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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : GEO494+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM

% Computer : n005.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep 25 01:21:09 PM UTC 2026

% Result   : Theorem 112.71s 30.75s
% Output   : CNFRefutation 112.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   85 (  24 unt;   0 def)
%            Number of atoms       :  186 (   7 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  198 (  97   ~;  92   |;   9   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-4 aty)
%            Number of functors    :   11 (  11 usr;   8 con; 0-4 aty)
%            Number of variables   :  306 (   0 sgn 300   !;   6   ?; 154   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1] : s_e(X0,X1,X1,X0),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO011+0.ax',aA1) ).

fof(f2,axiom,
    ! [X0,X1,X2,X3,X4,X5] :
      ( s_e(X2,X3,X4,X5)
      | ~ s_e(X0,X1,X4,X5)
      | ~ s_e(X0,X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO011+0.ax',aA2) ).

fof(f4,axiom,
    ! [X0,X1,X2,X3] :
      ( s_e(X1,ext(X0,X1,X2,X3),X2,X3)
      & s_t(X0,X1,ext(X0,X1,X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO011+0.ax',aA4) ).

fof(f10,axiom,
    ! [X0,X1,X2,X3] :
      ( s_e(X2,X3,X0,X1)
      | ~ s_e(X0,X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_2) ).

fof(f12,axiom,
    ! [X0,X1,X2,X3] :
      ( s_e(X1,X0,X2,X3)
      | ~ s_e(X0,X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_4) ).

fof(f13,axiom,
    ! [X0,X1,X2,X3] :
      ( s_e(X0,X1,X3,X2)
      | ~ s_e(X0,X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz2_5) ).

fof(f21,axiom,
    ! [X0,X1,X2] :
      ( s_t(X2,X1,X0)
      | ~ s_t(X0,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_2) ).

fof(f27,axiom,
    ! [X0,X1,X2,X3] :
      ( s_t(X0,X3,X2)
      | ~ s_t(X1,X3,X2)
      | ~ s_t(X0,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz3_5b) ).

fof(f56,axiom,
    ! [X0,X1,X2,X3] :
      ( ( ins(X2,X3,X0,X1) = ext(X0,X1,insert(X0,X1,X2,X3),X3)
        | ~ le(X0,X1,X2,X3) )
      & ( s_e(X0,ins(X2,X3,X0,X1),X2,X3)
        | ~ le(X0,X1,X2,X3) )
      & ( s_t(X0,X1,ins(X2,X3,X0,X1))
        | ~ le(X0,X1,X2,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_5a) ).

fof(f57,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( ~ s_e(X0,X4,X2,X3)
      | ~ s_t(X0,X1,X4)
      | le(X0,X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_5b) ).

fof(f58,axiom,
    ! [X0,X1,X2,X3,X4,X5,X6,X7] :
      ( le(X4,X5,X6,X7)
      | ~ s_e(X2,X3,X6,X7)
      | ~ s_e(X0,X1,X4,X5)
      | ~ le(X0,X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_6) ).

fof(f60,conjecture,
    ! [X0,X1,X2,X3,X4,X5] :
      ( le(X0,X1,X4,X5)
      | ~ le(X2,X3,X4,X5)
      | ~ le(X0,X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aSatz5_8) ).

fof(f61,negated_conjecture,
    ~ ! [X0,X1,X2,X3,X4,X5] :
        ( le(X0,X1,X4,X5)
        | ~ le(X2,X3,X4,X5)
        | ~ le(X0,X1,X2,X3) ),
    inference(negated_conjecture,[status(cth)],[f60]) ).

fof(f62,axiom,
    ! [X0,X1,X2,X3] : insert(X0,X1,X2,X3) = ext(ext(X3,X2,alpha,gamma),X2,X0,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_insert) ).

fof(f68,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( ( le(X0,X1,X2,X3)
        | ~ s_e(X0,X1,X2,X4)
        | ~ s_t(X2,X4,X3) )
      & ( s_e(X0,X1,X2,insert(X0,X1,X2,X3))
        | ~ le(X0,X1,X2,X3) )
      & ( s_t(X2,insert(X0,X1,X2,X3),X3)
        | ~ le(X0,X1,X2,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_Defn5_4) ).

fof(f69,plain,
    ? [X0,X1,X2,X3,X4,X5] :
      ( ~ le(X0,X1,X4,X5)
      & le(X2,X3,X4,X5)
      & le(X0,X1,X2,X3) ),
    inference(ennf_transformation,[],[f61]) ).

fof(f70,plain,
    ( ~ le(sK0,sK1,sK4,sK5)
    & le(sK2,sK3,sK4,sK5)
    & le(sK0,sK1,sK2,sK3) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f69]) ).

fof(f71,plain,
    ! [X0,X1] : s_e(X0,X1,X1,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f72,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( s_e(X2,X3,X4,X5)
      | ~ s_e(X0,X1,X4,X5)
      | ~ s_e(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f2]) ).

fof(f74,plain,
    ! [X2,X3,X0,X1] : s_e(X1,ext(X0,X1,X2,X3),X2,X3),
    inference(cnf_transformation,[],[f4]) ).

fof(f75,plain,
    ! [X2,X3,X0,X1] : s_t(X0,X1,ext(X0,X1,X2,X3)),
    inference(cnf_transformation,[],[f4]) ).

fof(f84,plain,
    ! [X2,X3,X0,X1] :
      ( s_e(X2,X3,X0,X1)
      | ~ s_e(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f10]) ).

fof(f86,plain,
    ! [X2,X3,X0,X1] :
      ( s_e(X1,X0,X2,X3)
      | ~ s_e(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f12]) ).

fof(f87,plain,
    ! [X2,X3,X0,X1] :
      ( s_e(X0,X1,X3,X2)
      | ~ s_e(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f95,plain,
    ! [X2,X0,X1] :
      ( s_t(X2,X1,X0)
      | ~ s_t(X0,X1,X2) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f101,plain,
    ! [X2,X3,X0,X1] :
      ( s_t(X0,X3,X2)
      | ~ s_t(X1,X3,X2)
      | ~ s_t(X0,X1,X2) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f132,plain,
    ! [X2,X3,X0,X1] :
      ( ins(X2,X3,X0,X1) = ext(X0,X1,insert(X0,X1,X2,X3),X3)
      | ~ le(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f133,plain,
    ! [X2,X3,X0,X1] :
      ( s_e(X0,ins(X2,X3,X0,X1),X2,X3)
      | ~ le(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f135,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ s_e(X0,X4,X2,X3)
      | ~ s_t(X0,X1,X4)
      | le(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f57]) ).

fof(f136,plain,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( le(X4,X5,X6,X7)
      | ~ s_e(X2,X3,X6,X7)
      | ~ s_e(X0,X1,X4,X5)
      | ~ le(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f138,plain,
    ~ le(sK0,sK1,sK4,sK5),
    inference(cnf_transformation,[],[f70]) ).

fof(f139,plain,
    le(sK2,sK3,sK4,sK5),
    inference(cnf_transformation,[],[f70]) ).

fof(f140,plain,
    le(sK0,sK1,sK2,sK3),
    inference(cnf_transformation,[],[f70]) ).

fof(f141,plain,
    ! [X2,X3,X0,X1] : insert(X0,X1,X2,X3) = ext(ext(X3,X2,alpha,gamma),X2,X0,X1),
    inference(cnf_transformation,[],[f62]) ).

fof(f169,plain,
    ! [X2,X3,X0,X1,X4] :
      ( le(X0,X1,X2,X3)
      | ~ s_e(X0,X1,X2,X4)
      | ~ s_t(X2,X4,X3) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f171,plain,
    ! [X2,X3,X0,X1] :
      ( s_t(X2,insert(X0,X1,X2,X3),X3)
      | ~ le(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f174,plain,
    ! [X2,X3,X0,X1] :
      ( ins(X2,X3,X0,X1) = ext(X0,X1,ext(ext(X3,X2,alpha,gamma),X2,X0,X1),X3)
      | ~ le(X0,X1,X2,X3) ),
    inference(definition_unfolding,[],[f132,f141]) ).

fof(f175,plain,
    ! [X2,X3,X0,X1] :
      ( s_t(X2,ext(ext(X3,X2,alpha,gamma),X2,X0,X1),X3)
      | ~ le(X0,X1,X2,X3) ),
    inference(definition_unfolding,[],[f171,f141]) ).

tcf(c_49,plain,
    ! [X0: $i,X1: $i] : s_e(X0,X1,X1,X0),
    inference(cnf_transformation,[],[f71]) ).

tcf(c_50,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( s_e(X2,X3,X4,X5)
      | ~ s_e(X0,X1,X4,X5)
      | ~ s_e(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f72]) ).

tcf(c_52,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : s_t(X0,X1,ext(X0,X1,X2,X3)),
    inference(cnf_transformation,[],[f75]) ).

tcf(c_53,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : s_e(X0,ext(X1,X0,X2,X3),X2,X3),
    inference(cnf_transformation,[],[f74]) ).

tcf(c_62,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( s_e(X2,X3,X0,X1)
      | ~ s_e(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f84]) ).

tcf(c_64,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( s_e(X1,X0,X2,X3)
      | ~ s_e(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f86]) ).

tcf(c_65,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( s_e(X0,X1,X3,X2)
      | ~ s_e(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f87]) ).

tcf(c_73,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( s_t(X2,X1,X0)
      | ~ s_t(X0,X1,X2) ),
    inference(cnf_transformation,[],[f95]) ).

tcf(c_79,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( s_t(X0,X3,X2)
      | ~ s_t(X1,X3,X2)
      | ~ s_t(X0,X1,X2) ),
    inference(cnf_transformation,[],[f101]) ).

tcf(c_111,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( s_e(X0,ins(X2,X3,X0,X1),X2,X3)
      | ~ le(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f133]) ).

tcf(c_112,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( ext(X0,X1,ext(ext(X3,X2,alpha,gamma),X2,X0,X1),X3) = ins(X2,X3,X0,X1) )
      | ~ le(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f174]) ).

tcf(c_113,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( le(X0,X4,X2,X3)
      | ~ s_t(X0,X4,X1)
      | ~ s_e(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f135]) ).

tcf(c_114,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
      ( le(X2,X3,X6,X7)
      | ~ le(X0,X1,X4,X5)
      | ~ s_e(X4,X5,X6,X7)
      | ~ s_e(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f136]) ).

tcf(c_116,negated_conjecture,
    le(sK0,sK1,sK2,sK3),
    inference(cnf_transformation,[],[f140]) ).

tcf(c_117,negated_conjecture,
    le(sK2,sK3,sK4,sK5),
    inference(cnf_transformation,[],[f139]) ).

tcf(c_118,negated_conjecture,
    ~ le(sK0,sK1,sK4,sK5),
    inference(cnf_transformation,[],[f138]) ).

tcf(c_146,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( s_t(X2,ext(ext(X3,X2,alpha,gamma),X2,X0,X1),X3)
      | ~ le(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f175]) ).

tcf(c_148,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( le(X0,X1,X2,X4)
      | ~ s_t(X2,X3,X4)
      | ~ s_e(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f169]) ).

tcf(c_3514,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( le(sK0,sK1,sK4,sK5)
      | ~ s_e(X2,X3,sK4,sK5)
      | ~ s_e(X0,X1,sK0,sK1)
      | ~ le(X0,X1,X2,X3) ),
    inference(instantiation,[status(thm)],[c_114]) ).

tcf(c_3579,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : s_t(ext(X0,X1,X2,X3),X1,X0),
    inference(superposition,[status(thm)],[c_52,c_73]) ).

tcf(c_3848,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( s_t(ext(X2,X0,X3,X4),X1,X2)
      | ~ s_t(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_3579,c_79]) ).

tcf(c_3966,plain,
    ! [X0: $i,X1: $i] :
      ( le(sK0,sK1,sK4,sK5)
      | ~ s_e(sK5,sK4,sK4,sK5)
      | ~ le(X0,X1,sK5,sK4)
      | ~ s_e(X0,X1,sK0,sK1) ),
    inference(instantiation,[status(thm)],[c_3514]) ).

tcf(c_3967,plain,
    s_e(sK5,sK4,sK4,sK5),
    inference(instantiation,[status(thm)],[c_49]) ).

tcf(c_4068,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( s_e(X0,ins(X2,X3,X0,X1),X3,X2)
      | ~ le(X0,X1,X2,X3) ),
    inference(superposition,[status(thm)],[c_111,c_65]) ).

tcf(c_31270,plain,
    s_e(sK1,sK0,sK0,sK1),
    inference(instantiation,[status(thm)],[c_49]) ).

tcf(c_79256,plain,
    ( le(sK0,sK1,sK4,sK5)
    | ~ le(sK1,sK0,sK5,sK4)
    | ~ s_e(sK5,sK4,sK4,sK5)
    | ~ s_e(sK1,sK0,sK0,sK1) ),
    inference(instantiation,[status(thm)],[c_3966]) ).

tcf(c_363150,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : s_e(X0,X1,X2,ext(X3,X2,X0,X1)),
    inference(superposition,[status(thm)],[c_53,c_62]) ).

tcf(c_363205,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] : s_e(X0,X1,X2,ext(X3,X2,X1,X0)),
    inference(superposition,[status(thm)],[c_363150,c_64]) ).

tcf(c_363408,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( s_t(X2,X1,ext(X2,X0,X3,X4))
      | ~ s_t(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_3848,c_73]) ).

tcf(c_363586,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( le(X3,X2,X0,X4)
      | ~ s_t(X0,ext(X1,X0,X2,X3),X4) ),
    inference(superposition,[status(thm)],[c_363205,c_148]) ).

tcf(c_363595,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( s_e(X4,ext(X5,X4,X0,X1),X2,X3)
      | ~ s_e(X0,X1,X2,X3) ),
    inference(superposition,[status(thm)],[c_363150,c_50]) ).

tcf(c_363820,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( s_t(X3,ext(ext(X3,X2,alpha,gamma),X2,X0,X1),X2)
      | ~ le(X0,X1,X2,X3) ),
    inference(superposition,[status(thm)],[c_146,c_73]) ).

tcf(c_364675,plain,
    ext(sK2,sK3,ext(ext(sK5,sK4,alpha,gamma),sK4,sK2,sK3),sK5) = ins(sK4,sK5,sK2,sK3),
    inference(superposition,[status(thm)],[c_117,c_112]) ).

tcf(c_364875,plain,
    ! [X0: $i] :
      ( s_t(sK2,X0,ins(sK4,sK5,sK2,sK3))
      | ~ s_t(sK3,X0,sK2) ),
    inference(superposition,[status(thm)],[c_364675,c_363408]) ).

tcf(c_366077,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( le(X1,X0,X2,X3)
      | ~ le(X0,X1,X2,X3) ),
    inference(superposition,[status(thm)],[c_146,c_363586]) ).

tcf(c_366258,plain,
    le(sK1,sK0,sK2,sK3),
    inference(superposition,[status(thm)],[c_116,c_366077]) ).

tcf(c_367018,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( le(X0,X1,X3,X2)
      | ~ le(X0,X4,X2,X3)
      | ~ s_t(X0,X1,ins(X2,X3,X0,X4)) ),
    inference(superposition,[status(thm)],[c_4068,c_113]) ).

tcf(c_367307,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( s_e(X2,X3,X4,ext(X5,X4,X0,X1))
      | ~ s_e(X0,X1,X2,X3) ),
    inference(superposition,[status(thm)],[c_363595,c_62]) ).

tcf(c_369049,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( le(X5,X6,X0,X4)
      | ~ s_e(X2,X3,X5,X6)
      | ~ s_t(X0,ext(X1,X0,X2,X3),X4) ),
    inference(superposition,[status(thm)],[c_367307,c_148]) ).

tcf(c_378450,plain,
    ! [X0: $i] :
      ( le(sK2,X0,sK5,sK4)
      | ~ s_t(sK3,X0,sK2)
      | ~ le(sK2,sK3,sK4,sK5) ),
    inference(superposition,[status(thm)],[c_364875,c_367018]) ).

tcf(c_378462,plain,
    ! [X0: $i] :
      ( le(sK2,X0,sK5,sK4)
      | ~ s_t(sK3,X0,sK2) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_378450,c_117]) ).

tcf(c_387497,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( le(X2,X3,X4,X5)
      | ~ le(X0,X1,X4,X5)
      | ~ s_e(X0,X1,X2,X3) ),
    inference(superposition,[status(thm)],[c_146,c_369049]) ).

tcf(c_406255,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( le(X2,X3,X4,X5)
      | ~ le(X0,ext(X1,X0,X2,X3),X4,X5) ),
    inference(superposition,[status(thm)],[c_53,c_387497]) ).

tcf(c_406667,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( le(X1,X2,sK5,sK4)
      | ~ s_t(sK3,ext(X0,sK2,X1,X2),sK2) ),
    inference(superposition,[status(thm)],[c_378462,c_406255]) ).

tcf(c_407030,plain,
    ! [X0: $i,X1: $i] :
      ( le(X0,X1,sK5,sK4)
      | ~ le(X0,X1,sK2,sK3) ),
    inference(superposition,[status(thm)],[c_363820,c_406667]) ).

tcf(c_407139,plain,
    le(sK1,sK0,sK5,sK4),
    inference(superposition,[status(thm)],[c_366258,c_407030]) ).

tcf(c_407161,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_407139,c_79256,c_31270,c_3967,c_118]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04  % Problem  : GEO494+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06  % Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.18/0.43  % Computer : n005.cluster.edu
% 0.18/0.43  % Model    : x86_64 x86_64
% 0.18/0.43  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43  % Memory   : 8046.5625MB
% 0.18/0.43  % OS       : Linux 6.8.0-71-generic
% 0.18/0.43  % CPULimit : 300
% 0.18/0.43  % WCLimit  : 300
% 0.18/0.43  % DateTime : Wed Sep 23 12:12:32 UTC 2026
% 0.18/0.43  % CPUTime  : 
% 0.18/0.43  Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.18/0.48  Running first-order theorem proving
% 0.18/0.48  Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.50  
% 0.18/0.50  % ======== iProver multi-core TPTP/SMT =========
% 0.18/0.50  
% 0.18/0.50  % Detected problem language: tptp
% 0.27/0.52  % Proving...
% 112.71/30.75  % SZS status Started for theBenchmark.p
% 112.71/30.75  % SZS status Theorem for theBenchmark.p
% 112.71/30.75  
% 112.71/30.75  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 112.71/30.75  
% 112.71/30.75  % ------  iProver source info
% 112.71/30.75  
% 112.71/30.75  % git: date: 2026-07-19 20:42:38 +0200
% 112.71/30.75  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 112.71/30.75  % git: non_committed_changes: false
% 112.71/30.75  
% 112.71/30.75  % ------ Parsing...
% 112.71/30.75  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 112.71/30.75  
% 112.71/30.75  % ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e % 
% 112.71/30.75  
% 112.71/30.75  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 112.71/30.75  
% 112.71/30.75  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 112.71/30.75  % ------ Proving...
% 112.71/30.75  % ------ Problem Properties 
% 112.71/30.75  
% 112.71/30.75  % 
% 112.71/30.75  % clauses                               79
% 112.71/30.75  % conjectures                           3
% 112.71/30.75  % EPR                                   63
% 112.71/30.75  % Horn                                  68
% 112.71/30.75  % unary                                 20
% 112.71/30.75  % binary                                23
% 112.71/30.75  % lits                                  210
% 112.71/30.75  % lits eq                               20
% 112.71/30.75  % fd_pure                               0
% 112.71/30.75  % fd_pseudo                             0
% 112.71/30.75  % fd_cond                               0
% 112.71/30.75  % fd_pseudo_cond                        13
% 112.71/30.75  % AC symbols                            0
% 112.71/30.75  
% 112.71/30.75  % ------ Input Options Time Limit: Unbounded
% 112.71/30.75  
% 112.71/30.75  
% 112.71/30.75  % ------ 
% 112.71/30.75  % Current options:
% 112.71/30.75  % ------ 
% 112.71/30.75  
% 112.71/30.75  
% 112.71/30.75  % 
% 112.71/30.75  
% 112.71/30.75  % ------ Proving...
% 112.71/30.75  % 
% 112.71/30.75  
% 112.71/30.75  % SZS status Theorem for theBenchmark.p
% 112.71/30.75  
% 112.71/30.75  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 112.71/30.75  
% 112.71/30.75  
%------------------------------------------------------------------------------