%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : HWV005-2 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n029.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 : Sat Jul 16 18:29:33 EDT 2022

% Result   : Unsatisfiable 0.19s 0.35s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   25
% Syntax   : Number of clauses     :   83 (  30 unt;   9 nHn;  83 RR)
%            Number of literals    :  159 (   0 equ;  73 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :   12 (  11 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   1 con; 0-1 aty)
%            Number of variables   :   20 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(value_propagation_zero1,axiom,
    ( ~ connection(P1,P2)
    | ~ zero(P1)
    | zero(P2) ) ).

cnf(value_propagation_one1,axiom,
    ( ~ connection(P1,P2)
    | ~ one(P1)
    | one(P2) ) ).

cnf(unique_value,axiom,
    ( ~ zero(P)
    | ~ one(P) ) ).

cnf(and_11_1,axiom,
    ( ~ and_ok(K)
    | ~ one(in1(K))
    | ~ one(in2(K))
    | one(out1(K)) ) ).

cnf(and_ok_or_abnormal,axiom,
    ( ~ logic_and(K)
    | and_ok(K)
    | abnormal(K) ) ).

cnf(or_1x_1,axiom,
    ( ~ or_ok(K)
    | ~ one(in1(K))
    | one(out1(K)) ) ).

cnf(or_ok_or_abnormal,axiom,
    ( ~ logic_or(K)
    | or_ok(K)
    | abnormal(K) ) ).

cnf(not_0_1_fw,axiom,
    ( ~ not_ok(K)
    | ~ zero(in1(K))
    | one(out1(K)) ) ).

cnf(not_ok_or_abnormal,axiom,
    ( ~ logic_not(K)
    | not_ok(K)
    | abnormal(K) ) ).

cnf(halfadder_and1,axiom,
    ( ~ halfadder(X)
    | logic_and(and1(X)) ) ).

cnf(halfadder_not1,axiom,
    ( ~ halfadder(X)
    | logic_not(not1(X)) ) ).

cnf(halfadder_or1,axiom,
    ( ~ halfadder(X)
    | logic_or(or1(X)) ) ).

cnf(halfadder_connection_in1_in1or1,axiom,
    ( ~ halfadder(X)
    | connection(in1(X),in1(or1(X))) ) ).

cnf(halfadder_connection_outs_out1and1,axiom,
    ( ~ halfadder(X)
    | connection(outs(X),out1(and1(X))) ) ).

cnf(halfadder_connection_outc_out1and2,axiom,
    ( ~ halfadder(X)
    | connection(outc(X),out1(and2(X))) ) ).

cnf(halfadder_connection_out1or1_in1_and1,axiom,
    ( ~ halfadder(X)
    | connection(out1(or1(X)),in1(and1(X))) ) ).

cnf(halfadder_connection_out1and2_in1not1,axiom,
    ( ~ halfadder(X)
    | connection(out1(and2(X)),in1(not1(X))) ) ).

cnf(halfadder_connection_out1not1_in2and1,axiom,
    ( ~ halfadder(X)
    | connection(out1(not1(X)),in2(and1(X))) ) ).

cnf(h_isa_halfadder,hypothesis,
    halfadder(h) ).

cnf(in1_1,hypothesis,
    one(in1(h)) ).

cnf(outs_0,hypothesis,
    zero(outs(h)) ).

cnf(outc_0,hypothesis,
    zero(outc(h)) ).

cnf(diagnosis_and1,negated_conjecture,
    ~ abnormal(and1(h)) ).

cnf(diagnosis_not1,negated_conjecture,
    ~ abnormal(not1(h)) ).

cnf(diagnosis_or1,negated_conjecture,
    ~ abnormal(or1(h)) ).

cnf(refute_0_0,plain,
    ( ~ halfadder(h)
    | connection(out1(not1(h)),in2(and1(h))) ),
    inference(subst,[],[halfadder_connection_out1not1_in2and1:[bind(X,$fot(h))]]) ).

cnf(refute_0_1,plain,
    connection(out1(not1(h)),in2(and1(h))),
    inference(resolve,[$cnf( halfadder(h) )],[h_isa_halfadder,refute_0_0]) ).

cnf(refute_0_2,plain,
    ( ~ connection(out1(not1(h)),in2(and1(h)))
    | ~ one(out1(not1(h)))
    | one(in2(and1(h))) ),
    inference(subst,[],[value_propagation_one1:[bind(P1,$fot(out1(not1(h)))),bind(P2,$fot(in2(and1(h))))]]) ).

cnf(refute_0_3,plain,
    ( ~ one(out1(not1(h)))
    | one(in2(and1(h))) ),
    inference(resolve,[$cnf( connection(out1(not1(h)),in2(and1(h))) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( ~ not_ok(not1(h))
    | ~ zero(in1(not1(h)))
    | one(out1(not1(h))) ),
    inference(subst,[],[not_0_1_fw:[bind(K,$fot(not1(h)))]]) ).

cnf(refute_0_5,plain,
    ( ~ halfadder(h)
    | connection(out1(and2(h)),in1(not1(h))) ),
    inference(subst,[],[halfadder_connection_out1and2_in1not1:[bind(X,$fot(h))]]) ).

cnf(refute_0_6,plain,
    connection(out1(and2(h)),in1(not1(h))),
    inference(resolve,[$cnf( halfadder(h) )],[h_isa_halfadder,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( ~ connection(out1(and2(h)),in1(not1(h)))
    | ~ zero(out1(and2(h)))
    | zero(in1(not1(h))) ),
    inference(subst,[],[value_propagation_zero1:[bind(P1,$fot(out1(and2(h)))),bind(P2,$fot(in1(not1(h))))]]) ).

cnf(refute_0_8,plain,
    ( ~ zero(out1(and2(h)))
    | zero(in1(not1(h))) ),
    inference(resolve,[$cnf( connection(out1(and2(h)),in1(not1(h))) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( ~ halfadder(h)
    | connection(outc(h),out1(and2(h))) ),
    inference(subst,[],[halfadder_connection_outc_out1and2:[bind(X,$fot(h))]]) ).

cnf(refute_0_10,plain,
    connection(outc(h),out1(and2(h))),
    inference(resolve,[$cnf( halfadder(h) )],[h_isa_halfadder,refute_0_9]) ).

cnf(refute_0_11,plain,
    ( ~ connection(outc(h),out1(and2(h)))
    | ~ zero(outc(h))
    | zero(out1(and2(h))) ),
    inference(subst,[],[value_propagation_zero1:[bind(P1,$fot(outc(h))),bind(P2,$fot(out1(and2(h))))]]) ).

cnf(refute_0_12,plain,
    ( ~ zero(outc(h))
    | zero(out1(and2(h))) ),
    inference(resolve,[$cnf( connection(outc(h),out1(and2(h))) )],[refute_0_10,refute_0_11]) ).

cnf(refute_0_13,plain,
    zero(out1(and2(h))),
    inference(resolve,[$cnf( zero(outc(h)) )],[outc_0,refute_0_12]) ).

cnf(refute_0_14,plain,
    zero(in1(not1(h))),
    inference(resolve,[$cnf( zero(out1(and2(h))) )],[refute_0_13,refute_0_8]) ).

cnf(refute_0_15,plain,
    ( ~ not_ok(not1(h))
    | one(out1(not1(h))) ),
    inference(resolve,[$cnf( zero(in1(not1(h))) )],[refute_0_14,refute_0_4]) ).

cnf(refute_0_16,plain,
    ( ~ halfadder(h)
    | logic_not(not1(h)) ),
    inference(subst,[],[halfadder_not1:[bind(X,$fot(h))]]) ).

cnf(refute_0_17,plain,
    logic_not(not1(h)),
    inference(resolve,[$cnf( halfadder(h) )],[h_isa_halfadder,refute_0_16]) ).

cnf(refute_0_18,plain,
    ( ~ logic_not(not1(h))
    | abnormal(not1(h))
    | not_ok(not1(h)) ),
    inference(subst,[],[not_ok_or_abnormal:[bind(K,$fot(not1(h)))]]) ).

cnf(refute_0_19,plain,
    ( abnormal(not1(h))
    | not_ok(not1(h)) ),
    inference(resolve,[$cnf( logic_not(not1(h)) )],[refute_0_17,refute_0_18]) ).

cnf(refute_0_20,plain,
    not_ok(not1(h)),
    inference(resolve,[$cnf( abnormal(not1(h)) )],[refute_0_19,diagnosis_not1]) ).

cnf(refute_0_21,plain,
    one(out1(not1(h))),
    inference(resolve,[$cnf( not_ok(not1(h)) )],[refute_0_20,refute_0_15]) ).

cnf(refute_0_22,plain,
    one(in2(and1(h))),
    inference(resolve,[$cnf( one(out1(not1(h))) )],[refute_0_21,refute_0_3]) ).

cnf(refute_0_23,plain,
    ( ~ and_ok(and1(h))
    | ~ one(in1(and1(h)))
    | ~ one(in2(and1(h)))
    | one(out1(and1(h))) ),
    inference(subst,[],[and_11_1:[bind(K,$fot(and1(h)))]]) ).

cnf(refute_0_24,plain,
    ( ~ and_ok(and1(h))
    | ~ one(in1(and1(h)))
    | one(out1(and1(h))) ),
    inference(resolve,[$cnf( one(in2(and1(h))) )],[refute_0_22,refute_0_23]) ).

cnf(refute_0_25,plain,
    ( ~ halfadder(h)
    | logic_and(and1(h)) ),
    inference(subst,[],[halfadder_and1:[bind(X,$fot(h))]]) ).

cnf(refute_0_26,plain,
    logic_and(and1(h)),
    inference(resolve,[$cnf( halfadder(h) )],[h_isa_halfadder,refute_0_25]) ).

cnf(refute_0_27,plain,
    ( ~ logic_and(and1(h))
    | abnormal(and1(h))
    | and_ok(and1(h)) ),
    inference(subst,[],[and_ok_or_abnormal:[bind(K,$fot(and1(h)))]]) ).

cnf(refute_0_28,plain,
    ( abnormal(and1(h))
    | and_ok(and1(h)) ),
    inference(resolve,[$cnf( logic_and(and1(h)) )],[refute_0_26,refute_0_27]) ).

cnf(refute_0_29,plain,
    and_ok(and1(h)),
    inference(resolve,[$cnf( abnormal(and1(h)) )],[refute_0_28,diagnosis_and1]) ).

cnf(refute_0_30,plain,
    ( ~ one(in1(and1(h)))
    | one(out1(and1(h))) ),
    inference(resolve,[$cnf( and_ok(and1(h)) )],[refute_0_29,refute_0_24]) ).

cnf(refute_0_31,plain,
    ( ~ halfadder(h)
    | connection(out1(or1(h)),in1(and1(h))) ),
    inference(subst,[],[halfadder_connection_out1or1_in1_and1:[bind(X,$fot(h))]]) ).

cnf(refute_0_32,plain,
    connection(out1(or1(h)),in1(and1(h))),
    inference(resolve,[$cnf( halfadder(h) )],[h_isa_halfadder,refute_0_31]) ).

cnf(refute_0_33,plain,
    ( ~ connection(out1(or1(h)),in1(and1(h)))
    | ~ one(out1(or1(h)))
    | one(in1(and1(h))) ),
    inference(subst,[],[value_propagation_one1:[bind(P1,$fot(out1(or1(h)))),bind(P2,$fot(in1(and1(h))))]]) ).

cnf(refute_0_34,plain,
    ( ~ one(out1(or1(h)))
    | one(in1(and1(h))) ),
    inference(resolve,[$cnf( connection(out1(or1(h)),in1(and1(h))) )],[refute_0_32,refute_0_33]) ).

cnf(refute_0_35,plain,
    ( ~ one(in1(or1(h)))
    | ~ or_ok(or1(h))
    | one(out1(or1(h))) ),
    inference(subst,[],[or_1x_1:[bind(K,$fot(or1(h)))]]) ).

cnf(refute_0_36,plain,
    ( ~ halfadder(h)
    | connection(in1(h),in1(or1(h))) ),
    inference(subst,[],[halfadder_connection_in1_in1or1:[bind(X,$fot(h))]]) ).

cnf(refute_0_37,plain,
    connection(in1(h),in1(or1(h))),
    inference(resolve,[$cnf( halfadder(h) )],[h_isa_halfadder,refute_0_36]) ).

cnf(refute_0_38,plain,
    ( ~ connection(in1(h),in1(or1(h)))
    | ~ one(in1(h))
    | one(in1(or1(h))) ),
    inference(subst,[],[value_propagation_one1:[bind(P1,$fot(in1(h))),bind(P2,$fot(in1(or1(h))))]]) ).

cnf(refute_0_39,plain,
    ( ~ one(in1(h))
    | one(in1(or1(h))) ),
    inference(resolve,[$cnf( connection(in1(h),in1(or1(h))) )],[refute_0_37,refute_0_38]) ).

cnf(refute_0_40,plain,
    one(in1(or1(h))),
    inference(resolve,[$cnf( one(in1(h)) )],[in1_1,refute_0_39]) ).

cnf(refute_0_41,plain,
    ( ~ or_ok(or1(h))
    | one(out1(or1(h))) ),
    inference(resolve,[$cnf( one(in1(or1(h))) )],[refute_0_40,refute_0_35]) ).

cnf(refute_0_42,plain,
    ( ~ halfadder(h)
    | logic_or(or1(h)) ),
    inference(subst,[],[halfadder_or1:[bind(X,$fot(h))]]) ).

cnf(refute_0_43,plain,
    logic_or(or1(h)),
    inference(resolve,[$cnf( halfadder(h) )],[h_isa_halfadder,refute_0_42]) ).

cnf(refute_0_44,plain,
    ( ~ logic_or(or1(h))
    | abnormal(or1(h))
    | or_ok(or1(h)) ),
    inference(subst,[],[or_ok_or_abnormal:[bind(K,$fot(or1(h)))]]) ).

cnf(refute_0_45,plain,
    ( abnormal(or1(h))
    | or_ok(or1(h)) ),
    inference(resolve,[$cnf( logic_or(or1(h)) )],[refute_0_43,refute_0_44]) ).

cnf(refute_0_46,plain,
    or_ok(or1(h)),
    inference(resolve,[$cnf( abnormal(or1(h)) )],[refute_0_45,diagnosis_or1]) ).

cnf(refute_0_47,plain,
    one(out1(or1(h))),
    inference(resolve,[$cnf( or_ok(or1(h)) )],[refute_0_46,refute_0_41]) ).

cnf(refute_0_48,plain,
    one(in1(and1(h))),
    inference(resolve,[$cnf( one(out1(or1(h))) )],[refute_0_47,refute_0_34]) ).

cnf(refute_0_49,plain,
    one(out1(and1(h))),
    inference(resolve,[$cnf( one(in1(and1(h))) )],[refute_0_48,refute_0_30]) ).

cnf(refute_0_50,plain,
    ( ~ one(out1(and1(h)))
    | ~ zero(out1(and1(h))) ),
    inference(subst,[],[unique_value:[bind(P,$fot(out1(and1(h))))]]) ).

cnf(refute_0_51,plain,
    ( ~ halfadder(h)
    | connection(outs(h),out1(and1(h))) ),
    inference(subst,[],[halfadder_connection_outs_out1and1:[bind(X,$fot(h))]]) ).

cnf(refute_0_52,plain,
    connection(outs(h),out1(and1(h))),
    inference(resolve,[$cnf( halfadder(h) )],[h_isa_halfadder,refute_0_51]) ).

cnf(refute_0_53,plain,
    ( ~ connection(outs(h),out1(and1(h)))
    | ~ zero(outs(h))
    | zero(out1(and1(h))) ),
    inference(subst,[],[value_propagation_zero1:[bind(P1,$fot(outs(h))),bind(P2,$fot(out1(and1(h))))]]) ).

cnf(refute_0_54,plain,
    ( ~ zero(outs(h))
    | zero(out1(and1(h))) ),
    inference(resolve,[$cnf( connection(outs(h),out1(and1(h))) )],[refute_0_52,refute_0_53]) ).

cnf(refute_0_55,plain,
    zero(out1(and1(h))),
    inference(resolve,[$cnf( zero(outs(h)) )],[outs_0,refute_0_54]) ).

cnf(refute_0_56,plain,
    ~ one(out1(and1(h))),
    inference(resolve,[$cnf( zero(out1(and1(h))) )],[refute_0_55,refute_0_50]) ).

cnf(refute_0_57,plain,
    $false,
    inference(resolve,[$cnf( one(out1(and1(h))) )],[refute_0_49,refute_0_56]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : HWV005-2 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.33  % Computer : n029.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Fri Jun 17 08:08:43 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.35  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.35  
% 0.19/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.36  
%------------------------------------------------------------------------------