TSTP Solution File: CAT003-1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : CAT003-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n002.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 : Sun May  5 04:43:42 EDT 2024

% Result   : Unsatisfiable 3.52s 0.87s
% Output   : Refutation 3.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   49 (  31 unt;   0 def)
%            Number of atoms       :   84 (   6 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   79 (  44   ~;  32   |;   0   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-4 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   74 (  74   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f44567,plain,
    $false,
    inference(subsumption_resolution,[],[f44566,f33420]) ).

fof(f33420,plain,
    ~ sP4(compose(h,c),c,d,a),
    inference(forward_demodulation,[],[f33403,f4605]) ).

fof(f4605,plain,
    d = compose(h,a),
    inference(unit_resulting_resolution,[],[f21,f69,f18]) ).

fof(f18,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ product(X0,X1,X6)
      | X2 = X6
      | ~ product(X0,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_is_well_defined) ).

fof(f69,plain,
    product(h,a,compose(h,a)),
    inference(unit_resulting_resolution,[],[f39,f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( ~ defined(X0,X1)
      | product(X0,X1,compose(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_composition) ).

fof(f39,plain,
    defined(h,a),
    inference(unit_resulting_resolution,[],[f21,f2]) ).

fof(f2,axiom,
    ! [X2,X0,X1] :
      ( ~ product(X0,X1,X2)
      | defined(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_property1) ).

fof(f21,axiom,
    product(h,a,d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ha_equals_d) ).

fof(f33403,plain,
    ~ sP4(compose(h,c),c,compose(h,a),a),
    inference(unit_resulting_resolution,[],[f69,f2926,f33]) ).

fof(f33,plain,
    ! [X3,X0,X1,X4,X5] :
      ( ~ sP4(X5,X4,X3,X1)
      | ~ product(X0,X4,X5)
      | ~ product(X0,X1,X3) ),
    inference(general_splitting,[],[f8,f32_D]) ).

fof(f32,plain,
    ! [X2,X3,X1,X4,X5] :
      ( ~ product(X1,X2,X4)
      | product(X3,X2,X5)
      | sP4(X5,X4,X3,X1) ),
    inference(cnf_transformation,[],[f32_D]) ).

fof(f32_D,plain,
    ! [X1,X3,X4,X5] :
      ( ! [X2] :
          ( ~ product(X1,X2,X4)
          | product(X3,X2,X5) )
    <=> ~ sP4(X5,X4,X3,X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP4])]) ).

fof(f8,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ product(X1,X2,X4)
      | ~ product(X0,X1,X3)
      | ~ product(X0,X4,X5)
      | product(X3,X2,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',category_theory_axiom5) ).

fof(f2926,plain,
    product(h,c,compose(h,c)),
    inference(unit_resulting_resolution,[],[f2466,f1]) ).

fof(f2466,plain,
    defined(h,c),
    inference(unit_resulting_resolution,[],[f678,f11,f13,f9]) ).

fof(f9,axiom,
    ! [X2,X0,X1] :
      ( ~ defined(X1,X2)
      | ~ identity_map(X1)
      | ~ defined(X0,X1)
      | defined(X0,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',category_theory_axiom6) ).

fof(f13,axiom,
    ! [X0] : defined(codomain(X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mapping_from_codomain_of_x_to_x) ).

fof(f11,axiom,
    ! [X0] : identity_map(codomain(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_is_an_identity_map) ).

fof(f678,plain,
    defined(h,codomain(c)),
    inference(unit_resulting_resolution,[],[f39,f664,f27]) ).

fof(f27,plain,
    ! [X0,X1,X4] :
      ( ~ sP1(X4,X1)
      | defined(X0,X1)
      | ~ defined(X0,X4) ),
    inference(general_splitting,[],[f6,f26_D]) ).

fof(f26,plain,
    ! [X2,X1,X4] :
      ( ~ product(X1,X2,X4)
      | sP1(X4,X1) ),
    inference(cnf_transformation,[],[f26_D]) ).

fof(f26_D,plain,
    ! [X1,X4] :
      ( ! [X2] : ~ product(X1,X2,X4)
    <=> ~ sP1(X4,X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP1])]) ).

fof(f6,axiom,
    ! [X2,X0,X1,X4] :
      ( ~ defined(X0,X4)
      | defined(X0,X1)
      | ~ product(X1,X2,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',category_theory_axiom3) ).

fof(f664,plain,
    sP1(a,codomain(c)),
    inference(unit_resulting_resolution,[],[f345,f26]) ).

fof(f345,plain,
    product(codomain(c),a,a),
    inference(unit_resulting_resolution,[],[f11,f295,f16]) ).

fof(f16,axiom,
    ! [X0,X1] :
      ( ~ defined(X0,X1)
      | ~ identity_map(X0)
      | product(X0,X1,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity1) ).

fof(f295,plain,
    defined(codomain(c),a),
    inference(unit_resulting_resolution,[],[f13,f58,f27]) ).

fof(f58,plain,
    sP1(c,a),
    inference(unit_resulting_resolution,[],[f19,f26]) ).

fof(f19,axiom,
    product(a,b,c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_equals_c) ).

fof(f44566,plain,
    sP4(compose(h,c),c,d,a),
    inference(forward_demodulation,[],[f44564,f4597]) ).

fof(f4597,plain,
    c = compose(a,b),
    inference(unit_resulting_resolution,[],[f19,f68,f18]) ).

fof(f68,plain,
    product(a,b,compose(a,b)),
    inference(unit_resulting_resolution,[],[f38,f1]) ).

fof(f38,plain,
    defined(a,b),
    inference(unit_resulting_resolution,[],[f19,f2]) ).

fof(f44564,plain,
    sP4(compose(h,c),compose(a,b),d,a),
    inference(unit_resulting_resolution,[],[f68,f44541,f32]) ).

fof(f44541,plain,
    ~ product(d,b,compose(h,c)),
    inference(unit_resulting_resolution,[],[f19,f39393,f34]) ).

fof(f34,plain,
    ! [X2,X3,X1,X4,X5] :
      ( ~ product(X1,X2,X4)
      | ~ product(X3,X2,X5)
      | sP5(X5,X4,X3,X1) ),
    inference(cnf_transformation,[],[f34_D]) ).

fof(f34_D,plain,
    ! [X1,X3,X4,X5] :
      ( ! [X2] :
          ( ~ product(X1,X2,X4)
          | ~ product(X3,X2,X5) )
    <=> ~ sP5(X5,X4,X3,X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP5])]) ).

fof(f39393,plain,
    ~ sP5(compose(h,c),c,d,a),
    inference(forward_demodulation,[],[f39229,f4617]) ).

fof(f4617,plain,
    d = compose(g,a),
    inference(unit_resulting_resolution,[],[f22,f70,f18]) ).

fof(f70,plain,
    product(g,a,compose(g,a)),
    inference(unit_resulting_resolution,[],[f40,f1]) ).

fof(f40,plain,
    defined(g,a),
    inference(unit_resulting_resolution,[],[f22,f2]) ).

fof(f22,axiom,
    product(g,a,d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ga_equals_d) ).

fof(f39229,plain,
    ~ sP5(compose(h,c),c,compose(g,a),a),
    inference(unit_resulting_resolution,[],[f70,f33322,f35]) ).

fof(f35,plain,
    ! [X3,X0,X1,X4,X5] :
      ( ~ sP5(X5,X4,X3,X1)
      | product(X0,X4,X5)
      | ~ product(X0,X1,X3) ),
    inference(general_splitting,[],[f5,f34_D]) ).

fof(f5,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ product(X0,X1,X3)
      | ~ product(X1,X2,X4)
      | ~ product(X3,X2,X5)
      | product(X0,X4,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',category_theory_axiom2) ).

fof(f33322,plain,
    ~ product(g,c,compose(h,c)),
    inference(unit_resulting_resolution,[],[f23,f2926,f20]) ).

fof(f20,axiom,
    ! [X0,X1,X6] :
      ( ~ product(X1,c,X6)
      | X0 = X1
      | ~ product(X0,c,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation_for_product) ).

fof(f23,axiom,
    h != g,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_h_equals_g) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : CAT003-1 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.34  % Computer : n002.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Fri May  3 18:11:07 EDT 2024
% 0.12/0.35  % CPUTime    : 
% 0.12/0.35  % (16966)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.36  % (16970)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.18/0.36  % (16969)WARNING: value z3 for option sas not known
% 0.18/0.36  % (16971)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)
% 0.18/0.36  % (16968)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.18/0.36  % (16972)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)
% 0.18/0.36  TRYING [1]
% 0.18/0.36  % (16973)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)
% 0.18/0.36  TRYING [2]
% 0.18/0.36  % (16969)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)
% 0.18/0.37  TRYING [3]
% 0.18/0.37  % (16967)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.18/0.37  TRYING [4]
% 0.18/0.37  TRYING [1]
% 0.18/0.37  TRYING [2]
% 0.18/0.38  TRYING [5]
% 0.18/0.38  TRYING [3]
% 0.18/0.41  TRYING [4]
% 0.18/0.41  TRYING [6]
% 0.18/0.46  TRYING [5]
% 0.18/0.50  TRYING [7]
% 1.67/0.62  TRYING [6]
% 2.65/0.72  TRYING [8]
% 3.52/0.87  % (16973)First to succeed.
% 3.52/0.87  % (16973)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-16966"
% 3.52/0.87  % (16973)Refutation found. Thanks to Tanya!
% 3.52/0.87  % SZS status Unsatisfiable for theBenchmark
% 3.52/0.87  % SZS output start Proof for theBenchmark
% See solution above
% 3.52/0.87  % (16973)------------------------------
% 3.52/0.87  % (16973)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 3.52/0.87  % (16973)Termination reason: Refutation
% 3.52/0.87  
% 3.52/0.87  % (16973)Memory used [KB]: 6277
% 3.52/0.87  % (16973)Time elapsed: 0.506 s
% 3.52/0.87  % (16973)Instructions burned: 1075 (million)
% 3.52/0.87  % (16966)Success in time 0.517 s
%------------------------------------------------------------------------------