%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HWV005-2 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 26
% Syntax : Number of formulae : 88 ( 25 unt; 0 def)
% Number of atoms : 189 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 204 ( 103 ~; 101 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 51 ( 0 sgn 22 !; 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_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_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(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_15,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_19,plain,
( one(out1(A))
| ~ one(in2(A))
| ~ one(in1(A))
| ~ and_ok(A) ),
inference(clausify,[status(thm)],[and_11_1]) ).
cnf(c_26,plain,
( abnormal(A)
| ~ logic_and(A)
| one(out1(A))
| ~ one(in2(A))
| ~ one(in1(A)) ),
inference(resolve,[status(thm)],[c_19,c_15]) ).
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_29,plain,
( abnormal(A)
| or_ok(A)
| ~ logic_or(A) ),
inference(clausify,[status(thm)],[or_ok_or_abnormal]) ).
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_31,plain,
( abnormal(A)
| not_ok(A)
| ~ logic_not(A) ),
inference(clausify,[status(thm)],[not_ok_or_abnormal]) ).
fof(diagnosis_and1,axiom,
~ abnormal(and1(h)),
file('theBenchmark.p',diagnosis_and1) ).
cnf(c_32,plain,
~ abnormal(and1(h)),
inference(clausify,[status(thm)],[diagnosis_and1]) ).
fof(diagnosis_not1,axiom,
~ abnormal(not1(h)),
file('theBenchmark.p',diagnosis_not1) ).
cnf(c_33,plain,
~ abnormal(not1(h)),
inference(clausify,[status(thm)],[diagnosis_not1]) ).
fof(diagnosis_or1,axiom,
~ abnormal(or1(h)),
file('theBenchmark.p',diagnosis_or1) ).
cnf(c_34,plain,
~ abnormal(or1(h)),
inference(clausify,[status(thm)],[diagnosis_or1]) ).
cnf(c_51,plain,
( ~ logic_and(and1(h))
| one(out1(and1(h)))
| ~ one(in2(and1(h)))
| ~ one(in1(and1(h))) ),
inference(resolve,[status(thm)],[c_32,c_26]) ).
fof(halfadder_and1,axiom,
! [VAR_0] :
( logic_and(and1(VAR_0))
| ~ halfadder(VAR_0) ),
file('theBenchmark.p',halfadder_and1) ).
cnf(c_66,plain,
( logic_and(and1(A))
| ~ halfadder(A) ),
inference(clausify,[status(thm)],[halfadder_and1]) ).
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_73,plain,
( one(out1(A))
| ~ one(in1(A))
| ~ or_ok(A) ),
inference(clausify,[status(thm)],[or_1x_1]) ).
cnf(c_85,plain,
( or_ok(or1(h))
| ~ logic_or(or1(h)) ),
inference(resolve,[status(thm)],[c_34,c_29]) ).
fof(halfadder_or1,axiom,
! [VAR_0] :
( logic_or(or1(VAR_0))
| ~ halfadder(VAR_0) ),
file('theBenchmark.p',halfadder_or1) ).
cnf(c_86,plain,
( logic_or(or1(A))
| ~ halfadder(A) ),
inference(clausify,[status(thm)],[halfadder_or1]) ).
cnf(c_125,plain,
( one(out1(or1(h)))
| ~ one(in1(or1(h)))
| ~ logic_or(or1(h)) ),
inference(resolve,[status(thm)],[c_85,c_73]) ).
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_145,plain,
( one(out1(A))
| ~ zero(in1(A))
| ~ not_ok(A) ),
inference(clausify,[status(thm)],[not_0_1_fw]) ).
cnf(c_150,plain,
( not_ok(not1(h))
| ~ logic_not(not1(h)) ),
inference(resolve,[status(thm)],[c_33,c_31]) ).
fof(halfadder_not1,axiom,
! [VAR_0] :
( logic_not(not1(VAR_0))
| ~ halfadder(VAR_0) ),
file('theBenchmark.p',halfadder_not1) ).
cnf(c_152,plain,
( logic_not(not1(A))
| ~ halfadder(A) ),
inference(clausify,[status(thm)],[halfadder_not1]) ).
cnf(c_176,plain,
( one(out1(not1(h)))
| ~ zero(in1(not1(h)))
| ~ logic_not(not1(h)) ),
inference(resolve,[status(thm)],[c_150,c_145]) ).
fof(h_isa_halfadder,axiom,
halfadder(h),
file('theBenchmark.p',h_isa_halfadder) ).
cnf(c_181,plain,
halfadder(h),
inference(clausify,[status(thm)],[h_isa_halfadder]) ).
cnf(c_185,plain,
( one(out1(and1(h)))
| ~ one(in2(and1(h)))
| ~ one(in1(and1(h)))
| ~ halfadder(h) ),
inference(resolve,[status(thm)],[c_66,c_51]) ).
cnf(c_193,plain,
( one(out1(or1(h)))
| ~ one(in1(or1(h)))
| ~ halfadder(h) ),
inference(resolve,[status(thm)],[c_86,c_125]) ).
cnf(c_197,plain,
( one(out1(not1(h)))
| ~ zero(in1(not1(h)))
| ~ halfadder(h) ),
inference(resolve,[status(thm)],[c_152,c_176]) ).
cnf(c_200,plain,
( one(in1(or1(A)))
| ~ one(in1(A))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_214,plain,
( one(outs(A))
| ~ one(out1(and1(A)))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_9,c_2]) ).
cnf(c_221,plain,
( zero(out1(and2(A)))
| ~ zero(outc(A))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_10,c_5]) ).
cnf(c_224,plain,
( one(in1(and1(A)))
| ~ one(out1(or1(A)))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_11,c_4]) ).
cnf(c_229,plain,
( zero(in1(not1(A)))
| ~ zero(out1(and2(A)))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_12,c_5]) ).
cnf(c_232,plain,
( one(in2(and1(A)))
| ~ one(out1(not1(A)))
| ~ halfadder(A) ),
inference(resolve,[status(thm)],[c_13,c_4]) ).
cnf(c_235,plain,
( one(in2(and1(h)))
| ~ one(out1(not1(h))) ),
inference(resolve,[status(thm)],[c_232,c_181]) ).
cnf(c_238,plain,
( zero(in1(not1(h)))
| ~ zero(out1(and2(h))) ),
inference(resolve,[status(thm)],[c_229,c_181]) ).
cnf(c_243,plain,
( one(in1(and1(h)))
| ~ one(out1(or1(h))) ),
inference(resolve,[status(thm)],[c_224,c_181]) ).
cnf(c_246,plain,
( zero(out1(and2(h)))
| ~ zero(outc(h)) ),
inference(resolve,[status(thm)],[c_221,c_181]) ).
cnf(c_253,plain,
( one(outs(h))
| ~ one(out1(and1(h))) ),
inference(resolve,[status(thm)],[c_214,c_181]) ).
cnf(c_267,plain,
( one(in1(or1(h)))
| ~ one(in1(h)) ),
inference(resolve,[status(thm)],[c_200,c_181]) ).
cnf(c_270,plain,
( one(out1(not1(h)))
| ~ zero(in1(not1(h))) ),
inference(resolve,[status(thm)],[c_181,c_197]) ).
cnf(c_274,plain,
( one(out1(or1(h)))
| ~ one(in1(or1(h))) ),
inference(resolve,[status(thm)],[c_181,c_193]) ).
cnf(c_282,plain,
( one(out1(and1(h)))
| ~ one(in2(and1(h)))
| ~ one(in1(and1(h))) ),
inference(resolve,[status(thm)],[c_181,c_185]) ).
fof(outc_0,axiom,
zero(outc(h)),
file('theBenchmark.p',outc_0) ).
cnf(c_286,plain,
zero(outc(h)),
inference(clausify,[status(thm)],[outc_0]) ).
fof(outs_0,axiom,
zero(outs(h)),
file('theBenchmark.p',outs_0) ).
cnf(c_287,plain,
zero(outs(h)),
inference(clausify,[status(thm)],[outs_0]) ).
fof(in1_1,axiom,
one(in1(h)),
file('theBenchmark.p',in1_1) ).
cnf(c_289,plain,
one(in1(h)),
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_290,plain,
( ~ one(A)
| ~ zero(A) ),
inference(clausify,[status(thm)],[unique_value]) ).
cnf(c_291,plain,
zero(out1(and2(h))),
inference(resolve,[status(thm)],[c_286,c_246]) ).
cnf(c_295,plain,
one(in1(or1(h))),
inference(resolve,[status(thm)],[c_289,c_267]) ).
cnf(c_297,plain,
zero(in1(not1(h))),
inference(resolve,[status(thm)],[c_291,c_238]) ).
cnf(c_300,plain,
one(out1(or1(h))),
inference(resolve,[status(thm)],[c_295,c_274]) ).
cnf(c_301,plain,
one(out1(not1(h))),
inference(resolve,[status(thm)],[c_297,c_270]) ).
cnf(c_302,plain,
one(in1(and1(h))),
inference(resolve,[status(thm)],[c_300,c_243]) ).
cnf(c_303,plain,
one(in2(and1(h))),
inference(resolve,[status(thm)],[c_301,c_235]) ).
cnf(c_309,plain,
( one(out1(and1(h)))
| ~ one(in2(and1(h))) ),
inference(resolve,[status(thm)],[c_302,c_282]) ).
cnf(c_304,plain,
one(out1(and1(h))),
inference(resolve,[status(thm)],[c_303,c_309]) ).
cnf(c_305,plain,
one(outs(h)),
inference(resolve,[status(thm)],[c_304,c_253]) ).
cnf(c_310,plain,
~ one(outs(h)),
inference(resolve,[status(thm)],[c_290,c_287]) ).
cnf(c_308,plain,
$false,
inference(resolve,[status(thm)],[c_305,c_310]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HWV005-2 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 15:55:34 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2702087 was started by sandbox2 on n017,
% 0.10/0.37 % Fri Sep 25 15:55:34 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.39
% 0.10/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.39
% 0.10/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.10/0.39 % Length of proof is 60.
% 0.10/0.39 % Level of proof is 9.
% 0.10/0.39 % Maximum clause weight is 27.000.
% 0.10/0.39 % Given clauses 24.
% 0.10/0.39
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------