) = '+'(X0,times(x,d(X0))),
    inference(forward_demodulation,[],[f977,f30]) ).

fof(f977,plain,
    ! [X0] : d(times(X0,x)) = '+'(times(X0,one),times(x,d(X0))),
    inference(superposition,[],[f14,f12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem    : ANA133-1 : TPTP v8.2.0. Released v8.1.0.
% 0.08/0.16  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.37  % Computer : n005.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Mon May 20 07:43:08 EDT 2024
% 0.16/0.37  % CPUTime    : 
% 0.16/0.38  % (8932)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.39  % (8935)WARNING: value z3 for option sas not known
% 0.16/0.39  % (8933)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.39  % (8936)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.39  % (8934)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.39  % (8935)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)
% 0.16/0.39  % (8937)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)
% 0.16/0.39  % (8938)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)
% 0.16/0.39  % (8939)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)
% 0.16/0.40  TRYING [1]
% 0.16/0.40  TRYING [2]
% 0.16/0.40  TRYING [3]
% 0.16/0.40  TRYING [1]
% 0.16/0.40  TRYING [2]
% 0.16/0.41  TRYING [4]
% 0.23/0.41  TRYING [3]
% 0.23/0.45  TRYING [4]
% 0.23/0.46  TRYING [5]
% 0.23/0.52  TRYING [5]
% 0.23/0.55  TRYING [6]
% 1.97/0.68  TRYING [6]
% 2.60/0.74  TRYING [7]
% 5.10/1.15  TRYING [8]
% 5.59/1.16  TRYING [7]
% 7.79/1.49  TRYING [1]
% 7.79/1.49  TRYING [2]
% 7.79/1.49  TRYING [3]
% 7.79/1.50  TRYING [4]
% 8.12/1.53  TRYING [5]
% 8.88/1.63  TRYING [6]
% 10.27/1.86  TRYING [7]
% 13.59/2.35  TRYING [9]
% 14.37/2.49  TRYING [8]
% 26.53/4.14  % (8935)First to succeed.
% 26.53/4.15  % (8935)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-8932"
% 26.53/4.15  % (8935)Refutation found. Thanks to Tanya!
% 26.53/4.15  % SZS status Unsatisfiable for theBenchmark
% 26.53/4.15  % SZS output start Proof for theBenchmark
% See solution above
% 26.53/4.15  % (8935)------------------------------
% 26.53/4.15  % (8935)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 26.53/4.15  % (8935)Termination reason: Refutation
% 26.53/4.15  
% 26.53/4.15  % (8935)Memory used [KB]: 53879
% 26.53/4.15  % (8935)Time elapsed: 3.753 s
% 26.53/4.15  % (8935)Instructions burned: 17748 (million)
% 26.53/4.15  % (8932)Success in time 3.726 s
%------------------------------------------------------------------------------