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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : LCL894+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM

% Computer : n026.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 02:08:38 PM UTC 2026

% Result   : Theorem 9.23s 4.25s
% Output   : CNFRefutation 9.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   13
% Syntax   : Number of formulae    :  115 (  60 unt;   2 def)
%            Number of atoms       :  238 (  27 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  152 (  65   ~;  70   |;  10   &)
%                                         (   3 <=>;   3  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    7 (   3 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;   3 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :  136 (   0 sgn 136   !;   0   ?;  75   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1,X2] : '+'('+'(X0,X1),X2) = '+'(X0,'+'(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_01) ).

fof(f2,axiom,
    ! [X0,X1] : '+'(X0,X1) = '+'(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_02) ).

fof(f3,axiom,
    ! [X0] : '+'(X0,'0') = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_03) ).

fof(f4,axiom,
    ! [X0] : '>='(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_04) ).

fof(f5,axiom,
    ! [X0,X1,X2] :
      ( ( '>='(X1,X2)
        & '>='(X0,X1) )
     => '>='(X0,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_05) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( ( '>='(X1,X0)
        & '>='(X0,X1) )
     => X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_06) ).

fof(f7,axiom,
    ! [X0,X1,X2] :
      ( '>='('+'(X0,X1),X2)
    <=> '>='(X1,'==>'(X0,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_07) ).

fof(f8,axiom,
    ! [X0] : '>='(X0,'0'),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_08) ).

fof(f9,axiom,
    ! [X0,X1,X2] :
      ( '>='(X0,X1)
     => '>='('+'(X0,X2),'+'(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_09) ).

fof(f12,axiom,
    ! [X0,X1] : '+'(X0,'==>'(X0,X1)) = '+'(X1,'==>'(X1,X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_12) ).

fof(f13,conjecture,
    ( ( '>='(c,b)
      & '>='(c,a) )
  <=> '>='(c,'+'(a,'==>'(a,b))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_13) ).

fof(f14,negated_conjecture,
    ~ ( ( '>='(c,b)
        & '>='(c,a) )
    <=> '>='(c,'+'(a,'==>'(a,b))) ),
    inference(negated_conjecture,[status(cth)],[f13]) ).

fof(f15,plain,
    ! [X0,X1,X2] :
      ( ~ '>='(X1,X2)
      | ~ '>='(X0,X1)
      | '>='(X0,X2) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f16,plain,
    ! [X0,X1,X2] :
      ( ~ '>='(X1,X2)
      | ~ '>='(X0,X1)
      | '>='(X0,X2) ),
    inference(flattening,[],[f15]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ~ '>='(X1,X0)
      | ~ '>='(X0,X1)
      | X0 = X1 ),
    inference(ennf_transformation,[],[f6]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ~ '>='(X1,X0)
      | ~ '>='(X0,X1)
      | X0 = X1 ),
    inference(flattening,[],[f17]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( ~ '>='(X0,X1)
      | '>='('+'(X0,X2),'+'(X1,X2)) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f22,plain,
    ( ( '>='(c,b)
      & '>='(c,a) )
  <~> '>='(c,'+'(a,'==>'(a,b))) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( ( ~ '>='('+'(X0,X1),X2)
        | '>='(X1,'==>'(X0,X2)) )
      & ( ~ '>='(X1,'==>'(X0,X2))
        | '>='('+'(X0,X1),X2) ) ),
    inference(nnf_transformation,[],[f7]) ).

fof(f24,plain,
    ( ( ( '>='(c,b)
        & '>='(c,a) )
      | '>='(c,'+'(a,'==>'(a,b))) )
    & ( ~ '>='(c,b)
      | ~ '>='(c,a)
      | ~ '>='(c,'+'(a,'==>'(a,b))) ) ),
    inference(nnf_transformation,[],[f22]) ).

fof(f25,plain,
    ( ( ( '>='(c,b)
        & '>='(c,a) )
      | '>='(c,'+'(a,'==>'(a,b))) )
    & ( ~ '>='(c,b)
      | ~ '>='(c,a)
      | ~ '>='(c,'+'(a,'==>'(a,b))) ) ),
    inference(flattening,[],[f24]) ).

fof(f26,plain,
    ! [X2,X0,X1] : '+'('+'(X0,X1),X2) = '+'(X0,'+'(X1,X2)),
    inference(cnf_transformation,[],[f1]) ).

fof(f27,plain,
    ! [X0,X1] : '+'(X0,X1) = '+'(X1,X0),
    inference(cnf_transformation,[],[f2]) ).

fof(f28,plain,
    ! [X0] : '+'(X0,'0') = X0,
    inference(cnf_transformation,[],[f3]) ).

fof(f29,plain,
    ! [X0] : '>='(X0,X0),
    inference(cnf_transformation,[],[f4]) ).

fof(f30,plain,
    ! [X2,X0,X1] :
      ( ~ '>='(X1,X2)
      | ~ '>='(X0,X1)
      | '>='(X0,X2) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ~ '>='(X1,X0)
      | ~ '>='(X0,X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f18]) ).

fof(f32,plain,
    ! [X2,X0,X1] :
      ( ~ '>='('+'(X0,X1),X2)
      | '>='(X1,'==>'(X0,X2)) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f33,plain,
    ! [X2,X0,X1] :
      ( ~ '>='(X1,'==>'(X0,X2))
      | '>='('+'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f34,plain,
    ! [X0] : '>='(X0,'0'),
    inference(cnf_transformation,[],[f8]) ).

fof(f35,plain,
    ! [X2,X0,X1] :
      ( ~ '>='(X0,X1)
      | '>='('+'(X0,X2),'+'(X1,X2)) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f38,plain,
    ! [X0,X1] : '+'(X0,'==>'(X0,X1)) = '+'(X1,'==>'(X1,X0)),
    inference(cnf_transformation,[],[f12]) ).

fof(f39,plain,
    ( '>='(c,b)
    | '>='(c,'+'(a,'==>'(a,b))) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f40,plain,
    ( '>='(c,a)
    | '>='(c,'+'(a,'==>'(a,b))) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f41,plain,
    ( ~ '>='(c,b)
    | ~ '>='(c,a)
    | ~ '>='(c,'+'(a,'==>'(a,b))) ),
    inference(cnf_transformation,[],[f25]) ).

tcf(c_49,plain,
    ! [X0: $i,X1: $i,X2: $i] : '+'('+'(X0,X1),X2) = '+'(X0,'+'(X1,X2)),
    inference(cnf_transformation,[],[f26]) ).

tcf(c_50,plain,
    ! [X0: $i,X1: $i] : '+'(X0,X1) = '+'(X1,X0),
    inference(cnf_transformation,[],[f27]) ).

tcf(c_51,plain,
    ! [X0: $i] : '+'(X0,'0') = X0,
    inference(cnf_transformation,[],[f28]) ).

tcf(c_52,plain,
    ! [X0: $i] : '>='(X0,X0),
    inference(cnf_transformation,[],[f29]) ).

tcf(c_53,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( '>='(X0,X2)
      | ~ '>='(X1,X2)
      | ~ '>='(X0,X1) ),
    inference(cnf_transformation,[],[f30]) ).

tcf(c_54,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ~ '>='(X1,X0)
      | ~ '>='(X0,X1) ),
    inference(cnf_transformation,[],[f31]) ).

tcf(c_55,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( '>='('+'(X1,X0),X2)
      | ~ '>='(X0,'==>'(X1,X2)) ),
    inference(cnf_transformation,[],[f33]) ).

tcf(c_56,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( '>='(X1,'==>'(X0,X2))
      | ~ '>='('+'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f32]) ).

tcf(c_57,plain,
    ! [X0: $i] : '>='(X0,'0'),
    inference(cnf_transformation,[],[f34]) ).

tcf(c_58,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( '>='('+'(X0,X2),'+'(X1,X2))
      | ~ '>='(X0,X1) ),
    inference(cnf_transformation,[],[f35]) ).

tcf(c_61,plain,
    ! [X0: $i,X1: $i] : '+'(X0,'==>'(X0,X1)) = '+'(X1,'==>'(X1,X0)),
    inference(cnf_transformation,[],[f38]) ).

tcf(c_62,negated_conjecture,
    ( ~ '>='(c,b)
    | ~ '>='(c,a)
    | ~ '>='(c,'+'(a,'==>'(a,b))) ),
    inference(cnf_transformation,[],[f41]) ).

tcf(c_63,negated_conjecture,
    ( '>='(c,a)
    | '>='(c,'+'(a,'==>'(a,b))) ),
    inference(cnf_transformation,[],[f40]) ).

tcf(c_64,negated_conjecture,
    ( '>='(c,b)
    | '>='(c,'+'(a,'==>'(a,b))) ),
    inference(cnf_transformation,[],[f39]) ).

tcf(c_66,plain,
    '>='(a,a),
    inference(instantiation,[status(thm)],[c_52]) ).

tcf(c_184,definition,
    iPr_def_10 = '==>'(a,b),
    introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).

tcf(c_185,definition,
    iPr_def_11 = '+'(a,iPr_def_10),
    introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).

tcf(c_186,negated_conjecture,
    ( '>='(c,iPr_def_11)
    | '>='(c,b) ),
    inference(demodulation,[status(thm)],[c_64,c_184,c_185]) ).

tcf(c_187,negated_conjecture,
    ( '>='(c,iPr_def_11)
    | '>='(c,a) ),
    inference(demodulation,[status(thm)],[c_63]) ).

tcf(c_188,negated_conjecture,
    ( ~ '>='(c,iPr_def_11)
    | ~ '>='(c,b)
    | ~ '>='(c,a) ),
    inference(demodulation,[status(thm)],[c_62]) ).

tcf(c_396,plain,
    '+'(iPr_def_10,a) = iPr_def_11,
    inference(theory_normalisation,[status(thm)],[c_185,c_49,c_50]) ).

tcf(c_404,plain,
    ! [X0: $i] : '+'('0',X0) = X0,
    inference(superposition,[status(thm)],[c_51,c_50]) ).

tcf(c_417,plain,
    ! [X0: $i] :
      ( '>='(c,iPr_def_11)
      | '>='(c,X0)
      | ~ '>='(a,X0) ),
    inference(superposition,[status(thm)],[c_187,c_53]) ).

tcf(c_418,plain,
    ! [X0: $i] :
      ( '>='(c,iPr_def_11)
      | '>='(c,X0)
      | ~ '>='(b,X0) ),
    inference(superposition,[status(thm)],[c_186,c_53]) ).

tcf(c_432,plain,
    ! [X0: $i,X1: $i] : '>='('+'(X0,'==>'(X0,X1)),X1),
    inference(superposition,[status(thm)],[c_52,c_55]) ).

tcf(c_442,plain,
    ! [X0: $i,X1: $i] : '>='(X0,'==>'(X1,'+'(X1,X0))),
    inference(superposition,[status(thm)],[c_52,c_56]) ).

tcf(c_446,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( '>='(X0,'==>'(X1,X2))
      | ~ '>='('+'(X0,X1),X2) ),
    inference(superposition,[status(thm)],[c_50,c_56]) ).

tcf(c_485,plain,
    ! [X0: $i] : '>='('==>'('0',X0),X0),
    inference(superposition,[status(thm)],[c_404,c_432]) ).

tcf(c_486,plain,
    '>='('+'(a,iPr_def_10),b),
    inference(superposition,[status(thm)],[c_184,c_432]) ).

tcf(c_490,plain,
    '>='('+'(iPr_def_10,a),b),
    inference(theory_normalisation,[status(thm)],[c_486,c_49,c_50]) ).

tcf(c_491,plain,
    '>='(iPr_def_11,b),
    inference(light_normalisation,[status(thm)],[c_490,c_396]) ).

tcf(c_521,plain,
    ! [X0: $i] :
      ( '>='(iPr_def_11,X0)
      | ~ '>='(b,X0) ),
    inference(superposition,[status(thm)],[c_491,c_53]) ).

tcf(c_534,plain,
    ! [X0: $i] : '>='(X0,'==>'('0',X0)),
    inference(superposition,[status(thm)],[c_404,c_442]) ).

tcf(c_679,plain,
    ! [X0: $i,X1: $i] :
      ( '>='('+'(X0,X1),X1)
      | ~ '>='(X0,'0') ),
    inference(superposition,[status(thm)],[c_404,c_58]) ).

tcf(c_685,plain,
    ! [X0: $i,X1: $i] : '>='('+'(X0,X1),X1),
    inference(forward_subsumption_resolution,[status(thm)],[c_679,c_57]) ).

tcf(c_724,plain,
    ! [X0: $i,X1: $i] :
      ( '>='(c,X1)
      | ~ '>='(c,X0)
      | ~ '>='(X0,X1) ),
    inference(instantiation,[status(thm)],[c_53]) ).

tcf(c_803,plain,
    ! [X0: $i] :
      ( ( X0 = '0' )
      | ~ '>='('0',X0) ),
    inference(superposition,[status(thm)],[c_57,c_54]) ).

tcf(c_888,plain,
    ! [X0: $i] :
      ( '>='(c,iPr_def_11)
      | '>='(c,X0)
      | ~ '>='(a,X0) ),
    inference(superposition,[status(thm)],[c_187,c_53]) ).

tcf(c_889,plain,
    ! [X0: $i] :
      ( '>='(c,iPr_def_11)
      | '>='(c,X0)
      | ~ '>='(b,X0) ),
    inference(superposition,[status(thm)],[c_186,c_53]) ).

tcf(c_929,plain,
    ! [X0: $i] :
      ( ( '==>'('0',X0) = X0 )
      | ~ '>='('==>'('0',X0),X0) ),
    inference(superposition,[status(thm)],[c_534,c_54]) ).

tcf(c_939,plain,
    ! [X0: $i] : '==>'('0',X0) = X0,
    inference(forward_subsumption_resolution,[status(thm)],[c_929,c_485]) ).

tcf(c_963,plain,
    ! [X0: $i,X1: $i,X2: $i] : '>='('+'(X0,'+'(X1,X2)),X2),
    inference(superposition,[status(thm)],[c_49,c_685]) ).

tcf(c_967,plain,
    '>='(iPr_def_11,a),
    inference(superposition,[status(thm)],[c_396,c_685]) ).

tcf(c_970,plain,
    ! [X0: $i,X1: $i] : '>='(X0,'==>'(X1,X0)),
    inference(superposition,[status(thm)],[c_685,c_56]) ).

tcf(c_1279,plain,
    ! [X0: $i,X1: $i] : '>='('==>'(X0,X1),'==>'(X0,'+'(X1,'==>'(X1,X0)))),
    inference(superposition,[status(thm)],[c_61,c_442]) ).

tcf(c_1336,plain,
    ! [X0: $i] :
      ( '>='(c,X0)
      | ~ '>='(c,iPr_def_11)
      | ~ '>='(iPr_def_11,X0) ),
    inference(instantiation,[status(thm)],[c_724]) ).

tcf(c_1367,plain,
    ! [X0: $i] :
      ( '>='(iPr_def_11,X0)
      | ~ '>='(a,X0) ),
    inference(superposition,[status(thm)],[c_967,c_53]) ).

tcf(c_1427,plain,
    ! [X0: $i] :
      ( ~ '>='(a,X0)
      | '>='(c,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_888,c_417,c_1336,c_1367]) ).

tcf(c_1428,plain,
    ! [X0: $i] :
      ( '>='(c,X0)
      | ~ '>='(a,X0) ),
    inference(renaming,[status(thm)],[c_1427]) ).

tcf(c_1429,plain,
    ( '>='(c,a)
    | ~ '>='(a,a) ),
    inference(instantiation,[status(thm)],[c_1428]) ).

tcf(c_1446,plain,
    ! [X0: $i] :
      ( '>='(c,iPr_def_11)
      | '>='(c,'==>'(X0,a)) ),
    inference(superposition,[status(thm)],[c_970,c_417]) ).

tcf(c_1472,plain,
    ! [X0: $i] :
      ( ~ '>='(b,X0)
      | '>='(c,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_889,c_418,c_521,c_1336]) ).

tcf(c_1473,plain,
    ! [X0: $i] :
      ( '>='(c,X0)
      | ~ '>='(b,X0) ),
    inference(renaming,[status(thm)],[c_1472]) ).

tcf(c_1478,plain,
    '>='(c,b),
    inference(superposition,[status(thm)],[c_52,c_1473]) ).

tcf(c_1591,plain,
    ! [X0: $i] : '>='(c,'==>'(X0,a)),
    inference(global_subsumption_just,[status(thm)],[c_1446,c_66,c_188,c_1429,c_1446,c_1478]) ).

tcf(c_1594,plain,
    '>='(c,a),
    inference(superposition,[status(thm)],[c_939,c_1591]) ).

tcf(c_1597,plain,
    ! [X0: $i] : '>='('+'(X0,c),a),
    inference(superposition,[status(thm)],[c_1591,c_55]) ).

tcf(c_1602,plain,
    ( ~ '>='(c,iPr_def_11)
    | ~ '>='(c,b) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_188,c_1594]) ).

tcf(c_1627,plain,
    ~ '>='(c,iPr_def_11),
    inference(global_subsumption_just,[status(thm)],[c_1602,c_66,c_188,c_1429,c_1478]) ).

tcf(c_1637,plain,
    ! [X0: $i] :
      ( '>='(c,X0)
      | ~ '>='(b,X0) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_418,c_1627]) ).

tcf(c_1865,plain,
    ! [X0: $i] : '>='('+'(c,X0),a),
    inference(superposition,[status(thm)],[c_50,c_1597]) ).

tcf(c_1892,plain,
    ! [X0: $i] : '>='('+'(X0,'==>'(X0,c)),a),
    inference(superposition,[status(thm)],[c_61,c_1865]) ).

tcf(c_1970,plain,
    ! [X0: $i] : '>='(c,'==>'(X0,b)),
    inference(superposition,[status(thm)],[c_970,c_1637]) ).

tcf(c_1992,plain,
    ! [X0: $i] : '>='('+'(X0,c),b),
    inference(superposition,[status(thm)],[c_1970,c_55]) ).

tcf(c_2021,plain,
    ! [X0: $i] : '>='(X0,'==>'(c,b)),
    inference(superposition,[status(thm)],[c_1992,c_446]) ).

tcf(c_2626,plain,
    ! [X0: $i] : '>='('+'(X0,iPr_def_11),a),
    inference(superposition,[status(thm)],[c_396,c_963]) ).

tcf(c_3133,plain,
    ! [X0: $i] : '>='('+'(iPr_def_11,X0),a),
    inference(superposition,[status(thm)],[c_50,c_2626]) ).

tcf(c_3286,plain,
    ! [X0: $i] : '>='('+'(X0,'==>'(X0,iPr_def_11)),a),
    inference(superposition,[status(thm)],[c_61,c_3133]) ).

tcf(c_5467,plain,
    ! [X0: $i] : '>='('==>'(X0,c),'==>'(X0,a)),
    inference(superposition,[status(thm)],[c_1892,c_56]) ).

tcf(c_6695,plain,
    ! [X0: $i] : '>='('==>'(X0,iPr_def_11),'==>'(X0,a)),
    inference(superposition,[status(thm)],[c_3286,c_56]) ).

tcf(c_34536,plain,
    '==>'(c,b) = '0',
    inference(superposition,[status(thm)],[c_2021,c_803]) ).

tcf(c_59836,plain,
    '>='('==>'(b,a),'==>'(b,'+'(a,iPr_def_10))),
    inference(superposition,[status(thm)],[c_184,c_1279]) ).

tcf(c_59896,plain,
    '>='('==>'(b,a),'==>'(b,'+'(iPr_def_10,a))),
    inference(theory_normalisation,[status(thm)],[c_59836,c_49,c_50]) ).

tcf(c_59897,plain,
    '>='('==>'(b,a),'==>'(b,iPr_def_11)),
    inference(light_normalisation,[status(thm)],[c_59896,c_396]) ).

tcf(c_60138,plain,
    ( ( '==>'(b,a) = '==>'(b,iPr_def_11) )
    | ~ '>='('==>'(b,iPr_def_11),'==>'(b,a)) ),
    inference(superposition,[status(thm)],[c_59897,c_54]) ).

tcf(c_60152,plain,
    '==>'(b,a) = '==>'(b,iPr_def_11),
    inference(forward_subsumption_resolution,[status(thm)],[c_60138,c_6695]) ).

tcf(c_61033,plain,
    '>='('==>'(b,c),'==>'(b,iPr_def_11)),
    inference(superposition,[status(thm)],[c_60152,c_5467]) ).

tcf(c_66188,plain,
    '>='('+'(b,'==>'(b,c)),iPr_def_11),
    inference(superposition,[status(thm)],[c_61033,c_55]) ).

tcf(c_67625,plain,
    '>='(c,iPr_def_11),
    inference(demodulation,[status(thm)],[c_66188,c_51,c_61,c_34536]) ).

tcf(c_67626,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_67625,c_1627]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : LCL894+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37  % Computer : n026.cluster.edu
% 0.09/0.37  % Model    : x86_64 x86_64
% 0.09/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37  % Memory   : 8046.5625MB
% 0.09/0.37  % OS       : Linux 6.8.0-71-generic
% 0.09/0.37  % CPULimit : 300
% 0.09/0.37  % WCLimit  : 300
% 0.09/0.37  % DateTime : Thu Sep 24 00:42:10 UTC 2026
% 0.09/0.37  % CPUTime  : 
% 0.09/0.37  Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41  Running first-order theorem proving
% 0.09/0.41  Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.42  
% 0.09/0.42  % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42  
% 0.09/0.42  % Detected problem language: tptp
% 0.09/0.43  % Proving...
% 9.23/4.25  % SZS status Started for theBenchmark.p
% 9.23/4.25  % SZS status Theorem for theBenchmark.p
% 9.23/4.25  
% 9.23/4.25  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 9.23/4.25  
% 9.23/4.25  % ------  iProver source info
% 9.23/4.25  
% 9.23/4.25  % git: date: 2026-07-19 20:42:38 +0200
% 9.23/4.25  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 9.23/4.25  % git: non_committed_changes: false
% 9.23/4.25  
% 9.23/4.25  % ------ Parsing...
% 9.23/4.25  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 9.23/4.25  
% 9.23/4.25  % ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e % 
% 9.23/4.25  
% 9.23/4.25  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 9.23/4.25  
% 9.23/4.25  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 9.23/4.25  % ------ Proving...
% 9.23/4.25  % ------ Problem Properties 
% 9.23/4.25  
% 9.23/4.25  % 
% 9.23/4.25  % clauses                               18
% 9.23/4.25  % conjectures                           3
% 9.23/4.25  % EPR                                   7
% 9.23/4.25  % Horn                                  16
% 9.23/4.25  % unary                                 8
% 9.23/4.25  % binary                                7
% 9.23/4.25  % lits                                  31
% 9.23/4.25  % lits eq                               7
% 9.23/4.25  % fd_pure                               0
% 9.23/4.25  % fd_pseudo                             0
% 9.23/4.25  % fd_cond                               0
% 9.23/4.25  % fd_pseudo_cond                        1
% 9.23/4.25  % AC symbols                            1
% 9.23/4.25  
% 9.23/4.25  % ------ Schedule dynamic 5 is on 
% 9.23/4.25  
% 9.23/4.25  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 9.23/4.25  
% 9.23/4.25  
% 9.23/4.25  % ------ 
% 9.23/4.25  % Current options:
% 9.23/4.25  % ------ 
% 9.23/4.25  
% 9.23/4.25  
% 9.23/4.25  % 
% 9.23/4.25  
% 9.23/4.25  % ------ Proving...
% 9.23/4.25  % 
% 9.23/4.25  
% 9.23/4.25  % SZS status Theorem for theBenchmark.p
% 9.23/4.25  
% 9.23/4.25  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 9.23/4.26  
% 9.23/4.26  
%------------------------------------------------------------------------------