↑ Up

iProver---3.9.4.THM-CRf.s

View TPTP
Problem
Process solution in
SystemOnTSTP
Download .tgz
%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : SET703+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM

% Computer : n006.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 02:47:50 PM UTC 2026

% Result   : Theorem 7.79s 1.69s
% Output   : CNFRefutation 7.79s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   88 (  22 unt;   0 def)
%            Number of atoms       :  211 (  66 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  209 (  86   ~; 101   |;  13   &)
%                                         (   5 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 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; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :  146 (   0 sgn 143   !;   3   ?;  66   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( equal_set(X0,X1)
    <=> ( subset(X1,X0)
        & subset(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).

fof(f5,axiom,
    ! [X0,X1,X2] :
      ( member(X0,union(X1,X2))
    <=> ( member(X0,X2)
        | member(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',union) ).

fof(f8,axiom,
    ! [X0,X1] :
      ( member(X0,singleton(X1))
    <=> X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',singleton) ).

fof(f9,axiom,
    ! [X0,X1,X2] :
      ( member(X0,unordered_pair(X1,X2))
    <=> ( X0 = X2
        | X0 = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',unordered_pair) ).

fof(f12,conjecture,
    ! [X0,X1] : equal_set(union(singleton(X0),singleton(X1)),unordered_pair(X0,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI41) ).

fof(f13,negated_conjecture,
    ~ ! [X0,X1] : equal_set(union(singleton(X0),singleton(X1)),unordered_pair(X0,X1)),
    inference(negated_conjecture,[status(cth)],[f12]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        & subset(X0,X1) )
     => equal_set(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f2]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) )
     => subset(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f1]) ).

fof(f16,plain,
    ? [X0,X1] : ~ equal_set(union(singleton(X0),singleton(X1)),unordered_pair(X0,X1)),
    inference(ennf_transformation,[],[f13]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | ~ subset(X0,X1)
      | equal_set(X0,X1) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | ~ subset(X0,X1)
      | equal_set(X0,X1) ),
    inference(flattening,[],[f17]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( member(X2,X0)
          & ~ member(X2,X1) )
      | subset(X0,X1) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f20,plain,
    ~ equal_set(union(singleton(sK0),singleton(sK1)),unordered_pair(sK0,sK1)),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f16]) ).

fof(f21,plain,
    ! [X0,X1,X2] :
      ( ( ~ member(X0,union(X1,X2))
        | member(X0,X2)
        | member(X0,X1) )
      & ( ( ~ member(X0,X2)
          & ~ member(X0,X1) )
        | member(X0,union(X1,X2)) ) ),
    inference(nnf_transformation,[],[f5]) ).

fof(f22,plain,
    ! [X0,X1,X2] :
      ( ( ~ member(X0,union(X1,X2))
        | member(X0,X2)
        | member(X0,X1) )
      & ( ( ~ member(X0,X2)
          & ~ member(X0,X1) )
        | member(X0,union(X1,X2)) ) ),
    inference(flattening,[],[f21]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ( ~ member(X0,singleton(X1))
        | X0 = X1 )
      & ( X0 != X1
        | member(X0,singleton(X1)) ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( ( ~ member(X0,unordered_pair(X1,X2))
        | X0 = X2
        | X0 = X1 )
      & ( ( X0 != X2
          & X0 != X1 )
        | member(X0,unordered_pair(X1,X2)) ) ),
    inference(nnf_transformation,[],[f9]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( ( ~ member(X0,unordered_pair(X1,X2))
        | X0 = X2
        | X0 = X1 )
      & ( ( X0 != X2
          & X0 != X1 )
        | member(X0,unordered_pair(X1,X2)) ) ),
    inference(flattening,[],[f24]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( member(sK2(X0,X1),X0)
        & ~ member(sK2(X0,X1),X1) )
      | subset(X0,X1) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f19]) ).

fof(f27,plain,
    ~ equal_set(union(singleton(sK0),singleton(sK1)),unordered_pair(sK0,sK1)),
    inference(cnf_transformation,[],[f20]) ).

fof(f28,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,union(X1,X2))
      | member(X0,X2)
      | member(X0,X1) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f29,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,X2)
      | member(X0,union(X1,X2)) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f30,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,X1)
      | member(X0,union(X1,X2)) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | ~ subset(X0,X1)
      | equal_set(X0,X1) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ~ member(X0,singleton(X1))
      | X0 = X1 ),
    inference(cnf_transformation,[],[f23]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( X0 != X1
      | member(X0,singleton(X1)) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f34,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,unordered_pair(X1,X2))
      | X0 = X2
      | X0 = X1 ),
    inference(cnf_transformation,[],[f25]) ).

fof(f35,plain,
    ! [X2,X0,X1] :
      ( X0 != X2
      | member(X0,unordered_pair(X1,X2)) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f36,plain,
    ! [X2,X0,X1] :
      ( X0 != X1
      | member(X0,unordered_pair(X1,X2)) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( member(sK2(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ~ member(sK2(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f39,plain,
    ! [X1] : member(X1,singleton(X1)),
    inference(equality_resolution,[],[f33]) ).

fof(f40,plain,
    ! [X2,X1] : member(X1,unordered_pair(X1,X2)),
    inference(equality_resolution,[],[f36]) ).

fof(f41,plain,
    ! [X2,X1] : member(X2,unordered_pair(X1,X2)),
    inference(equality_resolution,[],[f35]) ).

tcf(c_49,negated_conjecture,
    ~ equal_set(union(singleton(sK0),singleton(sK1)),unordered_pair(sK0,sK1)),
    inference(cnf_transformation,[],[f27]) ).

tcf(c_50,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[],[f30]) ).

tcf(c_51,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( member(X0,union(X2,X1))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[],[f29]) ).

tcf(c_52,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( member(X0,X2)
      | member(X0,X1)
      | ~ member(X0,union(X1,X2)) ),
    inference(cnf_transformation,[],[f28]) ).

tcf(c_53,plain,
    ! [X0: $i,X1: $i] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f31]) ).

tcf(c_54,plain,
    ! [X0: $i] : member(X0,singleton(X0)),
    inference(cnf_transformation,[],[f39]) ).

tcf(c_55,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ~ member(X0,singleton(X1)) ),
    inference(cnf_transformation,[],[f32]) ).

tcf(c_56,plain,
    ! [X0: $i,X1: $i] : member(X0,unordered_pair(X0,X1)),
    inference(cnf_transformation,[],[f40]) ).

tcf(c_57,plain,
    ! [X0: $i,X1: $i] : member(X0,unordered_pair(X1,X0)),
    inference(cnf_transformation,[],[f41]) ).

tcf(c_58,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0 = X2 )
      | ( X0 = X1 )
      | ~ member(X0,unordered_pair(X1,X2)) ),
    inference(cnf_transformation,[],[f34]) ).

tcf(c_59,plain,
    ! [X0: $i,X1: $i] :
      ( subset(X0,X1)
      | ~ member(sK2(X0,X1),X1) ),
    inference(cnf_transformation,[],[f38]) ).

tcf(c_60,plain,
    ! [X0: $i,X1: $i] :
      ( subset(X0,X1)
      | member(sK2(X0,X1),X0) ),
    inference(cnf_transformation,[],[f37]) ).

tcf(c_61,plain,
    member(sK0,singleton(sK0)),
    inference(instantiation,[status(thm)],[c_54]) ).

tcf(c_65,plain,
    ( ( sK0 = sK0 )
    | ~ member(sK0,singleton(sK0)) ),
    inference(instantiation,[status(thm)],[c_55]) ).

tcf(c_160,plain,
    ! [X0: $i,X1: $i] :
      ( ~ subset(X1,X0)
      | ~ subset(X0,X1)
      | ( unordered_pair(sK0,sK1) != X1 )
      | ( union(singleton(sK0),singleton(sK1)) != X0 ) ),
    inference(resolution_lifted,[status(thm)],[c_49,c_53]) ).

tcf(c_161,plain,
    ( ~ subset(unordered_pair(sK0,sK1),union(singleton(sK0),singleton(sK1)))
    | ~ subset(union(singleton(sK0),singleton(sK1)),unordered_pair(sK0,sK1)) ),
    inference(unflattening,[status(thm)],[c_160]) ).

tcf(c_254,plain,
    ! [X0: $i] : X0 = X0,
    theory(equality) ).

tcf(c_257,plain,
    ! [X0: $i,X1: $i] :
      ( ( singleton(X0) = singleton(X1) )
      | ( X0 != X1 ) ),
    theory(equality) ).

tcf(c_260,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( member(X0,X2)
      | ~ member(X1,X3)
      | ( X2 != X3 )
      | ( X0 != X1 ) ),
    theory(equality) ).

tcf(c_262,plain,
    ( ( singleton(sK0) = singleton(sK0) )
    | ( sK0 != sK0 ) ),
    inference(instantiation,[status(thm)],[c_257]) ).

tcf(c_464,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( subset(union(X0,X1),X2)
      | member(sK2(union(X0,X1),X2),X1)
      | member(sK2(union(X0,X1),X2),X0) ),
    inference(superposition,[status(thm)],[c_60,c_52]) ).

tcf(c_474,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( subset(X0,union(X1,X2))
      | ~ member(sK2(X0,union(X1,X2)),X2) ),
    inference(superposition,[status(thm)],[c_51,c_59]) ).

tcf(c_490,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( subset(unordered_pair(X0,X1),X2)
      | ( sK2(unordered_pair(X0,X1),X2) = X1 )
      | ( sK2(unordered_pair(X0,X1),X2) = X0 ) ),
    inference(superposition,[status(thm)],[c_60,c_58]) ).

tcf(c_591,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( subset(union(X0,singleton(X1)),X2)
      | member(sK2(union(X0,singleton(X1)),X2),X0)
      | ( sK2(union(X0,singleton(X1)),X2) = X1 ) ),
    inference(superposition,[status(thm)],[c_464,c_55]) ).

tcf(c_673,plain,
    ( subset(union(singleton(sK0),singleton(sK1)),unordered_pair(sK0,sK1))
    | ~ member(sK2(union(singleton(sK0),singleton(sK1)),unordered_pair(sK0,sK1)),unordered_pair(sK0,sK1)) ),
    inference(instantiation,[status(thm)],[c_59]) ).

tcf(c_675,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( member(X0,X2)
      | ~ member(X1,singleton(X1))
      | ( X2 != singleton(X1) )
      | ( X0 != X1 ) ),
    inference(instantiation,[status(thm)],[c_260]) ).

tcf(c_677,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( member(X0,X2)
      | ~ member(X1,unordered_pair(X1,X3))
      | ( X2 != unordered_pair(X1,X3) )
      | ( X0 != X1 ) ),
    inference(instantiation,[status(thm)],[c_260]) ).

tcf(c_683,plain,
    ( subset(unordered_pair(sK0,sK1),union(singleton(sK0),singleton(sK1)))
    | ~ member(sK2(unordered_pair(sK0,sK1),union(singleton(sK0),singleton(sK1))),union(singleton(sK0),singleton(sK1))) ),
    inference(instantiation,[status(thm)],[c_59]) ).

tcf(c_920,plain,
    ! [X0: $i,X1: $i] :
      ( member(X1,singleton(X0))
      | ~ member(X0,singleton(X0))
      | ( X1 != X0 )
      | ( singleton(X0) != singleton(X0) ) ),
    inference(instantiation,[status(thm)],[c_675]) ).

tcf(c_981,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( member(X2,unordered_pair(X0,X1))
      | ~ member(X0,unordered_pair(X0,X1))
      | ( X2 != X0 )
      | ( unordered_pair(X0,X1) != unordered_pair(X0,X1) ) ),
    inference(instantiation,[status(thm)],[c_677]) ).

tcf(c_982,plain,
    ! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X0,X1),
    inference(instantiation,[status(thm)],[c_254]) ).

tcf(c_1373,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( member(X0,union(singleton(X1),X2))
      | ~ member(X0,singleton(X1)) ),
    inference(instantiation,[status(thm)],[c_50]) ).

tcf(c_1486,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( subset(union(singleton(X0),singleton(X1)),X2)
      | ( sK2(union(singleton(X0),singleton(X1)),X2) = X1 )
      | ( sK2(union(singleton(X0),singleton(X1)),X2) = X0 ) ),
    inference(superposition,[status(thm)],[c_591,c_55]) ).

tcf(c_2203,plain,
    ( member(sK2(union(singleton(sK0),singleton(sK1)),unordered_pair(sK0,sK1)),unordered_pair(sK0,sK1))
    | ~ member(sK0,unordered_pair(sK0,sK1))
    | ( unordered_pair(sK0,sK1) != unordered_pair(sK0,sK1) )
    | ( sK2(union(singleton(sK0),singleton(sK1)),unordered_pair(sK0,sK1)) != sK0 ) ),
    inference(instantiation,[status(thm)],[c_981]) ).

tcf(c_2219,plain,
    member(sK0,unordered_pair(sK0,sK1)),
    inference(instantiation,[status(thm)],[c_56]) ).

tcf(c_2234,plain,
    unordered_pair(sK0,sK1) = unordered_pair(sK0,sK1),
    inference(instantiation,[status(thm)],[c_982]) ).

tcf(c_2431,plain,
    ( member(sK2(unordered_pair(sK0,sK1),union(singleton(sK0),singleton(sK1))),union(singleton(sK0),singleton(sK1)))
    | ~ member(sK2(unordered_pair(sK0,sK1),union(singleton(sK0),singleton(sK1))),singleton(sK0)) ),
    inference(instantiation,[status(thm)],[c_1373]) ).

tcf(c_6466,plain,
    ( member(sK2(unordered_pair(sK0,sK1),union(singleton(sK0),singleton(sK1))),singleton(sK0))
    | ~ member(sK0,singleton(sK0))
    | ( singleton(sK0) != singleton(sK0) )
    | ( sK2(unordered_pair(sK0,sK1),union(singleton(sK0),singleton(sK1))) != sK0 ) ),
    inference(instantiation,[status(thm)],[c_920]) ).

tcf(c_11141,plain,
    ( ( sK2(union(singleton(sK0),singleton(sK1)),unordered_pair(sK0,sK1)) = sK1 )
    | ( sK2(union(singleton(sK0),singleton(sK1)),unordered_pair(sK0,sK1)) = sK0 )
    | ~ subset(unordered_pair(sK0,sK1),union(singleton(sK0),singleton(sK1))) ),
    inference(superposition,[status(thm)],[c_1486,c_161]) ).

tcf(c_11644,plain,
    ( ( sK2(union(singleton(sK0),singleton(sK1)),unordered_pair(sK0,sK1)) = sK1 )
    | ~ subset(unordered_pair(sK0,sK1),union(singleton(sK0),singleton(sK1))) ),
    inference(global_subsumption_just,[status(thm)],[c_11141,c_161,c_673,c_2203,c_2219,c_2234,c_11141]) ).

tcf(c_11650,plain,
    ( ( sK2(unordered_pair(sK0,sK1),union(singleton(sK0),singleton(sK1))) = sK1 )
    | ( sK2(unordered_pair(sK0,sK1),union(singleton(sK0),singleton(sK1))) = sK0 )
    | ( sK2(union(singleton(sK0),singleton(sK1)),unordered_pair(sK0,sK1)) = sK1 ) ),
    inference(superposition,[status(thm)],[c_490,c_11644]) ).

tcf(c_11749,plain,
    ( ( sK2(unordered_pair(sK0,sK1),union(singleton(sK0),singleton(sK1))) = sK1 )
    | ( sK2(union(singleton(sK0),singleton(sK1)),unordered_pair(sK0,sK1)) = sK1 ) ),
    inference(global_subsumption_just,[status(thm)],[c_11650,c_61,c_65,c_262,c_683,c_2431,c_6466,c_11644,c_11650]) ).

tcf(c_11755,plain,
    ( subset(union(singleton(sK0),singleton(sK1)),unordered_pair(sK0,sK1))
    | ( sK2(unordered_pair(sK0,sK1),union(singleton(sK0),singleton(sK1))) = sK1 )
    | ~ member(sK1,unordered_pair(sK0,sK1)) ),
    inference(superposition,[status(thm)],[c_11749,c_59]) ).

tcf(c_11761,plain,
    ( subset(union(singleton(sK0),singleton(sK1)),unordered_pair(sK0,sK1))
    | ( sK2(unordered_pair(sK0,sK1),union(singleton(sK0),singleton(sK1))) = sK1 ) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11755,c_57]) ).

tcf(c_11782,plain,
    ( ( sK2(unordered_pair(sK0,sK1),union(singleton(sK0),singleton(sK1))) = sK1 )
    | ~ subset(unordered_pair(sK0,sK1),union(singleton(sK0),singleton(sK1))) ),
    inference(superposition,[status(thm)],[c_11761,c_161]) ).

tcf(c_11789,plain,
    ( ( sK2(unordered_pair(sK0,sK1),union(singleton(sK0),singleton(sK1))) = sK1 )
    | ( sK2(unordered_pair(sK0,sK1),union(singleton(sK0),singleton(sK1))) = sK0 ) ),
    inference(superposition,[status(thm)],[c_490,c_11782]) ).

tcf(c_11792,plain,
    sK2(unordered_pair(sK0,sK1),union(singleton(sK0),singleton(sK1))) = sK1,
    inference(global_subsumption_just,[status(thm)],[c_11789,c_61,c_65,c_262,c_683,c_2431,c_6466,c_11782,c_11789]) ).

tcf(c_11798,plain,
    ( subset(unordered_pair(sK0,sK1),union(singleton(sK0),singleton(sK1)))
    | ~ member(sK1,singleton(sK1)) ),
    inference(superposition,[status(thm)],[c_11792,c_474]) ).

tcf(c_11802,plain,
    subset(unordered_pair(sK0,sK1),union(singleton(sK0),singleton(sK1))),
    inference(forward_subsumption_resolution,[status(thm)],[c_11798,c_54]) ).

tcf(c_11803,plain,
    sK2(union(singleton(sK0),singleton(sK1)),unordered_pair(sK0,sK1)) = sK1,
    inference(backward_subsumption_resolution,[status(thm)],[c_11644,c_11802]) ).

tcf(c_11804,plain,
    ~ subset(union(singleton(sK0),singleton(sK1)),unordered_pair(sK0,sK1)),
    inference(backward_subsumption_resolution,[status(thm)],[c_161,c_11802]) ).

tcf(c_11807,plain,
    ( subset(union(singleton(sK0),singleton(sK1)),unordered_pair(sK0,sK1))
    | ~ member(sK1,unordered_pair(sK0,sK1)) ),
    inference(superposition,[status(thm)],[c_11803,c_59]) ).

tcf(c_11813,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_11807,c_11804,c_57]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SET703+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36  % Computer : n006.cluster.edu
% 0.09/0.36  % Model    : x86_64 x86_64
% 0.09/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36  % Memory   : 8046.5625MB
% 0.09/0.36  % OS       : Linux 6.8.0-71-generic
% 0.09/0.36  % CPULimit : 300
% 0.09/0.36  % WCLimit  : 300
% 0.09/0.36  % DateTime : Thu Sep 24 11:42:41 UTC 2026
% 0.09/0.36  % CPUTime  : 
% 0.09/0.36  Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40  Running first-order theorem proving
% 0.09/0.40  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
% 0.09/0.41  
% 0.09/0.41  % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41  
% 0.09/0.41  % Detected problem language: tptp
% 0.09/0.42  % Proving...
% 7.79/1.69  % SZS status Started for theBenchmark.p
% 7.79/1.69  % SZS status Theorem for theBenchmark.p
% 7.79/1.69  
% 7.79/1.69  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.79/1.69  
% 7.79/1.69  % ------  iProver source info
% 7.79/1.69  
% 7.79/1.69  % git: date: 2026-07-19 20:42:38 +0200
% 7.79/1.69  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.79/1.69  % git: non_committed_changes: false
% 7.79/1.69  
% 7.79/1.69  % ------ Parsing...
% 7.79/1.69  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 7.79/1.69  
% 7.79/1.69  % ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e % 
% 7.79/1.69  
% 7.79/1.69  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 7.79/1.69  
% 7.79/1.69  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 7.79/1.69  % ------ Proving...
% 7.79/1.69  % ------ Problem Properties 
% 7.79/1.69  
% 7.79/1.69  % 
% 7.79/1.69  % clauses                               11
% 7.79/1.69  % conjectures                           0
% 7.79/1.69  % EPR                                   0
% 7.79/1.69  % Horn                                  8
% 7.79/1.69  % unary                                 3
% 7.79/1.69  % binary                                6
% 7.79/1.69  % lits                                  21
% 7.79/1.69  % lits eq                               3
% 7.79/1.69  % fd_pure                               0
% 7.79/1.69  % fd_pseudo                             0
% 7.79/1.69  % fd_cond                               0
% 7.79/1.69  % fd_pseudo_cond                        2
% 7.79/1.69  % AC symbols                            0
% 7.79/1.69  
% 7.79/1.69  % ------ Schedule dynamic 5 is on 
% 7.79/1.69  
% 7.79/1.69  % ------ no conjectures: strip conj schedule 
% 7.79/1.69  
% 7.79/1.69  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 7.79/1.69  
% 7.79/1.69  
% 7.79/1.69  % ------ 
% 7.79/1.69  % Current options:
% 7.79/1.69  % ------ 
% 7.79/1.69  
% 7.79/1.69  
% 7.79/1.69  % 
% 7.79/1.69  
% 7.79/1.69  % ------ Proving...
% 7.79/1.69  % 
% 7.79/1.69  
% 7.79/1.69  % SZS status Theorem for theBenchmark.p
% 7.79/1.69  
% 7.79/1.69  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.79/1.69  
% 7.79/1.69  
%------------------------------------------------------------------------------