%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : HWV007-2 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 07:32:52 AM UTC 2026
% Result : Unsatisfiable 16.58s 3.59s
% Output : CNFRefutation 16.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 48
% Syntax : Number of clauses : 177 ( 23 unt; 30 nHn; 177 RR)
% Number of literals : 499 ( 0 equ; 305 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 3 ( 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 : 128 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(f_isa_fulladder,hypothesis,
fulladder(f) ).
cnf(in1_1,hypothesis,
zero(in1(f)) ).
cnf(in2_0,hypothesis,
one(in2(f)) ).
cnf(inc_1,hypothesis,
one(inc(f)) ).
cnf(outs_1,hypothesis,
one(outs(f)) ).
cnf(outc_0,hypothesis,
zero(outc(f)) ).
cnf(diagnosis_and2h1,negated_conjecture,
~ abnormal(and2(h1(f))) ).
cnf(diagnosis_or1_and1h1,negated_conjecture,
( ~ abnormal(and1(h1(f)))
| ~ abnormal(or1(f)) ) ).
cnf(diagnosis_or1_not1h1,negated_conjecture,
( ~ abnormal(not1(h1(f)))
| ~ abnormal(or1(f)) ) ).
cnf(diagnosis_or1_and1h2,negated_conjecture,
( ~ abnormal(and1(h2(f)))
| ~ abnormal(or1(f)) ) ).
cnf(diagnosis_or1_or1h2,negated_conjecture,
( ~ abnormal(or1(h2(f)))
| ~ abnormal(or1(f)) ) ).
cnf(value_propagation_zero1,axiom,
( zero(X1)
| ~ zero(X0)
| ~ connection(X0,X1) ) ).
cnf(value_propagation_one1,axiom,
( one(X1)
| ~ one(X0)
| ~ connection(X0,X1) ) ).
cnf(value_propagation_zero2,axiom,
( zero(X0)
| ~ zero(X1)
| ~ connection(X0,X1) ) ).
cnf(value_propagation_one2,axiom,
( one(X0)
| ~ one(X1)
| ~ connection(X0,X1) ) ).
cnf(unique_value,axiom,
( ~ one(X0)
| ~ zero(X0) ) ).
cnf(and_x0_0,axiom,
( zero(out1(X0))
| ~ zero(in2(X0))
| ~ 'and$uok'(X0) ) ).
cnf(and_11_1,axiom,
( one(out1(X0))
| ~ one(in2(X0))
| ~ one(in1(X0))
| ~ 'and$uok'(X0) ) ).
cnf(and_1_1x,axiom,
( one(in1(X0))
| ~ one(out1(X0))
| ~ 'and$uok'(X0) ) ).
cnf(and_ok_or_abnormal,axiom,
( abnormal(X0)
| 'and$uok'(X0)
| ~ 'logic$uand'(X0) ) ).
cnf(or_1_11,axiom,
( one(in2(X0))
| one(in1(X0))
| ~ one(out1(X0))
| ~ 'or$uok'(X0) ) ).
cnf(or_0_01,axiom,
( zero(in2(X0))
| ~ zero(out1(X0))
| ~ 'or$uok'(X0) ) ).
cnf(or_ok_or_abnormal,axiom,
( abnormal(X0)
| 'or$uok'(X0)
| ~ 'logic$uor'(X0) ) ).
cnf(not_1_0_fw,axiom,
( zero(out1(X0))
| ~ one(in1(X0))
| ~ 'not$uok'(X0) ) ).
cnf(not_ok_or_abnormal,axiom,
( abnormal(X0)
| 'not$uok'(X0)
| ~ 'logic$unot'(X0) ) ).
cnf(halfadder_and1,axiom,
( 'logic$uand'(and1(X0))
| ~ halfadder(X0) ) ).
cnf(halfadder_and2,axiom,
( 'logic$uand'(and2(X0))
| ~ halfadder(X0) ) ).
cnf(halfadder_not1,axiom,
( 'logic$unot'(not1(X0))
| ~ halfadder(X0) ) ).
cnf(halfadder_or1,axiom,
( 'logic$uor'(or1(X0))
| ~ halfadder(X0) ) ).
cnf(halfadder_connection_in1_in1or1,axiom,
( connection(in1(X0),in1(or1(X0)))
| ~ halfadder(X0) ) ).
cnf(halfadder_connection_in2_in2or1,axiom,
( connection(in2(X0),in2(or1(X0)))
| ~ halfadder(X0) ) ).
cnf(halfadder_connection_in1_in1and2,axiom,
( connection(in1(X0),in1(and2(X0)))
| ~ halfadder(X0) ) ).
cnf(halfadder_connection_in2_in2and2,axiom,
( connection(in2(X0),in2(and2(X0)))
| ~ halfadder(X0) ) ).
cnf(halfadder_connection_outs_out1and1,axiom,
( connection(outs(X0),out1(and1(X0)))
| ~ halfadder(X0) ) ).
cnf(halfadder_connection_outc_out1and2,axiom,
( connection(outc(X0),out1(and2(X0)))
| ~ halfadder(X0) ) ).
cnf(halfadder_connection_out1or1_in1_and1,axiom,
( connection(out1(or1(X0)),in1(and1(X0)))
| ~ halfadder(X0) ) ).
cnf(halfadder_connection_out1and2_in1not1,axiom,
( connection(out1(and2(X0)),in1(not1(X0)))
| ~ halfadder(X0) ) ).
cnf(halfadder_connection_out1not1_in2and1,axiom,
( connection(out1(not1(X0)),in2(and1(X0)))
| ~ halfadder(X0) ) ).
cnf(fulladder_halfadder1,axiom,
( halfadder(h1(X0))
| ~ fulladder(X0) ) ).
cnf(fulladder_halfadder2,axiom,
( halfadder(h2(X0))
| ~ fulladder(X0) ) ).
cnf(fulladder_or1,axiom,
( 'logic$uor'(or1(X0))
| ~ fulladder(X0) ) ).
cnf(fulladder_connection_outsh1_in2h2,axiom,
( connection(outs(h1(X0)),in2(h2(X0)))
| ~ fulladder(X0) ) ).
cnf(fulladder_connection_outch1_in2or1,axiom,
( connection(outc(h1(X0)),in2(or1(X0)))
| ~ fulladder(X0) ) ).
cnf(fulladder_connection_in1_in1h2,axiom,
( connection(in1(X0),in1(h2(X0)))
| ~ fulladder(X0) ) ).
cnf(fulladder_connection_in2_in1h1,axiom,
( connection(in2(X0),in1(h1(X0)))
| ~ fulladder(X0) ) ).
cnf(fulladder_connection_inc_in2h1,axiom,
( connection(inc(X0),in2(h1(X0)))
| ~ fulladder(X0) ) ).
cnf(fulladder_connection_outs_outsh2,axiom,
( connection(outs(X0),outs(h2(X0)))
| ~ fulladder(X0) ) ).
cnf(fulladder_connection_outc_out1or1,axiom,
( connection(outc(X0),out1(or1(X0)))
| ~ fulladder(X0) ) ).
cnf(c0,plain,
fulladder(f),
inference(clausification,[status(esa)],[f_isa_fulladder]) ).
cnf(c1,plain,
zero(in1(f)),
inference(clausification,[status(esa)],[in1_1]) ).
cnf(c2,plain,
one(in2(f)),
inference(clausification,[status(esa)],[in2_0]) ).
cnf(c3,plain,
one(inc(f)),
inference(clausification,[status(esa)],[inc_1]) ).
cnf(c4,plain,
one(outs(f)),
inference(clausification,[status(esa)],[outs_1]) ).
cnf(c5,plain,
zero(outc(f)),
inference(clausification,[status(esa)],[outc_0]) ).
cnf(c6,plain,
~ abnormal(and2(h1(f))),
inference(clausification,[status(esa)],[diagnosis_and2h1]) ).
cnf(c7,plain,
( ~ abnormal(and1(h1(f)))
| ~ abnormal(or1(f)) ),
inference(clausification,[status(esa)],[diagnosis_or1_and1h1]) ).
cnf(c8,plain,
( ~ abnormal(not1(h1(f)))
| ~ abnormal(or1(f)) ),
inference(clausification,[status(esa)],[diagnosis_or1_not1h1]) ).
cnf(c9,plain,
( ~ abnormal(and1(h2(f)))
| ~ abnormal(or1(f)) ),
inference(clausification,[status(esa)],[diagnosis_or1_and1h2]) ).
cnf(c10,plain,
( ~ abnormal(or1(h2(f)))
| ~ abnormal(or1(f)) ),
inference(clausification,[status(esa)],[diagnosis_or1_or1h2]) ).
cnf(c11,plain,
( zero(X1)
| ~ zero(X0)
| ~ connection(X0,X1) ),
inference(clausification,[status(esa)],[value_propagation_zero1]) ).
cnf(c12,plain,
( one(X1)
| ~ one(X0)
| ~ connection(X0,X1) ),
inference(clausification,[status(esa)],[value_propagation_one1]) ).
cnf(c13,plain,
( zero(X0)
| ~ zero(X1)
| ~ connection(X0,X1) ),
inference(clausification,[status(esa)],[value_propagation_zero2]) ).
cnf(c14,plain,
( one(X0)
| ~ one(X1)
| ~ connection(X0,X1) ),
inference(clausification,[status(esa)],[value_propagation_one2]) ).
cnf(c15,plain,
( ~ one(X0)
| ~ zero(X0) ),
inference(clausification,[status(esa)],[unique_value]) ).
cnf(c17,plain,
( zero(out1(X0))
| ~ zero(in2(X0))
| ~ 'and$uok'(X0) ),
inference(clausification,[status(esa)],[and_x0_0]) ).
cnf(c18,plain,
( one(out1(X0))
| ~ one(in2(X0))
| ~ one(in1(X0))
| ~ 'and$uok'(X0) ),
inference(clausification,[status(esa)],[and_11_1]) ).
cnf(c20,plain,
( one(in1(X0))
| ~ one(out1(X0))
| ~ 'and$uok'(X0) ),
inference(clausification,[status(esa)],[and_1_1x]) ).
cnf(c23,plain,
( abnormal(X0)
| 'and$uok'(X0)
| ~ 'logic$uand'(X0) ),
inference(clausification,[status(esa)],[and_ok_or_abnormal]) ).
cnf(c27,plain,
( one(in2(X0))
| one(in1(X0))
| ~ one(out1(X0))
| ~ 'or$uok'(X0) ),
inference(clausification,[status(esa)],[or_1_11]) ).
cnf(c29,plain,
( zero(in2(X0))
| ~ zero(out1(X0))
| ~ 'or$uok'(X0) ),
inference(clausification,[status(esa)],[or_0_01]) ).
cnf(c31,plain,
( abnormal(X0)
| 'or$uok'(X0)
| ~ 'logic$uor'(X0) ),
inference(clausification,[status(esa)],[or_ok_or_abnormal]) ).
cnf(c33,plain,
( zero(out1(X0))
| ~ one(in1(X0))
| ~ 'not$uok'(X0) ),
inference(clausification,[status(esa)],[not_1_0_fw]) ).
cnf(c37,plain,
( abnormal(X0)
| 'not$uok'(X0)
| ~ 'logic$unot'(X0) ),
inference(clausification,[status(esa)],[not_ok_or_abnormal]) ).
cnf(c38,plain,
( 'logic$uand'(and1(X0))
| ~ halfadder(X0) ),
inference(clausification,[status(esa)],[halfadder_and1]) ).
cnf(c39,plain,
( 'logic$uand'(and2(X0))
| ~ halfadder(X0) ),
inference(clausification,[status(esa)],[halfadder_and2]) ).
cnf(c40,plain,
( 'logic$unot'(not1(X0))
| ~ halfadder(X0) ),
inference(clausification,[status(esa)],[halfadder_not1]) ).
cnf(c41,plain,
( 'logic$uor'(or1(X0))
| ~ halfadder(X0) ),
inference(clausification,[status(esa)],[halfadder_or1]) ).
cnf(c42,plain,
( connection(in1(X0),in1(or1(X0)))
| ~ halfadder(X0) ),
inference(clausification,[status(esa)],[halfadder_connection_in1_in1or1]) ).
cnf(c43,plain,
( connection(in2(X0),in2(or1(X0)))
| ~ halfadder(X0) ),
inference(clausification,[status(esa)],[halfadder_connection_in2_in2or1]) ).
cnf(c44,plain,
( connection(in1(X0),in1(and2(X0)))
| ~ halfadder(X0) ),
inference(clausification,[status(esa)],[halfadder_connection_in1_in1and2]) ).
cnf(c45,plain,
( connection(in2(X0),in2(and2(X0)))
| ~ halfadder(X0) ),
inference(clausification,[status(esa)],[halfadder_connection_in2_in2and2]) ).
cnf(c46,plain,
( connection(outs(X0),out1(and1(X0)))
| ~ halfadder(X0) ),
inference(clausification,[status(esa)],[halfadder_connection_outs_out1and1]) ).
cnf(c47,plain,
( connection(outc(X0),out1(and2(X0)))
| ~ halfadder(X0) ),
inference(clausification,[status(esa)],[halfadder_connection_outc_out1and2]) ).
cnf(c48,plain,
( connection(out1(or1(X0)),in1(and1(X0)))
| ~ halfadder(X0) ),
inference(clausification,[status(esa)],[halfadder_connection_out1or1_in1_and1]) ).
cnf(c49,plain,
( connection(out1(and2(X0)),in1(not1(X0)))
| ~ halfadder(X0) ),
inference(clausification,[status(esa)],[halfadder_connection_out1and2_in1not1]) ).
cnf(c50,plain,
( connection(out1(not1(X0)),in2(and1(X0)))
| ~ halfadder(X0) ),
inference(clausification,[status(esa)],[halfadder_connection_out1not1_in2and1]) ).
cnf(c51,plain,
( halfadder(h1(X0))
| ~ fulladder(X0) ),
inference(clausification,[status(esa)],[fulladder_halfadder1]) ).
cnf(c52,plain,
( halfadder(h2(X0))
| ~ fulladder(X0) ),
inference(clausification,[status(esa)],[fulladder_halfadder2]) ).
cnf(c53,plain,
( 'logic$uor'(or1(X0))
| ~ fulladder(X0) ),
inference(clausification,[status(esa)],[fulladder_or1]) ).
cnf(c54,plain,
( connection(outs(h1(X0)),in2(h2(X0)))
| ~ fulladder(X0) ),
inference(clausification,[status(esa)],[fulladder_connection_outsh1_in2h2]) ).
cnf(c55,plain,
( connection(outc(h1(X0)),in2(or1(X0)))
| ~ fulladder(X0) ),
inference(clausification,[status(esa)],[fulladder_connection_outch1_in2or1]) ).
cnf(c57,plain,
( connection(in1(X0),in1(h2(X0)))
| ~ fulladder(X0) ),
inference(clausification,[status(esa)],[fulladder_connection_in1_in1h2]) ).
cnf(c58,plain,
( connection(in2(X0),in1(h1(X0)))
| ~ fulladder(X0) ),
inference(clausification,[status(esa)],[fulladder_connection_in2_in1h1]) ).
cnf(c59,plain,
( connection(inc(X0),in2(h1(X0)))
| ~ fulladder(X0) ),
inference(clausification,[status(esa)],[fulladder_connection_inc_in2h1]) ).
cnf(c60,plain,
( connection(outs(X0),outs(h2(X0)))
| ~ fulladder(X0) ),
inference(clausification,[status(esa)],[fulladder_connection_outs_outsh2]) ).
cnf(c61,plain,
( connection(outc(X0),out1(or1(X0)))
| ~ fulladder(X0) ),
inference(clausification,[status(esa)],[fulladder_connection_outc_out1or1]) ).
cnf(d0,plain,
( ~ one(in1(h2(X0)))
| one(in1(X0))
| ~ fulladder(X0) ),
inference(resolution,[status(thm)],[c57,c14]) ).
cnf(d1,plain,
( ~ zero(outs(h1(X0)))
| zero(in2(h2(X0)))
| ~ fulladder(X0) ),
inference(resolution,[status(thm)],[c54,c11]) ).
cnf(d2,plain,
( ~ halfadder(X0)
| 'and$uok'(and1(X0))
| abnormal(and1(X0)) ),
inference(resolution,[status(thm)],[c23,c38]) ).
cnf(d3,plain,
( ~ halfadder(X0)
| 'not$uok'(not1(X0))
| abnormal(not1(X0)) ),
inference(resolution,[status(thm)],[c37,c40]) ).
cnf(d4,plain,
( ~ zero(out1(and1(X0)))
| zero(outs(X0))
| ~ halfadder(X0) ),
inference(resolution,[status(thm)],[c46,c13]) ).
cnf(d5,plain,
( ~ zero(out1(not1(X0)))
| zero(in2(and1(X0)))
| ~ halfadder(X0) ),
inference(resolution,[status(thm)],[c50,c11]) ).
cnf(d6,plain,
( ~ one(outc(X0))
| one(out1(and2(X0)))
| ~ halfadder(X0) ),
inference(resolution,[status(thm)],[c47,c12]) ).
cnf(d7,plain,
( ~ one(out1(and2(X0)))
| one(in1(not1(X0)))
| ~ halfadder(X0) ),
inference(resolution,[status(thm)],[c49,c12]) ).
cnf(d8,plain,
( ~ halfadder(X0)
| ~ one(outc(X0))
| ~ halfadder(X0)
| one(in1(not1(X0))) ),
inference(resolution,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
( ~ 'not$uok'(not1(X0))
| zero(out1(not1(X0)))
| ~ halfadder(X0)
| ~ one(outc(X0)) ),
inference(resolution,[status(thm)],[d8,c33]) ).
cnf(d10,plain,
( ~ halfadder(X0)
| zero(in2(and1(X0)))
| ~ halfadder(X0)
| ~ 'not$uok'(not1(X0))
| ~ one(outc(X0)) ),
inference(resolution,[status(thm)],[d9,d5]) ).
cnf(d11,plain,
( ~ 'and$uok'(and1(X0))
| zero(out1(and1(X0)))
| ~ halfadder(X0)
| ~ 'not$uok'(not1(X0))
| ~ one(outc(X0)) ),
inference(resolution,[status(thm)],[d10,c17]) ).
cnf(d12,plain,
( ~ halfadder(X0)
| zero(outs(X0))
| ~ halfadder(X0)
| ~ 'not$uok'(not1(X0))
| ~ 'and$uok'(and1(X0))
| ~ one(outc(X0)) ),
inference(resolution,[status(thm)],[d11,d4]) ).
cnf(d13,plain,
( ~ halfadder(X0)
| abnormal(not1(X0))
| ~ halfadder(X0)
| ~ 'and$uok'(and1(X0))
| ~ one(outc(X0))
| zero(outs(X0)) ),
inference(resolution,[status(thm)],[d12,d3]) ).
cnf(d14,plain,
( ~ halfadder(X0)
| abnormal(and1(X0))
| ~ halfadder(X0)
| abnormal(not1(X0))
| ~ one(outc(X0))
| zero(outs(X0)) ),
inference(resolution,[status(thm)],[d13,d2]) ).
cnf(d15,plain,
( ~ one(in2(X0))
| one(in1(h1(X0)))
| ~ fulladder(X0) ),
inference(resolution,[status(thm)],[c58,c12]) ).
cnf(d16,plain,
( ~ one(inc(X0))
| one(in2(h1(X0)))
| ~ fulladder(X0) ),
inference(resolution,[status(thm)],[c59,c12]) ).
cnf(d17,plain,
( ~ halfadder(X0)
| 'and$uok'(and2(X0))
| abnormal(and2(X0)) ),
inference(resolution,[status(thm)],[c23,c39]) ).
cnf(d18,plain,
( ~ one(out1(and2(X0)))
| one(outc(X0))
| ~ halfadder(X0) ),
inference(resolution,[status(thm)],[c47,c14]) ).
cnf(d19,plain,
( ~ one(in1(X0))
| one(in1(and2(X0)))
| ~ halfadder(X0) ),
inference(resolution,[status(thm)],[c44,c12]) ).
cnf(d20,plain,
( ~ one(in2(X0))
| one(in2(and2(X0)))
| ~ halfadder(X0) ),
inference(resolution,[status(thm)],[c45,c12]) ).
cnf(d21,plain,
( ~ 'and$uok'(and2(X0))
| one(out1(and2(X0)))
| ~ one(in1(and2(X0)))
| ~ halfadder(X0)
| ~ one(in2(X0)) ),
inference(resolution,[status(thm)],[d20,c18]) ).
cnf(d22,plain,
( ~ halfadder(X0)
| ~ one(in1(X0))
| ~ halfadder(X0)
| ~ 'and$uok'(and2(X0))
| one(out1(and2(X0)))
| ~ one(in2(X0)) ),
inference(resolution,[status(thm)],[d21,d19]) ).
cnf(d23,plain,
( ~ halfadder(X0)
| one(outc(X0))
| ~ halfadder(X0)
| ~ 'and$uok'(and2(X0))
| ~ one(in2(X0))
| ~ one(in1(X0)) ),
inference(resolution,[status(thm)],[d22,d18]) ).
cnf(d24,plain,
( ~ halfadder(X0)
| abnormal(and2(X0))
| ~ halfadder(X0)
| one(outc(X0))
| ~ one(in2(X0))
| ~ one(in1(X0)) ),
inference(resolution,[status(thm)],[d23,d17]) ).
cnf(d25,plain,
( ~ one(inc(X0))
| ~ fulladder(X0)
| ~ halfadder(h1(X0))
| abnormal(and2(h1(X0)))
| one(outc(h1(X0)))
| ~ one(in1(h1(X0))) ),
inference(resolution,[status(thm)],[d24,d16]) ).
cnf(d26,plain,
( ~ one(in2(X0))
| ~ fulladder(X0)
| ~ halfadder(h1(X0))
| abnormal(and2(h1(X0)))
| one(outc(h1(X0)))
| ~ one(inc(X0))
| ~ fulladder(X0) ),
inference(resolution,[status(thm)],[d25,d15]) ).
cnf(d27,plain,
( ~ halfadder(h1(f))
| one(outc(h1(f)))
| ~ one(inc(f))
| ~ one(in2(f))
| ~ fulladder(f) ),
inference(resolution,[status(thm)],[d26,c6]) ).
cnf(d28,plain,
( ~ halfadder(h1(f))
| one(outc(h1(f)))
| ~ one(inc(f))
| ~ one(in2(f)) ),
inference(resolution,[status(thm)],[c0,d27]) ).
cnf(d29,plain,
( ~ halfadder(h1(f))
| one(outc(h1(f)))
| ~ one(inc(f)) ),
inference(resolution,[status(thm)],[c2,d28]) ).
cnf(d30,plain,
( ~ halfadder(h1(f))
| one(outc(h1(f))) ),
inference(resolution,[status(thm)],[c3,d29]) ).
cnf(d31,plain,
( ~ halfadder(h1(f))
| abnormal(not1(h1(f)))
| abnormal(and1(h1(f)))
| zero(outs(h1(f)))
| ~ halfadder(h1(f)) ),
inference(resolution,[status(thm)],[d30,d14]) ).
cnf(d32,plain,
( ~ fulladder(X0)
| 'or$uok'(or1(X0))
| abnormal(or1(X0)) ),
inference(resolution,[status(thm)],[c31,c53]) ).
cnf(d33,plain,
( ~ zero(in2(or1(X0)))
| zero(outc(h1(X0)))
| ~ fulladder(X0) ),
inference(resolution,[status(thm)],[c55,c13]) ).
cnf(d34,plain,
( ~ zero(outc(X0))
| zero(out1(or1(X0)))
| ~ fulladder(X0) ),
inference(resolution,[status(thm)],[c61,c11]) ).
cnf(d35,plain,
( ~ 'or$uok'(or1(X0))
| zero(in2(or1(X0)))
| ~ zero(outc(X0))
| ~ fulladder(X0) ),
inference(resolution,[status(thm)],[d34,c29]) ).
cnf(d36,plain,
( zero(outc(h1(X0)))
| ~ fulladder(X0)
| ~ 'or$uok'(or1(X0))
| ~ zero(outc(X0))
| ~ fulladder(X0) ),
inference(resolution,[status(thm)],[d35,d33]) ).
cnf(d37,plain,
( ~ zero(outc(h1(f)))
| ~ halfadder(h1(f)) ),
inference(resolution,[status(thm)],[d30,c15]) ).
cnf(d38,plain,
( ~ 'or$uok'(or1(f))
| ~ zero(outc(f))
| ~ fulladder(f)
| ~ halfadder(h1(f)) ),
inference(resolution,[status(thm)],[d37,d36]) ).
cnf(d39,plain,
( ~ halfadder(h1(f))
| ~ 'or$uok'(or1(f))
| ~ zero(outc(f)) ),
inference(resolution,[status(thm)],[c0,d38]) ).
cnf(d40,plain,
( ~ halfadder(h1(f))
| ~ 'or$uok'(or1(f)) ),
inference(resolution,[status(thm)],[c5,d39]) ).
cnf(d41,plain,
( ~ fulladder(f)
| ~ 'or$uok'(or1(f)) ),
inference(resolution,[status(thm)],[d40,c51]) ).
cnf(d42,plain,
~ 'or$uok'(or1(f)),
inference(resolution,[status(thm)],[c0,d41]) ).
cnf(d43,plain,
( abnormal(or1(f))
| ~ fulladder(f) ),
inference(resolution,[status(thm)],[d42,d32]) ).
cnf(d44,plain,
abnormal(or1(f)),
inference(resolution,[status(thm)],[c0,d43]) ).
cnf(d45,plain,
~ abnormal(and1(h1(f))),
inference(resolution,[status(thm)],[d44,c7]) ).
cnf(d46,plain,
( ~ halfadder(h1(f))
| abnormal(not1(h1(f)))
| zero(outs(h1(f))) ),
inference(resolution,[status(thm)],[d45,d31]) ).
cnf(d47,plain,
~ abnormal(not1(h1(f))),
inference(resolution,[status(thm)],[d44,c8]) ).
cnf(d48,plain,
( ~ halfadder(h1(f))
| zero(outs(h1(f))) ),
inference(resolution,[status(thm)],[d47,d46]) ).
cnf(d49,plain,
( zero(in2(h2(f)))
| ~ fulladder(f)
| ~ halfadder(h1(f)) ),
inference(resolution,[status(thm)],[d48,d1]) ).
cnf(d50,plain,
( ~ halfadder(h1(f))
| zero(in2(h2(f))) ),
inference(resolution,[status(thm)],[c0,d49]) ).
cnf(d51,plain,
~ abnormal(and1(h2(f))),
inference(resolution,[status(thm)],[d44,c9]) ).
cnf(d52,plain,
( ~ one(outs(X0))
| one(outs(h2(X0)))
| ~ fulladder(X0) ),
inference(resolution,[status(thm)],[c60,c12]) ).
cnf(d53,plain,
( ~ halfadder(X0)
| 'or$uok'(or1(X0))
| abnormal(or1(X0)) ),
inference(resolution,[status(thm)],[c31,c41]) ).
cnf(d54,plain,
( ~ one(in1(or1(X0)))
| one(in1(X0))
| ~ halfadder(X0) ),
inference(resolution,[status(thm)],[c42,c14]) ).
cnf(d55,plain,
( ~ one(in2(or1(X0)))
| one(in2(X0))
| ~ halfadder(X0) ),
inference(resolution,[status(thm)],[c43,c14]) ).
cnf(d56,plain,
( ~ one(in1(and1(X0)))
| one(out1(or1(X0)))
| ~ halfadder(X0) ),
inference(resolution,[status(thm)],[c48,c14]) ).
cnf(d57,plain,
( ~ one(outs(X0))
| one(out1(and1(X0)))
| ~ halfadder(X0) ),
inference(resolution,[status(thm)],[c46,c12]) ).
cnf(d58,plain,
( ~ 'and$uok'(and1(X0))
| one(in1(and1(X0)))
| ~ halfadder(X0)
| ~ one(outs(X0)) ),
inference(resolution,[status(thm)],[d57,c20]) ).
cnf(d59,plain,
( ~ halfadder(X0)
| one(out1(or1(X0)))
| ~ halfadder(X0)
| ~ 'and$uok'(and1(X0))
| ~ one(outs(X0)) ),
inference(resolution,[status(thm)],[d58,d56]) ).
cnf(d60,plain,
( ~ 'or$uok'(or1(X0))
| one(in2(or1(X0)))
| one(in1(or1(X0)))
| ~ halfadder(X0)
| ~ 'and$uok'(and1(X0))
| ~ one(outs(X0)) ),
inference(resolution,[status(thm)],[d59,c27]) ).
cnf(d61,plain,
( ~ halfadder(X0)
| one(in2(X0))
| ~ halfadder(X0)
| ~ 'or$uok'(or1(X0))
| ~ 'and$uok'(and1(X0))
| ~ one(outs(X0))
| one(in1(or1(X0))) ),
inference(resolution,[status(thm)],[d60,d55]) ).
cnf(d62,plain,
( ~ halfadder(X0)
| one(in1(X0))
| ~ halfadder(X0)
| ~ 'or$uok'(or1(X0))
| ~ 'and$uok'(and1(X0))
| ~ one(outs(X0))
| one(in2(X0)) ),
inference(resolution,[status(thm)],[d61,d54]) ).
cnf(d63,plain,
( ~ halfadder(X0)
| abnormal(or1(X0))
| ~ halfadder(X0)
| ~ 'and$uok'(and1(X0))
| ~ one(outs(X0))
| one(in2(X0))
| one(in1(X0)) ),
inference(resolution,[status(thm)],[d62,d53]) ).
cnf(d64,plain,
( ~ halfadder(X0)
| abnormal(and1(X0))
| ~ halfadder(X0)
| abnormal(or1(X0))
| ~ one(outs(X0))
| one(in2(X0))
| one(in1(X0)) ),
inference(resolution,[status(thm)],[d63,d2]) ).
cnf(d65,plain,
( ~ one(outs(X0))
| ~ fulladder(X0)
| ~ halfadder(h2(X0))
| abnormal(and1(h2(X0)))
| abnormal(or1(h2(X0)))
| one(in2(h2(X0)))
| one(in1(h2(X0))) ),
inference(resolution,[status(thm)],[d64,d52]) ).
cnf(d66,plain,
( ~ halfadder(h2(f))
| abnormal(or1(h2(f)))
| ~ one(outs(f))
| one(in2(h2(f)))
| one(in1(h2(f)))
| ~ fulladder(f) ),
inference(resolution,[status(thm)],[d65,d51]) ).
cnf(d67,plain,
( ~ halfadder(h2(f))
| abnormal(or1(h2(f)))
| ~ one(outs(f))
| one(in2(h2(f)))
| one(in1(h2(f))) ),
inference(resolution,[status(thm)],[c0,d66]) ).
cnf(d68,plain,
( ~ halfadder(h2(f))
| abnormal(or1(h2(f)))
| one(in2(h2(f)))
| one(in1(h2(f))) ),
inference(resolution,[status(thm)],[c4,d67]) ).
cnf(d69,plain,
~ abnormal(or1(h2(f))),
inference(resolution,[status(thm)],[d44,c10]) ).
cnf(d70,plain,
( ~ halfadder(h2(f))
| one(in2(h2(f)))
| one(in1(h2(f))) ),
inference(resolution,[status(thm)],[d69,d68]) ).
cnf(d71,plain,
( ~ zero(in2(h2(f)))
| ~ halfadder(h2(f))
| one(in1(h2(f))) ),
inference(resolution,[status(thm)],[d70,c15]) ).
cnf(d72,plain,
( ~ halfadder(h1(f))
| ~ halfadder(h2(f))
| one(in1(h2(f))) ),
inference(resolution,[status(thm)],[d71,d50]) ).
cnf(d73,plain,
( one(in1(f))
| ~ fulladder(f)
| ~ halfadder(h2(f))
| ~ halfadder(h1(f)) ),
inference(resolution,[status(thm)],[d72,d0]) ).
cnf(d74,plain,
( ~ halfadder(h2(f))
| ~ halfadder(h1(f))
| one(in1(f)) ),
inference(resolution,[status(thm)],[c0,d73]) ).
cnf(d75,plain,
( ~ fulladder(f)
| ~ halfadder(h1(f))
| one(in1(f)) ),
inference(resolution,[status(thm)],[d74,c52]) ).
cnf(d76,plain,
( ~ halfadder(h1(f))
| one(in1(f)) ),
inference(resolution,[status(thm)],[c0,d75]) ).
cnf(d77,plain,
( ~ fulladder(f)
| one(in1(f)) ),
inference(resolution,[status(thm)],[d76,c51]) ).
cnf(d78,plain,
one(in1(f)),
inference(resolution,[status(thm)],[c0,d77]) ).
cnf(d79,plain,
~ zero(in1(f)),
inference(resolution,[status(thm)],[d78,c15]) ).
cnf(d80,plain,
$false,
inference(resolution,[status(thm)],[c1,d79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HWV007-2 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 16:01:50 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.58/3.59 % SZS status Unsatisfiable for theBenchmark.p
% 16.58/3.59 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------