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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : CSR020+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM

% Computer : n014.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 01:09:54 PM UTC 2026

% Result   : Theorem 4.77s 1.53s
% Output   : CNFRefutation 4.77s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f241ERROR: Could not build tree for root c_7317ERROR: MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
fof(f10,axiom,
    ! [X0,X1,X2] :
      ( ( terminates(X0,X2,X1)
        & happens(X0,X1) )
     => ~ holdsAt(X2,plus(X1,n1)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+0.ax',happens_terminates_not_holds) ).

fof(f14,axiom,
    ! [X0,X1,X2] :
      ( terminates(X0,X1,X2)
    <=> ( ( ~ happens(push,X2)
          & X1 = spinning
          & X0 = pull )
        | ( ~ happens(pull,X2)
          & X1 = spinning
          & X0 = push )
        | ( happens(push,X2)
          & X1 = backwards
          & X0 = pull )
        | ( happens(push,X2)
          & X1 = forwards
          & X0 = pull )
        | ( ~ happens(push,X2)
          & X1 = forwards
          & X0 = pull )
        | ( ~ happens(pull,X2)
          & X1 = backwards
          & X0 = push ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+2.ax',terminates_all_defn) ).

fof(f16,axiom,
    ! [X0,X1] :
      ( happens(X0,X1)
    <=> ( ( X1 = n2
          & X0 = push )
        | ( X1 = n2
          & X0 = pull )
        | ( X1 = n1
          & X0 = pull )
        | ( X1 = n0
          & X0 = push ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+2.ax',happens_all_defn) ).

fof(f17,axiom,
    push != pull,
    file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+2.ax',push_not_pull) ).

fof(f25,axiom,
    plus(n1,n1) = n2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus1_1) ).

fof(f32,axiom,
    ! [X0,X1] :
      ( less_or_equal(X0,X1)
    <=> ( X0 = X1
        | less(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal) ).

fof(f34,axiom,
    ! [X0] :
      ( less(X0,n1)
    <=> less_or_equal(X0,n0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less1) ).

fof(f35,axiom,
    ! [X0] :
      ( less(X0,n2)
    <=> less_or_equal(X0,n1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less2) ).

fof(f43,axiom,
    ! [X0,X1] :
      ( less(X0,X1)
    <=> ( X1 != X0
        & ~ less(X1,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_property) ).

fof(f48,conjecture,
    ~ holdsAt(spinning,n2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_spinning_2) ).

fof(f49,negated_conjecture,
    ~ ~ holdsAt(spinning,n2),
    inference(negated_conjecture,[status(cth)],[f48]) ).

fof(f50,plain,
    holdsAt(spinning,n2),
    inference(flattening,[],[f49]) ).

fof(f52,plain,
    ! [X0,X1,X2] :
      ( ~ terminates(X0,X2,X1)
      | ~ happens(X0,X1)
      | ~ holdsAt(X2,plus(X1,n1)) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f53,plain,
    ! [X0,X1,X2] :
      ( ~ terminates(X0,X2,X1)
      | ~ happens(X0,X1)
      | ~ holdsAt(X2,plus(X1,n1)) ),
    inference(flattening,[],[f52]) ).

fof(f77,plain,
    ! [X0] :
      ( ( ~ less(X0,n1)
        | less_or_equal(X0,n0) )
      & ( ~ less_or_equal(X0,n0)
        | less(X0,n1) ) ),
    inference(nnf_transformation,[],[f34]) ).

fof(f78,plain,
    ! [X0,X1,X2] :
      ( ( ~ sP5(X0,X1,X2)
        | sP0(X0,X1,X2)
        | sP1(X0,X1,X2)
        | sP2(X0,X1,X2)
        | sP3(X0,X1,X2)
        | sP4(X0,X1,X2)
        | ( ~ happens(pull,X2)
          & X1 = backwards
          & X0 = push ) )
      & ( ( ~ sP0(X0,X1,X2)
          & ~ sP1(X0,X1,X2)
          & ~ sP2(X0,X1,X2)
          & ~ sP3(X0,X1,X2)
          & ~ sP4(X0,X1,X2)
          & ( happens(pull,X2)
            | backwards != X1
            | push != X0 ) )
        | sP5(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f69]) ).

fof(f79,plain,
    ! [X0,X1,X2] :
      ( ( ~ sP5(X0,X1,X2)
        | sP0(X0,X1,X2)
        | sP1(X0,X1,X2)
        | sP2(X0,X1,X2)
        | sP3(X0,X1,X2)
        | sP4(X0,X1,X2)
        | ( ~ happens(pull,X2)
          & X1 = backwards
          & X0 = push ) )
      & ( ( ~ sP0(X0,X1,X2)
          & ~ sP1(X0,X1,X2)
          & ~ sP2(X0,X1,X2)
          & ~ sP3(X0,X1,X2)
          & ~ sP4(X0,X1,X2)
          & ( happens(pull,X2)
            | backwards != X1
            | push != X0 ) )
        | sP5(X0,X1,X2) ) ),
    inference(flattening,[],[f78]) ).

fof(f90,plain,
    ! [X0,X1,X2] :
      ( ( ~ terminates(X0,X1,X2)
        | sP5(X0,X1,X2) )
      & ( ~ sP5(X0,X1,X2)
        | terminates(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f70]) ).

fof(f101,plain,
    ! [X0] :
      ( ( ~ less(X0,n2)
        | less_or_equal(X0,n1) )
      & ( ~ less_or_equal(X0,n1)
        | less(X0,n2) ) ),
    inference(nnf_transformation,[],[f35]) ).

fof(f102,plain,
    ! [X0,X1] :
      ( ( ~ less(X0,X1)
        | ( X1 != X0
          & ~ less(X1,X0) ) )
      & ( X0 = X1
        | less(X1,X0)
        | less(X0,X1) ) ),
    inference(nnf_transformation,[],[f43]) ).

fof(f103,plain,
    ! [X0,X1] :
      ( ( ~ less(X0,X1)
        | ( X1 != X0
          & ~ less(X1,X0) ) )
      & ( X0 = X1
        | less(X1,X0)
        | less(X0,X1) ) ),
    inference(flattening,[],[f102]) ).

fof(f104,plain,
    ! [X0,X1] :
      ( ( ~ less_or_equal(X0,X1)
        | X0 = X1
        | less(X0,X1) )
      & ( ( X0 != X1
          & ~ less(X0,X1) )
        | less_or_equal(X0,X1) ) ),
    inference(nnf_transformation,[],[f32]) ).

fof(f105,plain,
    ! [X0,X1] :
      ( ( ~ less_or_equal(X0,X1)
        | X0 = X1
        | less(X0,X1) )
      & ( ( X0 != X1
          & ~ less(X0,X1) )
        | less_or_equal(X0,X1) ) ),
    inference(flattening,[],[f104]) ).

fof(f106,plain,
    ! [X0,X1] :
      ( ( ~ sP9(X0,X1)
        | sP8(X0,X1)
        | ( X1 = n2
          & X0 = pull )
        | ( X1 = n1
          & X0 = pull )
        | ( X1 = n0
          & X0 = push ) )
      & ( ( ~ sP8(X0,X1)
          & ( n2 != X1
            | pull != X0 )
          & ( n1 != X1
            | pull != X0 )
          & ( n0 != X1
            | push != X0 ) )
        | sP9(X0,X1) ) ),
    inference(nnf_transformation,[],[f75]) ).

fof(f107,plain,
    ! [X0,X1] :
      ( ( ~ sP9(X0,X1)
        | sP8(X0,X1)
        | ( X1 = n2
          & X0 = pull )
        | ( X1 = n1
          & X0 = pull )
        | ( X1 = n0
          & X0 = push ) )
      & ( ( ~ sP8(X0,X1)
          & ( n2 != X1
            | pull != X0 )
          & ( n1 != X1
            | pull != X0 )
          & ( n0 != X1
            | push != X0 ) )
        | sP9(X0,X1) ) ),
    inference(flattening,[],[f106]) ).

fof(f110,plain,
    ! [X0,X1] :
      ( ( ~ happens(X0,X1)
        | sP9(X0,X1) )
      & ( ~ sP9(X0,X1)
        | happens(X0,X1) ) ),
    inference(nnf_transformation,[],[f76]) ).

fof(f115,plain,
    holdsAt(spinning,n2),
    inference(cnf_transformation,[],[f50]) ).

fof(f117,plain,
    ! [X0] :
      ( ~ less_or_equal(X0,n0)
      | less(X0,n1) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f127,plain,
    ! [X2,X0,X1] :
      ( ~ sP0(X0,X1,X2)
      | sP5(X0,X1,X2) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f154,plain,
    ! [X2,X0,X1] :
      ( ~ sP5(X0,X1,X2)
      | terminates(X0,X1,X2) ),
    inference(cnf_transformation,[],[f90]) ).

fof(f169,plain,
    ! [X2,X0,X1] :
      ( ~ terminates(X0,X2,X1)
      | ~ happens(X0,X1)
      | ~ holdsAt(X2,plus(X1,n1)) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f182,plain,
    ! [X0] :
      ( ~ less(X0,n2)
      | less_or_equal(X0,n1) ),
    inference(cnf_transformation,[],[f101]) ).

fof(f183,plain,
    ! [X0] :
      ( ~ less_or_equal(X0,n1)
      | less(X0,n2) ),
    inference(cnf_transformation,[],[f101]) ).

fof(f185,plain,
    n2 = plus(n1,n1),
    inference(cnf_transformation,[],[f25]) ).

fof(f186,plain,
    ! [X0,X1] :
      ( ~ less(X0,X1)
      | X0 != X1 ),
    inference(cnf_transformation,[],[f103]) ).

fof(f190,plain,
    ! [X0,X1] :
      ( X0 != X1
      | less_or_equal(X0,X1) ),
    inference(cnf_transformation,[],[f105]) ).

fof(f193,plain,
    push != pull,
    inference(cnf_transformation,[],[f17]) ).

fof(f196,plain,
    ! [X0,X1] :
      ( ~ sP9(X0,X1)
      | sP8(X0,X1)
      | n2 = X1
      | pull = X0
      | n0 = X1 ),
    inference(cnf_transformation,[],[f107]) ).

fof(f204,plain,
    ! [X0,X1] :
      ( n1 != X1
      | pull != X0
      | sP9(X0,X1) ),
    inference(cnf_transformation,[],[f107]) ).

fof(f209,plain,
    ! [X0,X1] :
      ( ~ happens(X0,X1)
      | sP9(X0,X1) ),
    inference(cnf_transformation,[],[f110]) ).

fof(f210,plain,
    ! [X0,X1] :
      ( ~ sP9(X0,X1)
      | happens(X0,X1) ),
    inference(cnf_transformation,[],[f110]) ).

fof(f230,plain,
    ! [X1] : ~ less(X1,X1),
    inference(equality_resolution,[],[f186]) ).

fof(f231,plain,
    ! [X1] : less_or_equal(X1,X1),
    inference(equality_resolution,[],[f190]) ).

fof(f234,plain,
    ! [X1] :
      ( n1 != X1
      | sP9(pull,X1) ),
    inference(equality_resolution,[],[f204]) ).

fof(f235,plain,
    sP9(pull,n1),
    inference(equality_resolution,[],[f234]) ).

tcf(c_53,negated_conjecture,
    holdsAt(spinning,n2),
    inference(cnf_transformation,[],[f115]) ).

tcf(c_54,plain,
    ! [X0: $i] :
      ( less(X0,n1)
      | ~ less_or_equal(X0,n0) ),
    inference(cnf_transformation,[],[f117]) ).

tcf(c_67,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( sP5(X0,X1,X2)
      | ~ sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f127]) ).

tcf(c_91,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( terminates(X0,X1,X2)
      | ~ sP5(X0,X1,X2) ),
    inference(cnf_transformation,[],[f154]) ).

tcf(c_107,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ happens(X2,X1)
      | ~ terminates(X2,X0,X1)
      | ~ holdsAt(X0,plus(X1,n1)) ),
    inference(cnf_transformation,[],[f169]) ).

tcf(c_120,plain,
    ! [X0: $i] :
      ( less(X0,n2)
      | ~ less_or_equal(X0,n1) ),
    inference(cnf_transformation,[],[f183]) ).

tcf(c_121,plain,
    ! [X0: $i] :
      ( less_or_equal(X0,n1)
      | ~ less(X0,n2) ),
    inference(cnf_transformation,[],[f182]) ).

tcf(c_123,plain,
    plus(n1,n1) = n2,
    inference(cnf_transformation,[],[f185]) ).

tcf(c_126,plain,
    ! [X0: $i] : ~ less(X0,X0),
    inference(cnf_transformation,[],[f230]) ).

tcf(c_128,plain,
    ! [X0: $i] : less_or_equal(X0,X0),
    inference(cnf_transformation,[],[f231]) ).

tcf(c_131,plain,
    push != pull,
    inference(cnf_transformation,[],[f193]) ).

tcf(c_133,plain,
    sP9(pull,n1),
    inference(cnf_transformation,[],[f235]) ).

tcf(c_140,plain,
    ! [X0: $i,X1: $i] :
      ( sP8(X0,X1)
      | ( X1 = n0 )
      | ( X0 = pull )
      | ~ sP9(X0,X1) ),
    inference(cnf_transformation,[],[f241]) ).

tcf(c_141,plain,
    ! [X0: $i,X1: $i] :
      ( sP8(X0,X1)
      | ( X1 = n2 )
      | ( X1 = n0 )
      | ( X0 = pull )
      | ~ sP9(X0,X1) ),
    inference(cnf_transformation,[],[f196]) ).

tcf(c_147,plain,
    ! [X0: $i,X1: $i] :
      ( happens(X0,X1)
      | ~ sP9(X0,X1) ),
    inference(cnf_transformation,[],[f210]) ).

tcf(c_148,plain,
    ! [X0: $i,X1: $i] :
      ( sP9(X0,X1)
      | ~ happens(X0,X1) ),
    inference(cnf_transformation,[],[f209]) ).

tcf(c_150,plain,
    less_or_equal(n1,n1),
    inference(instantiation,[status(thm)],[c_128]) ).

tcf(c_151,plain,
    ~ less(n1,n1),
    inference(instantiation,[status(thm)],[c_126]) ).

tcf(c_157,plain,
    ( less(n1,n2)
    | ~ less_or_equal(n1,n1) ),
    inference(instantiation,[status(thm)],[c_120]) ).

tcf(c_235,plain,
    ! [X0: $i,X1: $i] :
      ( sP8(X0,X1)
      | ~ sP9(X0,X1)
      | ( X0 = pull )
      | ( X1 = n0 ) ),
    inference(global_subsumption_just,[status(thm)],[c_141,c_140]) ).

tcf(c_236,plain,
    ! [X0: $i,X1: $i] :
      ( sP8(X0,X1)
      | ( X1 = n0 )
      | ( X0 = pull )
      | ~ sP9(X0,X1) ),
    inference(renaming,[status(thm)],[c_235]) ).

tcf(c_257,plain,
    ! [X0: $i] :
      ( less(X0,n1)
      | ~ less_or_equal(X0,n0) ),
    inference(prop_impl_just,[status(thm)],[c_54]) ).

tcf(c_263,plain,
    ! [X0: $i,X1: $i] :
      ( ~ happens(X0,X1)
      | sP9(X0,X1) ),
    inference(prop_impl_just,[status(thm)],[c_148]) ).

tcf(c_264,plain,
    ! [X0: $i,X1: $i] :
      ( sP9(X0,X1)
      | ~ happens(X0,X1) ),
    inference(renaming,[status(thm)],[c_263]) ).

tcf(c_265,plain,
    ! [X0: $i,X1: $i] :
      ( happens(X0,X1)
      | ~ sP9(X0,X1) ),
    inference(prop_impl_just,[status(thm)],[c_147]) ).

tcf(c_271,plain,
    ! [X0: $i] :
      ( ~ less(X0,n2)
      | less_or_equal(X0,n1) ),
    inference(prop_impl_just,[status(thm)],[c_121]) ).

tcf(c_272,plain,
    ! [X0: $i] :
      ( less_or_equal(X0,n1)
      | ~ less(X0,n2) ),
    inference(renaming,[status(thm)],[c_271]) ).

tcf(c_273,plain,
    ! [X0: $i] :
      ( less(X0,n2)
      | ~ less_or_equal(X0,n1) ),
    inference(prop_impl_just,[status(thm)],[c_120]) ).

tcf(c_315,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( terminates(X0,X1,X2)
      | ~ sP0(X0,X1,X2) ),
    inference(prop_impl_just,[status(thm)],[c_91,c_67]) ).

tcf(c_1522,plain,
    ! [X0: $i,X1: $i] :
      ( less(X0,n1)
      | ~ less(X1,n2)
      | ( n0 != n1 )
      | ( X0 != X1 ) ),
    inference(resolution_lifted,[status(thm)],[c_257,c_272]) ).

tcf(c_1523,plain,
    ! [X0: $i] :
      ( less(X0,n1)
      | ~ less(X0,n2)
      | ( n0 != n1 ) ),
    inference(unflattening,[status(thm)],[c_1522]) ).

tcf(c_1524,plain,
    ( less(n1,n1)
    | ~ less(n1,n2)
    | ( n0 != n1 ) ),
    inference(instantiation,[status(thm)],[c_1523]) ).

tcf(c_1525,plain,
    n0 != n1,
    inference(global_subsumption_just,[status(thm)],[c_1523,c_150,c_151,c_157,c_1524]) ).

tcf(c_1617,plain,
    ! [X0: $i,X1: $i] :
      ( less(X0,n2)
      | ( X1 != n1 )
      | ( X0 != X1 ) ),
    inference(resolution_lifted,[status(thm)],[c_273,c_128]) ).

tcf(c_1618,plain,
    less(n1,n2),
    inference(unflattening,[status(thm)],[c_1617]) ).

tcf(c_2403,plain,
    ! [X0: $i,X1: $i] :
      ( happens(X1,X0)
      | ( X1 != pull )
      | ( X0 != n1 ) ),
    inference(resolution_lifted,[status(thm)],[c_133,c_265]) ).

tcf(c_2404,plain,
    happens(pull,n1),
    inference(unflattening,[status(thm)],[c_2403]) ).

tcf(c_6102,plain,
    ! [X0: $i,X1: $i] :
      ( ~ happens(X0,n1)
      | ~ holdsAt(X1,n2)
      | ~ terminates(X0,X1,n1) ),
    inference(superposition,[status(thm)],[c_123,c_107]) ).

fof(f64,definition,
    ! [X0,X1,X2] :
      ( sP0(X0,X1,X2)
    <=> ( ~ happens(push,X2)
        & X1 = spinning
        & X0 = pull ) ),
    introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).

fof(f65,definition,
    ! [X0,X1,X2] :
      ( sP1(X0,X1,X2)
    <=> ( ~ happens(pull,X2)
        & X1 = spinning
        & X0 = push ) ),
    introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).

fof(f66,definition,
    ! [X0,X1,X2] :
      ( sP2(X0,X1,X2)
    <=> ( happens(push,X2)
        & X1 = backwards
        & X0 = pull ) ),
    introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).

fof(f67,definition,
    ! [X0,X1,X2] :
      ( sP3(X0,X1,X2)
    <=> ( happens(push,X2)
        & X1 = forwards
        & X0 = pull ) ),
    introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).

fof(f68,definition,
    ! [X0,X1,X2] :
      ( sP4(X0,X1,X2)
    <=> ( ~ happens(push,X2)
        & X1 = forwards
        & X0 = pull ) ),
    introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).

fof(f69,definition,
    ! [X0,X1,X2] :
      ( sP5(X0,X1,X2)
    <=> ( sP0(X0,X1,X2)
        | sP1(X0,X1,X2)
        | sP2(X0,X1,X2)
        | sP3(X0,X1,X2)
        | sP4(X0,X1,X2)
        | ( ~ happens(pull,X2)
          & X1 = backwards
          & X0 = push ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])],[predicate_definition_introduction]) ).

fof(f70,plain,
    ! [X0,X1,X2] :
      ( terminates(X0,X1,X2)
    <=> sP5(X0,X1,X2) ),
    inference(definition_folding,[],[f14,f69,f68,f67,f66,f65,f64]) ).

fof(f74,definition,
    ! [X0,X1] :
      ( sP8(X0,X1)
    <=> ( X1 = n2
        & X0 = push ) ),
    introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).

fof(f75,definition,
    ! [X0,X1] :
      ( sP9(X0,X1)
    <=> ( sP8(X0,X1)
        | ( X1 = n2
          & X0 = pull )
        | ( X1 = n1
          & X0 = pull )
        | ( X1 = n0
          & X0 = push ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])],[predicate_definition_introduction]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( happens(X0,X1)
    <=> sP9(X0,X1) ),
    inference(definition_folding,[],[f16,f75,f74]) ).

fof(f88,plain,
    ! [X0,X1,X2] :
      ( ( ~ sP0(X0,X1,X2)
        | ( ~ happens(push,X2)
          & X1 = spinning
          & X0 = pull ) )
      & ( happens(push,X2)
        | spinning != X1
        | pull != X0
        | sP0(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f64]) ).

fof(f89,plain,
    ! [X0,X1,X2] :
      ( ( ~ sP0(X0,X1,X2)
        | ( ~ happens(push,X2)
          & X1 = spinning
          & X0 = pull ) )
      & ( happens(push,X2)
        | spinning != X1
        | pull != X0
        | sP0(X0,X1,X2) ) ),
    inference(flattening,[],[f88]) ).

fof(f108,plain,
    ! [X0,X1] :
      ( ( ~ sP8(X0,X1)
        | ( X1 = n2
          & X0 = push ) )
      & ( n2 != X1
        | push != X0
        | sP8(X0,X1) ) ),
    inference(nnf_transformation,[],[f74]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( ( ~ sP8(X0,X1)
        | ( X1 = n2
          & X0 = push ) )
      & ( n2 != X1
        | push != X0
        | sP8(X0,X1) ) ),
    inference(flattening,[],[f108]) ).

fof(f152,plain,
    ! [X2,X0,X1] :
      ( happens(push,X2)
      | spinning != X1
      | pull != X0
      | sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f206,plain,
    ! [X0,X1] :
      ( ~ sP8(X0,X1)
      | n2 = X1 ),
    inference(cnf_transformation,[],[f109]) ).

fof(f222,plain,
    ! [X2,X1] :
      ( happens(push,X2)
      | spinning != X1
      | sP0(pull,X1,X2) ),
    inference(equality_resolution,[],[f152]) ).

fof(f223,plain,
    ! [X2] :
      ( happens(push,X2)
      | sP0(pull,spinning,X2) ),
    inference(equality_resolution,[],[f222]) ).

tcf(c_87,plain,
    ! [X0: $i] :
      ( happens(push,X0)
      | sP0(pull,spinning,X0) ),
    inference(cnf_transformation,[],[f223]) ).

tcf(c_146,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = n2 )
      | ~ sP8(X0,X1) ),
    inference(cnf_transformation,[],[f206]) ).

tcf(c_337,plain,
    ! [X0: $i] :
      ( sP0(pull,spinning,X0)
      | happens(push,X0) ),
    inference(prop_impl_just,[status(thm)],[c_87]) ).

tcf(c_338,plain,
    ! [X0: $i] :
      ( happens(push,X0)
      | sP0(pull,spinning,X0) ),
    inference(renaming,[status(thm)],[c_337]) ).

tcf(c_383,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = n2 )
      | ~ sP8(X0,X1) ),
    inference(prop_impl_just,[status(thm)],[c_146]) ).

tcf(c_1348,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( X3 = n2 )
      | ( X2 = n0 )
      | ( X0 = pull )
      | ~ sP9(X0,X2)
      | ( X2 != X3 )
      | ( X0 != X1 ) ),
    inference(resolution_lifted,[status(thm)],[c_236,c_383]) ).

tcf(c_1349,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = n2 )
      | ( X1 = n0 )
      | ( X0 = pull )
      | ~ sP9(X0,X1) ),
    inference(unflattening,[status(thm)],[c_1348]) ).

tcf(c_2323,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( X3 = n2 )
      | ( X3 = n0 )
      | ( X1 = pull )
      | ~ happens(X0,X2)
      | ( X2 != X3 )
      | ( X0 != X1 ) ),
    inference(resolution_lifted,[status(thm)],[c_264,c_1349]) ).

tcf(c_2324,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 = n2 )
      | ( X1 = n0 )
      | ( X0 = pull )
      | ~ happens(X0,X1) ),
    inference(unflattening,[status(thm)],[c_2323]) ).

tcf(c_3300,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( happens(push,X3)
      | terminates(X0,X1,X2)
      | ( X2 != X3 )
      | ( X1 != spinning )
      | ( X0 != pull ) ),
    inference(resolution_lifted,[status(thm)],[c_315,c_338]) ).

tcf(c_3301,plain,
    ! [X0: $i] :
      ( happens(push,X0)
      | terminates(pull,spinning,X0) ),
    inference(unflattening,[status(thm)],[c_3300]) ).

tcf(c_6573,plain,
    ( happens(push,n1)
    | ~ happens(pull,n1)
    | ~ holdsAt(spinning,n2) ),
    inference(superposition,[status(thm)],[c_3301,c_6102]) ).

tcf(c_6575,plain,
    happens(push,n1),
    inference(forward_subsumption_resolution,[status(thm)],[c_6573,c_2404,c_53]) ).

tcf(c_7241,plain,
    ( ( push = pull )
    | ( n2 = n1 )
    | ( n0 = n1 ) ),
    inference(superposition,[status(thm)],[c_6575,c_2324]) ).

tcf(c_7255,plain,
    n2 = n1,
    inference(forward_subsumption_resolution,[status(thm)],[c_7241,c_131,c_1525]) ).

tcf(c_7310,plain,
    less(n1,n1),
    inference(demodulation,[status(thm)],[c_1618,c_7255]) ).

tcf(c_7317,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_7310,c_126]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05  % Problem  : CSR020+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.07  % Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.19/0.45  % Computer : n014.cluster.edu
% 0.19/0.45  % Model    : x86_64 x86_64
% 0.19/0.45  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45  % Memory   : 8046.5625MB
% 0.19/0.45  % OS       : Linux 6.8.0-71-generic
% 0.19/0.45  % CPULimit : 300
% 0.19/0.45  % WCLimit  : 300
% 0.19/0.45  % DateTime : Fri Sep 25 08:06:47 UTC 2026
% 0.19/0.45  % CPUTime  : 
% 0.19/0.45  Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.26/0.51  Running first-order theorem proving
% 0.26/0.51  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
% 0.26/0.53  
% 0.26/0.53  % ======== iProver multi-core TPTP/SMT =========
% 0.26/0.53  
% 0.26/0.53  % Detected problem language: tptp
% 0.26/0.55  % Proving...
% 4.77/1.53  % SZS status Started for theBenchmark.p
% 4.77/1.53  % SZS status Theorem for theBenchmark.p
% 4.77/1.53  
% 4.77/1.53  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.77/1.53  
% 4.77/1.53  % ------  iProver source info
% 4.77/1.53  
% 4.77/1.53  % git: date: 2026-07-19 20:42:38 +0200
% 4.77/1.53  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.77/1.53  % git: non_committed_changes: false
% 4.77/1.53  
% 4.77/1.53  % ------ Parsing...
% 4.77/1.53  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 4.77/1.53  
% 4.77/1.53  % ------ Preprocessing... sup_sim: 1  sf_s  rm: 2 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e  sup_sim: 0  sf_s  rm: 10 0s  sf_e  pe_s  pe_e % 
% 4.77/1.53  
% 4.77/1.53  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 4.77/1.53  
% 4.77/1.53  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 4.77/1.53  % ------ Proving...
% 4.77/1.53  % ------ Problem Properties 
% 4.77/1.53  
% 4.77/1.53  % 
% 4.77/1.53  % clauses                               72
% 4.77/1.53  % conjectures                           1
% 4.77/1.53  % EPR                                   59
% 4.77/1.53  % Horn                                  46
% 4.77/1.53  % unary                                 27
% 4.77/1.53  % binary                                20
% 4.77/1.53  % lits                                  158
% 4.77/1.53  % lits eq                               54
% 4.77/1.53  % fd_pure                               0
% 4.77/1.53  % fd_pseudo                             0
% 4.77/1.53  % fd_cond                               21
% 4.77/1.53  % fd_pseudo_cond                        1
% 4.77/1.53  % AC symbols                            0
% 4.77/1.53  
% 4.77/1.53  % ------ Schedule dynamic 5 is on 
% 4.77/1.53  
% 4.77/1.53  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.77/1.53  
% 4.77/1.53  
% 4.77/1.53  % ------ 
% 4.77/1.53  % Current options:
% 4.77/1.53  % ------ 
% 4.77/1.53  
% 4.77/1.53  
% 4.77/1.53  % 
% 4.77/1.53  
% 4.77/1.53  % ------ Proving...
% 4.77/1.53  % 
% 4.77/1.53  
% 4.77/1.53  % SZS status Theorem for theBenchmark.p
% 4.77/1.53  
% 4.77/1.53  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.77/1.53  
% 4.77/1.53  
%------------------------------------------------------------------------------