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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : NUN085+1 : TPTP v9.3.1. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM

% Computer : n011.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 02:29:59 PM UTC 2026

% Result   : Theorem 15.53s 3.25s
% Output   : CNFRefutation 15.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   12
% Syntax   : Number of formulae    :  102 (  33 unt;   0 def)
%            Number of atoms       :  256 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  293 ( 139   ~; 118   |;  36   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :   12 (  12 usr;   6 con; 0-2 aty)
%            Number of variables   :  182 (   0 sgn 170   !;  12   ?;  86   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ? [X0] :
    ! [X1] :
      ( ( ~ id(X1,X0)
        & ~ r1(X1) )
      | ( r1(X1)
        & id(X1,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_1) ).

fof(f2,axiom,
    ! [X0] :
    ? [X1] :
    ! [X2] :
      ( ( ~ id(X2,X1)
        & ~ r2(X0,X2) )
      | ( r2(X0,X2)
        & id(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_2) ).

fof(f3,axiom,
    ! [X0,X1] :
    ? [X2] :
    ! [X3] :
      ( ( ~ id(X3,X2)
        & ~ r3(X0,X1,X3) )
      | ( r3(X0,X1,X3)
        & id(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_3) ).

fof(f5,axiom,
    ! [X0] : id(X0,X0),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_5) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( id(X1,X0)
      | ~ id(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_6) ).

fof(f7,axiom,
    ! [X0,X1,X2] :
      ( ~ id(X1,X2)
      | id(X0,X2)
      | ~ id(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_7) ).

fof(f8,axiom,
    ! [X0,X1] :
      ( ( r1(X1)
        & r1(X0) )
      | ( ~ r1(X1)
        & ~ r1(X0) )
      | ~ id(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_8) ).

fof(f9,axiom,
    ! [X0,X1,X2,X3] :
      ( ( r2(X2,X3)
        & r2(X0,X1) )
      | ( ~ r2(X2,X3)
        & ~ r2(X0,X1) )
      | ~ id(X1,X3)
      | ~ id(X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_9) ).

fof(f10,axiom,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ( r3(X3,X4,X5)
        & r3(X0,X1,X2) )
      | ( ~ r3(X3,X4,X5)
        & ~ r3(X0,X1,X2) )
      | ~ id(X2,X5)
      | ~ id(X1,X4)
      | ~ id(X0,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_10) ).

fof(f12,axiom,
    ! [X0,X1] :
    ? [X2] :
      ( ? [X5] :
          ( r3(X0,X1,X5)
          & r2(X5,X2) )
      & ? [X3] :
          ( ? [X4] :
              ( r3(X0,X4,X3)
              & r2(X1,X4) )
          & id(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_1a) ).

fof(f18,axiom,
    ! [X0,X1] :
      ( ~ r2(X0,X1)
      | ! [X2] :
          ( ~ r1(X2)
          | ~ id(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_7a) ).

fof(f19,conjecture,
    ! [X0] :
      ( ! [X4] :
          ( ~ r1(X4)
          | ~ id(X0,X4) )
      | ! [X1] :
          ( ! [X3] :
              ( ~ r2(X3,X1)
              | ~ r1(X3) )
          | ! [X2] :
              ( ~ r3(X2,X1,X0)
              | ~ r1(X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zeroplusoneidzero) ).

fof(f20,negated_conjecture,
    ~ ! [X0] :
        ( ! [X4] :
            ( ~ r1(X4)
            | ~ id(X0,X4) )
        | ! [X1] :
            ( ! [X3] :
                ( ~ r2(X3,X1)
                | ~ r1(X3) )
            | ! [X2] :
                ( ~ r3(X2,X1,X0)
                | ~ r1(X2) ) ) ),
    inference(negated_conjecture,[status(cth)],[f19]) ).

fof(f21,plain,
    ? [X0] :
      ( ? [X4] :
          ( r1(X4)
          & id(X0,X4) )
      & ? [X1] :
          ( ? [X3] :
              ( r2(X3,X1)
              & r1(X3) )
          & ? [X2] :
              ( r3(X2,X1,X0)
              & r1(X2) ) ) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f22,plain,
    ! [X1] :
      ( ( ~ id(X1,sK0)
        & ~ r1(X1) )
      | ( r1(X1)
        & id(X1,sK0) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f1]) ).

fof(f23,plain,
    ! [X0,X2] :
      ( ( ~ id(X2,sK1(X0))
        & ~ r2(X0,X2) )
      | ( r2(X0,X2)
        & id(X2,sK1(X0)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f2]) ).

fof(f24,plain,
    ! [X0,X1,X3] :
      ( ( ~ id(X3,sK2(X0,X1))
        & ~ r3(X0,X1,X3) )
      | ( r3(X0,X1,X3)
        & id(X3,sK2(X0,X1)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f3]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( r3(X0,X1,sK7(X0,X1))
      & r2(sK7(X0,X1),sK4(X0,X1))
      & r3(X0,sK6(X0,X1),sK5(X0,X1))
      & r2(X1,sK6(X0,X1))
      & id(sK5(X0,X1),sK4(X0,X1)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X2,sK4(X0,X1)),skolemize(X3,sK5(X0,X1)),skolemize(X4,sK6(X0,X1)),skolemize(X5,sK7(X0,X1))],[f12]) ).

fof(f31,plain,
    ( r1(sK24)
    & id(sK20,sK24)
    & r2(sK23,sK21)
    & r1(sK23)
    & r3(sK22,sK21,sK20)
    & r1(sK22) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23,sK24]),skolemize(X0,sK20),skolemize(X1,sK21),skolemize(X2,sK22),skolemize(X3,sK23),skolemize(X4,sK24)],[f21]) ).

fof(f35,plain,
    ! [X1] :
      ( ~ r1(X1)
      | id(X1,sK0) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f39,plain,
    ! [X2,X0] :
      ( ~ r2(X0,X2)
      | id(X2,sK1(X0)) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f43,plain,
    ! [X3,X0,X1] :
      ( ~ r3(X0,X1,X3)
      | id(X3,sK2(X0,X1)) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f48,plain,
    ! [X0] : id(X0,X0),
    inference(cnf_transformation,[],[f5]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( id(X1,X0)
      | ~ id(X0,X1) ),
    inference(cnf_transformation,[],[f6]) ).

fof(f50,plain,
    ! [X2,X0,X1] :
      ( ~ id(X1,X2)
      | id(X0,X2)
      | ~ id(X0,X1) ),
    inference(cnf_transformation,[],[f7]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( r1(X0)
      | ~ r1(X1)
      | ~ id(X0,X1) ),
    inference(cnf_transformation,[],[f8]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( r1(X1)
      | ~ r1(X0)
      | ~ id(X0,X1) ),
    inference(cnf_transformation,[],[f8]) ).

fof(f57,plain,
    ! [X2,X3,X0,X1] :
      ( r2(X2,X3)
      | ~ r2(X0,X1)
      | ~ id(X1,X3)
      | ~ id(X0,X2) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f61,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( r3(X3,X4,X5)
      | ~ r3(X0,X1,X2)
      | ~ id(X2,X5)
      | ~ id(X1,X4)
      | ~ id(X0,X3) ),
    inference(cnf_transformation,[],[f10]) ).

fof(f68,plain,
    ! [X0,X1] : r2(sK7(X0,X1),sK4(X0,X1)),
    inference(cnf_transformation,[],[f26]) ).

fof(f69,plain,
    ! [X0,X1] : r3(X0,sK6(X0,X1),sK5(X0,X1)),
    inference(cnf_transformation,[],[f26]) ).

fof(f70,plain,
    ! [X0,X1] : r2(X1,sK6(X0,X1)),
    inference(cnf_transformation,[],[f26]) ).

fof(f71,plain,
    ! [X0,X1] : id(sK5(X0,X1),sK4(X0,X1)),
    inference(cnf_transformation,[],[f26]) ).

fof(f89,plain,
    ! [X2,X0,X1] :
      ( ~ r2(X0,X1)
      | ~ r1(X2)
      | ~ id(X2,X1) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f90,plain,
    r1(sK24),
    inference(cnf_transformation,[],[f31]) ).

fof(f91,plain,
    id(sK20,sK24),
    inference(cnf_transformation,[],[f31]) ).

fof(f92,plain,
    r2(sK23,sK21),
    inference(cnf_transformation,[],[f31]) ).

fof(f93,plain,
    r1(sK23),
    inference(cnf_transformation,[],[f31]) ).

fof(f94,plain,
    r3(sK22,sK21,sK20),
    inference(cnf_transformation,[],[f31]) ).

fof(f95,plain,
    r1(sK22),
    inference(cnf_transformation,[],[f31]) ).

tcf(c_49,plain,
    ! [X0: $i] :
      ( id(X0,sK0)
      | ~ r1(X0) ),
    inference(cnf_transformation,[],[f35]) ).

tcf(c_51,plain,
    ! [X0: $i,X1: $i] :
      ( id(X1,sK1(X0))
      | ~ r2(X0,X1) ),
    inference(cnf_transformation,[],[f39]) ).

tcf(c_53,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( id(X2,sK2(X0,X1))
      | ~ r3(X0,X1,X2) ),
    inference(cnf_transformation,[],[f43]) ).

tcf(c_57,plain,
    ! [X0: $i] : id(X0,X0),
    inference(cnf_transformation,[],[f48]) ).

tcf(c_58,plain,
    ! [X0: $i,X1: $i] :
      ( id(X1,X0)
      | ~ id(X0,X1) ),
    inference(cnf_transformation,[],[f49]) ).

tcf(c_59,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( id(X2,X1)
      | ~ id(X2,X0)
      | ~ id(X0,X1) ),
    inference(cnf_transformation,[],[f50]) ).

tcf(c_60,plain,
    ! [X0: $i,X1: $i] :
      ( r1(X1)
      | ~ r1(X0)
      | ~ id(X0,X1) ),
    inference(cnf_transformation,[],[f53]) ).

tcf(c_61,plain,
    ! [X0: $i,X1: $i] :
      ( r1(X0)
      | ~ r1(X1)
      | ~ id(X0,X1) ),
    inference(cnf_transformation,[],[f52]) ).

tcf(c_62,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( r2(X3,X1)
      | ~ r2(X2,X0)
      | ~ id(X2,X3)
      | ~ id(X0,X1) ),
    inference(cnf_transformation,[],[f57]) ).

tcf(c_64,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( r3(X5,X3,X4)
      | ~ id(X2,X4)
      | ~ id(X1,X3)
      | ~ id(X0,X5)
      | ~ r3(X0,X1,X2) ),
    inference(cnf_transformation,[],[f61]) ).

tcf(c_68,plain,
    ! [X0: $i,X1: $i] : id(sK5(X0,X1),sK4(X0,X1)),
    inference(cnf_transformation,[],[f71]) ).

tcf(c_69,plain,
    ! [X0: $i,X1: $i] : r2(X0,sK6(X1,X0)),
    inference(cnf_transformation,[],[f70]) ).

tcf(c_70,plain,
    ! [X0: $i,X1: $i] : r3(X0,sK6(X0,X1),sK5(X0,X1)),
    inference(cnf_transformation,[],[f69]) ).

tcf(c_71,plain,
    ! [X0: $i,X1: $i] : r2(sK7(X0,X1),sK4(X0,X1)),
    inference(cnf_transformation,[],[f68]) ).

tcf(c_90,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ r1(X0)
      | ~ r2(X2,X1)
      | ~ id(X0,X1) ),
    inference(cnf_transformation,[],[f89]) ).

tcf(c_91,negated_conjecture,
    r1(sK22),
    inference(cnf_transformation,[],[f95]) ).

tcf(c_92,negated_conjecture,
    r3(sK22,sK21,sK20),
    inference(cnf_transformation,[],[f94]) ).

tcf(c_93,negated_conjecture,
    r1(sK23),
    inference(cnf_transformation,[],[f93]) ).

tcf(c_94,negated_conjecture,
    r2(sK23,sK21),
    inference(cnf_transformation,[],[f92]) ).

tcf(c_95,negated_conjecture,
    id(sK20,sK24),
    inference(cnf_transformation,[],[f91]) ).

tcf(c_96,negated_conjecture,
    r1(sK24),
    inference(cnf_transformation,[],[f90]) ).

tcf(c_104,plain,
    r2(sK0,sK6(sK0,sK0)),
    inference(instantiation,[status(thm)],[c_69]) ).

tcf(c_431,negated_conjecture,
    r1(sK24),
    inference(demodulation,[status(thm)],[c_96]) ).

tcf(c_432,negated_conjecture,
    id(sK20,sK24),
    inference(demodulation,[status(thm)],[c_95]) ).

tcf(c_435,negated_conjecture,
    r3(sK22,sK21,sK20),
    inference(demodulation,[status(thm)],[c_92]) ).

tcf(c_437,plain,
    ! [X0: $i,X1: $i] :
      ( id(sK6(X1,X0),sK1(X0))
      | ~ r2(X0,sK6(X1,X0)) ),
    inference(instantiation,[status(thm)],[c_51]) ).

tcf(c_438,plain,
    ( id(sK6(sK0,sK0),sK1(sK0))
    | ~ r2(sK0,sK6(sK0,sK0)) ),
    inference(instantiation,[status(thm)],[c_437]) ).

tcf(c_459,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ r1(X2)
      | ~ id(X2,sK4(X0,X1))
      | ~ r2(sK7(X0,X1),sK4(X0,X1)) ),
    inference(instantiation,[status(thm)],[c_90]) ).

tcf(c_509,plain,
    ! [X0: $i,X1: $i] :
      ( r2(X1,X0)
      | ~ r2(sK23,sK21)
      | ~ id(sK23,X1)
      | ~ id(sK21,X0) ),
    inference(instantiation,[status(thm)],[c_62]) ).

tcf(c_565,plain,
    id(sK21,sK21),
    inference(instantiation,[status(thm)],[c_57]) ).

tcf(c_579,plain,
    ! [X0: $i,X1: $i] :
      ( id(sK21,X1)
      | ~ id(sK21,X0)
      | ~ id(X0,X1) ),
    inference(instantiation,[status(thm)],[c_59]) ).

tcf(c_598,plain,
    ( id(sK22,sK0)
    | ~ r1(sK22) ),
    inference(instantiation,[status(thm)],[c_49]) ).

tcf(c_641,plain,
    ! [X0: $i,X1: $i] :
      ( id(sK1(X1),X0)
      | ~ id(X0,sK1(X1)) ),
    inference(instantiation,[status(thm)],[c_58]) ).

tcf(c_756,plain,
    ! [X0: $i,X1: $i] :
      ( ~ r1(sK5(X0,X1))
      | ~ r2(sK7(X0,X1),sK4(X0,X1))
      | ~ id(sK5(X0,X1),sK4(X0,X1)) ),
    inference(instantiation,[status(thm)],[c_459]) ).

tcf(c_913,plain,
    id(sK24,sK20),
    inference(superposition,[status(thm)],[c_432,c_58]) ).

tcf(c_1271,plain,
    ( r1(sK20)
    | ~ r1(sK24) ),
    inference(superposition,[status(thm)],[c_913,c_60]) ).

tcf(c_1275,plain,
    r1(sK20),
    inference(forward_subsumption_resolution,[status(thm)],[c_1271,c_431]) ).

tcf(c_1771,plain,
    ! [X0: $i] :
      ( r2(X0,sK21)
      | ~ r2(sK23,sK21)
      | ~ id(sK21,sK21)
      | ~ id(sK23,X0) ),
    inference(instantiation,[status(thm)],[c_509]) ).

tcf(c_1772,plain,
    ( r2(sK0,sK21)
    | ~ r2(sK23,sK21)
    | ~ id(sK23,sK0)
    | ~ id(sK21,sK21) ),
    inference(instantiation,[status(thm)],[c_1771]) ).

tcf(c_1877,plain,
    ( id(sK23,sK0)
    | ~ r1(sK23) ),
    inference(instantiation,[status(thm)],[c_49]) ).

tcf(c_2653,plain,
    ! [X0: $i,X1: $i] :
      ( id(sK1(X1),sK6(X0,X1))
      | ~ id(sK6(X0,X1),sK1(X1)) ),
    inference(instantiation,[status(thm)],[c_641]) ).

tcf(c_2654,plain,
    ( id(sK1(sK0),sK6(sK0,sK0))
    | ~ id(sK6(sK0,sK0),sK1(sK0)) ),
    inference(instantiation,[status(thm)],[c_2653]) ).

tcf(c_8178,plain,
    ! [X0: $i] :
      ( id(sK21,sK1(X0))
      | ~ r2(X0,sK21) ),
    inference(instantiation,[status(thm)],[c_51]) ).

tcf(c_8179,plain,
    ( id(sK21,sK1(sK0))
    | ~ r2(sK0,sK21) ),
    inference(instantiation,[status(thm)],[c_8178]) ).

tcf(c_19534,plain,
    ! [X0: $i,X1: $i] :
      ( r1(sK4(X0,X1))
      | ~ r1(sK5(X0,X1)) ),
    inference(superposition,[status(thm)],[c_68,c_60]) ).

tcf(c_19575,plain,
    ! [X0: $i,X1: $i] : ~ r1(sK5(X0,X1)),
    inference(global_subsumption_just,[status(thm)],[c_19534,c_71,c_68,c_756]) ).

tcf(c_19657,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( r1(X2)
      | ~ r1(sK2(X0,X1))
      | ~ r3(X0,X1,X2) ),
    inference(superposition,[status(thm)],[c_53,c_61]) ).

tcf(c_19748,plain,
    ! [X0: $i,X1: $i] :
      ( r1(sK5(X0,X1))
      | ~ r1(sK2(X0,sK6(X0,X1))) ),
    inference(superposition,[status(thm)],[c_70,c_19657]) ).

tcf(c_19764,plain,
    ! [X0: $i,X1: $i] : ~ r1(sK2(X0,sK6(X0,X1))),
    inference(forward_subsumption_resolution,[status(thm)],[c_19748,c_19575]) ).

tcf(c_19809,plain,
    ! [X0: $i] :
      ( id(sK20,X0)
      | ~ id(sK24,X0) ),
    inference(superposition,[status(thm)],[c_432,c_59]) ).

tcf(c_20064,plain,
    ! [X0: $i,X1: $i] :
      ( id(sK20,sK2(X0,X1))
      | ~ r3(X0,X1,sK24) ),
    inference(superposition,[status(thm)],[c_53,c_19809]) ).

tcf(c_20340,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( r3(X0,X1,X2)
      | ~ id(sK20,X2)
      | ~ id(sK21,X1)
      | ~ id(sK22,X0) ),
    inference(superposition,[status(thm)],[c_435,c_64]) ).

tcf(c_21117,plain,
    ! [X0: $i,X1: $i] :
      ( r1(sK2(X0,X1))
      | ~ r1(sK20)
      | ~ r3(X0,X1,sK24) ),
    inference(superposition,[status(thm)],[c_20064,c_60]) ).

tcf(c_21126,plain,
    ! [X0: $i,X1: $i] :
      ( r1(sK2(X0,X1))
      | ~ r3(X0,X1,sK24) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_21117,c_1275]) ).

tcf(c_21140,plain,
    ! [X0: $i,X1: $i] :
      ( r1(sK2(X0,X1))
      | ~ id(sK20,sK24)
      | ~ id(sK21,X1)
      | ~ id(sK22,X0) ),
    inference(superposition,[status(thm)],[c_20340,c_21126]) ).

tcf(c_21146,plain,
    ! [X0: $i,X1: $i] :
      ( r1(sK2(X0,X1))
      | ~ id(sK21,X1)
      | ~ id(sK22,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_21140,c_432]) ).

tcf(c_21247,plain,
    ! [X0: $i,X1: $i] :
      ( ~ id(sK22,X0)
      | ~ id(sK21,sK6(X0,X1)) ),
    inference(superposition,[status(thm)],[c_21146,c_19764]) ).

tcf(c_21250,plain,
    ( ~ id(sK22,sK0)
    | ~ id(sK21,sK6(sK0,sK0)) ),
    inference(instantiation,[status(thm)],[c_21247]) ).

tcf(c_23871,plain,
    ! [X0: $i,X1: $i] :
      ( id(sK21,X1)
      | ~ id(sK21,sK1(X0))
      | ~ id(sK1(X0),X1) ),
    inference(instantiation,[status(thm)],[c_579]) ).

tcf(c_65153,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( id(sK21,sK6(X1,X2))
      | ~ id(sK21,sK1(X0))
      | ~ id(sK1(X0),sK6(X1,X2)) ),
    inference(instantiation,[status(thm)],[c_23871]) ).

tcf(c_65163,plain,
    ( id(sK21,sK6(sK0,sK0))
    | ~ id(sK21,sK1(sK0))
    | ~ id(sK1(sK0),sK6(sK0,sK0)) ),
    inference(instantiation,[status(thm)],[c_65153]) ).

tcf(c_65164,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_65163,c_21250,c_8179,c_2654,c_1877,c_1772,c_598,c_565,c_438,c_104,c_94,c_91,c_93]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : NUN085+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.35  % Computer : n011.cluster.edu
% 0.08/0.35  % Model    : x86_64 x86_64
% 0.08/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35  % Memory   : 8046.5625MB
% 0.08/0.35  % OS       : Linux 6.8.0-71-generic
% 0.08/0.35  % CPULimit : 300
% 0.08/0.35  % WCLimit  : 300
% 0.08/0.35  % DateTime : Thu Sep 24 05:59:13 UTC 2026
% 0.08/0.35  % CPUTime  : 
% 0.08/0.35  Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39  Running first-order theorem proving
% 0.12/0.39  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
% 0.12/0.40  
% 0.12/0.40  % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40  
% 0.12/0.40  % Detected problem language: tptp
% 0.12/0.42  % Proving...
% 15.53/3.25  % SZS status Started for theBenchmark.p
% 15.53/3.25  % SZS status Theorem for theBenchmark.p
% 15.53/3.25  
% 15.53/3.25  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 15.53/3.25  
% 15.53/3.25  % ------  iProver source info
% 15.53/3.25  
% 15.53/3.25  % git: date: 2026-07-19 20:42:38 +0200
% 15.53/3.25  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 15.53/3.25  % git: non_committed_changes: false
% 15.53/3.25  
% 15.53/3.25  % ------ Parsing...
% 15.53/3.25  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 15.53/3.25  
% 15.53/3.25  % ------ Preprocessing... sf_s  rm: 0 0s  sf_e  pe_s  pe_e % 
% 15.53/3.25  
% 15.53/3.25  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 15.53/3.25  % ------ Proving...
% 15.53/3.25  % ------ Problem Properties 
% 15.53/3.25  
% 15.53/3.25  % 
% 15.53/3.25  % clauses                               48
% 15.53/3.25  % conjectures                           6
% 15.53/3.25  % EPR                                   21
% 15.53/3.25  % Horn                                  44
% 15.53/3.25  % unary                                 24
% 15.53/3.25  % binary                                13
% 15.53/3.25  % lits                                  94
% 15.53/3.25  % lits eq                               0
% 15.53/3.25  % fd_pure                               0
% 15.53/3.25  % fd_pseudo                             0
% 15.53/3.25  % fd_cond                               0
% 15.53/3.25  % fd_pseudo_cond                        0
% 15.53/3.25  % AC symbols                            0
% 15.53/3.25  
% 15.53/3.25  % ------ Schedule dynamic 5 is on 
% 15.53/3.25  
% 15.53/3.25  % ------ no equalities: superposition off 
% 15.53/3.25  
% 15.53/3.25  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 15.53/3.25  
% 15.53/3.25  
% 15.53/3.25  % ------ 
% 15.53/3.25  % Current options:
% 15.53/3.25  % ------ 
% 15.53/3.25  
% 15.53/3.25  
% 15.53/3.25  % 
% 15.53/3.25  
% 15.53/3.25  % ------ Proving...
% 15.53/3.25  % 
% 15.53/3.25  
% 15.53/3.25  % SZS status Theorem for theBenchmark.p
% 15.53/3.25  
% 15.53/3.25  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 15.53/3.25  
% 15.53/3.25  
%------------------------------------------------------------------------------