TSTP Solution File: COL076-1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : COL076-1 : TPTP v8.2.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n018.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 19:06:21 EDT 2024

% Result   : Unsatisfiable 138.02s 20.09s
% Output   : Refutation 138.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   31
%            Number of leaves      :   11
% Syntax   : Number of formulae    :  119 ( 114 unt;   0 def)
%            Number of atoms       :  124 ( 123 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   16 (  11   ~;   5   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    8 (   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   :  192 ( 192   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f618254,plain,
    $false,
    inference(unit_resulting_resolution,[],[f1133,f618227]) ).

fof(f618227,plain,
    ! [X0] : apply(X0,pair(X0,projection2)) != apply(eq,apply(f,pair(X0,projection2))),
    inference(forward_demodulation,[],[f617381,f3232]) ).

fof(f3232,plain,
    ! [X0,X1] : apply(f,X0) = apply(k,apply(apply(f,X0),X1)),
    inference(forward_demodulation,[],[f3168,f771]) ).

fof(f771,plain,
    ! [X0] : apply(f,X0) = apply(f,apply(f,X0)),
    inference(unit_resulting_resolution,[],[f44,f9]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( apply(X0,n(X0,X1)) != apply(X1,n(X0,X1))
      | X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality2) ).

fof(f44,plain,
    ! [X2,X0,X1] : apply(apply(f,X0),X1) = apply(apply(f,apply(f,X0)),X2),
    inference(superposition,[],[f15,f11]) ).

fof(f11,axiom,
    ! [X0,X1] : apply(apply(f,X0),X1) = apply(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagonal_combinator) ).

fof(f15,plain,
    ! [X0,X1] : apply(X0,X0) = apply(apply(f,apply(f,X0)),X1),
    inference(superposition,[],[f11,f11]) ).

fof(f3168,plain,
    ! [X0,X1] : apply(f,apply(f,X0)) = apply(k,apply(apply(f,X0),X1)),
    inference(unit_resulting_resolution,[],[f44,f772]) ).

fof(f772,plain,
    ! [X0,X1] :
      ( apply(X1,n(apply(k,X0),X1)) != X0
      | apply(k,X0) = X1 ),
    inference(superposition,[],[f9,f1]) ).

fof(f1,axiom,
    ! [X0,X1] : apply(apply(k,X0),X1) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).

fof(f617381,plain,
    ! [X0,X1] : apply(X0,pair(X0,projection2)) != apply(eq,apply(k,apply(apply(f,pair(X0,projection2)),X1))),
    inference(superposition,[],[f420142,f593903]) ).

fof(f593903,plain,
    ! [X0,X1] : apply(apply(f,pair(X0,projection2)),X1) = pair(apply(X0,pair(X0,projection2)),projection2),
    inference(forward_demodulation,[],[f593902,f591246]) ).

fof(f591246,plain,
    ! [X0] : apply(f,pair(X0,projection2)) = apply(f,apply(pair(apply(projection1,f),projection2),pair(X0,projection2))),
    inference(forward_demodulation,[],[f591245,f3234]) ).

fof(f3234,plain,
    ! [X0] : apply(f,X0) = apply(k,apply(X0,X0)),
    inference(forward_demodulation,[],[f3233,f771]) ).

fof(f3233,plain,
    ! [X0] : apply(f,apply(f,X0)) = apply(k,apply(X0,X0)),
    inference(forward_demodulation,[],[f3166,f771]) ).

fof(f3166,plain,
    ! [X0] : apply(f,apply(f,apply(f,X0))) = apply(k,apply(X0,X0)),
    inference(unit_resulting_resolution,[],[f46,f772]) ).

fof(f46,plain,
    ! [X0,X1] : apply(X0,X0) = apply(apply(f,apply(f,apply(f,X0))),X1),
    inference(superposition,[],[f15,f11]) ).

fof(f591245,plain,
    ! [X0] : apply(k,apply(pair(X0,projection2),pair(X0,projection2))) = apply(f,apply(pair(apply(projection1,f),projection2),pair(X0,projection2))),
    inference(forward_demodulation,[],[f591244,f132]) ).

fof(f132,plain,
    ! [X2,X0,X1] : apply(pair(X2,projection2),pair(X0,X1)) = pair(apply(X2,pair(X0,X1)),X1),
    inference(superposition,[],[f5,f3]) ).

fof(f3,axiom,
    ! [X0,X1] : apply(projection2,pair(X0,X1)) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',projection2) ).

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

fof(f591244,plain,
    ! [X0] : apply(k,pair(apply(X0,pair(X0,projection2)),projection2)) = apply(f,apply(pair(apply(projection1,f),projection2),pair(X0,projection2))),
    inference(forward_demodulation,[],[f590954,f118086]) ).

fof(f118086,plain,
    ! [X2,X0,X1] : apply(pair(apply(projection1,X0),projection2),pair(X1,X2)) = pair(apply(projection1,apply(X0,pair(X1,X2))),X2),
    inference(superposition,[],[f132,f183]) ).

fof(f183,plain,
    ! [X0,X1] : apply(apply(projection1,X0),X1) = apply(projection1,apply(X0,X1)),
    inference(superposition,[],[f143,f4]) ).

fof(f4,axiom,
    ! [X0] : pair(apply(projection1,X0),apply(projection2,X0)) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pairing) ).

fof(f143,plain,
    ! [X2,X0,X1] : apply(X0,X1) = apply(projection1,apply(pair(X0,X2),X1)),
    inference(superposition,[],[f2,f5]) ).

fof(f2,axiom,
    ! [X0,X1] : apply(projection1,pair(X0,X1)) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',projection1) ).

fof(f590954,plain,
    ! [X0] : apply(k,pair(apply(X0,pair(X0,projection2)),projection2)) = apply(f,pair(apply(projection1,apply(f,pair(X0,projection2))),projection2)),
    inference(superposition,[],[f121188,f465390]) ).

fof(f465390,plain,
    ! [X0] : apply(projection1,apply(f,pair(X0,projection2))) = apply(k,apply(X0,pair(X0,projection2))),
    inference(forward_demodulation,[],[f464909,f53945]) ).

fof(f53945,plain,
    ! [X0,X1] : pair(X1,X0) = apply(pair(projection2,projection1),pair(X0,X1)),
    inference(superposition,[],[f116,f2]) ).

fof(f116,plain,
    ! [X2,X0,X1] : apply(pair(projection2,X2),pair(X0,X1)) = pair(X1,apply(X2,pair(X0,X1))),
    inference(superposition,[],[f5,f3]) ).

fof(f464909,plain,
    ! [X0] : apply(projection1,apply(f,apply(pair(projection2,projection1),pair(projection2,X0)))) = apply(k,apply(X0,apply(pair(projection2,projection1),pair(projection2,X0)))),
    inference(superposition,[],[f353863,f14442]) ).

fof(f14442,plain,
    ! [X0,X1] : apply(X0,X1) = apply(projection1,apply(apply(pair(projection2,projection1),pair(projection2,X0)),X1)),
    inference(superposition,[],[f183,f14258]) ).

fof(f14258,plain,
    ! [X0] : apply(projection1,apply(pair(projection2,projection1),pair(projection2,X0))) = X0,
    inference(superposition,[],[f8978,f1]) ).

fof(f8978,plain,
    ! [X0] : apply(X0,X0) = apply(projection1,apply(pair(projection2,projection1),pair(projection2,apply(X0,X0)))),
    inference(forward_demodulation,[],[f8870,f131]) ).

fof(f131,plain,
    ! [X2,X0,X1] : apply(pair(X2,projection1),pair(X0,X1)) = pair(apply(X2,pair(X0,X1)),X0),
    inference(superposition,[],[f5,f2]) ).

fof(f8870,plain,
    ! [X0] : apply(X0,X0) = apply(projection1,pair(apply(projection2,pair(projection2,apply(X0,X0))),projection2)),
    inference(superposition,[],[f6927,f3094]) ).

fof(f3094,plain,
    ! [X0] : apply(apply(f,X0),n(projection1,projection2)) = apply(projection2,pair(projection2,apply(X0,X0))),
    inference(superposition,[],[f142,f1010]) ).

fof(f1010,plain,
    ! [X0] : apply(pair(eq,apply(f,X0)),n(projection1,projection2)) = pair(projection2,apply(X0,X0)),
    inference(superposition,[],[f879,f11]) ).

fof(f879,plain,
    ! [X0] : apply(pair(eq,X0),n(projection1,projection2)) = pair(projection2,apply(X0,n(projection1,projection2))),
    inference(superposition,[],[f5,f872]) ).

fof(f872,plain,
    projection2 = apply(eq,n(projection1,projection2)),
    inference(forward_demodulation,[],[f867,f4]) ).

fof(f867,plain,
    projection2 = apply(eq,pair(apply(projection1,n(projection1,projection2)),apply(projection2,n(projection1,projection2)))),
    inference(unit_resulting_resolution,[],[f811,f8]) ).

fof(f8,axiom,
    ! [X0,X1] :
      ( projection2 = apply(eq,pair(X0,X1))
      | X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality1) ).

fof(f811,plain,
    apply(projection1,n(projection1,projection2)) != apply(projection2,n(projection1,projection2)),
    inference(forward_demodulation,[],[f767,f144]) ).

fof(f144,plain,
    ! [X0,X1] : projection1 = apply(eq,apply(pair(X0,X0),X1)),
    inference(superposition,[],[f7,f5]) ).

fof(f7,axiom,
    ! [X0] : projection1 = apply(eq,pair(X0,X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality) ).

fof(f767,plain,
    apply(apply(eq,apply(pair(k,k),projection2)),n(apply(eq,apply(pair(k,k),projection2)),projection2)) != apply(projection2,n(apply(eq,apply(pair(k,k),projection2)),projection2)),
    inference(unit_resulting_resolution,[],[f140,f9]) ).

fof(f140,plain,
    projection2 != apply(eq,apply(pair(k,k),projection2)),
    inference(superposition,[],[f12,f5]) ).

fof(f12,axiom,
    ! [X1] : apply(eq,pair(apply(k,X1),apply(k,projection2))) != X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_self_referential) ).

fof(f142,plain,
    ! [X2,X0,X1] : apply(X2,X1) = apply(projection2,apply(pair(X0,X2),X1)),
    inference(superposition,[],[f3,f5]) ).

fof(f6927,plain,
    ! [X0,X1] : apply(X0,X0) = apply(projection1,pair(apply(apply(f,X0),X1),projection2)),
    inference(superposition,[],[f6685,f16]) ).

fof(f16,plain,
    ! [X2,X0,X1] : apply(apply(f,X0),X1) = apply(apply(f,X0),X2),
    inference(superposition,[],[f11,f11]) ).

fof(f6685,plain,
    ! [X0] : apply(X0,X0) = apply(projection1,pair(apply(apply(f,X0),projection2),projection2)),
    inference(forward_demodulation,[],[f6684,f152]) ).

fof(f152,plain,
    ! [X0,X1] : apply(pair(X1,pair(projection1,projection2)),X0) = pair(apply(X1,X0),X0),
    inference(superposition,[],[f5,f138]) ).

fof(f138,plain,
    ! [X0] : apply(pair(projection1,projection2),X0) = X0,
    inference(superposition,[],[f5,f4]) ).

fof(f6684,plain,
    ! [X0] : apply(X0,X0) = apply(projection1,apply(pair(apply(f,X0),pair(projection1,projection2)),projection2)),
    inference(forward_demodulation,[],[f6493,f399]) ).

fof(f399,plain,
    ! [X2,X0,X1] : apply(pair(apply(f,X0),pair(projection1,projection2)),X1) = pair(apply(apply(f,X0),X2),X1),
    inference(superposition,[],[f152,f16]) ).

fof(f6493,plain,
    ! [X0] : apply(X0,X0) = apply(projection1,pair(apply(apply(f,X0),apply(f,X0)),projection2)),
    inference(superposition,[],[f6296,f15]) ).

fof(f6296,plain,
    ! [X0,X1] : apply(apply(f,X0),X1) = apply(projection1,pair(apply(X0,X0),projection2)),
    inference(superposition,[],[f1095,f16]) ).

fof(f1095,plain,
    ! [X0] : apply(apply(f,X0),n(projection1,projection2)) = apply(projection1,pair(apply(X0,X0),projection2)),
    inference(superposition,[],[f143,f932]) ).

fof(f932,plain,
    ! [X0] : apply(pair(apply(f,X0),eq),n(projection1,projection2)) = pair(apply(X0,X0),projection2),
    inference(superposition,[],[f878,f11]) ).

fof(f878,plain,
    ! [X0] : apply(pair(X0,eq),n(projection1,projection2)) = pair(apply(X0,n(projection1,projection2)),projection2),
    inference(superposition,[],[f5,f872]) ).

fof(f353863,plain,
    ! [X0] : apply(projection1,apply(f,X0)) = apply(k,apply(projection1,apply(X0,X0))),
    inference(superposition,[],[f352537,f3234]) ).

fof(f352537,plain,
    ! [X0] : apply(projection1,apply(k,X0)) = apply(k,apply(projection1,X0)),
    inference(unit_resulting_resolution,[],[f352422,f791]) ).

fof(f791,plain,
    ! [X0,X1] :
      ( apply(X1,n(X1,apply(k,X0))) != X0
      | apply(k,X0) = X1 ),
    inference(superposition,[],[f9,f1]) ).

fof(f352422,plain,
    ! [X0,X1] : apply(projection1,X1) = apply(apply(projection1,apply(k,X1)),X0),
    inference(forward_demodulation,[],[f352070,f1]) ).

fof(f352070,plain,
    ! [X0,X1] : apply(apply(projection1,apply(k,X1)),X0) = apply(apply(apply(k,projection1),apply(k,X0)),X1),
    inference(superposition,[],[f1156,f3169]) ).

fof(f3169,plain,
    apply(k,projection1) = apply(abstraction,projection1),
    inference(unit_resulting_resolution,[],[f1387,f772]) ).

fof(f1387,plain,
    ! [X0] : projection1 = apply(apply(abstraction,projection1),X0),
    inference(unit_resulting_resolution,[],[f1266,f9]) ).

fof(f1266,plain,
    ! [X0,X1] : apply(projection1,X0) = apply(apply(apply(abstraction,projection1),X1),X0),
    inference(forward_demodulation,[],[f1215,f1]) ).

fof(f1215,plain,
    ! [X0,X1] : apply(projection1,apply(apply(k,X0),apply(X1,X0))) = apply(apply(apply(abstraction,projection1),X1),X0),
    inference(superposition,[],[f6,f183]) ).

fof(f6,axiom,
    ! [X2,X0,X1] : apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,apply(k,X2)),apply(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstraction) ).

fof(f1156,plain,
    ! [X2,X0,X1] : apply(apply(apply(abstraction,X2),apply(k,X0)),X1) = apply(apply(X2,apply(k,X1)),X0),
    inference(superposition,[],[f6,f1]) ).

fof(f121188,plain,
    ! [X0] : apply(k,pair(X0,projection2)) = apply(f,pair(apply(k,X0),projection2)),
    inference(unit_resulting_resolution,[],[f118073,f3206]) ).

fof(f3206,plain,
    ! [X0,X1] :
      ( apply(X0,X0) != X1
      | apply(f,X0) = apply(k,X1) ),
    inference(superposition,[],[f772,f11]) ).

fof(f118073,plain,
    ! [X2,X0,X1] : pair(X0,X2) = apply(pair(apply(k,X0),projection2),pair(X1,X2)),
    inference(superposition,[],[f132,f1]) ).

fof(f593902,plain,
    ! [X0,X1] : pair(apply(X0,pair(X0,projection2)),projection2) = apply(apply(f,apply(pair(apply(projection1,f),projection2),pair(X0,projection2))),X1),
    inference(forward_demodulation,[],[f593901,f118086]) ).

fof(f593901,plain,
    ! [X0,X1] : pair(apply(X0,pair(X0,projection2)),projection2) = apply(apply(f,pair(apply(projection1,apply(f,pair(X0,projection2))),projection2)),X1),
    inference(forward_demodulation,[],[f592692,f397797]) ).

fof(f397797,plain,
    ! [X0] : apply(projection1,apply(f,X0)) = apply(f,apply(projection1,apply(f,X0))),
    inference(forward_demodulation,[],[f397567,f353863]) ).

fof(f397567,plain,
    ! [X0] : apply(k,apply(projection1,apply(X0,X0))) = apply(f,apply(projection1,apply(f,X0))),
    inference(superposition,[],[f352541,f3234]) ).

fof(f352541,plain,
    ! [X0] : apply(k,apply(projection1,X0)) = apply(f,apply(projection1,apply(k,X0))),
    inference(unit_resulting_resolution,[],[f352422,f3206]) ).

fof(f592692,plain,
    ! [X0,X1] : pair(apply(X0,pair(X0,projection2)),projection2) = apply(apply(f,pair(apply(f,apply(projection1,apply(f,pair(X0,projection2)))),projection2)),X1),
    inference(superposition,[],[f540490,f398904]) ).

fof(f398904,plain,
    ! [X0,X1] : apply(X0,pair(X0,projection2)) = apply(apply(projection1,apply(f,pair(X0,projection2))),X1),
    inference(forward_demodulation,[],[f398218,f53945]) ).

fof(f398218,plain,
    ! [X0,X1] : apply(X0,apply(pair(projection2,projection1),pair(projection2,X0))) = apply(apply(projection1,apply(f,apply(pair(projection2,projection1),pair(projection2,X0)))),X1),
    inference(superposition,[],[f352552,f14442]) ).

fof(f352552,plain,
    ! [X0,X1] : apply(projection1,apply(X0,X0)) = apply(apply(projection1,apply(f,X0)),X1),
    inference(superposition,[],[f352422,f3234]) ).

fof(f540490,plain,
    ! [X0,X1] : pair(apply(X0,X0),projection2) = apply(apply(f,pair(apply(f,X0),projection2)),X1),
    inference(forward_demodulation,[],[f540489,f771]) ).

fof(f540489,plain,
    ! [X0,X1] : pair(apply(X0,X0),projection2) = apply(apply(f,apply(f,pair(apply(f,X0),projection2))),X1),
    inference(forward_demodulation,[],[f539936,f420337]) ).

fof(f420337,plain,
    ! [X0] : pair(apply(f,X0),apply(k,projection2)) = apply(f,pair(apply(f,X0),projection2)),
    inference(forward_demodulation,[],[f420026,f121901]) ).

fof(f121901,plain,
    ! [X0,X1] : apply(k,pair(apply(apply(f,X0),X1),projection2)) = apply(f,pair(apply(f,X0),projection2)),
    inference(superposition,[],[f121188,f3232]) ).

fof(f420026,plain,
    ! [X0,X1] : pair(apply(f,X0),apply(k,projection2)) = apply(k,pair(apply(apply(f,X0),X1),projection2)),
    inference(superposition,[],[f418203,f3232]) ).

fof(f418203,plain,
    ! [X0] : pair(apply(k,X0),apply(k,projection2)) = apply(k,pair(X0,projection2)),
    inference(forward_demodulation,[],[f418202,f2]) ).

fof(f418202,plain,
    ! [X0] : apply(k,pair(X0,projection2)) = pair(apply(k,apply(projection1,pair(X0,projection2))),apply(k,projection2)),
    inference(forward_demodulation,[],[f418149,f352537]) ).

fof(f418149,plain,
    ! [X0] : apply(k,pair(X0,projection2)) = pair(apply(projection1,apply(k,pair(X0,projection2))),apply(k,projection2)),
    inference(superposition,[],[f4,f417832]) ).

fof(f417832,plain,
    ! [X0] : apply(k,projection2) = apply(projection2,apply(k,pair(X0,projection2))),
    inference(superposition,[],[f417066,f121188]) ).

fof(f417066,plain,
    ! [X0] : apply(k,projection2) = apply(projection2,apply(f,pair(X0,projection2))),
    inference(unit_resulting_resolution,[],[f416773,f791]) ).

fof(f416773,plain,
    ! [X0,X1] : projection2 = apply(apply(projection2,apply(f,pair(X0,projection2))),X1),
    inference(forward_demodulation,[],[f415983,f771]) ).

fof(f415983,plain,
    ! [X0,X1] : projection2 = apply(apply(projection2,apply(f,apply(f,pair(X0,projection2)))),X1),
    inference(superposition,[],[f353189,f8352]) ).

fof(f8352,plain,
    ! [X0,X1] : projection2 = apply(projection2,apply(apply(f,pair(X0,projection2)),X1)),
    inference(superposition,[],[f3029,f927]) ).

fof(f927,plain,
    ! [X0] : pair(X0,projection2) = apply(pair(apply(k,X0),eq),n(projection1,projection2)),
    inference(superposition,[],[f878,f1]) ).

fof(f3029,plain,
    ! [X0,X1] : projection2 = apply(projection2,apply(apply(f,apply(pair(X0,eq),n(projection1,projection2))),X1)),
    inference(forward_demodulation,[],[f3028,f872]) ).

fof(f3028,plain,
    ! [X0,X1] : apply(eq,n(projection1,projection2)) = apply(projection2,apply(apply(f,apply(pair(X0,eq),n(projection1,projection2))),X1)),
    inference(forward_demodulation,[],[f3027,f142]) ).

fof(f3027,plain,
    ! [X0,X1] : apply(projection2,apply(pair(X0,eq),n(projection1,projection2))) = apply(projection2,apply(apply(f,apply(pair(X0,eq),n(projection1,projection2))),X1)),
    inference(forward_demodulation,[],[f3026,f771]) ).

fof(f3026,plain,
    ! [X0,X1] : apply(projection2,apply(pair(X0,eq),n(projection1,projection2))) = apply(projection2,apply(apply(f,apply(f,apply(pair(X0,eq),n(projection1,projection2)))),X1)),
    inference(forward_demodulation,[],[f3012,f771]) ).

fof(f3012,plain,
    ! [X0,X1] : apply(projection2,apply(pair(X0,eq),n(projection1,projection2))) = apply(projection2,apply(apply(f,apply(f,apply(f,apply(pair(X0,eq),n(projection1,projection2))))),X1)),
    inference(superposition,[],[f952,f46]) ).

fof(f952,plain,
    ! [X0,X1] : apply(projection2,X1) = apply(projection2,apply(apply(pair(X0,eq),n(projection1,projection2)),X1)),
    inference(superposition,[],[f142,f878]) ).

fof(f353189,plain,
    ! [X0,X1] : apply(projection2,apply(X0,X0)) = apply(apply(projection2,apply(f,X0)),X1),
    inference(superposition,[],[f352423,f3234]) ).

fof(f352423,plain,
    ! [X0,X1] : apply(projection2,X1) = apply(apply(projection2,apply(k,X1)),X0),
    inference(forward_demodulation,[],[f352071,f1]) ).

fof(f352071,plain,
    ! [X0,X1] : apply(apply(projection2,apply(k,X1)),X0) = apply(apply(apply(k,projection2),apply(k,X0)),X1),
    inference(superposition,[],[f1156,f3177]) ).

fof(f3177,plain,
    apply(k,projection2) = apply(abstraction,projection2),
    inference(unit_resulting_resolution,[],[f1439,f772]) ).

fof(f1439,plain,
    ! [X0] : projection2 = apply(apply(abstraction,projection2),X0),
    inference(unit_resulting_resolution,[],[f1267,f9]) ).

fof(f1267,plain,
    ! [X0,X1] : apply(projection2,X0) = apply(apply(apply(abstraction,projection2),X1),X0),
    inference(forward_demodulation,[],[f1216,f1]) ).

fof(f1216,plain,
    ! [X0,X1] : apply(projection2,apply(apply(k,X0),apply(X1,X0))) = apply(apply(apply(abstraction,projection2),X1),X0),
    inference(superposition,[],[f6,f175]) ).

fof(f175,plain,
    ! [X0,X1] : apply(apply(projection2,X0),X1) = apply(projection2,apply(X0,X1)),
    inference(superposition,[],[f142,f4]) ).

fof(f539936,plain,
    ! [X0,X1] : pair(apply(X0,X0),projection2) = apply(apply(f,pair(apply(f,X0),apply(k,projection2))),X1),
    inference(superposition,[],[f17,f420024]) ).

fof(f420024,plain,
    ! [X0] : pair(apply(f,X0),apply(k,projection2)) = apply(k,pair(apply(X0,X0),projection2)),
    inference(superposition,[],[f418203,f3234]) ).

fof(f17,plain,
    ! [X0,X1] : apply(apply(f,apply(k,X0)),X1) = X0,
    inference(superposition,[],[f11,f1]) ).

fof(f420142,plain,
    ! [X0] : apply(eq,apply(k,pair(X0,projection2))) != X0,
    inference(superposition,[],[f12,f418203]) ).

fof(f1133,plain,
    ! [X2,X0,X1] : apply(apply(apply(abstraction,apply(k,X0)),X2),X1) = apply(X0,apply(X2,X1)),
    inference(superposition,[],[f6,f1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : COL076-1 : TPTP v8.2.0. Released v1.2.0.
% 0.13/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n018.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sat May 18 13:05:38 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.35  % (19262)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.36  % (19263)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.37  TRYING [1]
% 0.21/0.37  TRYING [2]
% 0.21/0.38  % (19265)WARNING: value z3 for option sas not known
% 0.21/0.38  % (19264)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38  % (19266)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.38  % (19267)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)
% 0.21/0.38  % (19265)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)
% 0.21/0.38  % (19268)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)
% 0.21/0.38  TRYING [3]
% 0.21/0.38  % (19269)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)
% 0.21/0.38  TRYING [1]
% 0.21/0.38  TRYING [2]
% 0.21/0.39  TRYING [3]
% 0.21/0.40  TRYING [4]
% 0.21/0.40  TRYING [4]
% 0.21/0.44  TRYING [5]
% 0.21/0.47  TRYING [5]
% 0.21/0.50  TRYING [6]
% 1.78/0.64  TRYING [7]
% 2.22/0.70  TRYING [6]
% 3.89/0.93  TRYING [8]
% 7.40/1.41  TRYING [7]
% 7.90/1.48  TRYING [1]
% 7.90/1.48  TRYING [2]
% 7.90/1.48  TRYING [3]
% 7.90/1.49  TRYING [4]
% 8.21/1.52  TRYING [5]
% 8.45/1.58  TRYING [6]
% 9.53/1.72  TRYING [9]
% 9.53/1.74  TRYING [7]
% 12.16/2.09  TRYING [8]
% 18.10/2.94  TRYING [9]
% 30.79/4.74  TRYING [10]
% 32.24/4.96  TRYING [10]
% 34.23/5.29  TRYING [8]
% 56.00/8.43  TRYING [11]
% 63.92/9.50  TRYING [11]
% 103.42/15.16  TRYING [12]
% 138.02/20.07  % (19269)First to succeed.
% 138.02/20.08  % (19269)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-19262"
% 138.02/20.09  % (19269)Refutation found. Thanks to Tanya!
% 138.02/20.09  % SZS status Unsatisfiable for theBenchmark
% 138.02/20.09  % SZS output start Proof for theBenchmark
% See solution above
% 138.02/20.09  % (19269)------------------------------
% 138.02/20.09  % (19269)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 138.02/20.09  % (19269)Termination reason: Refutation
% 138.02/20.09  
% 138.02/20.09  % (19269)Memory used [KB]: 102056
% 138.02/20.09  % (19269)Time elapsed: 19.710 s
% 138.02/20.09  % (19269)Instructions burned: 47572 (million)
% 138.02/20.09  % (19262)Success in time 19.671 s
%------------------------------------------------------------------------------