%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HWV007-2 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 : Sun Sep 27 07:34:16 AM UTC 2026
% Result : Unsatisfiable 0.15s 10.58s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 48
% Syntax : Number of formulae : 200 ( 44 unt; 0 def)
% Number of atoms : 462 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 511 ( 249 ~; 262 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 1 con; 0-1 aty)
% Number of variables : 125 ( 0 sgn 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(halfadder_connection_in1_in1or1,axiom,
! [VAR_0] :
( connection(in1(VAR_0),in1(or1(VAR_0)))
| ~ halfadder(VAR_0) ),
file('theBenchmark.p',halfadder_connection_in1_in1or1) ).
cnf(c_1,plain,
( connection(in1(A),in1(or1(A)))
| ~ halfadder(A) ),
inference(clausify,[status(thm)],[halfadder_connection_in1_in1or1]) ).
fof(value_propagation_one2,axiom,
! [VAR_0,VAR_1] :
( one(VAR_0)
| ~ one(VAR_1)
| ~ connection(VAR_0,VAR_1) ),
file('theBenchmark.p',value_propagation_one2) ).
cnf(c_2,plain,
( one(A)
| ~ one(B)
| ~ connection(A,B) ),
inference(clausify,[status(thm)],[value_propagation_one2]) ).
fof(value_propagation_zero2,axiom,
! [VAR_0,VAR_1] :
( zero(VAR_0)
| ~ zero(VAR_1)
| ~ connection(VAR_0,VAR_1) ),
file('theBenchmark.p',value_propagation_zero2) ).
cnf(c_3,plain,
( zero(A)
| ~ zero(B)
| ~ connection(A,B) ),
inference(clausify,[status(thm)],[value_propagation_zero2]) ).
fof(value_propagation_one1,axiom,
! [VAR_0,VAR_1] :
( one(VAR_1)
| ~ one(VAR_0)
| ~ connection(VAR_0,VAR_1) ),
file('theBenchmark.p',value_propagation_one1) ).
cnf(c_4,plain,
( one(B)
| ~ one(A)
| ~ connection(A,B) ),
inference(clausify,[status(thm)],[value_propagation_one1]) ).
fof(value_propagation_zero1,axiom,
! [VAR_0,VAR_1] :
( zero(VAR_1)
| ~ zero(VAR_0)
| ~ connection(VAR_0,VAR_1) ),
file('theBenchmark.p',value_propagation_zero1) ).
cnf(c_5,plain,
( zero(B)
| ~ zero(A)
| ~ connection(A,B) ),
inference(clausify,[status(thm)],[value_propagation_zero1]) ).
fof(halfadder_connection_in2_in2or1,axiom,
! [VAR_0] :
( connection(in2(VAR_0),in2(or1(VAR_0)))
| ~ halfadder(VAR_0) ),
file('theBenchmark.p',halfadder_connection_in2_in2or1) ).
cnf(c_6,plain,
( connection(in2(A),in2(or1(A)))
| ~ halfadder(A) ),
inference(clausify,[status(thm)],[halfadder_connection_in2_in2or1]) ).
fof(halfadder_connection_in1_in1and2,axiom,
! [VAR_0] :
( connection(in1(VAR_0),in1(and2(VAR_0)))
| ~ halfadder(VAR_0) ),
file('theBenchmark.p',halfadder_connection_in1_in1and2) ).
cnf(c_7,plain,
( connection(in1(A),in1(and2(A)))
| ~ halfadder(A) ),
inference(clausify,[status(thm)],[halfadder_connection_in1_in1and2]) ).
fof(halfadder_connection_in2_in2and2,axiom,
! [VAR_0] :
( connection(in2(VAR_0),in2(and2(VAR_0)))
| ~ halfadder(VAR_0) ),
file('theBenchmark.p',halfadder_connection_in2_in2and2) ).
cnf(c_8,plain,
( connection(in2(A),in2(and2(A)))
| ~ halfadder(A) ),
inference(clausify,[status(thm)],[halfadder_connection_in2_in2and2]) ).
fof(halfadder_connection_outs_out1and1,axiom,
! [VAR_0] :
( connection(outs(VAR_0),out1(and1(VAR_0)))
| ~ halfadder(VAR_0) ),
file('theBenchmark.p',halfadder_connection_outs_out1and1) ).
cnf(c_9,plain,
( connection(outs(A),out1(and1(A)))
| ~ halfadder(A) ),
inference(clausify,[status(thm)],[halfadder_connection_outs_out1and1]) ).
fof(halfadder_connection_outc_out1and2,axiom,
! [VAR_0] :
( connection(outc(VAR_0),out1(and2(VAR_0)))
| ~ halfadder(VAR_0) ),
file('theBenchmark.p',halfadder_connection_outc_out1and2) ).
cnf(c_10,plain,
( connection(outc(A),out1(and2(A)))
| ~ halfadder(A) ),
inference(clausify,[status(thm)],[halfadder_connection_outc_out1and2]) ).
fof(halfadder_connection_out1or1_in1_and1,axiom,
! [VAR_0] :
( connection(out1(or1(VAR_0)),in1(and1(VAR_0)))
| ~ halfadder(VAR_0) ),
file('theBenchmark.p',halfadder_connection_out1or1_in1_and1) ).
cnf(c_11,plain,
( connection(out1(or1(A)),in1(and1(A)))
| ~ halfadder(A) ),
inference(clausify,[status(thm)],[halfadder_connection_out1or1_in1_and1]) ).
fof(halfadder_connection_out1and2_in1not1,axiom,
! [VAR_0] :
( connection(out1(and2(VAR_0)),in1(not1(VAR_0)))
| ~ halfadder(VAR_0) ),
file('theBenchmark.p',halfadder_connection_out1and2_in1not1) ).
cnf(c_12,plain,
( connection(out1(and2(A)),in1(not1(A)))
| ~ halfadder(A) ),
inference(clausify,[status(thm)],[halfadder_connection_out1and2_in1not1]) ).
fof(halfadder_connection_out1not1_in2and1,axiom,
! [VAR_0] :
( connection(out1(not1(VAR_0)),in2(and1(VAR_0)))
| ~ halfadder(VAR_0) ),
file('theBenchmark.p',halfadder_connection_out1not1_in2and1) ).
cnf(c_13,plain,
( connection(out1(not1(A)),in2(and1(A)))
| ~ halfadder(A) ),
inference(clausify,[status(thm)],[halfadder_connection_out1not1_in2and1]) ).
fof(fulladder_connection_outsh1_in2h2,axiom,
! [VAR_0] :
( connection(outs(h1(VAR_0)),in2(h2(VAR_0)))
| ~ fulladder(VAR_0) ),
file('theBenchmark.p',fulladder_connection_outsh1_in2h2) ).
cnf(c_14,plain,
( connection(outs(h1(A)),in2(h2(A)))
| ~ fulladder(A) ),
inference(clausify,[status(thm)],[fulladder_connection_outsh1_in2h2]) ).
fof(fulladder_connection_outch1_in2or1,axiom,
! [VAR_0] :
( connection(outc(h1(VAR_0)),in2(or1(VAR_0)))
| ~ fulladder(VAR_0) ),
file('theBenchmark.p',fulladder_connection_outch1_in2or1) ).
cnf(c_15,plain,
( connection(outc(h1(A)),in2(or1(A)))
| ~ fulladder(A) ),
inference(clausify,[status(thm)],[fulladder_connection_outch1_in2or1]) ).
fof(fulladder_connection_in1_in1h2,axiom,
! [VAR_0] :
( connection(in1(VAR_0),in1(h2(VAR_0)))
| ~ fulladder(VAR_0) ),
file('theBenchmark.p',fulladder_connection_in1_in1h2) ).
cnf(c_17,plain,
( connection(in1(A),in1(h2(A)))
| ~ fulladder(A) ),
inference(clausify,[status(thm)],[fulladder_connection_in1_in1h2]) ).
fof(fulladder_connection_in2_in1h1,axiom,
! [VAR_0] :
( connection(in2(VAR_0),in1(h1(VAR_0)))
| ~ fulladder(VAR_0) ),
file('theBenchmark.p',fulladder_connection_in2_in1h1) ).
cnf(c_18,plain,
( connection(in2(A),in1(h1(A)))
| ~ fulladder(A) ),
inference(clausify,[status(thm)],[fulladder_connection_in2_in1h1]) ).
fof(fulladder_connection_inc_in2h1,axiom,
! [VAR_0] :
( connection(inc(VAR_0),in2(h1(VAR_0)))
| ~ fulladder(VAR_0) ),
file('theBenchmark.p',fulladder_connection_inc_in2h1) ).
cnf(c_19,plain,
( connection(inc(A),in2(h1(A)))
| ~ fulladder(A) ),
inference(clausify,[status(thm)],[fulladder_connection_inc_in2h1]) ).
fof(fulladder_connection_outs_outsh2,axiom,
! [VAR_0] :
( connection(outs(VAR_0),outs(h2(VAR_0)))
| ~ fulladder(VAR_0) ),
file('theBenchmark.p',fulladder_connection_outs_outsh2) ).
cnf(c_20,plain,
( connection(outs(A),outs(h2(A)))
| ~ fulladder(A) ),
inference(clausify,[status(thm)],[fulladder_connection_outs_outsh2]) ).
fof(fulladder_connection_outc_out1or1,axiom,
! [VAR_0] :
( connection(outc(VAR_0),out1(or1(VAR_0)))
| ~ fulladder(VAR_0) ),
file('theBenchmark.p',fulladder_connection_outc_out1or1) ).
cnf(c_21,plain,
( connection(outc(A),out1(or1(A)))
| ~ fulladder(A) ),
inference(clausify,[status(thm)],[fulladder_connection_outc_out1or1]) ).
fof(and_ok_or_abnormal,axiom,
! [VAR_0] :
( abnormal(VAR_0)
| and_ok(VAR_0)
| ~ logic_and(VAR_0) ),
file('theBenchmark.p',and_ok_or_abnormal) ).
cnf(c_23,plain,
( abnormal(A)
| and_ok(A)
| ~ logic_and(A) ),
inference(clausify,[status(thm)],[and_ok_or_abnormal]) ).
fof(and_11_1,axiom,
! [VAR_0] :
( one(out1(VAR_0))
| ~ one(in2(VAR_0))
| ~ one(in1(VAR_0))
| ~ and_ok(VAR_0) ),
file('theBenchmark.p',and_11_1) ).
cnf(c_27,plain,
( one(out1(A))
| ~ one(in2(A))
| ~ one(in1(A))
| ~ and_ok(A) ),
inference(clausify,[status(thm)],[and_11_1]) ).
fof(and_x0_0,axiom,
! [VAR_0] :
( zero(out1(VAR_0))
| ~ zero(in2(VAR_0))
| ~ and_ok(VAR_0) ),
file('theBenchmark.p',and_x0_0) ).
cnf(c_28,plain,
( zero(out1(A))
| ~ zero(in2(A))
| ~ and_ok(A) ),
inference(clausify,[status(thm)],[and_x0_0]) ).
fof(and_0x_0,axiom,
! [VAR_0] :
( zero(out1(VAR_0))
| ~ zero(in1(VAR_0))
| ~ and_ok(VAR_0) ),
file('theBenchmark.p',and_0x_0) ).
cnf(c_29,plain,
( zero(out1(A))
| ~ zero(in1(A))
| ~ and_ok(A) ),
inference(clausify,[status(thm)],[and_0x_0]) ).
fof(halfadder_and1,axiom,
! [VAR_0] :
( logic_and(and1(VAR_0))
| ~ halfadder(VAR_0) ),
file('theBenchmark.p',halfadder_and1) ).
cnf(c_30,plain,
( logic_and(and1(A))
| ~ halfadder(A) ),
inference(clausify,[status(thm)],[halfadder_and1]) ).
cnf(c_34,plain,
( abnormal(A)
| ~ logic_and(A)
| one(out1(A))
| ~ one(in2(A))
| ~ one(in1(A)) ),
inference(resolve,[status(thm)],[c_27,c_23]) ).
cnf(c_35,plain,
( abnormal(A)
| ~ logic_and(A)
| zero(out1(A))
| ~ zero(in2(A)) ),
inference(resolve,[status(thm)],[c_28,c_23]) ).
cnf(c_36,plain,
( abnormal(A)
| ~ logic_and(A)
| zero(out1(A))
| ~ zero(in1(A)) ),
inference(resolve,[status(thm)],[c_29,c_23]) ).
fof(halfadder_and2,axiom,
! [VAR_0] :
( logic_and(and2(VAR_0))
| ~ halfadder(VAR_0) ),
file('theBenchmark.p',halfadder_and2) ).
cnf(c_37,plain,
( logic_and(and2(A))
| ~ halfadder(A) ),
inference(clausify,[status(thm)],[halfadder_and2]) ).
fof(or_ok_or_abnormal,axiom,
! [VAR_0] :
( abnormal(VAR_0)
| or_ok(VAR_0)
| ~ logic_or(VAR_0) ),
file('theBenchmark.p',or_ok_or_abnormal) ).
cnf(c_39,plain,
( abnormal(A)
| or_ok(A)
| ~ logic_or(A) ),
inference(clausify,[status(thm)],[or_ok_or_abnormal]) ).
fof(or_00_0,axiom,
! [VAR_0] :
( zero(out1(VAR_0))
| ~ zero(in2(VAR_0))
| ~ zero(in1(VAR_0))
| ~ or_ok(VAR_0) ),
file('theBenchmark.p',or_00_0) ).
cnf(c_43,plain,
( zero(out1(A))
| ~ zero(in2(A))
| ~ zero(in1(A))
| ~ or_ok(A) ),
inference(clausify,[status(thm)],[or_00_0]) ).
fof(or_x1_1,axiom,
! [VAR_0] :
( one(out1(VAR_0))
| ~ one(in2(VAR_0))
| ~ or_ok(VAR_0) ),
file('theBenchmark.p',or_x1_1) ).
cnf(c_44,plain,
( one(out1(A))
| ~ one(in2(A))
| ~ or_ok(A) ),
inference(clausify,[status(thm)],[or_x1_1]) ).
fof(halfadder_or1,axiom,
! [VAR_0] :
( logic_or(or1(VAR_0))
| ~ halfadder(VAR_0) ),
file('theBenchmark.p',halfadder_or1) ).
cnf(c_46,plain,
( logic_or(or1(A))
| ~ halfadder(A) ),
inference(clausify,[status(thm)],[halfadder_or1]) ).
cnf(c_50,plain,
( abnormal(A)
| ~ logic_or(A)
| zero(out1(A))
| ~ zero(in2(A))
| ~ zero(in1(A)) ),
inference(resolve,[status(thm)],[c_43,c_39]) ).
cnf(c_51,plain,
( abnormal(A)
| ~ logic_or(A)
| one(out1(A))
| ~ one(in2(A)) ),
inference(resolve,[status(thm)],[c_44,c_39]) ).
fof(fulladder_or1,axiom,
! [VAR_0] :
( logic_or(or1(VAR_0))
| ~ fulladder(VAR_0) ),
file('theBenchmark.p',fulladder_or1) ).
cnf(c_53,plain,
( logic_or(or1(A))
| ~ fulladder(A) ),
inference(clausify,[status(thm)],[fulladder_or1]) ).
fof(not_ok_or_abnormal,axiom,
! [VAR_0] :
( abnormal(VAR_0)
| not_ok(VAR_0)
| ~ logic_not(VAR_0) ),
file('theBenchmark.p',not_ok_or_abnormal) ).
cnf(c_55,plain,
( abnormal(A)
| not_ok(A)
| ~ logic_not(A) ),
inference(clausify,[status(thm)],[not_ok_or_abnormal]) ).
fof(not_1_0_fw,axiom,
! [VAR_0] :
( zero(out1(VAR_0))
| ~ one(in1(VAR_0))
| ~ not_ok(VAR_0) ),
file('theBenchmark.p',not_1_0_fw) ).
cnf(c_58,plain,
( zero(out1(A))
| ~ one(in1(A))
| ~ not_ok(A) ),
inference(clausify,[status(thm)],[not_1_0_fw]) ).
fof(halfadder_not1,axiom,
! [VAR_0] :
( logic_not(not1(VAR_0))
| ~ halfadder(VAR_0) ),
file('theBenchmark.p',halfadder_not1) ).
cnf(c_60,plain,
( logic_not(not1(A))
| ~ halfadder(A) ),
inference(clausify,[status(thm)],[halfadder_not1]) ).
cnf(c_63,plain,
( abnormal(A)
| ~ logic_not(A)
| zero(out1(A))
| ~ one(in1(A)) ),
inference(resolve,[status(thm)],[c_58,c_55]) ).
fof(fulladder_halfadder2,axiom,
! [VAR_0] :
( halfadder(h2(VAR_0))
| ~ fulladder(VAR_0) ),
file('theBenchmark.p',fulladder_halfadder2) ).
cnf(c_65,plain,
( halfadder(h2(A))
| ~ fulladder(A) ),
inference(clausify,[status(thm)],[fulladder_halfadder2]) ).
cnf(c_69,plain,
( zero(in1(or1(A)))
| ~ zero(in1(A))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_73,plain,
( zero(in2(or1(A)))
| ~ zero(in2(A))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_76,plain,
( one(in1(and2(A)))
| ~ one(in1(A))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_7,c_4]) ).
cnf(c_80,plain,
( one(in2(and2(A)))
| ~ one(in2(A))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_8,c_4]) ).
cnf(c_83,plain,
( zero(outs(A))
| ~ zero(out1(and1(A)))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_9,c_3]) ).
cnf(c_86,plain,
( one(outc(A))
| ~ one(out1(and2(A)))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_10,c_2]) ).
cnf(c_93,plain,
( zero(in1(and1(A)))
| ~ zero(out1(or1(A)))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_11,c_5]) ).
cnf(c_96,plain,
( one(in1(not1(A)))
| ~ one(out1(and2(A)))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_12,c_4]) ).
cnf(c_101,plain,
( zero(in2(and1(A)))
| ~ zero(out1(not1(A)))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_13,c_5]) ).
cnf(c_106,plain,
( abnormal(and1(A))
| zero(out1(and1(A)))
| ~ zero(in2(and1(A)))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_30,c_35]) ).
cnf(c_107,plain,
( abnormal(and1(A))
| zero(out1(and1(A)))
| ~ zero(in1(and1(A)))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_30,c_36]) ).
cnf(c_111,plain,
( abnormal(and2(A))
| one(out1(and2(A)))
| ~ one(in2(and2(A)))
| ~ one(in1(and2(A)))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_37,c_34]) ).
cnf(c_117,plain,
( abnormal(or1(A))
| zero(out1(or1(A)))
| ~ zero(in2(or1(A)))
| ~ zero(in1(or1(A)))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_46,c_50]) ).
cnf(c_122,plain,
( abnormal(not1(A))
| zero(out1(not1(A)))
| ~ one(in1(not1(A)))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_60,c_63]) ).
fof(fulladder_halfadder1,axiom,
! [VAR_0] :
( halfadder(h1(VAR_0))
| ~ fulladder(VAR_0) ),
file('theBenchmark.p',fulladder_halfadder1) ).
cnf(c_124,plain,
( halfadder(h1(A))
| ~ fulladder(A) ),
inference(clausify,[status(thm)],[fulladder_halfadder1]) ).
fof(f_isa_fulladder,axiom,
fulladder(f),
file('theBenchmark.p',f_isa_fulladder) ).
cnf(c_125,plain,
fulladder(f),
inference(clausify,[status(thm)],[f_isa_fulladder]) ).
cnf(c_129,plain,
( zero(in1(or1(h2(A))))
| ~ zero(in1(h2(A)))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_65,c_69]) ).
cnf(c_133,plain,
( zero(in2(or1(h2(A))))
| ~ zero(in2(h2(A)))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_65,c_73]) ).
cnf(c_143,plain,
( zero(outs(h2(A)))
| ~ zero(out1(and1(h2(A))))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_65,c_83]) ).
cnf(c_153,plain,
( zero(in1(and1(h2(A))))
| ~ zero(out1(or1(h2(A))))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_65,c_93]) ).
cnf(c_167,plain,
( abnormal(and1(h2(A)))
| zero(out1(and1(h2(A))))
| ~ zero(in1(and1(h2(A))))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_65,c_107]) ).
cnf(c_177,plain,
( abnormal(or1(h2(A)))
| zero(out1(or1(h2(A))))
| ~ zero(in2(or1(h2(A))))
| ~ zero(in1(or1(h2(A))))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_65,c_117]) ).
cnf(c_194,plain,
( one(in1(and2(h1(A))))
| ~ one(in1(h1(A)))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_124,c_76]) ).
cnf(c_198,plain,
( one(in2(and2(h1(A))))
| ~ one(in2(h1(A)))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_124,c_80]) ).
cnf(c_201,plain,
( zero(outs(h1(A)))
| ~ zero(out1(and1(h1(A))))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_124,c_83]) ).
cnf(c_204,plain,
( one(outc(h1(A)))
| ~ one(out1(and2(h1(A))))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_124,c_86]) ).
cnf(c_214,plain,
( one(in1(not1(h1(A))))
| ~ one(out1(and2(h1(A))))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_124,c_96]) ).
cnf(c_219,plain,
( zero(in2(and1(h1(A))))
| ~ zero(out1(not1(h1(A))))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_124,c_101]) ).
cnf(c_224,plain,
( abnormal(and1(h1(A)))
| zero(out1(and1(h1(A))))
| ~ zero(in2(and1(h1(A))))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_124,c_106]) ).
cnf(c_229,plain,
( abnormal(and2(h1(A)))
| one(out1(and2(h1(A))))
| ~ one(in2(and2(h1(A))))
| ~ one(in1(and2(h1(A))))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_124,c_111]) ).
cnf(c_240,plain,
( abnormal(not1(h1(A)))
| zero(out1(not1(h1(A))))
| ~ one(in1(not1(h1(A))))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_124,c_122]) ).
cnf(c_245,plain,
( zero(in2(h2(A)))
| ~ zero(outs(h1(A)))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_14,c_5]) ).
cnf(c_248,plain,
( one(in2(or1(A)))
| ~ one(outc(h1(A)))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_15,c_4]) ).
cnf(c_257,plain,
( zero(in1(h2(A)))
| ~ zero(in1(A))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_17,c_5]) ).
cnf(c_260,plain,
( one(in1(h1(A)))
| ~ one(in2(A))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_18,c_4]) ).
cnf(c_264,plain,
( one(in2(h1(A)))
| ~ one(inc(A))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_19,c_4]) ).
cnf(c_267,plain,
( zero(outs(A))
| ~ zero(outs(h2(A)))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_20,c_3]) ).
cnf(c_270,plain,
( one(outc(A))
| ~ one(out1(or1(A)))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_21,c_2]) ).
cnf(c_278,plain,
( abnormal(or1(A))
| one(out1(or1(A)))
| ~ one(in2(or1(A)))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_53,c_51]) ).
cnf(c_281,plain,
( abnormal(or1(f))
| one(out1(or1(f)))
| ~ one(in2(or1(f))) ),
inference(resolve,[status(thm)],[c_278,c_125]) ).
cnf(c_289,plain,
( one(outc(f))
| ~ one(out1(or1(f))) ),
inference(resolve,[status(thm)],[c_270,c_125]) ).
cnf(c_292,plain,
( zero(outs(f))
| ~ zero(outs(h2(f))) ),
inference(resolve,[status(thm)],[c_267,c_125]) ).
cnf(c_295,plain,
( one(in2(h1(f)))
| ~ one(inc(f)) ),
inference(resolve,[status(thm)],[c_264,c_125]) ).
cnf(c_299,plain,
( one(in1(h1(f)))
| ~ one(in2(f)) ),
inference(resolve,[status(thm)],[c_260,c_125]) ).
cnf(c_302,plain,
( zero(in1(h2(f)))
| ~ zero(in1(f)) ),
inference(resolve,[status(thm)],[c_257,c_125]) ).
cnf(c_311,plain,
( one(in2(or1(f)))
| ~ one(outc(h1(f))) ),
inference(resolve,[status(thm)],[c_248,c_125]) ).
cnf(c_314,plain,
( zero(in2(h2(f)))
| ~ zero(outs(h1(f))) ),
inference(resolve,[status(thm)],[c_245,c_125]) ).
cnf(c_319,plain,
( abnormal(not1(h1(f)))
| zero(out1(not1(h1(f))))
| ~ one(in1(not1(h1(f)))) ),
inference(resolve,[status(thm)],[c_125,c_240]) ).
cnf(c_330,plain,
( abnormal(and2(h1(f)))
| one(out1(and2(h1(f))))
| ~ one(in2(and2(h1(f))))
| ~ one(in1(and2(h1(f)))) ),
inference(resolve,[status(thm)],[c_125,c_229]) ).
cnf(c_335,plain,
( abnormal(and1(h1(f)))
| zero(out1(and1(h1(f))))
| ~ zero(in2(and1(h1(f)))) ),
inference(resolve,[status(thm)],[c_125,c_224]) ).
cnf(c_340,plain,
( zero(in2(and1(h1(f))))
| ~ zero(out1(not1(h1(f)))) ),
inference(resolve,[status(thm)],[c_125,c_219]) ).
cnf(c_345,plain,
( one(in1(not1(h1(f))))
| ~ one(out1(and2(h1(f)))) ),
inference(resolve,[status(thm)],[c_125,c_214]) ).
cnf(c_355,plain,
( one(outc(h1(f)))
| ~ one(out1(and2(h1(f)))) ),
inference(resolve,[status(thm)],[c_125,c_204]) ).
cnf(c_358,plain,
( zero(outs(h1(f)))
| ~ zero(out1(and1(h1(f)))) ),
inference(resolve,[status(thm)],[c_125,c_201]) ).
cnf(c_361,plain,
( one(in2(and2(h1(f))))
| ~ one(in2(h1(f))) ),
inference(resolve,[status(thm)],[c_125,c_198]) ).
cnf(c_365,plain,
( one(in1(and2(h1(f))))
| ~ one(in1(h1(f))) ),
inference(resolve,[status(thm)],[c_125,c_194]) ).
cnf(c_382,plain,
( abnormal(or1(h2(f)))
| zero(out1(or1(h2(f))))
| ~ zero(in2(or1(h2(f))))
| ~ zero(in1(or1(h2(f)))) ),
inference(resolve,[status(thm)],[c_125,c_177]) ).
cnf(c_392,plain,
( abnormal(and1(h2(f)))
| zero(out1(and1(h2(f))))
| ~ zero(in1(and1(h2(f)))) ),
inference(resolve,[status(thm)],[c_125,c_167]) ).
cnf(c_406,plain,
( zero(in1(and1(h2(f))))
| ~ zero(out1(or1(h2(f)))) ),
inference(resolve,[status(thm)],[c_125,c_153]) ).
cnf(c_416,plain,
( zero(outs(h2(f)))
| ~ zero(out1(and1(h2(f)))) ),
inference(resolve,[status(thm)],[c_125,c_143]) ).
cnf(c_426,plain,
( zero(in2(or1(h2(f))))
| ~ zero(in2(h2(f))) ),
inference(resolve,[status(thm)],[c_125,c_133]) ).
cnf(c_430,plain,
( zero(in1(or1(h2(f))))
| ~ zero(in1(h2(f))) ),
inference(resolve,[status(thm)],[c_125,c_129]) ).
fof(diagnosis_or1_or1h2,axiom,
( ~ abnormal(or1(h2(f)))
| ~ abnormal(or1(f)) ),
file('theBenchmark.p',diagnosis_or1_or1h2) ).
cnf(c_434,plain,
( ~ abnormal(or1(h2(f)))
| ~ abnormal(or1(f)) ),
inference(clausify,[status(thm)],[diagnosis_or1_or1h2]) ).
fof(diagnosis_or1_and1h2,axiom,
( ~ abnormal(and1(h2(f)))
| ~ abnormal(or1(f)) ),
file('theBenchmark.p',diagnosis_or1_and1h2) ).
cnf(c_435,plain,
( ~ abnormal(and1(h2(f)))
| ~ abnormal(or1(f)) ),
inference(clausify,[status(thm)],[diagnosis_or1_and1h2]) ).
fof(diagnosis_or1_not1h1,axiom,
( ~ abnormal(not1(h1(f)))
| ~ abnormal(or1(f)) ),
file('theBenchmark.p',diagnosis_or1_not1h1) ).
cnf(c_436,plain,
( ~ abnormal(not1(h1(f)))
| ~ abnormal(or1(f)) ),
inference(clausify,[status(thm)],[diagnosis_or1_not1h1]) ).
fof(diagnosis_or1_and1h1,axiom,
( ~ abnormal(and1(h1(f)))
| ~ abnormal(or1(f)) ),
file('theBenchmark.p',diagnosis_or1_and1h1) ).
cnf(c_437,plain,
( ~ abnormal(and1(h1(f)))
| ~ abnormal(or1(f)) ),
inference(clausify,[status(thm)],[diagnosis_or1_and1h1]) ).
fof(diagnosis_and2h1,axiom,
~ abnormal(and2(h1(f))),
file('theBenchmark.p',diagnosis_and2h1) ).
cnf(c_438,plain,
~ abnormal(and2(h1(f))),
inference(clausify,[status(thm)],[diagnosis_and2h1]) ).
fof(outc_0,axiom,
zero(outc(f)),
file('theBenchmark.p',outc_0) ).
cnf(c_439,plain,
zero(outc(f)),
inference(clausify,[status(thm)],[outc_0]) ).
fof(outs_1,axiom,
one(outs(f)),
file('theBenchmark.p',outs_1) ).
cnf(c_440,plain,
one(outs(f)),
inference(clausify,[status(thm)],[outs_1]) ).
fof(inc_1,axiom,
one(inc(f)),
file('theBenchmark.p',inc_1) ).
cnf(c_441,plain,
one(inc(f)),
inference(clausify,[status(thm)],[inc_1]) ).
fof(in2_0,axiom,
one(in2(f)),
file('theBenchmark.p',in2_0) ).
cnf(c_442,plain,
one(in2(f)),
inference(clausify,[status(thm)],[in2_0]) ).
fof(in1_1,axiom,
zero(in1(f)),
file('theBenchmark.p',in1_1) ).
cnf(c_443,plain,
zero(in1(f)),
inference(clausify,[status(thm)],[in1_1]) ).
fof(unique_value,axiom,
! [VAR_0] :
( ~ one(VAR_0)
| ~ zero(VAR_0) ),
file('theBenchmark.p',unique_value) ).
cnf(c_444,plain,
( ~ one(A)
| ~ zero(A) ),
inference(clausify,[status(thm)],[unique_value]) ).
cnf(c_448,plain,
( one(out1(and2(h1(f))))
| ~ one(in2(and2(h1(f))))
| ~ one(in1(and2(h1(f)))) ),
inference(resolve,[status(thm)],[c_438,c_330]) ).
cnf(c_453,plain,
one(in2(h1(f))),
inference(resolve,[status(thm)],[c_441,c_295]) ).
cnf(c_454,plain,
one(in1(h1(f))),
inference(resolve,[status(thm)],[c_442,c_299]) ).
cnf(c_455,plain,
zero(in1(h2(f))),
inference(resolve,[status(thm)],[c_443,c_302]) ).
cnf(c_460,plain,
one(in2(and2(h1(f)))),
inference(resolve,[status(thm)],[c_453,c_361]) ).
cnf(c_462,plain,
one(in1(and2(h1(f)))),
inference(resolve,[status(thm)],[c_454,c_365]) ).
cnf(c_463,plain,
zero(in1(or1(h2(f)))),
inference(resolve,[status(thm)],[c_455,c_430]) ).
cnf(c_536,plain,
( one(out1(and2(h1(f))))
| ~ one(in2(and2(h1(f)))) ),
inference(resolve,[status(thm)],[c_462,c_448]) ).
cnf(c_468,plain,
one(out1(and2(h1(f)))),
inference(resolve,[status(thm)],[c_460,c_536]) ).
cnf(c_469,plain,
( abnormal(or1(h2(f)))
| zero(out1(or1(h2(f))))
| ~ zero(in2(or1(h2(f)))) ),
inference(resolve,[status(thm)],[c_463,c_382]) ).
cnf(c_471,plain,
one(outc(h1(f))),
inference(resolve,[status(thm)],[c_468,c_355]) ).
cnf(c_472,plain,
one(in1(not1(h1(f)))),
inference(resolve,[status(thm)],[c_468,c_345]) ).
cnf(c_473,plain,
one(in2(or1(f))),
inference(resolve,[status(thm)],[c_471,c_311]) ).
cnf(c_474,plain,
( abnormal(not1(h1(f)))
| zero(out1(not1(h1(f)))) ),
inference(resolve,[status(thm)],[c_472,c_319]) ).
cnf(c_475,plain,
( abnormal(or1(f))
| one(out1(or1(f))) ),
inference(resolve,[status(thm)],[c_473,c_281]) ).
cnf(c_477,plain,
~ one(outc(f)),
inference(resolve,[status(thm)],[c_444,c_439]) ).
cnf(c_479,plain,
~ one(out1(or1(f))),
inference(resolve,[status(thm)],[c_477,c_289]) ).
cnf(c_482,plain,
abnormal(or1(f)),
inference(resolve,[status(thm)],[c_479,c_475]) ).
cnf(c_485,plain,
~ abnormal(and1(h1(f))),
inference(resolve,[status(thm)],[c_482,c_437]) ).
cnf(c_486,plain,
~ abnormal(not1(h1(f))),
inference(resolve,[status(thm)],[c_482,c_436]) ).
cnf(c_487,plain,
~ abnormal(and1(h2(f))),
inference(resolve,[status(thm)],[c_482,c_435]) ).
cnf(c_488,plain,
~ abnormal(or1(h2(f))),
inference(resolve,[status(thm)],[c_482,c_434]) ).
cnf(c_493,plain,
( zero(out1(and1(h1(f))))
| ~ zero(in2(and1(h1(f)))) ),
inference(resolve,[status(thm)],[c_485,c_335]) ).
cnf(c_495,plain,
zero(out1(not1(h1(f)))),
inference(resolve,[status(thm)],[c_486,c_474]) ).
cnf(c_502,plain,
( zero(out1(and1(h2(f))))
| ~ zero(in1(and1(h2(f)))) ),
inference(resolve,[status(thm)],[c_487,c_392]) ).
cnf(c_504,plain,
( zero(out1(or1(h2(f))))
| ~ zero(in2(or1(h2(f)))) ),
inference(resolve,[status(thm)],[c_488,c_469]) ).
cnf(c_507,plain,
zero(in2(and1(h1(f)))),
inference(resolve,[status(thm)],[c_495,c_340]) ).
cnf(c_510,plain,
zero(out1(and1(h1(f)))),
inference(resolve,[status(thm)],[c_507,c_493]) ).
cnf(c_513,plain,
zero(outs(h1(f))),
inference(resolve,[status(thm)],[c_510,c_358]) ).
cnf(c_515,plain,
zero(in2(h2(f))),
inference(resolve,[status(thm)],[c_513,c_314]) ).
cnf(c_518,plain,
zero(in2(or1(h2(f)))),
inference(resolve,[status(thm)],[c_515,c_426]) ).
cnf(c_521,plain,
zero(out1(or1(h2(f)))),
inference(resolve,[status(thm)],[c_518,c_504]) ).
cnf(c_524,plain,
zero(in1(and1(h2(f)))),
inference(resolve,[status(thm)],[c_521,c_406]) ).
cnf(c_527,plain,
zero(out1(and1(h2(f)))),
inference(resolve,[status(thm)],[c_524,c_502]) ).
cnf(c_529,plain,
zero(outs(h2(f))),
inference(resolve,[status(thm)],[c_527,c_416]) ).
cnf(c_531,plain,
zero(outs(f)),
inference(resolve,[status(thm)],[c_529,c_292]) ).
cnf(c_537,plain,
~ one(outs(f)),
inference(resolve,[status(thm)],[c_531,c_444]) ).
cnf(c_535,plain,
$false,
inference(resolve,[status(thm)],[c_440,c_537]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HWV007-2 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/10.44 % Computer : n010.cluster.edu
% 0.11/10.44 % Model : x86_64 x86_64
% 0.11/10.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.44 % Memory : 8046.5625MB
% 0.11/10.44 % OS : Linux 6.8.0-71-generic
% 0.11/10.44 % CPULimit : 300
% 0.11/10.44 % WCLimit : 300
% 0.11/10.44 % DateTime : Fri Sep 25 16:00:31 UTC 2026
% 0.11/10.44 % CPUTime :
% 0.11/10.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/10.45 % Process 1167575 was started by sandbox on n010,
% 0.11/10.45 % Fri Sep 25 16:00:31 2026
% 0.11/10.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/10.45
% 0.11/10.45 % From the command line: assign(max_seconds, 300).
% 0.15/10.58
% 0.15/10.58 % SZS status Unsatisfiable for theBenchmark
% 0.15/10.58
% 0.15/10.58 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.15/10.58 % Length of proof is 150.
% 0.15/10.58 % Level of proof is 23.
% 0.15/10.58 % Maximum clause weight is 39.000.
% 0.15/10.58 % Given clauses 136.
% 0.15/10.58
% 0.15/10.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------