%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : TOP051-1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 99.76s 21.48s
% Output : CNFRefutation 99.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 14
% Syntax : Number of clauses : 140 ( 140 unt; 0 nHn; 114 RR)
% Number of literals : 140 ( 139 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 : 13 ( 13 usr; 11 con; 0-10 aty)
% Number of variables : 36 ( 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,
product(a1,a6) = a2 ).
cnf(knot_03,axiom,
product(a2,a7) = a3 ).
cnf(knot_04,axiom,
product(a3,a1) = a4 ).
cnf(knot_05,axiom,
product(a4,a10) = a5 ).
cnf(knot_06,axiom,
product(a5,a9) = a6 ).
cnf(knot_07,axiom,
product(a6,a2) = a7 ).
cnf(knot_08,axiom,
product(a7,a3) = a8 ).
cnf(knot_09,axiom,
product(a8,a6) = a9 ).
cnf(knot_10,axiom,
product(a9,a4) = a10 ).
cnf(knot_11,axiom,
product(a10,a5) = a11 ).
cnf(goal,negated_conjecture,
tuple(a1,a6,a5,a2,a7,a3,a4,a9,a10,a8) != tuple(a2,a7,a6,a3,a8,a4,a5,a10,a11,a9) ).
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,
product(a1,a6) = a2,
inference(clausification,[status(esa)],[knot]) ).
cnf(c4,plain,
product(a2,a7) = a3,
inference(clausification,[status(esa)],[knot_03]) ).
cnf(c5,plain,
product(a3,a1) = a4,
inference(clausification,[status(esa)],[knot_04]) ).
cnf(c6,plain,
product(a4,a10) = a5,
inference(clausification,[status(esa)],[knot_05]) ).
cnf(c7,plain,
product(a5,a9) = a6,
inference(clausification,[status(esa)],[knot_06]) ).
cnf(c8,plain,
product(a6,a2) = a7,
inference(clausification,[status(esa)],[knot_07]) ).
cnf(c9,plain,
product(a7,a3) = a8,
inference(clausification,[status(esa)],[knot_08]) ).
cnf(c10,plain,
product(a8,a6) = a9,
inference(clausification,[status(esa)],[knot_09]) ).
cnf(c11,plain,
product(a9,a4) = a10,
inference(clausification,[status(esa)],[knot_10]) ).
cnf(c12,plain,
product(a10,a5) = a11,
inference(clausification,[status(esa)],[knot_11]) ).
cnf(c13,plain,
tuple(a1,a6,a5,a2,a7,a3,a4,a9,a10,a8) != tuple(a2,a7,a6,a3,a8,a4,a5,a10,a11,a9),
inference(clausification,[status(esa)],[goal]) ).
cnf(d0,plain,
product(product(X0,X0),X1) = product(X0,X1),
inference(superposition,[status(thm)],[c2,c0]) ).
cnf(d1,plain,
product(X0,X1) = product(X0,X1),
inference(demodulation,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
X0 = product(product(X0,X1),X1),
inference(superposition,[status(thm)],[c1,d1]) ).
cnf(d3,plain,
product(a2,a6) = a1,
inference(superposition,[status(thm)],[c3,c1]) ).
cnf(d4,plain,
product(product(X0,a2),a6) = product(product(X0,a6),a1),
inference(superposition,[status(thm)],[d3,c2]) ).
cnf(d5,plain,
product(a7,a2) = a6,
inference(superposition,[status(thm)],[c8,c1]) ).
cnf(d6,plain,
product(product(X0,a7),a2) = product(product(X0,a2),a6),
inference(superposition,[status(thm)],[d5,c2]) ).
cnf(d7,plain,
product(product(X0,a7),a2) = product(product(X0,a6),a1),
inference(demodulation,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
product(a3,a7) = a2,
inference(superposition,[status(thm)],[c4,c1]) ).
cnf(d9,plain,
product(product(X0,a3),a7) = product(product(X0,a7),a2),
inference(superposition,[status(thm)],[d8,c2]) ).
cnf(d10,plain,
product(a8,a3) = a7,
inference(superposition,[status(thm)],[c9,c1]) ).
cnf(d11,plain,
product(a7,a7) = product(product(a8,a7),a2),
inference(superposition,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
a7 = product(product(a8,a7),a2),
inference(demodulation,[status(thm)],[d11,c0]) ).
cnf(d13,plain,
a7 = product(product(a8,a6),a1),
inference(demodulation,[status(thm)],[d12,d7]) ).
cnf(d14,plain,
a7 = product(a9,a1),
inference(demodulation,[status(thm)],[d13,c10]) ).
cnf(d15,plain,
a9 = product(a7,a1),
inference(superposition,[status(thm)],[d14,d2]) ).
cnf(d16,plain,
product(product(a3,X0),a1) = product(a4,product(X0,a1)),
inference(superposition,[status(thm)],[c5,c2]) ).
cnf(d17,plain,
product(a2,a1) = product(a4,product(a7,a1)),
inference(superposition,[status(thm)],[d8,d16]) ).
cnf(d18,plain,
product(a2,a1) = product(a4,a9),
inference(demodulation,[status(thm)],[d17,d15]) ).
cnf(d19,plain,
product(product(a5,X0),a9) = product(a6,product(X0,a9)),
inference(superposition,[status(thm)],[c7,c2]) ).
cnf(d20,plain,
product(a10,a4) = a9,
inference(superposition,[status(thm)],[c11,c1]) ).
cnf(d21,plain,
product(product(X0,a10),a4) = product(product(X0,a4),a9),
inference(superposition,[status(thm)],[d20,c2]) ).
cnf(d22,plain,
product(a5,a10) = a4,
inference(superposition,[status(thm)],[c6,c1]) ).
cnf(d23,plain,
product(product(X0,a5),a10) = product(product(X0,a10),a4),
inference(superposition,[status(thm)],[d22,c2]) ).
cnf(d24,plain,
X0 = product(X0,X0),
inference(superposition,[status(thm)],[c0,d1]) ).
cnf(d25,plain,
product(a5,a10) = product(product(a5,a10),a4),
inference(superposition,[status(thm)],[d24,d23]) ).
cnf(d26,plain,
a4 = product(product(a5,a10),a4),
inference(demodulation,[status(thm)],[d25,d22]) ).
cnf(d27,plain,
a4 = product(product(a5,a4),a9),
inference(demodulation,[status(thm)],[d26,d21]) ).
cnf(d28,plain,
a4 = product(a6,product(a4,a9)),
inference(demodulation,[status(thm)],[d27,d19]) ).
cnf(d29,plain,
a4 = product(a6,product(a2,a1)),
inference(demodulation,[status(thm)],[d28,d18]) ).
cnf(d30,plain,
a6 = product(a4,product(a2,a1)),
inference(superposition,[status(thm)],[d29,d2]) ).
cnf(d31,plain,
product(product(X0,X1),X0) = product(X0,product(X1,X0)),
inference(superposition,[status(thm)],[c0,c2]) ).
cnf(d32,plain,
a1 = product(a2,a6),
inference(superposition,[status(thm)],[d3,d1]) ).
cnf(d33,plain,
product(a1,a2) = product(a2,product(a6,a2)),
inference(superposition,[status(thm)],[d32,d31]) ).
cnf(d34,plain,
product(a1,a2) = product(a2,a7),
inference(demodulation,[status(thm)],[d33,c8]) ).
cnf(d35,plain,
product(a1,a2) = a3,
inference(demodulation,[status(thm)],[d34,c4]) ).
cnf(d36,plain,
product(a3,a1) = product(a1,product(a2,a1)),
inference(superposition,[status(thm)],[d35,d31]) ).
cnf(d37,plain,
a4 = product(a1,product(a2,a1)),
inference(demodulation,[status(thm)],[d36,c5]) ).
cnf(d38,plain,
product(a4,product(a2,a1)) = a1,
inference(superposition,[status(thm)],[d37,c1]) ).
cnf(d39,plain,
a6 = a1,
inference(demodulation,[status(thm)],[d38,d30]) ).
cnf(d40,plain,
a7 = product(a9,a6),
inference(demodulation,[status(thm)],[d14,d39]) ).
cnf(d41,plain,
product(a9,a6) = a8,
inference(superposition,[status(thm)],[c10,c1]) ).
cnf(d42,plain,
a7 = a8,
inference(demodulation,[status(thm)],[d41,d40]) ).
cnf(d43,plain,
a8 = product(a7,a3),
inference(superposition,[status(thm)],[c9,d1]) ).
cnf(d44,plain,
product(a8,a7) = product(a7,product(a3,a7)),
inference(superposition,[status(thm)],[d43,d31]) ).
cnf(d45,plain,
product(a8,a7) = product(a7,a2),
inference(demodulation,[status(thm)],[d44,d8]) ).
cnf(d46,plain,
product(a8,a7) = a6,
inference(demodulation,[status(thm)],[d45,d5]) ).
cnf(d47,plain,
a6 = product(a8,a7),
inference(superposition,[status(thm)],[d46,d1]) ).
cnf(d48,plain,
a6 = product(a7,a7),
inference(demodulation,[status(thm)],[d47,d42]) ).
cnf(d49,plain,
a6 = a7,
inference(demodulation,[status(thm)],[d48,c0]) ).
cnf(d50,plain,
a2 = product(a1,a6),
inference(superposition,[status(thm)],[c3,d1]) ).
cnf(d51,plain,
a2 = product(a6,a6),
inference(demodulation,[status(thm)],[d50,d39]) ).
cnf(d52,plain,
a2 = a6,
inference(demodulation,[status(thm)],[d51,c0]) ).
cnf(d53,plain,
product(a6,a2) = a3,
inference(demodulation,[status(thm)],[d35,d39]) ).
cnf(d54,plain,
product(a6,a6) = a3,
inference(demodulation,[status(thm)],[d53,d52]) ).
cnf(d55,plain,
a6 = a3,
inference(demodulation,[status(thm)],[d54,c0]) ).
cnf(d56,plain,
a7 = product(a7,a3),
inference(demodulation,[status(thm)],[d43,d42]) ).
cnf(d57,plain,
a7 = product(a7,a6),
inference(demodulation,[status(thm)],[d56,d55]) ).
cnf(d58,plain,
a9 = product(a7,a6),
inference(demodulation,[status(thm)],[d15,d39]) ).
cnf(d59,plain,
a9 = a7,
inference(demodulation,[status(thm)],[d58,d57]) ).
cnf(d60,plain,
a9 = a6,
inference(demodulation,[status(thm)],[d59,d49]) ).
cnf(d61,plain,
product(a3,a2) = a1,
inference(superposition,[status(thm)],[d35,c1]) ).
cnf(d62,plain,
product(a3,a2) = a6,
inference(demodulation,[status(thm)],[d61,d39]) ).
cnf(d63,plain,
product(a3,a6) = a6,
inference(demodulation,[status(thm)],[d62,d52]) ).
cnf(d64,plain,
product(a3,a6) = a4,
inference(demodulation,[status(thm)],[c5,d39]) ).
cnf(d65,plain,
a6 = a4,
inference(demodulation,[status(thm)],[d64,d63]) ).
cnf(d66,plain,
product(a9,a6) = a10,
inference(demodulation,[status(thm)],[c11,d65]) ).
cnf(d67,plain,
product(a6,a6) = a10,
inference(demodulation,[status(thm)],[d66,d60]) ).
cnf(d68,plain,
a6 = a10,
inference(demodulation,[status(thm)],[d67,c0]) ).
cnf(d69,plain,
product(a11,a10) = product(a10,product(a5,a10)),
inference(superposition,[status(thm)],[c12,d31]) ).
cnf(d70,plain,
product(a11,a10) = product(a10,a4),
inference(demodulation,[status(thm)],[d69,d22]) ).
cnf(d71,plain,
product(a11,a10) = a9,
inference(demodulation,[status(thm)],[d70,d20]) ).
cnf(d72,plain,
product(a9,a10) = a11,
inference(superposition,[status(thm)],[d71,c1]) ).
cnf(d73,plain,
product(a7,a10) = a11,
inference(demodulation,[status(thm)],[d72,d59]) ).
cnf(d74,plain,
product(a6,a10) = a11,
inference(demodulation,[status(thm)],[d73,d49]) ).
cnf(d75,plain,
product(a6,a6) = a11,
inference(demodulation,[status(thm)],[d74,d68]) ).
cnf(d76,plain,
a6 = a11,
inference(demodulation,[status(thm)],[d75,c0]) ).
cnf(d77,plain,
product(a6,a9) = a5,
inference(superposition,[status(thm)],[c7,c1]) ).
cnf(d78,plain,
a5 = product(a6,a9),
inference(superposition,[status(thm)],[d77,d1]) ).
cnf(d79,plain,
a5 = product(a6,a7),
inference(demodulation,[status(thm)],[d78,d59]) ).
cnf(d80,plain,
a5 = product(a6,a6),
inference(demodulation,[status(thm)],[d79,d49]) ).
cnf(d81,plain,
a5 = a6,
inference(demodulation,[status(thm)],[d80,c0]) ).
cnf(d82,plain,
a8 = product(a9,a6),
inference(superposition,[status(thm)],[d41,d1]) ).
cnf(d83,plain,
a8 = a7,
inference(demodulation,[status(thm)],[d82,d40]) ).
cnf(d84,plain,
a8 = a6,
inference(demodulation,[status(thm)],[d83,d49]) ).
cnf(d85,plain,
tuple(a6,a6,a5,a2,a7,a3,a4,a9,a10,a8) != tuple(a2,a7,a6,a3,a8,a4,a5,a10,a11,a9),
inference(demodulation,[status(thm)],[c13,d39]) ).
cnf(d86,plain,
tuple(a6,a6,a6,a2,a7,a3,a4,a9,a10,a8) != tuple(a2,a7,a6,a3,a8,a4,a5,a10,a11,a9),
inference(demodulation,[status(thm)],[d85,d81]) ).
cnf(d87,plain,
tuple(a6,a6,a6,a6,a7,a3,a4,a9,a10,a8) != tuple(a2,a7,a6,a3,a8,a4,a5,a10,a11,a9),
inference(demodulation,[status(thm)],[d86,d52]) ).
cnf(d88,plain,
tuple(a6,a6,a6,a6,a6,a3,a4,a9,a10,a8) != tuple(a2,a7,a6,a3,a8,a4,a5,a10,a11,a9),
inference(demodulation,[status(thm)],[d87,d49]) ).
cnf(d89,plain,
tuple(a6,a6,a6,a6,a6,a6,a4,a9,a10,a8) != tuple(a2,a7,a6,a3,a8,a4,a5,a10,a11,a9),
inference(demodulation,[status(thm)],[d88,d55]) ).
cnf(d90,plain,
tuple(a6,a6,a6,a6,a6,a6,a6,a9,a10,a8) != tuple(a2,a7,a6,a3,a8,a4,a5,a10,a11,a9),
inference(demodulation,[status(thm)],[d89,d65]) ).
cnf(d91,plain,
tuple(a6,a6,a6,a6,a6,a6,a6,a6,a10,a8) != tuple(a2,a7,a6,a3,a8,a4,a5,a10,a11,a9),
inference(demodulation,[status(thm)],[d90,d60]) ).
cnf(d92,plain,
tuple(a6,a6,a6,a6,a6,a6,a6,a6,a6,a8) != tuple(a2,a7,a6,a3,a8,a4,a5,a10,a11,a9),
inference(demodulation,[status(thm)],[d91,d68]) ).
cnf(d93,plain,
tuple(a6,a6,a6,a6,a6,a6,a6,a6,a6,a6) != tuple(a2,a7,a6,a3,a8,a4,a5,a10,a11,a9),
inference(demodulation,[status(thm)],[d92,d84]) ).
cnf(d94,plain,
tuple(a6,a6,a6,a6,a6,a6,a6,a6,a6,a6) != tuple(a6,a7,a6,a3,a8,a4,a5,a10,a11,a9),
inference(demodulation,[status(thm)],[d93,d52]) ).
cnf(d95,plain,
tuple(a6,a6,a6,a6,a6,a6,a6,a6,a6,a6) != tuple(a6,a6,a6,a3,a8,a4,a5,a10,a11,a9),
inference(demodulation,[status(thm)],[d94,d49]) ).
cnf(d96,plain,
tuple(a6,a6,a6,a6,a6,a6,a6,a6,a6,a6) != tuple(a6,a6,a6,a6,a8,a4,a5,a10,a11,a9),
inference(demodulation,[status(thm)],[d95,d55]) ).
cnf(d97,plain,
tuple(a6,a6,a6,a6,a6,a6,a6,a6,a6,a6) != tuple(a6,a6,a6,a6,a6,a4,a5,a10,a11,a9),
inference(demodulation,[status(thm)],[d96,d84]) ).
cnf(d98,plain,
tuple(a6,a6,a6,a6,a6,a6,a6,a6,a6,a6) != tuple(a6,a6,a6,a6,a6,a6,a5,a10,a11,a9),
inference(demodulation,[status(thm)],[d97,d65]) ).
cnf(d99,plain,
tuple(a6,a6,a6,a6,a6,a6,a6,a6,a6,a6) != tuple(a6,a6,a6,a6,a6,a6,a6,a10,a11,a9),
inference(demodulation,[status(thm)],[d98,d81]) ).
cnf(d100,plain,
tuple(a6,a6,a6,a6,a6,a6,a6,a6,a6,a6) != tuple(a6,a6,a6,a6,a6,a6,a6,a6,a11,a9),
inference(demodulation,[status(thm)],[d99,d68]) ).
cnf(d101,plain,
tuple(a6,a6,a6,a6,a6,a6,a6,a6,a6,a6) != tuple(a6,a6,a6,a6,a6,a6,a6,a6,a6,a9),
inference(demodulation,[status(thm)],[d100,d76]) ).
cnf(d102,plain,
tuple(a6,a6,a6,a6,a6,a6,a6,a6,a6,a6) != tuple(a6,a6,a6,a6,a6,a6,a6,a6,a6,a6),
inference(demodulation,[status(thm)],[d101,d60]) ).
cnf(d103,plain,
a4 = product(a3,a1),
inference(superposition,[status(thm)],[c5,d1]) ).
cnf(d104,plain,
product(product(X0,a3),a1) = product(product(X0,a1),a4),
inference(superposition,[status(thm)],[d103,c2]) ).
cnf(d105,plain,
product(product(X0,a6),a1) = product(product(X0,a1),a4),
inference(demodulation,[status(thm)],[d104,d55]) ).
cnf(d106,plain,
product(product(X0,a6),a6) = product(product(X0,a1),a4),
inference(demodulation,[status(thm)],[d105,d39]) ).
cnf(d107,plain,
X0 = product(product(X0,a1),a4),
inference(demodulation,[status(thm)],[d106,c1]) ).
cnf(d108,plain,
X0 = product(product(X0,a6),a4),
inference(demodulation,[status(thm)],[d107,d39]) ).
cnf(d109,plain,
X0 = product(product(X0,a6),a6),
inference(demodulation,[status(thm)],[d108,d65]) ).
cnf(d110,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d109,c1]) ).
cnf(d111,plain,
$false,
inference(resolution,[status(thm)],[d110,d102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP051-1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 20:50:39 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 99.76/21.48 % SZS status Unsatisfiable for theBenchmark.p
% 99.76/21.48 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------