%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SWC254-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Tue Jul 19 21:27:21 EDT 2022

% Result   : Unsatisfiable 0.52s 0.70s
% Output   : CNFRefutation 0.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   15
% Syntax   : Number of clauses     :   39 (  12 unt;   1 nHn;  37 RR)
%            Number of literals    :   79 (  29 equ;  42 neg)
%            Maximal clause size   :    4 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   10 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(clause116,axiom,
    ( cons(U,nil) != V
    | ~ ssItem(U)
    | ~ ssList(V)
    | singletonP(V) ) ).

cnf(co1_1,negated_conjecture,
    ssList(sk1) ).

cnf(co1_5,negated_conjecture,
    sk2 = sk4 ).

cnf(co1_6,negated_conjecture,
    sk1 = sk3 ).

cnf(co1_7,negated_conjecture,
    ( neq(sk2,nil)
    | neq(sk2,nil) ) ).

cnf(co1_14,negated_conjecture,
    ( ssItem(sk5)
    | ~ neq(sk4,nil) ) ).

cnf(co1_16,negated_conjecture,
    ( cons(sk5,nil) = sk3
    | ~ neq(sk4,nil) ) ).

cnf(co1_18,negated_conjecture,
    ( ~ singletonP(sk1)
    | ~ neq(sk4,nil) ) ).

cnf(refute_0_0,plain,
    ( cons(U,nil) != cons(U,nil)
    | ~ ssItem(U)
    | ~ ssList(cons(U,nil))
    | singletonP(cons(U,nil)) ),
    inference(subst,[],[clause116:[bind(V,$fot(cons(U,nil)))]]) ).

cnf(refute_0_1,plain,
    cons(U,nil) = cons(U,nil),
    introduced(tautology,[refl,[$fot(cons(U,nil))]]) ).

cnf(refute_0_2,plain,
    ( ~ ssItem(U)
    | ~ ssList(cons(U,nil))
    | singletonP(cons(U,nil)) ),
    inference(resolve,[$cnf( $equal(cons(U,nil),cons(U,nil)) )],[refute_0_1,refute_0_0]) ).

cnf(refute_0_3,plain,
    ( ~ ssItem(sk5)
    | ~ ssList(cons(sk5,nil))
    | singletonP(cons(sk5,nil)) ),
    inference(subst,[],[refute_0_2:[bind(U,$fot(sk5))]]) ).

cnf(refute_0_4,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_5,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_6,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_4,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( sk2 != sk4
    | sk4 = sk2 ),
    inference(subst,[],[refute_0_6:[bind(X,$fot(sk2)),bind(Y,$fot(sk4))]]) ).

cnf(refute_0_8,plain,
    sk4 = sk2,
    inference(resolve,[$cnf( $equal(sk2,sk4) )],[co1_5,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( sk4 != sk2
    | ~ neq(sk2,nil)
    | neq(sk4,nil) ),
    introduced(tautology,[equality,[$cnf( ~ neq(sk4,nil) ),[0],$fot(sk2)]]) ).

cnf(refute_0_10,plain,
    ( ~ neq(sk2,nil)
    | neq(sk4,nil) ),
    inference(resolve,[$cnf( $equal(sk4,sk2) )],[refute_0_8,refute_0_9]) ).

cnf(refute_0_11,plain,
    ( ~ neq(sk2,nil)
    | cons(sk5,nil) = sk3 ),
    inference(resolve,[$cnf( neq(sk4,nil) )],[refute_0_10,co1_16]) ).

cnf(refute_0_12,plain,
    ( sk1 != sk3
    | sk3 = sk1 ),
    inference(subst,[],[refute_0_6:[bind(X,$fot(sk1)),bind(Y,$fot(sk3))]]) ).

cnf(refute_0_13,plain,
    sk3 = sk1,
    inference(resolve,[$cnf( $equal(sk1,sk3) )],[co1_6,refute_0_12]) ).

cnf(refute_0_14,plain,
    ( cons(sk5,nil) != sk3
    | sk3 != sk1
    | cons(sk5,nil) = sk1 ),
    introduced(tautology,[equality,[$cnf( ~ $equal(cons(sk5,nil),sk1) ),[0],$fot(sk3)]]) ).

cnf(refute_0_15,plain,
    ( cons(sk5,nil) != sk3
    | cons(sk5,nil) = sk1 ),
    inference(resolve,[$cnf( $equal(sk3,sk1) )],[refute_0_13,refute_0_14]) ).

cnf(refute_0_16,plain,
    ( ~ neq(sk2,nil)
    | cons(sk5,nil) = sk1 ),
    inference(resolve,[$cnf( $equal(cons(sk5,nil),sk3) )],[refute_0_11,refute_0_15]) ).

cnf(refute_0_17,plain,
    cons(sk5,nil) = sk1,
    inference(resolve,[$cnf( neq(sk2,nil) )],[co1_7,refute_0_16]) ).

cnf(refute_0_18,plain,
    ( cons(sk5,nil) != sk1
    | ~ ssList(sk1)
    | ssList(cons(sk5,nil)) ),
    introduced(tautology,[equality,[$cnf( ~ ssList(cons(sk5,nil)) ),[0],$fot(sk1)]]) ).

cnf(refute_0_19,plain,
    ( ~ ssList(sk1)
    | ssList(cons(sk5,nil)) ),
    inference(resolve,[$cnf( $equal(cons(sk5,nil),sk1) )],[refute_0_17,refute_0_18]) ).

cnf(refute_0_20,plain,
    ( ~ ssItem(sk5)
    | ~ ssList(sk1)
    | singletonP(cons(sk5,nil)) ),
    inference(resolve,[$cnf( ssList(cons(sk5,nil)) )],[refute_0_19,refute_0_3]) ).

cnf(refute_0_21,plain,
    ( cons(sk5,nil) != sk1
    | ~ singletonP(cons(sk5,nil))
    | singletonP(sk1) ),
    introduced(tautology,[equality,[$cnf( singletonP(cons(sk5,nil)) ),[0],$fot(sk1)]]) ).

cnf(refute_0_22,plain,
    ( ~ singletonP(cons(sk5,nil))
    | singletonP(sk1) ),
    inference(resolve,[$cnf( $equal(cons(sk5,nil),sk1) )],[refute_0_17,refute_0_21]) ).

cnf(refute_0_23,plain,
    ( ~ ssItem(sk5)
    | ~ ssList(sk1)
    | singletonP(sk1) ),
    inference(resolve,[$cnf( singletonP(cons(sk5,nil)) )],[refute_0_20,refute_0_22]) ).

cnf(refute_0_24,plain,
    ( ~ neq(sk2,nil)
    | ssItem(sk5) ),
    inference(resolve,[$cnf( neq(sk4,nil) )],[refute_0_10,co1_14]) ).

cnf(refute_0_25,plain,
    ssItem(sk5),
    inference(resolve,[$cnf( neq(sk2,nil) )],[co1_7,refute_0_24]) ).

cnf(refute_0_26,plain,
    ( ~ ssList(sk1)
    | singletonP(sk1) ),
    inference(resolve,[$cnf( ssItem(sk5) )],[refute_0_25,refute_0_23]) ).

cnf(refute_0_27,plain,
    singletonP(sk1),
    inference(resolve,[$cnf( ssList(sk1) )],[co1_1,refute_0_26]) ).

cnf(refute_0_28,plain,
    ( ~ neq(sk2,nil)
    | ~ singletonP(sk1) ),
    inference(resolve,[$cnf( neq(sk4,nil) )],[refute_0_10,co1_18]) ).

cnf(refute_0_29,plain,
    ~ singletonP(sk1),
    inference(resolve,[$cnf( neq(sk2,nil) )],[co1_7,refute_0_28]) ).

cnf(refute_0_30,plain,
    $false,
    inference(resolve,[$cnf( singletonP(sk1) )],[refute_0_27,refute_0_29]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SWC254-1 : TPTP v8.1.0. Released v2.4.0.
% 0.04/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n026.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sun Jun 12 15:01:50 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.52/0.70  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.52/0.70  
% 0.52/0.70  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.52/0.70  
%------------------------------------------------------------------------------