%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HWC003-2 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 07:32:06 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.44s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 11
% Syntax : Number of formulae : 87 ( 75 unt; 0 def)
% Number of atoms : 101 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 35 ( 21 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-10 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-8 aty)
% Number of variables : 164 ( 63 sgn 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(create_test,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8,VAR_9] :
( basic_output(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8)
| ~ test(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8,VAR_9) ),
file('theBenchmark.p',create_test) ).
cnf(c_1,plain,
( basic_output(A,B,C,D,E,F,V6,V7,V8)
| ~ test(A,B,C,D,E,F,V6,V7,V8,V9) ),
inference(clausify,[status(thm)],[create_test]) ).
fof(inverter_test,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8] :
( test(not(VAR_0),not(VAR_1),not(VAR_2),not(VAR_3),not(VAR_4),not(VAR_5),not(VAR_6),not(VAR_7),add_inverter(VAR_8,inverter_table(not(VAR_0),not(VAR_1),not(VAR_2),not(VAR_3),not(VAR_4),not(VAR_5),not(VAR_6),not(VAR_7))),make_reverse_list(list(inverter_table(not(VAR_0),not(VAR_1),not(VAR_2),not(VAR_3),not(VAR_4),not(VAR_5),not(VAR_6),not(VAR_7)),VAR_8)))
| ~ output(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8) ),
file('theBenchmark.p',inverter_test) ).
cnf(c_2,plain,
( test(not(A),not(B),not(C),not(D),not(E),not(F),not(V6),not(V7),add_inverter(V8,inverter_table(not(A),not(B),not(C),not(D),not(E),not(F),not(V6),not(V7))),make_reverse_list(list(inverter_table(not(A),not(B),not(C),not(D),not(E),not(F),not(V6),not(V7)),V8)))
| ~ output(A,B,C,D,E,F,V6,V7,V8) ),
inference(clausify,[status(thm)],[inverter_test]) ).
cnf(c_3,plain,
( ~ output(A,B,C,D,E,F,V6,V7,V8)
| basic_output(not(A),not(B),not(C),not(D),not(E),not(F),not(V6),not(V7),add_inverter(V8,inverter_table(not(A),not(B),not(C),not(D),not(E),not(F),not(V6),not(V7)))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(prove_cannot_construct_this,axiom,
! [VAR_0] :
( ~ output(n1,n0,n1,n0,n1,n0,n1,n0,VAR_0)
| ~ output(n1,n1,n0,n0,n1,n1,n0,n0,VAR_0)
| ~ output(n1,n1,n1,n1,n0,n0,n0,n0,VAR_0) ),
file('theBenchmark.p',prove_cannot_construct_this) ).
cnf(c_4,plain,
( ~ output(n1,n0,n1,n0,n1,n0,n1,n0,A)
| ~ output(n1,n1,n0,n0,n1,n1,n0,n0,A)
| ~ output(n1,n1,n1,n1,n0,n0,n0,n0,A) ),
inference(clausify,[status(thm)],[prove_cannot_construct_this]) ).
fof(input3,axiom,
! [VAR_0] : output(n0,n1,n0,n1,n0,n1,n0,n1,VAR_0),
file('theBenchmark.p',input3) ).
cnf(c_5,plain,
output(n0,n1,n0,n1,n0,n1,n0,n1,A),
inference(clausify,[status(thm)],[input3]) ).
fof(input2,axiom,
! [VAR_0] : output(n0,n0,n1,n1,n0,n0,n1,n1,VAR_0),
file('theBenchmark.p',input2) ).
cnf(c_6,plain,
output(n0,n0,n1,n1,n0,n0,n1,n1,A),
inference(clausify,[status(thm)],[input2]) ).
fof(input1,axiom,
! [VAR_0] : output(n0,n0,n0,n0,n1,n1,n1,n1,VAR_0),
file('theBenchmark.p',input1) ).
cnf(c_7,plain,
output(n0,n0,n0,n0,n1,n1,n1,n1,A),
inference(clausify,[status(thm)],[input1]) ).
fof(basic_output_definition,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8] :
( output(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8)
| ~ basic_output(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8) ),
file('theBenchmark.p',basic_output_definition) ).
cnf(c_8,plain,
( output(A,B,C,D,E,F,V6,V7,V8)
| ~ basic_output(A,B,C,D,E,F,V6,V7,V8) ),
inference(clausify,[status(thm)],[basic_output_definition]) ).
fof(add_inverter_definition2,axiom,
! [VAR_0,VAR_1] : add_inverter(VAR_0,VAR_1) = list(VAR_1,VAR_0),
file('theBenchmark.p',add_inverter_definition2) ).
cnf(c_20,plain,
add_inverter(A,B) = list(B,A),
inference(clausify,[status(thm)],[add_inverter_definition2]) ).
fof(add_inverter_definition1,axiom,
! [VAR_0,VAR_1,VAR_2] : add_inverter(list(VAR_0,VAR_1),VAR_2) = list(VAR_0,add_inverter(VAR_1,VAR_2)),
file('theBenchmark.p',add_inverter_definition1) ).
cnf(c_21,plain,
add_inverter(list(A,B),C) = list(A,add_inverter(B,C)),
inference(clausify,[status(thm)],[add_inverter_definition1]) ).
cnf(c_122,plain,
list(C,list(A,B)) = list(A,add_inverter(B,C)),
inference(paramod,[status(thm)],[c_20,c_21]) ).
cnf(c_22,plain,
list(A,list(B,C)) = list(B,list(A,C)),
inference(paramod,[status(thm)],[c_20,c_122]) ).
fof(not_definition2,axiom,
not(n1) = n0,
file('theBenchmark.p',not_definition2) ).
cnf(c_23,plain,
not(n1) = n0,
inference(clausify,[status(thm)],[not_definition2]) ).
fof(not_definition1,axiom,
not(n0) = n1,
file('theBenchmark.p',not_definition1) ).
cnf(c_24,plain,
not(n0) = n1,
inference(clausify,[status(thm)],[not_definition1]) ).
cnf(c_29,plain,
( ~ output(A,B,C,D,E,F,V6,V7,V8)
| basic_output(not(A),not(B),not(C),not(D),not(E),not(F),not(V6),not(V7),list(inverter_table(not(A),not(B),not(C),not(D),not(E),not(F),not(V6),not(V7)),V8)) ),
inference(paramod,[status(thm)],[c_20,c_3]) ).
cnf(c_33,plain,
list(A,list(B,list(C,D))) = list(C,list(A,list(B,D))),
inference(paramod,[status(thm)],[c_22,c_22]) ).
cnf(c_123,plain,
basic_output(not(n0),not(n0),not(n0),not(n0),not(n1),not(n1),not(n1),not(n1),list(inverter_table(not(n0),not(n0),not(n0),not(n0),not(n1),not(n1),not(n1),not(n1)),A)),
inference(resolve,[status(thm)],[c_29,c_7]) ).
cnf(c_124,plain,
basic_output(n1,not(n0),not(n0),not(n0),not(n1),not(n1),not(n1),not(n1),list(inverter_table(not(n0),not(n0),not(n0),not(n0),not(n1),not(n1),not(n1),not(n1)),A)),
inference(paramod,[status(thm)],[c_24,c_123]) ).
cnf(c_125,plain,
basic_output(n1,n1,not(n0),not(n0),not(n1),not(n1),not(n1),not(n1),list(inverter_table(not(n0),not(n0),not(n0),not(n0),not(n1),not(n1),not(n1),not(n1)),A)),
inference(paramod,[status(thm)],[c_24,c_124]) ).
cnf(c_126,plain,
basic_output(n1,n1,n1,not(n0),not(n1),not(n1),not(n1),not(n1),list(inverter_table(not(n0),not(n0),not(n0),not(n0),not(n1),not(n1),not(n1),not(n1)),A)),
inference(paramod,[status(thm)],[c_24,c_125]) ).
cnf(c_127,plain,
basic_output(n1,n1,n1,n1,not(n1),not(n1),not(n1),not(n1),list(inverter_table(not(n0),not(n0),not(n0),not(n0),not(n1),not(n1),not(n1),not(n1)),A)),
inference(paramod,[status(thm)],[c_24,c_126]) ).
cnf(c_128,plain,
basic_output(n1,n1,n1,n1,n0,not(n1),not(n1),not(n1),list(inverter_table(not(n0),not(n0),not(n0),not(n0),not(n1),not(n1),not(n1),not(n1)),A)),
inference(paramod,[status(thm)],[c_23,c_127]) ).
cnf(c_129,plain,
basic_output(n1,n1,n1,n1,n0,n0,not(n1),not(n1),list(inverter_table(not(n0),not(n0),not(n0),not(n0),not(n1),not(n1),not(n1),not(n1)),A)),
inference(paramod,[status(thm)],[c_23,c_128]) ).
cnf(c_130,plain,
basic_output(n1,n1,n1,n1,n0,n0,n0,not(n1),list(inverter_table(not(n0),not(n0),not(n0),not(n0),not(n1),not(n1),not(n1),not(n1)),A)),
inference(paramod,[status(thm)],[c_23,c_129]) ).
cnf(c_131,plain,
basic_output(n1,n1,n1,n1,n0,n0,n0,n0,list(inverter_table(not(n0),not(n0),not(n0),not(n0),not(n1),not(n1),not(n1),not(n1)),A)),
inference(paramod,[status(thm)],[c_23,c_130]) ).
cnf(c_132,plain,
basic_output(n1,n1,n1,n1,n0,n0,n0,n0,list(inverter_table(n1,not(n0),not(n0),not(n0),not(n1),not(n1),not(n1),not(n1)),A)),
inference(paramod,[status(thm)],[c_24,c_131]) ).
cnf(c_133,plain,
basic_output(n1,n1,n1,n1,n0,n0,n0,n0,list(inverter_table(n1,n1,not(n0),not(n0),not(n1),not(n1),not(n1),not(n1)),A)),
inference(paramod,[status(thm)],[c_24,c_132]) ).
cnf(c_134,plain,
basic_output(n1,n1,n1,n1,n0,n0,n0,n0,list(inverter_table(n1,n1,n1,not(n0),not(n1),not(n1),not(n1),not(n1)),A)),
inference(paramod,[status(thm)],[c_24,c_133]) ).
cnf(c_135,plain,
basic_output(n1,n1,n1,n1,n0,n0,n0,n0,list(inverter_table(n1,n1,n1,n1,not(n1),not(n1),not(n1),not(n1)),A)),
inference(paramod,[status(thm)],[c_24,c_134]) ).
cnf(c_136,plain,
basic_output(n1,n1,n1,n1,n0,n0,n0,n0,list(inverter_table(n1,n1,n1,n1,n0,not(n1),not(n1),not(n1)),A)),
inference(paramod,[status(thm)],[c_23,c_135]) ).
cnf(c_137,plain,
basic_output(n1,n1,n1,n1,n0,n0,n0,n0,list(inverter_table(n1,n1,n1,n1,n0,n0,not(n1),not(n1)),A)),
inference(paramod,[status(thm)],[c_23,c_136]) ).
cnf(c_138,plain,
basic_output(n1,n1,n1,n1,n0,n0,n0,n0,list(inverter_table(n1,n1,n1,n1,n0,n0,n0,not(n1)),A)),
inference(paramod,[status(thm)],[c_23,c_137]) ).
cnf(c_34,plain,
basic_output(n1,n1,n1,n1,n0,n0,n0,n0,list(inverter_table(n1,n1,n1,n1,n0,n0,n0,n0),A)),
inference(paramod,[status(thm)],[c_23,c_138]) ).
cnf(c_139,plain,
basic_output(not(n0),not(n0),not(n1),not(n1),not(n0),not(n0),not(n1),not(n1),list(inverter_table(not(n0),not(n0),not(n1),not(n1),not(n0),not(n0),not(n1),not(n1)),A)),
inference(resolve,[status(thm)],[c_29,c_6]) ).
cnf(c_140,plain,
basic_output(n1,not(n0),not(n1),not(n1),not(n0),not(n0),not(n1),not(n1),list(inverter_table(not(n0),not(n0),not(n1),not(n1),not(n0),not(n0),not(n1),not(n1)),A)),
inference(paramod,[status(thm)],[c_24,c_139]) ).
cnf(c_141,plain,
basic_output(n1,n1,not(n1),not(n1),not(n0),not(n0),not(n1),not(n1),list(inverter_table(not(n0),not(n0),not(n1),not(n1),not(n0),not(n0),not(n1),not(n1)),A)),
inference(paramod,[status(thm)],[c_24,c_140]) ).
cnf(c_142,plain,
basic_output(n1,n1,n0,not(n1),not(n0),not(n0),not(n1),not(n1),list(inverter_table(not(n0),not(n0),not(n1),not(n1),not(n0),not(n0),not(n1),not(n1)),A)),
inference(paramod,[status(thm)],[c_23,c_141]) ).
cnf(c_143,plain,
basic_output(n1,n1,n0,n0,not(n0),not(n0),not(n1),not(n1),list(inverter_table(not(n0),not(n0),not(n1),not(n1),not(n0),not(n0),not(n1),not(n1)),A)),
inference(paramod,[status(thm)],[c_23,c_142]) ).
cnf(c_144,plain,
basic_output(n1,n1,n0,n0,n1,not(n0),not(n1),not(n1),list(inverter_table(not(n0),not(n0),not(n1),not(n1),not(n0),not(n0),not(n1),not(n1)),A)),
inference(paramod,[status(thm)],[c_24,c_143]) ).
cnf(c_145,plain,
basic_output(n1,n1,n0,n0,n1,n1,not(n1),not(n1),list(inverter_table(not(n0),not(n0),not(n1),not(n1),not(n0),not(n0),not(n1),not(n1)),A)),
inference(paramod,[status(thm)],[c_24,c_144]) ).
cnf(c_146,plain,
basic_output(n1,n1,n0,n0,n1,n1,n0,not(n1),list(inverter_table(not(n0),not(n0),not(n1),not(n1),not(n0),not(n0),not(n1),not(n1)),A)),
inference(paramod,[status(thm)],[c_23,c_145]) ).
cnf(c_147,plain,
basic_output(n1,n1,n0,n0,n1,n1,n0,n0,list(inverter_table(not(n0),not(n0),not(n1),not(n1),not(n0),not(n0),not(n1),not(n1)),A)),
inference(paramod,[status(thm)],[c_23,c_146]) ).
cnf(c_148,plain,
basic_output(n1,n1,n0,n0,n1,n1,n0,n0,list(inverter_table(n1,not(n0),not(n1),not(n1),not(n0),not(n0),not(n1),not(n1)),A)),
inference(paramod,[status(thm)],[c_24,c_147]) ).
cnf(c_149,plain,
basic_output(n1,n1,n0,n0,n1,n1,n0,n0,list(inverter_table(n1,n1,not(n1),not(n1),not(n0),not(n0),not(n1),not(n1)),A)),
inference(paramod,[status(thm)],[c_24,c_148]) ).
cnf(c_150,plain,
basic_output(n1,n1,n0,n0,n1,n1,n0,n0,list(inverter_table(n1,n1,n0,not(n1),not(n0),not(n0),not(n1),not(n1)),A)),
inference(paramod,[status(thm)],[c_23,c_149]) ).
cnf(c_151,plain,
basic_output(n1,n1,n0,n0,n1,n1,n0,n0,list(inverter_table(n1,n1,n0,n0,not(n0),not(n0),not(n1),not(n1)),A)),
inference(paramod,[status(thm)],[c_23,c_150]) ).
cnf(c_152,plain,
basic_output(n1,n1,n0,n0,n1,n1,n0,n0,list(inverter_table(n1,n1,n0,n0,n1,not(n0),not(n1),not(n1)),A)),
inference(paramod,[status(thm)],[c_24,c_151]) ).
cnf(c_153,plain,
basic_output(n1,n1,n0,n0,n1,n1,n0,n0,list(inverter_table(n1,n1,n0,n0,n1,n1,not(n1),not(n1)),A)),
inference(paramod,[status(thm)],[c_24,c_152]) ).
cnf(c_154,plain,
basic_output(n1,n1,n0,n0,n1,n1,n0,n0,list(inverter_table(n1,n1,n0,n0,n1,n1,n0,not(n1)),A)),
inference(paramod,[status(thm)],[c_23,c_153]) ).
cnf(c_35,plain,
basic_output(n1,n1,n0,n0,n1,n1,n0,n0,list(inverter_table(n1,n1,n0,n0,n1,n1,n0,n0),A)),
inference(paramod,[status(thm)],[c_23,c_154]) ).
cnf(c_155,plain,
basic_output(not(n0),not(n1),not(n0),not(n1),not(n0),not(n1),not(n0),not(n1),list(inverter_table(not(n0),not(n1),not(n0),not(n1),not(n0),not(n1),not(n0),not(n1)),A)),
inference(resolve,[status(thm)],[c_29,c_5]) ).
cnf(c_156,plain,
basic_output(n1,not(n1),not(n0),not(n1),not(n0),not(n1),not(n0),not(n1),list(inverter_table(not(n0),not(n1),not(n0),not(n1),not(n0),not(n1),not(n0),not(n1)),A)),
inference(paramod,[status(thm)],[c_24,c_155]) ).
cnf(c_157,plain,
basic_output(n1,n0,not(n0),not(n1),not(n0),not(n1),not(n0),not(n1),list(inverter_table(not(n0),not(n1),not(n0),not(n1),not(n0),not(n1),not(n0),not(n1)),A)),
inference(paramod,[status(thm)],[c_23,c_156]) ).
cnf(c_158,plain,
basic_output(n1,n0,n1,not(n1),not(n0),not(n1),not(n0),not(n1),list(inverter_table(not(n0),not(n1),not(n0),not(n1),not(n0),not(n1),not(n0),not(n1)),A)),
inference(paramod,[status(thm)],[c_24,c_157]) ).
cnf(c_159,plain,
basic_output(n1,n0,n1,n0,not(n0),not(n1),not(n0),not(n1),list(inverter_table(not(n0),not(n1),not(n0),not(n1),not(n0),not(n1),not(n0),not(n1)),A)),
inference(paramod,[status(thm)],[c_23,c_158]) ).
cnf(c_160,plain,
basic_output(n1,n0,n1,n0,n1,not(n1),not(n0),not(n1),list(inverter_table(not(n0),not(n1),not(n0),not(n1),not(n0),not(n1),not(n0),not(n1)),A)),
inference(paramod,[status(thm)],[c_24,c_159]) ).
cnf(c_161,plain,
basic_output(n1,n0,n1,n0,n1,n0,not(n0),not(n1),list(inverter_table(not(n0),not(n1),not(n0),not(n1),not(n0),not(n1),not(n0),not(n1)),A)),
inference(paramod,[status(thm)],[c_23,c_160]) ).
cnf(c_162,plain,
basic_output(n1,n0,n1,n0,n1,n0,n1,not(n1),list(inverter_table(not(n0),not(n1),not(n0),not(n1),not(n0),not(n1),not(n0),not(n1)),A)),
inference(paramod,[status(thm)],[c_24,c_161]) ).
cnf(c_163,plain,
basic_output(n1,n0,n1,n0,n1,n0,n1,n0,list(inverter_table(not(n0),not(n1),not(n0),not(n1),not(n0),not(n1),not(n0),not(n1)),A)),
inference(paramod,[status(thm)],[c_23,c_162]) ).
cnf(c_164,plain,
basic_output(n1,n0,n1,n0,n1,n0,n1,n0,list(inverter_table(n1,not(n1),not(n0),not(n1),not(n0),not(n1),not(n0),not(n1)),A)),
inference(paramod,[status(thm)],[c_24,c_163]) ).
cnf(c_165,plain,
basic_output(n1,n0,n1,n0,n1,n0,n1,n0,list(inverter_table(n1,n0,not(n0),not(n1),not(n0),not(n1),not(n0),not(n1)),A)),
inference(paramod,[status(thm)],[c_23,c_164]) ).
cnf(c_166,plain,
basic_output(n1,n0,n1,n0,n1,n0,n1,n0,list(inverter_table(n1,n0,n1,not(n1),not(n0),not(n1),not(n0),not(n1)),A)),
inference(paramod,[status(thm)],[c_24,c_165]) ).
cnf(c_167,plain,
basic_output(n1,n0,n1,n0,n1,n0,n1,n0,list(inverter_table(n1,n0,n1,n0,not(n0),not(n1),not(n0),not(n1)),A)),
inference(paramod,[status(thm)],[c_23,c_166]) ).
cnf(c_168,plain,
basic_output(n1,n0,n1,n0,n1,n0,n1,n0,list(inverter_table(n1,n0,n1,n0,n1,not(n1),not(n0),not(n1)),A)),
inference(paramod,[status(thm)],[c_24,c_167]) ).
cnf(c_169,plain,
basic_output(n1,n0,n1,n0,n1,n0,n1,n0,list(inverter_table(n1,n0,n1,n0,n1,n0,not(n0),not(n1)),A)),
inference(paramod,[status(thm)],[c_23,c_168]) ).
cnf(c_170,plain,
basic_output(n1,n0,n1,n0,n1,n0,n1,n0,list(inverter_table(n1,n0,n1,n0,n1,n0,n1,not(n1)),A)),
inference(paramod,[status(thm)],[c_24,c_169]) ).
cnf(c_36,plain,
basic_output(n1,n0,n1,n0,n1,n0,n1,n0,list(inverter_table(n1,n0,n1,n0,n1,n0,n1,n0),A)),
inference(paramod,[status(thm)],[c_23,c_170]) ).
cnf(c_47,plain,
output(n1,n1,n1,n1,n0,n0,n0,n0,list(inverter_table(n1,n1,n1,n1,n0,n0,n0,n0),A)),
inference(resolve,[status(thm)],[c_34,c_8]) ).
cnf(c_55,plain,
output(n1,n1,n0,n0,n1,n1,n0,n0,list(inverter_table(n1,n1,n0,n0,n1,n1,n0,n0),A)),
inference(resolve,[status(thm)],[c_35,c_8]) ).
cnf(c_84,plain,
( ~ output(n1,n0,n1,n0,n1,n0,n1,n0,list(inverter_table(n1,n1,n1,n1,n0,n0,n0,n0),A))
| ~ output(n1,n1,n0,n0,n1,n1,n0,n0,list(inverter_table(n1,n1,n1,n1,n0,n0,n0,n0),A)) ),
inference(resolve,[status(thm)],[c_47,c_4]) ).
cnf(c_100,plain,
basic_output(n1,n0,n1,n0,n1,n0,n1,n0,list(A,list(B,list(inverter_table(n1,n0,n1,n0,n1,n0,n1,n0),C)))),
inference(paramod,[status(thm)],[c_33,c_36]) ).
cnf(c_114,plain,
( ~ output(n1,n0,n1,n0,n1,n0,n1,n0,list(inverter_table(n1,n1,n1,n1,n0,n0,n0,n0),list(A,B)))
| ~ output(n1,n1,n0,n0,n1,n1,n0,n0,list(A,list(inverter_table(n1,n1,n1,n1,n0,n0,n0,n0),B))) ),
inference(paramod,[status(thm)],[c_22,c_84]) ).
cnf(c_171,plain,
~ output(n1,n0,n1,n0,n1,n0,n1,n0,list(inverter_table(n1,n1,n1,n1,n0,n0,n0,n0),list(inverter_table(n1,n1,n0,n0,n1,n1,n0,n0),A))),
inference(resolve,[status(thm)],[c_114,c_55]) ).
cnf(c_117,plain,
~ output(n1,n0,n1,n0,n1,n0,n1,n0,list(inverter_table(n1,n1,n0,n0,n1,n1,n0,n0),list(inverter_table(n1,n1,n1,n1,n0,n0,n0,n0),A))),
inference(paramod,[status(thm)],[c_22,c_171]) ).
cnf(c_120,plain,
~ basic_output(n1,n0,n1,n0,n1,n0,n1,n0,list(inverter_table(n1,n1,n0,n0,n1,n1,n0,n0),list(inverter_table(n1,n1,n1,n1,n0,n0,n0,n0),A))),
inference(resolve,[status(thm)],[c_8,c_117]) ).
cnf(c_121,plain,
$false,
inference(resolve,[status(thm)],[c_120,c_100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HWC003-2 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n005.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 15:58:17 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 3885273 was started by sandbox2 on n005,
% 0.09/0.35 % Fri Sep 25 15:58:17 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.44
% 0.13/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.44
% 0.13/0.44 % Proof 1 at 0.03 (+ 0.00) seconds.
% 0.13/0.44 % Length of proof is 26.
% 0.13/0.44 % Level of proof is 9.
% 0.13/0.44 % Maximum clause weight is 74.000.
% 0.13/0.44 % Given clauses 42.
% 0.13/0.44
% 0.13/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------