%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : TOP049-1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/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 09:52:46 AM UTC 2026
% Result : Unsatisfiable 99.94s 14.97s
% Output : CNFRefutation 99.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 13
% Syntax : Number of clauses : 119 ( 119 unt; 0 nHn; 102 RR)
% Number of literals : 119 ( 118 equ; 20 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-9 aty)
% Number of variables : 27 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(involutory_quandle,axiom,
product(X0,X0) = X0 ).
cnf(involutory_quandle_01,axiom,
product(product(X0,X1),X1) = X0 ).
cnf(involutory_quandle_02,axiom,
product(product(X0,X1),X2) = product(product(X0,X2),product(X1,X2)) ).
cnf(knot,axiom,
a1 = product(a9,a7) ).
cnf(knot_03,axiom,
a3 = product(a1,a2) ).
cnf(knot_04,axiom,
a2 = product(a3,a4) ).
cnf(knot_05,axiom,
a5 = product(a2,a10) ).
cnf(knot_06,axiom,
a6 = product(a5,a4) ).
cnf(knot_08,axiom,
a8 = product(a7,a4) ).
cnf(knot_09,axiom,
a10 = product(a8,a9) ).
cnf(knot_10,axiom,
a4 = product(a10,a3) ).
cnf(knot_11,axiom,
a9 = product(a4,a8) ).
cnf(goal,negated_conjecture,
tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) != tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6) ).
cnf(c0,plain,
product(X0,X0) = X0,
inference(clausification,[status(esa)],[involutory_quandle]) ).
cnf(c1,plain,
product(product(X0,X1),X1) = X0,
inference(clausification,[status(esa)],[involutory_quandle_01]) ).
cnf(c2,plain,
product(product(X0,X1),X2) = product(product(X0,X2),product(X1,X2)),
inference(clausification,[status(esa)],[involutory_quandle_02]) ).
cnf(c3,plain,
a1 = product(a9,a7),
inference(clausification,[status(esa)],[knot]) ).
cnf(c4,plain,
a3 = product(a1,a2),
inference(clausification,[status(esa)],[knot_03]) ).
cnf(c5,plain,
a2 = product(a3,a4),
inference(clausification,[status(esa)],[knot_04]) ).
cnf(c6,plain,
a5 = product(a2,a10),
inference(clausification,[status(esa)],[knot_05]) ).
cnf(c7,plain,
a6 = product(a5,a4),
inference(clausification,[status(esa)],[knot_06]) ).
cnf(c9,plain,
a8 = product(a7,a4),
inference(clausification,[status(esa)],[knot_08]) ).
cnf(c10,plain,
a10 = product(a8,a9),
inference(clausification,[status(esa)],[knot_09]) ).
cnf(c11,plain,
a4 = product(a10,a3),
inference(clausification,[status(esa)],[knot_10]) ).
cnf(c12,plain,
a9 = product(a4,a8),
inference(clausification,[status(esa)],[knot_11]) ).
cnf(c13,plain,
tuple(a1,a9,a8,a6,a7,a2,a3,a4,a5) != tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(clausification,[status(esa)],[goal]) ).
cnf(d0,plain,
product(a3,a2) = a1,
inference(superposition,[status(thm)],[c4,c1]) ).
cnf(d1,plain,
product(product(X0,X1),X0) = product(X0,product(X1,X0)),
inference(superposition,[status(thm)],[c0,c2]) ).
cnf(d2,plain,
product(a2,a4) = a3,
inference(superposition,[status(thm)],[c5,c1]) ).
cnf(d3,plain,
product(a3,a2) = product(a2,product(a4,a2)),
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
a1 = product(a2,product(a4,a2)),
inference(demodulation,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
product(a1,product(a4,a2)) = a2,
inference(superposition,[status(thm)],[d4,c1]) ).
cnf(d6,plain,
product(a8,a4) = a7,
inference(superposition,[status(thm)],[c9,c1]) ).
cnf(d7,plain,
product(product(X0,X0),X1) = product(X0,X1),
inference(superposition,[status(thm)],[c2,c0]) ).
cnf(d8,plain,
product(X0,X1) = product(X0,X1),
inference(demodulation,[status(thm)],[d7,c0]) ).
cnf(d9,plain,
product(a4,a3) = a10,
inference(superposition,[status(thm)],[c11,c1]) ).
cnf(d10,plain,
a10 = product(a4,a3),
inference(superposition,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
product(a10,a4) = product(a4,product(a3,a4)),
inference(superposition,[status(thm)],[d10,d1]) ).
cnf(d12,plain,
product(a10,a4) = product(a4,a2),
inference(demodulation,[status(thm)],[d11,c5]) ).
cnf(d13,plain,
product(product(a7,X0),a4) = product(a8,product(X0,a4)),
inference(superposition,[status(thm)],[c9,c2]) ).
cnf(d14,plain,
product(a9,a8) = a4,
inference(superposition,[status(thm)],[c12,c1]) ).
cnf(d15,plain,
product(a10,a8) = product(a8,product(a9,a8)),
inference(superposition,[status(thm)],[c10,d1]) ).
cnf(d16,plain,
product(a10,a8) = product(a8,a4),
inference(demodulation,[status(thm)],[d15,d14]) ).
cnf(d17,plain,
product(a10,a8) = a7,
inference(demodulation,[status(thm)],[d16,d6]) ).
cnf(d18,plain,
product(a7,a8) = a10,
inference(superposition,[status(thm)],[d17,c1]) ).
cnf(d19,plain,
product(a10,a4) = product(a8,product(a8,a4)),
inference(superposition,[status(thm)],[d18,d13]) ).
cnf(d20,plain,
product(a4,a2) = product(a8,product(a8,a4)),
inference(demodulation,[status(thm)],[d19,d12]) ).
cnf(d21,plain,
product(a4,a2) = product(a8,a7),
inference(demodulation,[status(thm)],[d20,d6]) ).
cnf(d22,plain,
product(product(a9,X0),a7) = product(a1,product(X0,a7)),
inference(superposition,[status(thm)],[c3,c2]) ).
cnf(d23,plain,
a4 = product(a9,a8),
inference(superposition,[status(thm)],[d14,d8]) ).
cnf(d24,plain,
product(a4,a7) = product(a1,product(a8,a7)),
inference(superposition,[status(thm)],[d23,d22]) ).
cnf(d25,plain,
product(a4,a7) = product(a1,product(a4,a2)),
inference(demodulation,[status(thm)],[d24,d21]) ).
cnf(d26,plain,
product(a4,a7) = a2,
inference(demodulation,[status(thm)],[d25,d5]) ).
cnf(d27,plain,
product(a9,a4) = product(a4,product(a8,a4)),
inference(superposition,[status(thm)],[c12,d1]) ).
cnf(d28,plain,
product(a9,a4) = product(a4,a7),
inference(demodulation,[status(thm)],[d27,d6]) ).
cnf(d29,plain,
product(a4,a7) = product(a9,a4),
inference(superposition,[status(thm)],[d28,d8]) ).
cnf(d30,plain,
a2 = product(a9,a4),
inference(demodulation,[status(thm)],[d29,d26]) ).
cnf(d31,plain,
product(a2,a4) = a9,
inference(superposition,[status(thm)],[d30,c1]) ).
cnf(d32,plain,
a3 = product(a2,a4),
inference(superposition,[status(thm)],[d2,d8]) ).
cnf(d33,plain,
a3 = a9,
inference(demodulation,[status(thm)],[d32,d31]) ).
cnf(d34,plain,
product(a4,a9) = a10,
inference(demodulation,[status(thm)],[d9,d33]) ).
cnf(d35,plain,
X0 = product(product(X0,X1),X1),
inference(superposition,[status(thm)],[c1,d8]) ).
cnf(d36,plain,
product(a4,a9) = product(a9,product(a8,a9)),
inference(superposition,[status(thm)],[d23,d1]) ).
cnf(d37,plain,
product(a4,a9) = product(a9,a10),
inference(demodulation,[status(thm)],[d36,c10]) ).
cnf(d38,plain,
a9 = product(product(a4,a9),a10),
inference(superposition,[status(thm)],[d37,d35]) ).
cnf(d39,plain,
a9 = product(a10,a10),
inference(demodulation,[status(thm)],[d38,d34]) ).
cnf(d40,plain,
a9 = a10,
inference(demodulation,[status(thm)],[d39,c0]) ).
cnf(d41,plain,
product(a10,a9) = a4,
inference(superposition,[status(thm)],[d34,c1]) ).
cnf(d42,plain,
product(a9,a9) = a4,
inference(demodulation,[status(thm)],[d41,d40]) ).
cnf(d43,plain,
a9 = a4,
inference(demodulation,[status(thm)],[d42,c0]) ).
cnf(d44,plain,
product(a9,a4) = a2,
inference(demodulation,[status(thm)],[d28,d26]) ).
cnf(d45,plain,
product(a4,a4) = a2,
inference(demodulation,[status(thm)],[d44,d43]) ).
cnf(d46,plain,
a4 = a2,
inference(demodulation,[status(thm)],[d45,c0]) ).
cnf(d47,plain,
product(a5,a10) = a2,
inference(superposition,[status(thm)],[c6,c1]) ).
cnf(d48,plain,
product(a5,a9) = a2,
inference(demodulation,[status(thm)],[d47,d40]) ).
cnf(d49,plain,
product(a5,a4) = a2,
inference(demodulation,[status(thm)],[d48,d43]) ).
cnf(d50,plain,
a6 = a2,
inference(demodulation,[status(thm)],[c7,d49]) ).
cnf(d51,plain,
a6 = a4,
inference(demodulation,[status(thm)],[d50,d46]) ).
cnf(d52,plain,
a9 = product(a2,a4),
inference(superposition,[status(thm)],[d30,d35]) ).
cnf(d53,plain,
a4 = product(a2,a4),
inference(demodulation,[status(thm)],[d52,d43]) ).
cnf(d54,plain,
product(a2,a10) = a5,
inference(superposition,[status(thm)],[d47,c1]) ).
cnf(d55,plain,
product(a2,a9) = a5,
inference(demodulation,[status(thm)],[d54,d40]) ).
cnf(d56,plain,
product(a2,a4) = a5,
inference(demodulation,[status(thm)],[d55,d43]) ).
cnf(d57,plain,
a4 = a5,
inference(demodulation,[status(thm)],[d56,d53]) ).
cnf(d58,plain,
product(a10,a3) = a4,
inference(superposition,[status(thm)],[d9,c1]) ).
cnf(d59,plain,
product(a10,a9) = a4,
inference(demodulation,[status(thm)],[d58,d33]) ).
cnf(d60,plain,
product(a10,a9) = a8,
inference(superposition,[status(thm)],[c10,c1]) ).
cnf(d61,plain,
a4 = a8,
inference(demodulation,[status(thm)],[d60,d59]) ).
cnf(d62,plain,
a7 = product(a8,a4),
inference(superposition,[status(thm)],[d6,d8]) ).
cnf(d63,plain,
a7 = product(a4,a4),
inference(demodulation,[status(thm)],[d62,d61]) ).
cnf(d64,plain,
a7 = a4,
inference(demodulation,[status(thm)],[d63,c0]) ).
cnf(d65,plain,
a4 = a10,
inference(demodulation,[status(thm)],[d40,d43]) ).
cnf(d66,plain,
a1 = product(a4,a7),
inference(demodulation,[status(thm)],[c3,d43]) ).
cnf(d67,plain,
a1 = product(a4,a4),
inference(demodulation,[status(thm)],[d66,d64]) ).
cnf(d68,plain,
a1 = a4,
inference(demodulation,[status(thm)],[d67,c0]) ).
cnf(d69,plain,
tuple(a1,a9,a8,a6,a7,a2,a9,a4,a5) != tuple(a2,a10,a9,a7,a8,a3,a4,a5,a6),
inference(demodulation,[status(thm)],[c13,d33]) ).
cnf(d70,plain,
tuple(a1,a9,a8,a6,a7,a2,a9,a4,a5) != tuple(a2,a10,a9,a7,a8,a9,a4,a5,a6),
inference(demodulation,[status(thm)],[d69,d33]) ).
cnf(d71,plain,
tuple(a4,a9,a8,a6,a7,a2,a9,a4,a5) != tuple(a2,a10,a9,a7,a8,a9,a4,a5,a6),
inference(demodulation,[status(thm)],[d70,d68]) ).
cnf(d72,plain,
tuple(a4,a4,a8,a6,a7,a2,a9,a4,a5) != tuple(a2,a10,a9,a7,a8,a9,a4,a5,a6),
inference(demodulation,[status(thm)],[d71,d43]) ).
cnf(d73,plain,
tuple(a4,a4,a4,a6,a7,a2,a9,a4,a5) != tuple(a2,a10,a9,a7,a8,a9,a4,a5,a6),
inference(demodulation,[status(thm)],[d72,d61]) ).
cnf(d74,plain,
tuple(a4,a4,a4,a4,a7,a2,a9,a4,a5) != tuple(a2,a10,a9,a7,a8,a9,a4,a5,a6),
inference(demodulation,[status(thm)],[d73,d51]) ).
cnf(d75,plain,
tuple(a4,a4,a4,a4,a4,a2,a9,a4,a5) != tuple(a2,a10,a9,a7,a8,a9,a4,a5,a6),
inference(demodulation,[status(thm)],[d74,d64]) ).
cnf(d76,plain,
tuple(a4,a4,a4,a4,a4,a4,a9,a4,a5) != tuple(a2,a10,a9,a7,a8,a9,a4,a5,a6),
inference(demodulation,[status(thm)],[d75,d46]) ).
cnf(d77,plain,
tuple(a4,a4,a4,a4,a4,a4,a4,a4,a5) != tuple(a2,a10,a9,a7,a8,a9,a4,a5,a6),
inference(demodulation,[status(thm)],[d76,d43]) ).
cnf(d78,plain,
tuple(a4,a4,a4,a4,a4,a4,a4,a4,a4) != tuple(a2,a10,a9,a7,a8,a9,a4,a5,a6),
inference(demodulation,[status(thm)],[d77,d57]) ).
cnf(d79,plain,
tuple(a4,a4,a4,a4,a4,a4,a4,a4,a4) != tuple(a4,a10,a9,a7,a8,a9,a4,a5,a6),
inference(demodulation,[status(thm)],[d78,d46]) ).
cnf(d80,plain,
tuple(a4,a4,a4,a4,a4,a4,a4,a4,a4) != tuple(a4,a4,a9,a7,a8,a9,a4,a5,a6),
inference(demodulation,[status(thm)],[d79,d65]) ).
cnf(d81,plain,
tuple(a4,a4,a4,a4,a4,a4,a4,a4,a4) != tuple(a4,a4,a4,a7,a8,a9,a4,a5,a6),
inference(demodulation,[status(thm)],[d80,d43]) ).
cnf(d82,plain,
tuple(a4,a4,a4,a4,a4,a4,a4,a4,a4) != tuple(a4,a4,a4,a4,a8,a9,a4,a5,a6),
inference(demodulation,[status(thm)],[d81,d64]) ).
cnf(d83,plain,
tuple(a4,a4,a4,a4,a4,a4,a4,a4,a4) != tuple(a4,a4,a4,a4,a4,a9,a4,a5,a6),
inference(demodulation,[status(thm)],[d82,d61]) ).
cnf(d84,plain,
tuple(a4,a4,a4,a4,a4,a4,a4,a4,a4) != tuple(a4,a4,a4,a4,a4,a4,a4,a5,a6),
inference(demodulation,[status(thm)],[d83,d43]) ).
cnf(d85,plain,
tuple(a4,a4,a4,a4,a4,a4,a4,a4,a4) != tuple(a4,a4,a4,a4,a4,a4,a4,a4,a6),
inference(demodulation,[status(thm)],[d84,d57]) ).
cnf(d86,plain,
tuple(a4,a4,a4,a4,a4,a4,a4,a4,a4) != tuple(a4,a4,a4,a4,a4,a4,a4,a4,a4),
inference(demodulation,[status(thm)],[d85,d51]) ).
cnf(d87,plain,
product(product(X0,a8),a4) = product(product(X0,a4),a7),
inference(superposition,[status(thm)],[d6,c2]) ).
cnf(d88,plain,
product(product(X0,a4),a4) = product(product(X0,a4),a7),
inference(demodulation,[status(thm)],[d87,d61]) ).
cnf(d89,plain,
X0 = product(product(X0,a4),a7),
inference(demodulation,[status(thm)],[d88,c1]) ).
cnf(d90,plain,
X0 = product(product(X0,a4),a4),
inference(demodulation,[status(thm)],[d89,d64]) ).
cnf(d91,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d90,c1]) ).
cnf(d92,plain,
$false,
inference(resolution,[status(thm)],[d91,d86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP049-1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n018.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 : Sat Sep 26 20:52:22 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 99.94/14.97 % SZS status Unsatisfiable for theBenchmark.p
% 99.94/14.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------