%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HWV006-2 : 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 : n019.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 0.10s 0.59s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 50
% Syntax : Number of formulae : 222 ( 54 unt; 0 def)
% Number of atoms : 512 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 563 ( 273 ~; 290 |; 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 : 135 ( 0 sgn 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_outch2_in1or1,axiom,
! [VAR_0] :
( connection(outc(h2(VAR_0)),in1(or1(VAR_0)))
| ~ fulladder(VAR_0) ),
file('theBenchmark.p',fulladder_connection_outch2_in1or1) ).
cnf(c_16,plain,
( connection(outc(h2(A)),in1(or1(A)))
| ~ fulladder(A) ),
inference(clausify,[status(thm)],[fulladder_connection_outch2_in1or1]) ).
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_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(or_1x_1,axiom,
! [VAR_0] :
( one(out1(VAR_0))
| ~ one(in1(VAR_0))
| ~ or_ok(VAR_0) ),
file('theBenchmark.p',or_1x_1) ).
cnf(c_45,plain,
( one(out1(A))
| ~ one(in1(A))
| ~ or_ok(A) ),
inference(clausify,[status(thm)],[or_1x_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_51,plain,
( abnormal(A)
| ~ logic_or(A)
| one(out1(A))
| ~ one(in2(A)) ),
inference(resolve,[status(thm)],[c_44,c_39]) ).
cnf(c_52,plain,
( abnormal(A)
| ~ logic_or(A)
| one(out1(A))
| ~ one(in1(A)) ),
inference(resolve,[status(thm)],[c_45,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(not_0_1_fw,axiom,
! [VAR_0] :
( one(out1(VAR_0))
| ~ zero(in1(VAR_0))
| ~ not_ok(VAR_0) ),
file('theBenchmark.p',not_0_1_fw) ).
cnf(c_59,plain,
( one(out1(A))
| ~ zero(in1(A))
| ~ not_ok(A) ),
inference(clausify,[status(thm)],[not_0_1_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]) ).
cnf(c_64,plain,
( abnormal(A)
| ~ logic_not(A)
| one(out1(A))
| ~ zero(in1(A)) ),
inference(resolve,[status(thm)],[c_59,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_72,plain,
( one(in2(or1(A)))
| ~ one(in2(A))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_6,c_4]) ).
cnf(c_76,plain,
( one(in1(and2(A)))
| ~ one(in1(A))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_7,c_4]) ).
cnf(c_77,plain,
( zero(in1(and2(A)))
| ~ zero(in1(A))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_7,c_5]) ).
cnf(c_80,plain,
( one(in2(and2(A)))
| ~ one(in2(A))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_8,c_4]) ).
cnf(c_82,plain,
( one(outs(A))
| ~ one(out1(and1(A)))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_9,c_2]) ).
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_92,plain,
( one(in1(and1(A)))
| ~ one(out1(or1(A)))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_11,c_4]) ).
cnf(c_96,plain,
( one(in1(not1(A)))
| ~ one(out1(and2(A)))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_12,c_4]) ).
cnf(c_97,plain,
( zero(in1(not1(A)))
| ~ zero(out1(and2(A)))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_12,c_5]) ).
cnf(c_100,plain,
( one(in2(and1(A)))
| ~ one(out1(not1(A)))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_13,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_105,plain,
( abnormal(and1(A))
| one(out1(and1(A)))
| ~ one(in2(and1(A)))
| ~ one(in1(and1(A)))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_30,c_34]) ).
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_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_113,plain,
( abnormal(and2(A))
| zero(out1(and2(A)))
| ~ zero(in1(and2(A)))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_37,c_36]) ).
cnf(c_118,plain,
( abnormal(or1(A))
| one(out1(or1(A)))
| ~ one(in2(or1(A)))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_46,c_51]) ).
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]) ).
cnf(c_123,plain,
( abnormal(not1(A))
| one(out1(not1(A)))
| ~ zero(in1(not1(A)))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_60,c_64]) ).
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_136,plain,
( one(in1(and2(h2(A))))
| ~ one(in1(h2(A)))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_65,c_76]) ).
cnf(c_140,plain,
( one(in2(and2(h2(A))))
| ~ one(in2(h2(A)))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_65,c_80]) ).
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_146,plain,
( one(outc(h2(A)))
| ~ one(out1(and2(h2(A))))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_65,c_86]) ).
cnf(c_156,plain,
( one(in1(not1(h2(A))))
| ~ one(out1(and2(h2(A))))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_65,c_96]) ).
cnf(c_161,plain,
( zero(in2(and1(h2(A))))
| ~ zero(out1(not1(h2(A))))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_65,c_101]) ).
cnf(c_166,plain,
( abnormal(and1(h2(A)))
| zero(out1(and1(h2(A))))
| ~ zero(in2(and1(h2(A))))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_65,c_106]) ).
cnf(c_171,plain,
( abnormal(and2(h2(A)))
| one(out1(and2(h2(A))))
| ~ one(in2(and2(h2(A))))
| ~ one(in1(and2(h2(A))))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_65,c_111]) ).
cnf(c_182,plain,
( abnormal(not1(h2(A)))
| zero(out1(not1(h2(A))))
| ~ one(in1(not1(h2(A))))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_65,c_122]) ).
cnf(c_190,plain,
( one(in2(or1(h1(A))))
| ~ one(in2(h1(A)))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_124,c_72]) ).
cnf(c_195,plain,
( zero(in1(and2(h1(A))))
| ~ zero(in1(h1(A)))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_124,c_77]) ).
cnf(c_200,plain,
( one(outs(h1(A)))
| ~ one(out1(and1(h1(A))))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_124,c_82]) ).
cnf(c_210,plain,
( one(in1(and1(h1(A))))
| ~ one(out1(or1(h1(A))))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_124,c_92]) ).
cnf(c_215,plain,
( zero(in1(not1(h1(A))))
| ~ zero(out1(and2(h1(A))))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_124,c_97]) ).
cnf(c_218,plain,
( one(in2(and1(h1(A))))
| ~ one(out1(not1(h1(A))))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_124,c_100]) ).
cnf(c_223,plain,
( abnormal(and1(h1(A)))
| one(out1(and1(h1(A))))
| ~ one(in2(and1(h1(A))))
| ~ one(in1(and1(h1(A))))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_124,c_105]) ).
cnf(c_231,plain,
( abnormal(and2(h1(A)))
| zero(out1(and2(h1(A))))
| ~ zero(in1(and2(h1(A))))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_124,c_113]) ).
cnf(c_236,plain,
( abnormal(or1(h1(A)))
| one(out1(or1(h1(A))))
| ~ one(in2(or1(h1(A))))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_124,c_118]) ).
cnf(c_241,plain,
( abnormal(not1(h1(A)))
| one(out1(not1(h1(A))))
| ~ zero(in1(not1(h1(A))))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_124,c_123]) ).
cnf(c_244,plain,
( one(in2(h2(A)))
| ~ one(outs(h1(A)))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_14,c_4]) ).
cnf(c_252,plain,
( one(in1(or1(A)))
| ~ one(outc(h2(A)))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_256,plain,
( one(in1(h2(A)))
| ~ one(in1(A))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_17,c_4]) ).
cnf(c_261,plain,
( zero(in1(h1(A)))
| ~ zero(in2(A))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_18,c_5]) ).
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_279,plain,
( abnormal(or1(A))
| one(out1(or1(A)))
| ~ one(in1(or1(A)))
| ~ fulladder(A) ),
inference(resolve,[status(thm)],[c_53,c_52]) ).
cnf(c_280,plain,
( abnormal(or1(f))
| one(out1(or1(f)))
| ~ one(in1(or1(f))) ),
inference(resolve,[status(thm)],[c_279,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_298,plain,
( zero(in1(h1(f)))
| ~ zero(in2(f)) ),
inference(resolve,[status(thm)],[c_261,c_125]) ).
cnf(c_303,plain,
( one(in1(h2(f)))
| ~ one(in1(f)) ),
inference(resolve,[status(thm)],[c_256,c_125]) ).
cnf(c_307,plain,
( one(in1(or1(f)))
| ~ one(outc(h2(f))) ),
inference(resolve,[status(thm)],[c_252,c_125]) ).
cnf(c_315,plain,
( one(in2(h2(f)))
| ~ one(outs(h1(f))) ),
inference(resolve,[status(thm)],[c_244,c_125]) ).
cnf(c_318,plain,
( abnormal(not1(h1(f)))
| one(out1(not1(h1(f))))
| ~ zero(in1(not1(h1(f)))) ),
inference(resolve,[status(thm)],[c_125,c_241]) ).
cnf(c_323,plain,
( abnormal(or1(h1(f)))
| one(out1(or1(h1(f))))
| ~ one(in2(or1(h1(f)))) ),
inference(resolve,[status(thm)],[c_125,c_236]) ).
cnf(c_328,plain,
( abnormal(and2(h1(f)))
| zero(out1(and2(h1(f))))
| ~ zero(in1(and2(h1(f)))) ),
inference(resolve,[status(thm)],[c_125,c_231]) ).
cnf(c_336,plain,
( abnormal(and1(h1(f)))
| one(out1(and1(h1(f))))
| ~ one(in2(and1(h1(f))))
| ~ one(in1(and1(h1(f)))) ),
inference(resolve,[status(thm)],[c_125,c_223]) ).
cnf(c_341,plain,
( one(in2(and1(h1(f))))
| ~ one(out1(not1(h1(f)))) ),
inference(resolve,[status(thm)],[c_125,c_218]) ).
cnf(c_344,plain,
( zero(in1(not1(h1(f))))
| ~ zero(out1(and2(h1(f)))) ),
inference(resolve,[status(thm)],[c_125,c_215]) ).
cnf(c_349,plain,
( one(in1(and1(h1(f))))
| ~ one(out1(or1(h1(f)))) ),
inference(resolve,[status(thm)],[c_125,c_210]) ).
cnf(c_359,plain,
( one(outs(h1(f)))
| ~ one(out1(and1(h1(f)))) ),
inference(resolve,[status(thm)],[c_125,c_200]) ).
cnf(c_364,plain,
( zero(in1(and2(h1(f))))
| ~ zero(in1(h1(f))) ),
inference(resolve,[status(thm)],[c_125,c_195]) ).
cnf(c_369,plain,
( one(in2(or1(h1(f))))
| ~ one(in2(h1(f))) ),
inference(resolve,[status(thm)],[c_125,c_190]) ).
cnf(c_377,plain,
( abnormal(not1(h2(f)))
| zero(out1(not1(h2(f))))
| ~ one(in1(not1(h2(f)))) ),
inference(resolve,[status(thm)],[c_125,c_182]) ).
cnf(c_388,plain,
( abnormal(and2(h2(f)))
| one(out1(and2(h2(f))))
| ~ one(in2(and2(h2(f))))
| ~ one(in1(and2(h2(f)))) ),
inference(resolve,[status(thm)],[c_125,c_171]) ).
cnf(c_393,plain,
( abnormal(and1(h2(f)))
| zero(out1(and1(h2(f))))
| ~ zero(in2(and1(h2(f)))) ),
inference(resolve,[status(thm)],[c_125,c_166]) ).
cnf(c_398,plain,
( zero(in2(and1(h2(f))))
| ~ zero(out1(not1(h2(f)))) ),
inference(resolve,[status(thm)],[c_125,c_161]) ).
cnf(c_403,plain,
( one(in1(not1(h2(f))))
| ~ one(out1(and2(h2(f)))) ),
inference(resolve,[status(thm)],[c_125,c_156]) ).
cnf(c_413,plain,
( one(outc(h2(f)))
| ~ one(out1(and2(h2(f)))) ),
inference(resolve,[status(thm)],[c_125,c_146]) ).
cnf(c_416,plain,
( zero(outs(h2(f)))
| ~ zero(out1(and1(h2(f)))) ),
inference(resolve,[status(thm)],[c_125,c_143]) ).
cnf(c_419,plain,
( one(in2(and2(h2(f))))
| ~ one(in2(h2(f))) ),
inference(resolve,[status(thm)],[c_125,c_140]) ).
cnf(c_423,plain,
( one(in1(and2(h2(f))))
| ~ one(in1(h2(f))) ),
inference(resolve,[status(thm)],[c_125,c_136]) ).
fof(diagnosis_and1h1,axiom,
~ abnormal(and1(h1(f))),
file('theBenchmark.p',diagnosis_and1h1) ).
cnf(c_434,plain,
~ abnormal(and1(h1(f))),
inference(clausify,[status(thm)],[diagnosis_and1h1]) ).
fof(diagnosis_and2h1,axiom,
~ abnormal(and2(h1(f))),
file('theBenchmark.p',diagnosis_and2h1) ).
cnf(c_435,plain,
~ abnormal(and2(h1(f))),
inference(clausify,[status(thm)],[diagnosis_and2h1]) ).
fof(diagnosis_not1h1,axiom,
~ abnormal(not1(h1(f))),
file('theBenchmark.p',diagnosis_not1h1) ).
cnf(c_436,plain,
~ abnormal(not1(h1(f))),
inference(clausify,[status(thm)],[diagnosis_not1h1]) ).
fof(diagnosis_or1h1,axiom,
~ abnormal(or1(h1(f))),
file('theBenchmark.p',diagnosis_or1h1) ).
cnf(c_437,plain,
~ abnormal(or1(h1(f))),
inference(clausify,[status(thm)],[diagnosis_or1h1]) ).
fof(diagnosis_or1_and1h2,axiom,
( ~ abnormal(and1(h2(f)))
| ~ abnormal(or1(f)) ),
file('theBenchmark.p',diagnosis_or1_and1h2) ).
cnf(c_438,plain,
( ~ abnormal(and1(h2(f)))
| ~ abnormal(or1(f)) ),
inference(clausify,[status(thm)],[diagnosis_or1_and1h2]) ).
fof(diagnosis_and2,axiom,
~ abnormal(and2(h2(f))),
file('theBenchmark.p',diagnosis_and2) ).
cnf(c_439,plain,
~ abnormal(and2(h2(f))),
inference(clausify,[status(thm)],[diagnosis_and2]) ).
fof(diagnosis_or1_not1h2,axiom,
( ~ abnormal(not1(h2(f)))
| ~ abnormal(or1(f)) ),
file('theBenchmark.p',diagnosis_or1_not1h2) ).
cnf(c_440,plain,
( ~ abnormal(not1(h2(f)))
| ~ abnormal(or1(f)) ),
inference(clausify,[status(thm)],[diagnosis_or1_not1h2]) ).
fof(outc_0,axiom,
zero(outc(f)),
file('theBenchmark.p',outc_0) ).
cnf(c_441,plain,
zero(outc(f)),
inference(clausify,[status(thm)],[outc_0]) ).
fof(outs_1,axiom,
one(outs(f)),
file('theBenchmark.p',outs_1) ).
cnf(c_442,plain,
one(outs(f)),
inference(clausify,[status(thm)],[outs_1]) ).
fof(inc_1,axiom,
one(inc(f)),
file('theBenchmark.p',inc_1) ).
cnf(c_443,plain,
one(inc(f)),
inference(clausify,[status(thm)],[inc_1]) ).
fof(in2_0,axiom,
zero(in2(f)),
file('theBenchmark.p',in2_0) ).
cnf(c_444,plain,
zero(in2(f)),
inference(clausify,[status(thm)],[in2_0]) ).
fof(in1_1,axiom,
one(in1(f)),
file('theBenchmark.p',in1_1) ).
cnf(c_445,plain,
one(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_446,plain,
( ~ one(A)
| ~ zero(A) ),
inference(clausify,[status(thm)],[unique_value]) ).
cnf(c_450,plain,
( one(out1(and1(h1(f))))
| ~ one(in2(and1(h1(f))))
| ~ one(in1(and1(h1(f)))) ),
inference(resolve,[status(thm)],[c_434,c_336]) ).
cnf(c_458,plain,
( zero(out1(and2(h1(f))))
| ~ zero(in1(and2(h1(f)))) ),
inference(resolve,[status(thm)],[c_435,c_328]) ).
cnf(c_462,plain,
( one(out1(not1(h1(f))))
| ~ zero(in1(not1(h1(f)))) ),
inference(resolve,[status(thm)],[c_436,c_318]) ).
cnf(c_467,plain,
( one(out1(or1(h1(f))))
| ~ one(in2(or1(h1(f)))) ),
inference(resolve,[status(thm)],[c_437,c_323]) ).
cnf(c_472,plain,
( one(out1(and2(h2(f))))
| ~ one(in2(and2(h2(f))))
| ~ one(in1(and2(h2(f)))) ),
inference(resolve,[status(thm)],[c_439,c_388]) ).
cnf(c_477,plain,
one(in2(h1(f))),
inference(resolve,[status(thm)],[c_443,c_295]) ).
cnf(c_478,plain,
zero(in1(h1(f))),
inference(resolve,[status(thm)],[c_444,c_298]) ).
cnf(c_479,plain,
one(in1(h2(f))),
inference(resolve,[status(thm)],[c_445,c_303]) ).
cnf(c_483,plain,
one(in2(or1(h1(f)))),
inference(resolve,[status(thm)],[c_477,c_369]) ).
cnf(c_486,plain,
zero(in1(and2(h1(f)))),
inference(resolve,[status(thm)],[c_478,c_364]) ).
cnf(c_488,plain,
one(in1(and2(h2(f)))),
inference(resolve,[status(thm)],[c_479,c_423]) ).
cnf(c_491,plain,
one(out1(or1(h1(f)))),
inference(resolve,[status(thm)],[c_483,c_467]) ).
cnf(c_494,plain,
zero(out1(and2(h1(f)))),
inference(resolve,[status(thm)],[c_486,c_458]) ).
cnf(c_496,plain,
( one(out1(and2(h2(f))))
| ~ one(in2(and2(h2(f)))) ),
inference(resolve,[status(thm)],[c_488,c_472]) ).
cnf(c_497,plain,
one(in1(and1(h1(f)))),
inference(resolve,[status(thm)],[c_491,c_349]) ).
cnf(c_499,plain,
zero(in1(not1(h1(f)))),
inference(resolve,[status(thm)],[c_494,c_344]) ).
cnf(c_500,plain,
( one(out1(and1(h1(f))))
| ~ one(in2(and1(h1(f)))) ),
inference(resolve,[status(thm)],[c_497,c_450]) ).
cnf(c_502,plain,
one(out1(not1(h1(f)))),
inference(resolve,[status(thm)],[c_499,c_462]) ).
cnf(c_503,plain,
one(in2(and1(h1(f)))),
inference(resolve,[status(thm)],[c_502,c_341]) ).
cnf(c_504,plain,
one(out1(and1(h1(f)))),
inference(resolve,[status(thm)],[c_503,c_500]) ).
cnf(c_505,plain,
one(outs(h1(f))),
inference(resolve,[status(thm)],[c_504,c_359]) ).
cnf(c_506,plain,
one(in2(h2(f))),
inference(resolve,[status(thm)],[c_505,c_315]) ).
cnf(c_508,plain,
one(in2(and2(h2(f)))),
inference(resolve,[status(thm)],[c_506,c_419]) ).
cnf(c_509,plain,
one(out1(and2(h2(f)))),
inference(resolve,[status(thm)],[c_508,c_496]) ).
cnf(c_510,plain,
one(outc(h2(f))),
inference(resolve,[status(thm)],[c_509,c_413]) ).
cnf(c_511,plain,
one(in1(not1(h2(f)))),
inference(resolve,[status(thm)],[c_509,c_403]) ).
cnf(c_512,plain,
one(in1(or1(f))),
inference(resolve,[status(thm)],[c_510,c_307]) ).
cnf(c_513,plain,
( abnormal(not1(h2(f)))
| zero(out1(not1(h2(f)))) ),
inference(resolve,[status(thm)],[c_511,c_377]) ).
cnf(c_514,plain,
( abnormal(or1(f))
| one(out1(or1(f))) ),
inference(resolve,[status(thm)],[c_512,c_280]) ).
cnf(c_516,plain,
~ one(outc(f)),
inference(resolve,[status(thm)],[c_446,c_441]) ).
cnf(c_518,plain,
~ one(out1(or1(f))),
inference(resolve,[status(thm)],[c_516,c_289]) ).
cnf(c_521,plain,
abnormal(or1(f)),
inference(resolve,[status(thm)],[c_518,c_514]) ).
cnf(c_523,plain,
~ abnormal(not1(h2(f))),
inference(resolve,[status(thm)],[c_521,c_440]) ).
cnf(c_524,plain,
~ abnormal(and1(h2(f))),
inference(resolve,[status(thm)],[c_521,c_438]) ).
cnf(c_527,plain,
zero(out1(not1(h2(f)))),
inference(resolve,[status(thm)],[c_523,c_513]) ).
cnf(c_533,plain,
( zero(out1(and1(h2(f))))
| ~ zero(in2(and1(h2(f)))) ),
inference(resolve,[status(thm)],[c_524,c_393]) ).
cnf(c_537,plain,
zero(in2(and1(h2(f)))),
inference(resolve,[status(thm)],[c_527,c_398]) ).
cnf(c_541,plain,
zero(out1(and1(h2(f)))),
inference(resolve,[status(thm)],[c_537,c_533]) ).
cnf(c_544,plain,
zero(outs(h2(f))),
inference(resolve,[status(thm)],[c_541,c_416]) ).
cnf(c_546,plain,
zero(outs(f)),
inference(resolve,[status(thm)],[c_544,c_292]) ).
cnf(c_551,plain,
~ one(outs(f)),
inference(resolve,[status(thm)],[c_546,c_446]) ).
cnf(c_550,plain,
$false,
inference(resolve,[status(thm)],[c_442,c_551]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HWV006-2 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.55 % Computer : n019.cluster.edu
% 0.09/0.55 % Model : x86_64 x86_64
% 0.09/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.55 % Memory : 8046.5625MB
% 0.09/0.55 % OS : Linux 6.8.0-71-generic
% 0.10/0.55 % CPULimit : 300
% 0.10/0.55 % WCLimit : 300
% 0.10/0.55 % DateTime : Fri Sep 25 16:00:08 UTC 2026
% 0.10/0.56 % CPUTime :
% 0.10/0.56 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.56 % Process 3181472 was started by sandbox on n019,
% 0.10/0.56 % Fri Sep 25 16:00:08 2026
% 0.10/0.56 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.56
% 0.10/0.56 % From the command line: assign(max_seconds, 300).
% 0.10/0.59
% 0.10/0.59 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.59
% 0.10/0.59 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.10/0.59 % Length of proof is 171.
% 0.10/0.59 % Level of proof is 25.
% 0.10/0.59 % Maximum clause weight is 39.000.
% 0.10/0.59 % Given clauses 116.
% 0.10/0.59
% 0.10/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------