TSTP Solution File: BOO015-2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : BOO015-2 : TPTP v8.2.0. Bugfixed v1.0.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n027.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 18:58:50 EDT 2024

% Result   : Unsatisfiable 2.76s 0.80s
% Output   : Refutation 2.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   97 (  97 unt;   0 def)
%            Number of atoms       :   97 (  96 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    :    4 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :  109 ( 109   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f16651,plain,
    $false,
    inference(subsumption_resolution,[],[f16650,f17]) ).

fof(f17,axiom,
    d != inverse(c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_inverse_is_d) ).

fof(f16650,plain,
    d = inverse(c),
    inference(forward_demodulation,[],[f16649,f16]) ).

fof(f16,axiom,
    add(inverse(a),inverse(b)) = d,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_inverse_plus_b_inverse_is_d) ).

fof(f16649,plain,
    add(inverse(a),inverse(b)) = inverse(c),
    inference(forward_demodulation,[],[f16648,f12433]) ).

fof(f12433,plain,
    inverse(c) = multiply(d,inverse(c)),
    inference(forward_demodulation,[],[f12395,f12]) ).

fof(f12,axiom,
    ! [X0] : multiply(multiplicative_identity,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_id2) ).

fof(f12395,plain,
    multiply(multiplicative_identity,inverse(c)) = multiply(d,inverse(c)),
    inference(superposition,[],[f313,f12329]) ).

fof(f12329,plain,
    multiplicative_identity = add(c,d),
    inference(superposition,[],[f787,f12328]) ).

fof(f12328,plain,
    c = add(c,inverse(d)),
    inference(forward_demodulation,[],[f2763,f2830]) ).

fof(f2830,plain,
    inverse(d) = multiply(b,inverse(d)),
    inference(superposition,[],[f615,f2809]) ).

fof(f2809,plain,
    b = add(b,inverse(d)),
    inference(forward_demodulation,[],[f2792,f13]) ).

fof(f13,axiom,
    ! [X0] : add(X0,additive_identity) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_id1) ).

fof(f2792,plain,
    add(b,additive_identity) = add(b,inverse(d)),
    inference(superposition,[],[f159,f2616]) ).

fof(f2616,plain,
    additive_identity = multiply(inverse(b),inverse(d)),
    inference(superposition,[],[f1827,f969]) ).

fof(f969,plain,
    inverse(b) = multiply(inverse(b),d),
    inference(superposition,[],[f619,f16]) ).

fof(f619,plain,
    ! [X0,X1] : multiply(X0,add(X1,X0)) = X0,
    inference(forward_demodulation,[],[f618,f329]) ).

fof(f329,plain,
    ! [X0,X1] : add(X1,multiply(X1,X0)) = X1,
    inference(superposition,[],[f316,f2]) ).

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

fof(f316,plain,
    ! [X0,X1] : add(X0,multiply(X1,X0)) = X0,
    inference(forward_demodulation,[],[f315,f12]) ).

fof(f315,plain,
    ! [X0,X1] : multiply(multiplicative_identity,X0) = add(X0,multiply(X1,X0)),
    inference(forward_demodulation,[],[f287,f99]) ).

fof(f99,plain,
    ! [X0] : multiplicative_identity = add(multiplicative_identity,X0),
    inference(forward_demodulation,[],[f86,f8]) ).

fof(f8,axiom,
    ! [X0] : multiplicative_identity = add(inverse(X0),X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse2) ).

fof(f86,plain,
    ! [X0] : add(inverse(X0),X0) = add(multiplicative_identity,X0),
    inference(superposition,[],[f78,f11]) ).

fof(f11,axiom,
    ! [X0] : multiply(X0,multiplicative_identity) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_id1) ).

fof(f78,plain,
    ! [X0,X1] : add(X1,X0) = add(multiply(inverse(X0),X1),X0),
    inference(forward_demodulation,[],[f63,f12]) ).

fof(f63,plain,
    ! [X0,X1] : add(multiply(inverse(X0),X1),X0) = multiply(multiplicative_identity,add(X1,X0)),
    inference(superposition,[],[f3,f8]) ).

fof(f3,axiom,
    ! [X2,X0,X1] : add(multiply(X0,X1),X2) = multiply(add(X0,X2),add(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).

fof(f287,plain,
    ! [X0,X1] : add(X0,multiply(X1,X0)) = multiply(add(multiplicative_identity,X1),X0),
    inference(superposition,[],[f5,f12]) ).

fof(f5,axiom,
    ! [X2,X0,X1] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity3) ).

fof(f618,plain,
    ! [X0,X1] : multiply(X0,add(X1,X0)) = add(X0,multiply(X0,X1)),
    inference(forward_demodulation,[],[f607,f1]) ).

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

fof(f607,plain,
    ! [X0,X1] : multiply(X0,add(X1,X0)) = add(multiply(X0,X1),X0),
    inference(superposition,[],[f6,f579]) ).

fof(f579,plain,
    ! [X0] : multiply(X0,X0) = X0,
    inference(forward_demodulation,[],[f545,f12]) ).

fof(f545,plain,
    ! [X0] : multiply(multiplicative_identity,X0) = multiply(X0,X0),
    inference(superposition,[],[f314,f8]) ).

fof(f314,plain,
    ! [X0,X1] : multiply(X1,X0) = multiply(add(inverse(X0),X1),X0),
    inference(forward_demodulation,[],[f286,f14]) ).

fof(f14,axiom,
    ! [X0] : add(additive_identity,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_id2) ).

fof(f286,plain,
    ! [X0,X1] : add(additive_identity,multiply(X1,X0)) = multiply(add(inverse(X0),X1),X0),
    inference(superposition,[],[f5,f10]) ).

fof(f10,axiom,
    ! [X0] : additive_identity = multiply(inverse(X0),X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse2) ).

fof(f6,axiom,
    ! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity4) ).

fof(f1827,plain,
    ! [X0,X1] : additive_identity = multiply(multiply(X1,X0),inverse(X0)),
    inference(superposition,[],[f584,f644]) ).

fof(f644,plain,
    ! [X0] : inverse(inverse(X0)) = X0,
    inference(forward_demodulation,[],[f633,f100]) ).

fof(f100,plain,
    ! [X0] : add(inverse(inverse(X0)),X0) = X0,
    inference(forward_demodulation,[],[f87,f14]) ).

fof(f87,plain,
    ! [X0] : add(additive_identity,X0) = add(inverse(inverse(X0)),X0),
    inference(superposition,[],[f78,f9]) ).

fof(f9,axiom,
    ! [X0] : multiply(X0,inverse(X0)) = additive_identity,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse1) ).

fof(f633,plain,
    ! [X0] : inverse(inverse(X0)) = add(inverse(inverse(X0)),X0),
    inference(superposition,[],[f329,f587]) ).

fof(f587,plain,
    ! [X0] : multiply(inverse(inverse(X0)),X0) = X0,
    inference(forward_demodulation,[],[f553,f12]) ).

fof(f553,plain,
    ! [X0] : multiply(multiplicative_identity,X0) = multiply(inverse(inverse(X0)),X0),
    inference(superposition,[],[f314,f7]) ).

fof(f7,axiom,
    ! [X0] : add(X0,inverse(X0)) = multiplicative_identity,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse1) ).

fof(f584,plain,
    ! [X0,X1] : additive_identity = multiply(multiply(X1,inverse(X0)),X0),
    inference(forward_demodulation,[],[f583,f9]) ).

fof(f583,plain,
    ! [X0,X1] : multiply(X0,inverse(X0)) = multiply(multiply(X1,inverse(X0)),X0),
    inference(forward_demodulation,[],[f551,f2]) ).

fof(f551,plain,
    ! [X0,X1] : multiply(inverse(X0),X0) = multiply(multiply(X1,inverse(X0)),X0),
    inference(superposition,[],[f314,f316]) ).

fof(f159,plain,
    ! [X0,X1] : add(X0,X1) = add(X0,multiply(inverse(X0),X1)),
    inference(forward_demodulation,[],[f134,f12]) ).

fof(f134,plain,
    ! [X0,X1] : add(X0,multiply(inverse(X0),X1)) = multiply(multiplicative_identity,add(X0,X1)),
    inference(superposition,[],[f4,f7]) ).

fof(f4,axiom,
    ! [X2,X0,X1] : add(X0,multiply(X1,X2)) = multiply(add(X0,X1),add(X0,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).

fof(f615,plain,
    ! [X0,X1] : multiply(add(X1,X0),X0) = X0,
    inference(forward_demodulation,[],[f614,f316]) ).

fof(f614,plain,
    ! [X0,X1] : multiply(add(X1,X0),X0) = add(X0,multiply(X1,X0)),
    inference(forward_demodulation,[],[f604,f1]) ).

fof(f604,plain,
    ! [X0,X1] : multiply(add(X1,X0),X0) = add(multiply(X1,X0),X0),
    inference(superposition,[],[f5,f579]) ).

fof(f2763,plain,
    c = add(c,multiply(b,inverse(d))),
    inference(forward_demodulation,[],[f2762,f15]) ).

fof(f15,axiom,
    multiply(a,b) = c,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).

fof(f2762,plain,
    multiply(a,b) = add(c,multiply(b,inverse(d))),
    inference(forward_demodulation,[],[f2751,f2]) ).

fof(f2751,plain,
    multiply(a,b) = add(c,multiply(inverse(d),b)),
    inference(superposition,[],[f288,f2737]) ).

fof(f2737,plain,
    a = add(a,inverse(d)),
    inference(forward_demodulation,[],[f2720,f13]) ).

fof(f2720,plain,
    add(a,additive_identity) = add(a,inverse(d)),
    inference(superposition,[],[f159,f2615]) ).

fof(f2615,plain,
    additive_identity = multiply(inverse(a),inverse(d)),
    inference(superposition,[],[f1827,f888]) ).

fof(f888,plain,
    inverse(a) = multiply(inverse(a),d),
    inference(superposition,[],[f617,f16]) ).

fof(f617,plain,
    ! [X0,X1] : multiply(X0,add(X0,X1)) = X0,
    inference(forward_demodulation,[],[f606,f329]) ).

fof(f606,plain,
    ! [X0,X1] : add(X0,multiply(X0,X1)) = multiply(X0,add(X0,X1)),
    inference(superposition,[],[f6,f579]) ).

fof(f288,plain,
    ! [X0] : multiply(add(a,X0),b) = add(c,multiply(X0,b)),
    inference(superposition,[],[f5,f15]) ).

fof(f787,plain,
    ! [X0,X1] : multiplicative_identity = add(add(X0,inverse(X1)),X1),
    inference(forward_demodulation,[],[f786,f7]) ).

fof(f786,plain,
    ! [X0,X1] : add(X1,inverse(X1)) = add(add(X0,inverse(X1)),X1),
    inference(forward_demodulation,[],[f775,f1]) ).

fof(f775,plain,
    ! [X0,X1] : add(add(X0,inverse(X1)),X1) = add(inverse(X1),X1),
    inference(superposition,[],[f81,f615]) ).

fof(f81,plain,
    ! [X0,X1] : add(X1,X0) = add(multiply(X1,inverse(X0)),X0),
    inference(forward_demodulation,[],[f70,f11]) ).

fof(f70,plain,
    ! [X0,X1] : add(multiply(X1,inverse(X0)),X0) = multiply(add(X1,X0),multiplicative_identity),
    inference(superposition,[],[f3,f8]) ).

fof(f313,plain,
    ! [X0,X1] : multiply(X1,inverse(X0)) = multiply(add(X0,X1),inverse(X0)),
    inference(forward_demodulation,[],[f281,f14]) ).

fof(f281,plain,
    ! [X0,X1] : multiply(add(X0,X1),inverse(X0)) = add(additive_identity,multiply(X1,inverse(X0))),
    inference(superposition,[],[f5,f9]) ).

fof(f16648,plain,
    add(inverse(a),inverse(b)) = multiply(d,inverse(c)),
    inference(forward_demodulation,[],[f16647,f2691]) ).

fof(f2691,plain,
    inverse(c) = add(inverse(b),inverse(c)),
    inference(forward_demodulation,[],[f2678,f14]) ).

fof(f2678,plain,
    add(inverse(b),inverse(c)) = add(additive_identity,inverse(c)),
    inference(superposition,[],[f77,f2623]) ).

fof(f2623,plain,
    additive_identity = multiply(c,inverse(b)),
    inference(superposition,[],[f1827,f15]) ).

fof(f77,plain,
    ! [X0,X1] : add(multiply(X0,X1),inverse(X0)) = add(X1,inverse(X0)),
    inference(forward_demodulation,[],[f59,f12]) ).

fof(f59,plain,
    ! [X0,X1] : add(multiply(X0,X1),inverse(X0)) = multiply(multiplicative_identity,add(X1,inverse(X0))),
    inference(superposition,[],[f3,f7]) ).

fof(f16647,plain,
    add(inverse(a),inverse(b)) = multiply(d,add(inverse(b),inverse(c))),
    inference(forward_demodulation,[],[f16569,f1]) ).

fof(f16569,plain,
    add(inverse(a),inverse(b)) = multiply(d,add(inverse(c),inverse(b))),
    inference(superposition,[],[f64,f5313]) ).

fof(f5313,plain,
    inverse(a) = multiply(inverse(a),inverse(c)),
    inference(forward_demodulation,[],[f5232,f11]) ).

fof(f5232,plain,
    multiply(inverse(a),inverse(c)) = multiply(inverse(a),multiplicative_identity),
    inference(superposition,[],[f474,f2159]) ).

fof(f2159,plain,
    multiplicative_identity = add(a,inverse(c)),
    inference(forward_demodulation,[],[f2101,f7]) ).

fof(f2101,plain,
    add(a,inverse(c)) = add(c,inverse(c)),
    inference(superposition,[],[f77,f894]) ).

fof(f894,plain,
    c = multiply(c,a),
    inference(superposition,[],[f617,f514]) ).

fof(f514,plain,
    a = add(c,a),
    inference(superposition,[],[f479,f15]) ).

fof(f479,plain,
    ! [X0,X1] : add(multiply(X0,X1),X0) = X0,
    inference(forward_demodulation,[],[f478,f11]) ).

fof(f478,plain,
    ! [X0,X1] : multiply(X0,multiplicative_identity) = add(multiply(X0,X1),X0),
    inference(forward_demodulation,[],[f442,f111]) ).

fof(f111,plain,
    ! [X0] : multiplicative_identity = add(X0,multiplicative_identity),
    inference(superposition,[],[f99,f1]) ).

fof(f442,plain,
    ! [X0,X1] : add(multiply(X0,X1),X0) = multiply(X0,add(X1,multiplicative_identity)),
    inference(superposition,[],[f6,f11]) ).

fof(f474,plain,
    ! [X0,X1] : multiply(inverse(X0),X1) = multiply(inverse(X0),add(X0,X1)),
    inference(forward_demodulation,[],[f435,f14]) ).

fof(f435,plain,
    ! [X0,X1] : multiply(inverse(X0),add(X0,X1)) = add(additive_identity,multiply(inverse(X0),X1)),
    inference(superposition,[],[f6,f10]) ).

fof(f64,plain,
    ! [X0] : add(multiply(inverse(a),X0),inverse(b)) = multiply(d,add(X0,inverse(b))),
    inference(superposition,[],[f3,f16]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : BOO015-2 : TPTP v8.2.0. Bugfixed v1.0.1.
% 0.04/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.37  % Computer : n027.cluster.edu
% 0.14/0.37  % Model    : x86_64 x86_64
% 0.14/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37  % Memory   : 8042.1875MB
% 0.14/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37  % CPULimit   : 300
% 0.14/0.38  % WCLimit    : 300
% 0.14/0.38  % DateTime   : Sat May 18 14:37:53 EDT 2024
% 0.14/0.38  % CPUTime    : 
% 0.14/0.38  % (1099)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.39  % (1102)WARNING: value z3 for option sas not known
% 0.14/0.40  % (1103)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.40  % (1100)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.40  % (1101)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.40  % (1105)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)
% 0.14/0.40  % (1104)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)
% 0.14/0.40  % (1102)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)
% 0.14/0.40  % (1106)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)
% 0.14/0.40  TRYING [1]
% 0.14/0.40  TRYING [2]
% 0.14/0.40  TRYING [3]
% 0.14/0.40  TRYING [1]
% 0.14/0.40  TRYING [2]
% 0.14/0.41  TRYING [3]
% 0.14/0.42  TRYING [4]
% 0.14/0.45  TRYING [4]
% 0.23/0.47  TRYING [5]
% 1.41/0.61  TRYING [6]
% 1.41/0.63  TRYING [5]
% 2.76/0.79  % (1102)First to succeed.
% 2.76/0.79  % (1102)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1099"
% 2.76/0.80  % (1102)Refutation found. Thanks to Tanya!
% 2.76/0.80  % SZS status Unsatisfiable for theBenchmark
% 2.76/0.80  % SZS output start Proof for theBenchmark
% See solution above
% 2.76/0.80  % (1102)------------------------------
% 2.76/0.80  % (1102)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.76/0.80  % (1102)Termination reason: Refutation
% 2.76/0.80  
% 2.76/0.80  % (1102)Memory used [KB]: 5515
% 2.76/0.80  % (1102)Time elapsed: 0.400 s
% 2.76/0.80  % (1102)Instructions burned: 857 (million)
% 2.76/0.80  % (1099)Success in time 0.405 s
%------------------------------------------------------------------------------