%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : HWV001-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 07:32:50 AM UTC 2026
% Result : Unsatisfiable 133.89s 24.95s
% Output : CNFRefutation 133.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 42
% Syntax : Number of clauses : 331 ( 331 unt; 0 nHn; 220 RR)
% Number of literals : 331 ( 324 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 19 con; 0-2 aty)
% Number of variables : 171 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(and_commutativity,axiom,
and(X0,X1) = and(X1,X0) ).
cnf(or_commutativity,axiom,
or(X0,X1) = or(X1,X0) ).
cnf(and_associativity,axiom,
and(X0,and(X1,X2)) = and(and(X0,X1),X2) ).
cnf(or_associativity,axiom,
or(X0,or(X1,X2)) = or(or(X0,X1),X2) ).
cnf(or_sorting,axiom,
or(or(X0,X1),X2) = or(or(X0,X2),X1) ).
cnf(and_sorting,axiom,
and(and(X0,X1),X2) = and(and(X0,X2),X1) ).
cnf(not_canonicalization1,axiom,
not(and(X0,X1)) = or(not(X0),not(X1)) ).
cnf(not_canonicalization2,axiom,
not(or(X0,X1)) = and(not(X0),not(X1)) ).
cnf(and_or_canonicalization,axiom,
and(or(X0,X1),X2) = or(and(X0,X2),and(X1,X2)) ).
cnf(and_simplification1,axiom,
and(X0,X0) = X0 ).
cnf(and_simplification2,axiom,
and(and(X0,X1),X1) = and(X0,X1) ).
cnf(and_simplification3,axiom,
and(and(X0,X1),X0) = and(X0,X1) ).
cnf(or_simplification1,axiom,
or(X0,X0) = X0 ).
cnf(or_simplification2,axiom,
or(or(X0,X1),X1) = or(X0,X1) ).
cnf(or_simplification3,axiom,
or(or(X0,X1),X0) = or(X0,X1) ).
cnf(and_not_simplification1,axiom,
and(X0,not(X0)) = n0 ).
cnf(and_not_simplification3,axiom,
and(and(X0,X1),not(X0)) = n0 ).
cnf(or_not_simplification1,axiom,
or(X0,not(X0)) = n1 ).
cnf(not_simplification,axiom,
not(not(X0)) = X0 ).
cnf(and_or_not_simplification1,axiom,
or(and(X0,X1),and(X0,not(X1))) = X0 ).
cnf(constructor1,negated_conjecture,
a1 = and(b1,b3) ).
cnf(constructor2,negated_conjecture,
a2 = and(b2,b3) ).
cnf(constructor3,negated_conjecture,
b1 = not(d1) ).
cnf(constructor4,negated_conjecture,
b2 = not(d2) ).
cnf(constructor5,negated_conjecture,
b3 = or(c1,c2) ).
cnf(constructor6,negated_conjecture,
c1 = or(d1,d3) ).
cnf(constructor7,negated_conjecture,
c2 = or(d2,d3) ).
cnf(constructor8,negated_conjecture,
d3 = f3 ).
cnf(constructor9,negated_conjecture,
d1 = not(e1) ).
cnf(constructor10,negated_conjecture,
d2 = not(e2) ).
cnf(constructor11,negated_conjecture,
e1 = or(f1,f3) ).
cnf(constructor12,negated_conjecture,
e2 = or(f2,f3) ).
cnf(constructor13,negated_conjecture,
f1 = not(i1) ).
cnf(constructor14,negated_conjecture,
f2 = not(i2) ).
cnf(constructor15,negated_conjecture,
f3 = and(i1,i2) ).
cnf(circuit_description,negated_conjecture,
circuit(input(i1,i2),output(a1,a2)) ).
cnf(prove_interchange,negated_conjecture,
~ circuit(input(i1,i2),output(i2,i1)) ).
cnf(and_definition2,axiom,
and(X0,n1) = X0 ).
cnf(or_definition1,axiom,
or(X0,n0) = X0 ).
cnf(or_definition2,axiom,
or(X0,n1) = n1 ).
cnf(not_definition1,axiom,
not(n0) = n1 ).
cnf(not_definition2,axiom,
not(n1) = n0 ).
cnf(c0,plain,
and(X0,X1) = and(X1,X0),
inference(clausification,[status(esa)],[and_commutativity]) ).
cnf(c1,plain,
or(X0,X1) = or(X1,X0),
inference(clausification,[status(esa)],[or_commutativity]) ).
cnf(c2,plain,
and(X0,and(X1,X2)) = and(and(X0,X1),X2),
inference(clausification,[status(esa)],[and_associativity]) ).
cnf(c3,plain,
or(X0,or(X1,X2)) = or(or(X0,X1),X2),
inference(clausification,[status(esa)],[or_associativity]) ).
cnf(c4,plain,
or(or(X0,X1),X2) = or(or(X0,X2),X1),
inference(clausification,[status(esa)],[or_sorting]) ).
cnf(c5,plain,
and(and(X0,X1),X2) = and(and(X0,X2),X1),
inference(clausification,[status(esa)],[and_sorting]) ).
cnf(c6,plain,
not(and(X0,X1)) = or(not(X0),not(X1)),
inference(clausification,[status(esa)],[not_canonicalization1]) ).
cnf(c7,plain,
not(or(X0,X1)) = and(not(X0),not(X1)),
inference(clausification,[status(esa)],[not_canonicalization2]) ).
cnf(c8,plain,
and(or(X0,X1),X2) = or(and(X0,X2),and(X1,X2)),
inference(clausification,[status(esa)],[and_or_canonicalization]) ).
cnf(c9,plain,
and(X0,X0) = X0,
inference(clausification,[status(esa)],[and_simplification1]) ).
cnf(c10,plain,
and(and(X0,X1),X1) = and(X0,X1),
inference(clausification,[status(esa)],[and_simplification2]) ).
cnf(c11,plain,
and(and(X0,X1),X0) = and(X0,X1),
inference(clausification,[status(esa)],[and_simplification3]) ).
cnf(c12,plain,
or(X0,X0) = X0,
inference(clausification,[status(esa)],[or_simplification1]) ).
cnf(c13,plain,
or(or(X0,X1),X1) = or(X0,X1),
inference(clausification,[status(esa)],[or_simplification2]) ).
cnf(c14,plain,
or(or(X0,X1),X0) = or(X0,X1),
inference(clausification,[status(esa)],[or_simplification3]) ).
cnf(c15,plain,
and(X0,not(X0)) = n0,
inference(clausification,[status(esa)],[and_not_simplification1]) ).
cnf(c17,plain,
and(and(X0,X1),not(X0)) = n0,
inference(clausification,[status(esa)],[and_not_simplification3]) ).
cnf(c18,plain,
or(X0,not(X0)) = n1,
inference(clausification,[status(esa)],[or_not_simplification1]) ).
cnf(c21,plain,
not(not(X0)) = X0,
inference(clausification,[status(esa)],[not_simplification]) ).
cnf(c22,plain,
or(and(X0,X1),and(X0,not(X1))) = X0,
inference(clausification,[status(esa)],[and_or_not_simplification1]) ).
cnf(c24,plain,
a1 = and(b1,b3),
inference(clausification,[status(esa)],[constructor1]) ).
cnf(c25,plain,
a2 = and(b2,b3),
inference(clausification,[status(esa)],[constructor2]) ).
cnf(c26,plain,
b1 = not(d1),
inference(clausification,[status(esa)],[constructor3]) ).
cnf(c27,plain,
b2 = not(d2),
inference(clausification,[status(esa)],[constructor4]) ).
cnf(c28,plain,
b3 = or(c1,c2),
inference(clausification,[status(esa)],[constructor5]) ).
cnf(c29,plain,
c1 = or(d1,d3),
inference(clausification,[status(esa)],[constructor6]) ).
cnf(c30,plain,
c2 = or(d2,d3),
inference(clausification,[status(esa)],[constructor7]) ).
cnf(c31,plain,
d3 = f3,
inference(clausification,[status(esa)],[constructor8]) ).
cnf(c32,plain,
d1 = not(e1),
inference(clausification,[status(esa)],[constructor9]) ).
cnf(c33,plain,
d2 = not(e2),
inference(clausification,[status(esa)],[constructor10]) ).
cnf(c34,plain,
e1 = or(f1,f3),
inference(clausification,[status(esa)],[constructor11]) ).
cnf(c35,plain,
e2 = or(f2,f3),
inference(clausification,[status(esa)],[constructor12]) ).
cnf(c36,plain,
f1 = not(i1),
inference(clausification,[status(esa)],[constructor13]) ).
cnf(c37,plain,
f2 = not(i2),
inference(clausification,[status(esa)],[constructor14]) ).
cnf(c38,plain,
f3 = and(i1,i2),
inference(clausification,[status(esa)],[constructor15]) ).
cnf(c39,plain,
circuit(input(i1,i2),output(a1,a2)),
inference(clausification,[status(esa)],[circuit_description]) ).
cnf(c40,plain,
~ circuit(input(i1,i2),output(i2,i1)),
inference(clausification,[status(esa)],[prove_interchange]) ).
cnf(c42,plain,
and(X0,n1) = X0,
inference(clausification,[status(esa)],[and_definition2]) ).
cnf(c43,plain,
or(X0,n0) = X0,
inference(clausification,[status(esa)],[or_definition1]) ).
cnf(c44,plain,
or(X0,n1) = n1,
inference(clausification,[status(esa)],[or_definition2]) ).
cnf(c45,plain,
not(n0) = n1,
inference(clausification,[status(esa)],[not_definition1]) ).
cnf(c46,plain,
not(n1) = n0,
inference(clausification,[status(esa)],[not_definition2]) ).
cnf(d0,plain,
and(X0,and(X0,X1)) = and(X0,X1),
inference(superposition,[status(thm)],[c9,c2]) ).
cnf(d1,plain,
and(X0,and(X1,X1)) = and(X0,X1),
inference(demodulation,[status(thm)],[c10,c2]) ).
cnf(d2,plain,
and(X1,X0) = and(X1,X0),
inference(demodulation,[status(thm)],[d1,c9]) ).
cnf(d3,plain,
and(i1,i2) = f3,
inference(superposition,[status(thm)],[c38,d2]) ).
cnf(d4,plain,
and(i1,f3) = and(i1,i2),
inference(superposition,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
and(i1,f3) = f3,
inference(demodulation,[status(thm)],[d4,c38]) ).
cnf(d6,plain,
not(b1) = d1,
inference(superposition,[status(thm)],[c26,c21]) ).
cnf(d7,plain,
not(f1) = i1,
inference(superposition,[status(thm)],[c36,c21]) ).
cnf(d8,plain,
not(or(X0,f1)) = and(not(X0),i1),
inference(superposition,[status(thm)],[d7,c7]) ).
cnf(d9,plain,
not(or(X0,f1)) = and(i1,not(X0)),
inference(demodulation,[status(thm)],[d8,c0]) ).
cnf(d10,plain,
or(X0,or(X1,X1)) = or(X0,X1),
inference(demodulation,[status(thm)],[c13,c3]) ).
cnf(d11,plain,
or(X1,X0) = or(X1,X0),
inference(demodulation,[status(thm)],[d10,c12]) ).
cnf(d12,plain,
not(d1) = e1,
inference(superposition,[status(thm)],[c32,c21]) ).
cnf(d13,plain,
b1 = e1,
inference(demodulation,[status(thm)],[d12,c26]) ).
cnf(d14,plain,
b1 = or(f1,f3),
inference(demodulation,[status(thm)],[c34,d13]) ).
cnf(d15,plain,
b1 = or(f3,f1),
inference(demodulation,[status(thm)],[d14,c1]) ).
cnf(d16,plain,
or(f3,f1) = b1,
inference(superposition,[status(thm)],[d15,d11]) ).
cnf(d17,plain,
not(b1) = and(i1,not(f3)),
inference(superposition,[status(thm)],[d16,d9]) ).
cnf(d18,plain,
d1 = and(i1,not(f3)),
inference(demodulation,[status(thm)],[d17,d6]) ).
cnf(d19,plain,
or(and(i1,f3),d1) = i1,
inference(superposition,[status(thm)],[d18,c22]) ).
cnf(d20,plain,
or(d1,and(i1,f3)) = i1,
inference(demodulation,[status(thm)],[d19,c1]) ).
cnf(d21,plain,
or(d1,f3) = i1,
inference(demodulation,[status(thm)],[d20,d5]) ).
cnf(d22,plain,
or(f3,d1) = i1,
inference(demodulation,[status(thm)],[d21,c1]) ).
cnf(d23,plain,
and(i1,and(i2,X0)) = and(f3,X0),
inference(superposition,[status(thm)],[c38,c2]) ).
cnf(d24,plain,
not(f2) = i2,
inference(superposition,[status(thm)],[c37,c21]) ).
cnf(d25,plain,
not(or(X0,f2)) = and(not(X0),i2),
inference(superposition,[status(thm)],[d24,c7]) ).
cnf(d26,plain,
not(or(X0,f2)) = and(i2,not(X0)),
inference(demodulation,[status(thm)],[d25,c0]) ).
cnf(d27,plain,
or(c1,or(c2,X0)) = or(b3,X0),
inference(superposition,[status(thm)],[c28,c3]) ).
cnf(d28,plain,
not(b2) = d2,
inference(superposition,[status(thm)],[c27,c21]) ).
cnf(d29,plain,
not(d2) = b2,
inference(superposition,[status(thm)],[d28,c21]) ).
cnf(d30,plain,
or(d2,b2) = n1,
inference(superposition,[status(thm)],[d29,c18]) ).
cnf(d31,plain,
not(d2) = e2,
inference(superposition,[status(thm)],[c33,c21]) ).
cnf(d32,plain,
b2 = e2,
inference(demodulation,[status(thm)],[d31,c27]) ).
cnf(d33,plain,
b2 = or(f2,f3),
inference(demodulation,[status(thm)],[c35,d32]) ).
cnf(d34,plain,
b2 = or(f3,f2),
inference(demodulation,[status(thm)],[d33,c1]) ).
cnf(d35,plain,
or(f3,or(f2,X0)) = or(b2,X0),
inference(superposition,[status(thm)],[d34,c3]) ).
cnf(d36,plain,
or(X0,or(X1,X2)) = or(or(X0,X2),X1),
inference(demodulation,[status(thm)],[c4,c3]) ).
cnf(d37,plain,
c2 = or(d2,f3),
inference(demodulation,[status(thm)],[c30,c31]) ).
cnf(d38,plain,
c2 = or(f3,d2),
inference(demodulation,[status(thm)],[d37,c1]) ).
cnf(d39,plain,
or(f3,or(X0,d2)) = or(c2,X0),
inference(superposition,[status(thm)],[d38,d36]) ).
cnf(d40,plain,
or(c2,f2) = or(b2,d2),
inference(superposition,[status(thm)],[d39,d35]) ).
cnf(d41,plain,
or(c2,f2) = or(d2,b2),
inference(demodulation,[status(thm)],[d40,c1]) ).
cnf(d42,plain,
or(c2,f2) = n1,
inference(demodulation,[status(thm)],[d41,d30]) ).
cnf(d43,plain,
or(c1,n1) = or(b3,f2),
inference(superposition,[status(thm)],[d42,d27]) ).
cnf(d44,plain,
n1 = or(b3,f2),
inference(demodulation,[status(thm)],[d43,c44]) ).
cnf(d45,plain,
or(b3,f2) = n1,
inference(superposition,[status(thm)],[d44,d11]) ).
cnf(d46,plain,
not(n1) = and(i2,not(b3)),
inference(superposition,[status(thm)],[d45,d26]) ).
cnf(d47,plain,
n0 = and(i2,not(b3)),
inference(demodulation,[status(thm)],[d46,c46]) ).
cnf(d48,plain,
or(and(i2,b3),n0) = i2,
inference(superposition,[status(thm)],[d47,c22]) ).
cnf(d49,plain,
and(i2,b3) = i2,
inference(demodulation,[status(thm)],[d48,c43]) ).
cnf(d50,plain,
and(i1,i2) = and(f3,b3),
inference(superposition,[status(thm)],[d49,d23]) ).
cnf(d51,plain,
f3 = and(f3,b3),
inference(demodulation,[status(thm)],[d50,c38]) ).
cnf(d52,plain,
and(X0,and(X1,X2)) = and(and(X0,X2),X1),
inference(demodulation,[status(thm)],[c5,c2]) ).
cnf(d53,plain,
a2 = and(b3,b2),
inference(demodulation,[status(thm)],[c25,c0]) ).
cnf(d54,plain,
and(b3,and(X0,b2)) = and(a2,X0),
inference(superposition,[status(thm)],[d53,d52]) ).
cnf(d55,plain,
and(n1,X0) = X0,
inference(superposition,[status(thm)],[c42,c0]) ).
cnf(d56,plain,
n1 = or(n1,X0),
inference(superposition,[status(thm)],[c44,c1]) ).
cnf(d57,plain,
X0 = and(n1,X0),
inference(superposition,[status(thm)],[c42,c0]) ).
cnf(d58,plain,
and(or(n1,X1),X0) = or(X0,and(X1,X0)),
inference(superposition,[status(thm)],[d57,c8]) ).
cnf(d59,plain,
and(n1,X1) = or(X1,and(X0,X1)),
inference(demodulation,[status(thm)],[d58,d56]) ).
cnf(d60,plain,
X0 = or(X0,and(X1,X0)),
inference(demodulation,[status(thm)],[d59,d55]) ).
cnf(d61,plain,
and(or(X0,X1),X0) = or(X0,and(X1,X0)),
inference(superposition,[status(thm)],[c9,c8]) ).
cnf(d62,plain,
and(X0,or(X0,X1)) = or(X0,and(X1,X0)),
inference(demodulation,[status(thm)],[d61,c0]) ).
cnf(d63,plain,
and(X0,or(X0,X1)) = X0,
inference(demodulation,[status(thm)],[d62,d60]) ).
cnf(d64,plain,
X0 = or(X0,X0),
inference(superposition,[status(thm)],[c12,c1]) ).
cnf(d65,plain,
or(X0,or(X0,X1)) = or(X0,X1),
inference(superposition,[status(thm)],[d64,c3]) ).
cnf(d66,plain,
or(f3,b2) = or(f3,f2),
inference(superposition,[status(thm)],[d34,d65]) ).
cnf(d67,plain,
or(f3,b2) = b2,
inference(demodulation,[status(thm)],[d66,d34]) ).
cnf(d68,plain,
and(f3,b2) = f3,
inference(superposition,[status(thm)],[d67,d63]) ).
cnf(d69,plain,
and(d2,b2) = n0,
inference(superposition,[status(thm)],[d29,c15]) ).
cnf(d70,plain,
and(or(X0,d2),b2) = or(and(X0,b2),n0),
inference(superposition,[status(thm)],[d69,c8]) ).
cnf(d71,plain,
and(b2,or(X0,d2)) = or(and(X0,b2),n0),
inference(demodulation,[status(thm)],[d70,c0]) ).
cnf(d72,plain,
and(b2,or(X0,d2)) = and(X0,b2),
inference(demodulation,[status(thm)],[d71,c43]) ).
cnf(d73,plain,
and(X0,and(X1,X0)) = and(X0,X1),
inference(demodulation,[status(thm)],[c11,c2]) ).
cnf(d74,plain,
and(i2,f3) = and(i2,i1),
inference(superposition,[status(thm)],[c38,d73]) ).
cnf(d75,plain,
and(i2,f3) = and(i1,i2),
inference(demodulation,[status(thm)],[d74,c0]) ).
cnf(d76,plain,
and(i2,f3) = f3,
inference(demodulation,[status(thm)],[d75,c38]) ).
cnf(d77,plain,
not(b2) = and(i2,not(f3)),
inference(superposition,[status(thm)],[d34,d26]) ).
cnf(d78,plain,
d2 = and(i2,not(f3)),
inference(demodulation,[status(thm)],[d77,d28]) ).
cnf(d79,plain,
or(and(i2,f3),d2) = i2,
inference(superposition,[status(thm)],[d78,c22]) ).
cnf(d80,plain,
or(d2,and(i2,f3)) = i2,
inference(demodulation,[status(thm)],[d79,c1]) ).
cnf(d81,plain,
or(d2,f3) = i2,
inference(demodulation,[status(thm)],[d80,d76]) ).
cnf(d82,plain,
or(f3,d2) = i2,
inference(demodulation,[status(thm)],[d81,c1]) ).
cnf(d83,plain,
i2 = or(f3,d2),
inference(superposition,[status(thm)],[d82,d11]) ).
cnf(d84,plain,
and(b2,i2) = and(f3,b2),
inference(superposition,[status(thm)],[d83,d72]) ).
cnf(d85,plain,
and(i2,b2) = and(f3,b2),
inference(demodulation,[status(thm)],[d84,c0]) ).
cnf(d86,plain,
and(i2,b2) = f3,
inference(demodulation,[status(thm)],[d85,d68]) ).
cnf(d87,plain,
and(b3,f3) = and(a2,i2),
inference(superposition,[status(thm)],[d86,d54]) ).
cnf(d88,plain,
and(f3,b3) = and(a2,i2),
inference(demodulation,[status(thm)],[d87,c0]) ).
cnf(d89,plain,
f3 = and(a2,i2),
inference(demodulation,[status(thm)],[d88,d51]) ).
cnf(d90,plain,
f3 = and(i2,a2),
inference(demodulation,[status(thm)],[d89,c0]) ).
cnf(d91,plain,
or(and(X0,f2),and(X0,i2)) = X0,
inference(superposition,[status(thm)],[d24,c22]) ).
cnf(d92,plain,
or(and(X0,i2),and(X0,f2)) = X0,
inference(demodulation,[status(thm)],[d91,c1]) ).
cnf(d93,plain,
not(or(i2,X0)) = and(f2,not(X0)),
inference(superposition,[status(thm)],[c37,c7]) ).
cnf(d94,plain,
not(d1) = b1,
inference(superposition,[status(thm)],[d6,c21]) ).
cnf(d95,plain,
not(and(d1,X0)) = or(b1,not(X0)),
inference(superposition,[status(thm)],[d94,c6]) ).
cnf(d96,plain,
X0 = or(n0,X0),
inference(superposition,[status(thm)],[c43,c1]) ).
cnf(d97,plain,
or(and(X0,d2),and(X0,b2)) = X0,
inference(superposition,[status(thm)],[d29,c22]) ).
cnf(d98,plain,
not(or(b1,X0)) = and(d1,not(X0)),
inference(superposition,[status(thm)],[d6,c7]) ).
cnf(d99,plain,
or(f3,or(X0,f1)) = or(b1,X0),
inference(superposition,[status(thm)],[d15,d36]) ).
cnf(d100,plain,
not(i1) = f1,
inference(superposition,[status(thm)],[d7,c21]) ).
cnf(d101,plain,
not(and(i1,X0)) = or(f1,not(X0)),
inference(superposition,[status(thm)],[d100,c6]) ).
cnf(d102,plain,
and(X0,and(X1,not(X0))) = n0,
inference(demodulation,[status(thm)],[c17,c2]) ).
cnf(d103,plain,
n0 = and(X0,and(X1,not(X0))),
inference(superposition,[status(thm)],[d102,d2]) ).
cnf(d104,plain,
d2 = not(b2),
inference(demodulation,[status(thm)],[c33,d32]) ).
cnf(d105,plain,
not(or(X0,b2)) = and(not(X0),d2),
inference(superposition,[status(thm)],[d104,c7]) ).
cnf(d106,plain,
not(or(X0,b2)) = and(d2,not(X0)),
inference(demodulation,[status(thm)],[d105,c0]) ).
cnf(d107,plain,
not(b2) = and(d2,not(f3)),
inference(superposition,[status(thm)],[d67,d106]) ).
cnf(d108,plain,
d2 = and(d2,not(f3)),
inference(demodulation,[status(thm)],[d107,d28]) ).
cnf(d109,plain,
n0 = and(f3,d2),
inference(superposition,[status(thm)],[d108,d103]) ).
cnf(d110,plain,
not(or(b2,X0)) = and(d2,not(X0)),
inference(superposition,[status(thm)],[d104,c7]) ).
cnf(d111,plain,
or(X0,or(X1,X0)) = or(X0,X1),
inference(demodulation,[status(thm)],[c14,c3]) ).
cnf(d112,plain,
or(f2,b2) = or(f2,f3),
inference(superposition,[status(thm)],[d34,d111]) ).
cnf(d113,plain,
or(b2,f2) = or(f2,f3),
inference(demodulation,[status(thm)],[d112,c1]) ).
cnf(d114,plain,
or(b2,f2) = or(f3,f2),
inference(demodulation,[status(thm)],[d113,c1]) ).
cnf(d115,plain,
or(b2,f2) = b2,
inference(demodulation,[status(thm)],[d114,d34]) ).
cnf(d116,plain,
not(b2) = and(d2,not(f2)),
inference(superposition,[status(thm)],[d115,d110]) ).
cnf(d117,plain,
d2 = and(d2,not(f2)),
inference(demodulation,[status(thm)],[d116,d28]) ).
cnf(d118,plain,
d2 = and(d2,i2),
inference(demodulation,[status(thm)],[d117,d24]) ).
cnf(d119,plain,
d2 = and(i2,d2),
inference(demodulation,[status(thm)],[d118,c0]) ).
cnf(d120,plain,
and(i1,d2) = and(f3,d2),
inference(superposition,[status(thm)],[d119,d23]) ).
cnf(d121,plain,
and(f3,d2) = and(i1,d2),
inference(superposition,[status(thm)],[d120,d2]) ).
cnf(d122,plain,
n0 = and(i1,d2),
inference(demodulation,[status(thm)],[d121,d109]) ).
cnf(d123,plain,
not(n0) = or(f1,not(d2)),
inference(superposition,[status(thm)],[d122,d101]) ).
cnf(d124,plain,
n1 = or(f1,not(d2)),
inference(demodulation,[status(thm)],[d123,c45]) ).
cnf(d125,plain,
n1 = or(f1,b2),
inference(demodulation,[status(thm)],[d124,c27]) ).
cnf(d126,plain,
n1 = or(b2,f1),
inference(demodulation,[status(thm)],[d125,c1]) ).
cnf(d127,plain,
or(f3,n1) = or(b1,b2),
inference(superposition,[status(thm)],[d126,d99]) ).
cnf(d128,plain,
n1 = or(b1,b2),
inference(demodulation,[status(thm)],[d127,c44]) ).
cnf(d129,plain,
not(n1) = and(d1,not(b2)),
inference(superposition,[status(thm)],[d128,d98]) ).
cnf(d130,plain,
n0 = and(d1,not(b2)),
inference(demodulation,[status(thm)],[d129,c46]) ).
cnf(d131,plain,
n0 = and(d1,d2),
inference(demodulation,[status(thm)],[d130,d28]) ).
cnf(d132,plain,
and(d1,d2) = n0,
inference(superposition,[status(thm)],[d131,d2]) ).
cnf(d133,plain,
or(n0,and(d1,b2)) = d1,
inference(superposition,[status(thm)],[d132,d97]) ).
cnf(d134,plain,
and(d1,b2) = d1,
inference(demodulation,[status(thm)],[d133,d96]) ).
cnf(d135,plain,
not(d1) = or(b1,not(b2)),
inference(superposition,[status(thm)],[d134,d95]) ).
cnf(d136,plain,
b1 = or(b1,not(b2)),
inference(demodulation,[status(thm)],[d135,c26]) ).
cnf(d137,plain,
b1 = or(b1,d2),
inference(demodulation,[status(thm)],[d136,d28]) ).
cnf(d138,plain,
b1 = or(d2,b1),
inference(demodulation,[status(thm)],[d137,c1]) ).
cnf(d139,plain,
c2 = i2,
inference(demodulation,[status(thm)],[d38,d82]) ).
cnf(d140,plain,
or(f3,or(f1,X0)) = or(b1,X0),
inference(superposition,[status(thm)],[d15,c3]) ).
cnf(d141,plain,
or(c2,f1) = or(b1,d2),
inference(superposition,[status(thm)],[d39,d140]) ).
cnf(d142,plain,
or(c2,f1) = or(d2,b1),
inference(demodulation,[status(thm)],[d141,c1]) ).
cnf(d143,plain,
or(i2,f1) = or(d2,b1),
inference(demodulation,[status(thm)],[d142,d139]) ).
cnf(d144,plain,
or(i2,f1) = b1,
inference(demodulation,[status(thm)],[d143,d138]) ).
cnf(d145,plain,
not(b1) = and(f2,not(f1)),
inference(superposition,[status(thm)],[d144,d93]) ).
cnf(d146,plain,
d1 = and(f2,not(f1)),
inference(demodulation,[status(thm)],[d145,d6]) ).
cnf(d147,plain,
d1 = and(f2,i1),
inference(demodulation,[status(thm)],[d146,d7]) ).
cnf(d148,plain,
d1 = and(i1,f2),
inference(demodulation,[status(thm)],[d147,c0]) ).
cnf(d149,plain,
and(f2,i2) = n0,
inference(superposition,[status(thm)],[d24,c15]) ).
cnf(d150,plain,
and(i2,f2) = n0,
inference(demodulation,[status(thm)],[d149,c0]) ).
cnf(d151,plain,
and(or(X0,i2),f2) = or(and(X0,f2),n0),
inference(superposition,[status(thm)],[d150,c8]) ).
cnf(d152,plain,
and(f2,or(X0,i2)) = or(and(X0,f2),n0),
inference(demodulation,[status(thm)],[d151,c0]) ).
cnf(d153,plain,
and(f2,or(X0,i2)) = and(X0,f2),
inference(demodulation,[status(thm)],[d152,c43]) ).
cnf(d154,plain,
c1 = or(d1,f3),
inference(demodulation,[status(thm)],[c29,c31]) ).
cnf(d155,plain,
c1 = or(f3,d1),
inference(demodulation,[status(thm)],[d154,c1]) ).
cnf(d156,plain,
or(f3,d1) = c1,
inference(superposition,[status(thm)],[d155,d11]) ).
cnf(d157,plain,
i1 = c1,
inference(demodulation,[status(thm)],[d156,d22]) ).
cnf(d158,plain,
b3 = or(i1,c2),
inference(demodulation,[status(thm)],[c28,d157]) ).
cnf(d159,plain,
b3 = or(i1,i2),
inference(demodulation,[status(thm)],[d158,d139]) ).
cnf(d160,plain,
and(f2,b3) = and(i1,f2),
inference(superposition,[status(thm)],[d159,d153]) ).
cnf(d161,plain,
and(b3,f2) = and(i1,f2),
inference(demodulation,[status(thm)],[d160,c0]) ).
cnf(d162,plain,
and(b3,and(b2,X0)) = and(a2,X0),
inference(superposition,[status(thm)],[d53,c2]) ).
cnf(d163,plain,
not(or(d2,X0)) = and(b2,not(X0)),
inference(superposition,[status(thm)],[d29,c7]) ).
cnf(d164,plain,
or(d2,c2) = or(d2,f3),
inference(superposition,[status(thm)],[d38,d111]) ).
cnf(d165,plain,
or(d2,c2) = or(f3,d2),
inference(demodulation,[status(thm)],[d164,c1]) ).
cnf(d166,plain,
or(d2,c2) = c2,
inference(demodulation,[status(thm)],[d165,d38]) ).
cnf(d167,plain,
not(c2) = and(b2,not(c2)),
inference(superposition,[status(thm)],[d166,d163]) ).
cnf(d168,plain,
and(b2,not(c2)) = not(c2),
inference(superposition,[status(thm)],[d167,d2]) ).
cnf(d169,plain,
and(b2,not(i2)) = not(c2),
inference(demodulation,[status(thm)],[d168,d139]) ).
cnf(d170,plain,
and(b2,not(i2)) = not(i2),
inference(demodulation,[status(thm)],[d169,d139]) ).
cnf(d171,plain,
and(b2,f2) = not(i2),
inference(demodulation,[status(thm)],[d170,c37]) ).
cnf(d172,plain,
and(b2,f2) = f2,
inference(demodulation,[status(thm)],[d171,c37]) ).
cnf(d173,plain,
and(b3,f2) = and(a2,f2),
inference(superposition,[status(thm)],[d172,d162]) ).
cnf(d174,plain,
and(a2,f2) = and(b3,f2),
inference(superposition,[status(thm)],[d173,d2]) ).
cnf(d175,plain,
and(a2,f2) = and(b3,f2),
inference(superposition,[status(thm)],[d174,d2]) ).
cnf(d176,plain,
and(a2,f2) = and(i1,f2),
inference(demodulation,[status(thm)],[d175,d161]) ).
cnf(d177,plain,
and(a2,f2) = d1,
inference(demodulation,[status(thm)],[d176,d148]) ).
cnf(d178,plain,
or(and(a2,i2),d1) = a2,
inference(superposition,[status(thm)],[d177,d92]) ).
cnf(d179,plain,
or(d1,and(a2,i2)) = a2,
inference(demodulation,[status(thm)],[d178,c1]) ).
cnf(d180,plain,
or(d1,and(i2,a2)) = a2,
inference(demodulation,[status(thm)],[d179,c0]) ).
cnf(d181,plain,
or(d1,f3) = a2,
inference(demodulation,[status(thm)],[d180,d90]) ).
cnf(d182,plain,
or(f3,d1) = a2,
inference(demodulation,[status(thm)],[d181,c1]) ).
cnf(d183,plain,
i1 = a2,
inference(demodulation,[status(thm)],[d182,d22]) ).
cnf(d184,plain,
a1 = and(b3,b1),
inference(demodulation,[status(thm)],[c24,c0]) ).
cnf(d185,plain,
and(b3,and(X0,b1)) = and(a1,X0),
inference(superposition,[status(thm)],[d184,d52]) ).
cnf(d186,plain,
or(f3,b1) = or(f3,f1),
inference(superposition,[status(thm)],[d16,d65]) ).
cnf(d187,plain,
or(f3,b1) = b1,
inference(demodulation,[status(thm)],[d186,d15]) ).
cnf(d188,plain,
and(f3,b1) = f3,
inference(superposition,[status(thm)],[d187,d63]) ).
cnf(d189,plain,
and(d1,b1) = n0,
inference(superposition,[status(thm)],[d94,c15]) ).
cnf(d190,plain,
and(or(X0,d1),b1) = or(and(X0,b1),n0),
inference(superposition,[status(thm)],[d189,c8]) ).
cnf(d191,plain,
and(b1,or(X0,d1)) = or(and(X0,b1),n0),
inference(demodulation,[status(thm)],[d190,c0]) ).
cnf(d192,plain,
and(b1,or(X0,d1)) = and(X0,b1),
inference(demodulation,[status(thm)],[d191,c43]) ).
cnf(d193,plain,
i1 = or(f3,d1),
inference(superposition,[status(thm)],[d22,d11]) ).
cnf(d194,plain,
and(b1,i1) = and(f3,b1),
inference(superposition,[status(thm)],[d193,d192]) ).
cnf(d195,plain,
and(i1,b1) = and(f3,b1),
inference(demodulation,[status(thm)],[d194,c0]) ).
cnf(d196,plain,
and(i1,b1) = f3,
inference(demodulation,[status(thm)],[d195,d188]) ).
cnf(d197,plain,
and(b3,f3) = and(a1,i1),
inference(superposition,[status(thm)],[d196,d185]) ).
cnf(d198,plain,
and(f3,b3) = and(a1,i1),
inference(demodulation,[status(thm)],[d197,c0]) ).
cnf(d199,plain,
f3 = and(a1,i1),
inference(demodulation,[status(thm)],[d198,d51]) ).
cnf(d200,plain,
f3 = and(i1,a1),
inference(demodulation,[status(thm)],[d199,c0]) ).
cnf(d201,plain,
or(and(X0,f1),and(X0,i1)) = X0,
inference(superposition,[status(thm)],[d7,c22]) ).
cnf(d202,plain,
or(and(X0,i1),and(X0,f1)) = X0,
inference(demodulation,[status(thm)],[d201,c1]) ).
cnf(d203,plain,
not(or(i1,X0)) = and(f1,not(X0)),
inference(superposition,[status(thm)],[d100,c7]) ).
cnf(d204,plain,
b2 = or(b2,d1),
inference(superposition,[status(thm)],[d134,d60]) ).
cnf(d205,plain,
b2 = or(d1,b2),
inference(demodulation,[status(thm)],[d204,c1]) ).
cnf(d206,plain,
or(f3,or(X0,d1)) = or(c1,X0),
inference(superposition,[status(thm)],[d155,d36]) ).
cnf(d207,plain,
or(b2,d1) = or(c1,f2),
inference(superposition,[status(thm)],[d35,d206]) ).
cnf(d208,plain,
or(d1,b2) = or(c1,f2),
inference(demodulation,[status(thm)],[d207,c1]) ).
cnf(d209,plain,
or(d1,b2) = or(i1,f2),
inference(demodulation,[status(thm)],[d208,d157]) ).
cnf(d210,plain,
b2 = or(i1,f2),
inference(demodulation,[status(thm)],[d209,d205]) ).
cnf(d211,plain,
not(b2) = and(f1,not(f2)),
inference(superposition,[status(thm)],[d210,d203]) ).
cnf(d212,plain,
d2 = and(f1,not(f2)),
inference(demodulation,[status(thm)],[d211,d28]) ).
cnf(d213,plain,
d2 = and(f1,i2),
inference(demodulation,[status(thm)],[d212,d24]) ).
cnf(d214,plain,
d2 = and(i2,f1),
inference(demodulation,[status(thm)],[d213,c0]) ).
cnf(d215,plain,
and(f1,i1) = n0,
inference(superposition,[status(thm)],[d7,c15]) ).
cnf(d216,plain,
and(i1,f1) = n0,
inference(demodulation,[status(thm)],[d215,c0]) ).
cnf(d217,plain,
and(or(i1,X0),f1) = or(n0,and(X0,f1)),
inference(superposition,[status(thm)],[d216,c8]) ).
cnf(d218,plain,
and(f1,or(i1,X0)) = or(n0,and(X0,f1)),
inference(demodulation,[status(thm)],[d217,c0]) ).
cnf(d219,plain,
and(f1,or(i1,X0)) = and(X0,f1),
inference(demodulation,[status(thm)],[d218,d96]) ).
cnf(d220,plain,
and(f1,b3) = and(i2,f1),
inference(superposition,[status(thm)],[d159,d219]) ).
cnf(d221,plain,
and(b3,f1) = and(i2,f1),
inference(demodulation,[status(thm)],[d220,c0]) ).
cnf(d222,plain,
and(b3,and(b1,X0)) = and(a1,X0),
inference(superposition,[status(thm)],[d184,c2]) ).
cnf(d223,plain,
not(or(d1,X0)) = and(b1,not(X0)),
inference(superposition,[status(thm)],[d94,c7]) ).
cnf(d224,plain,
or(d1,c1) = or(d1,f3),
inference(superposition,[status(thm)],[d155,d111]) ).
cnf(d225,plain,
or(d1,c1) = or(f3,d1),
inference(demodulation,[status(thm)],[d224,c1]) ).
cnf(d226,plain,
or(d1,c1) = c1,
inference(demodulation,[status(thm)],[d225,d155]) ).
cnf(d227,plain,
not(c1) = and(b1,not(c1)),
inference(superposition,[status(thm)],[d226,d223]) ).
cnf(d228,plain,
and(b1,not(c1)) = not(c1),
inference(superposition,[status(thm)],[d227,d2]) ).
cnf(d229,plain,
and(b1,not(i1)) = not(c1),
inference(demodulation,[status(thm)],[d228,d157]) ).
cnf(d230,plain,
and(b1,not(i1)) = not(i1),
inference(demodulation,[status(thm)],[d229,d157]) ).
cnf(d231,plain,
and(b1,f1) = not(i1),
inference(demodulation,[status(thm)],[d230,c36]) ).
cnf(d232,plain,
and(b1,f1) = f1,
inference(demodulation,[status(thm)],[d231,c36]) ).
cnf(d233,plain,
and(b3,f1) = and(a1,f1),
inference(superposition,[status(thm)],[d232,d222]) ).
cnf(d234,plain,
and(a1,f1) = and(b3,f1),
inference(superposition,[status(thm)],[d233,d2]) ).
cnf(d235,plain,
and(b3,f1) = and(a1,f1),
inference(superposition,[status(thm)],[d234,d2]) ).
cnf(d236,plain,
and(i2,f1) = and(a1,f1),
inference(demodulation,[status(thm)],[d235,d221]) ).
cnf(d237,plain,
d2 = and(a1,f1),
inference(demodulation,[status(thm)],[d236,d214]) ).
cnf(d238,plain,
or(and(a1,i1),d2) = a1,
inference(superposition,[status(thm)],[d237,d202]) ).
cnf(d239,plain,
or(d2,and(a1,i1)) = a1,
inference(demodulation,[status(thm)],[d238,c1]) ).
cnf(d240,plain,
or(d2,and(i1,a1)) = a1,
inference(demodulation,[status(thm)],[d239,c0]) ).
cnf(d241,plain,
or(d2,f3) = a1,
inference(demodulation,[status(thm)],[d240,d200]) ).
cnf(d242,plain,
or(f3,d2) = a1,
inference(demodulation,[status(thm)],[d241,c1]) ).
cnf(d243,plain,
i2 = a1,
inference(demodulation,[status(thm)],[d242,d82]) ).
cnf(d244,plain,
circuit(input(i1,i2),output(i2,a2)),
inference(demodulation,[status(thm)],[c39,d243]) ).
cnf(d245,plain,
circuit(input(i1,i2),output(i2,i1)),
inference(demodulation,[status(thm)],[d244,d183]) ).
cnf(d246,plain,
$false,
inference(resolution,[status(thm)],[c40,d245]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HWV001-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/5.47 % Computer : n006.cluster.edu
% 0.20/5.47 % Model : x86_64 x86_64
% 0.20/5.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/5.47 % Memory : 8046.5625MB
% 0.20/5.47 % OS : Linux 6.8.0-71-generic
% 0.20/5.47 % CPULimit : 300
% 0.20/5.47 % WCLimit : 300
% 0.20/5.47 % DateTime : Fri Sep 25 15:59:04 UTC 2026
% 0.20/5.47 % CPUTime :
% 0.20/5.47 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 133.89/24.95 % SZS status Unsatisfiable for theBenchmark.p
% 133.89/24.95 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------