%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP002-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 07:22:03 AM UTC 2026
% Result : Unsatisfiable 25.57s 4.11s
% Output : CNFRefutation 25.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 12
% Syntax : Number of clauses : 110 ( 110 unt; 0 nHn; 40 RR)
% Number of literals : 110 ( 109 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 114 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(right_identity,axiom,
multiply(X0,identity) = X0 ).
cnf(right_inverse,axiom,
multiply(X0,inverse(X0)) = identity ).
cnf(x_cubed_is_identity,hypothesis,
multiply(X0,multiply(X0,X0)) = identity ).
cnf(a_times_b_is_c,negated_conjecture,
multiply(a,b) = c ).
cnf(c_times_inverse_a_is_d,negated_conjecture,
multiply(c,inverse(a)) = d ).
cnf(d_times_inverse_b_is_h,negated_conjecture,
multiply(d,inverse(b)) = h ).
cnf(h_times_b_is_j,negated_conjecture,
multiply(h,b) = j ).
cnf(j_times_inverse_h_is_k,negated_conjecture,
multiply(j,inverse(h)) = k ).
cnf(prove_k_times_inverse_b_is_e,negated_conjecture,
multiply(k,inverse(b)) != identity ).
cnf(left_identity,axiom,
multiply(identity,X0) = X0 ).
cnf(left_inverse,axiom,
multiply(inverse(X0),X0) = identity ).
cnf(associativity,axiom,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)) ).
cnf(c0,plain,
multiply(X0,identity) = X0,
inference(clausification,[status(esa)],[right_identity]) ).
cnf(c1,plain,
multiply(X0,inverse(X0)) = identity,
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c2,plain,
multiply(X0,multiply(X0,X0)) = identity,
inference(clausification,[status(esa)],[x_cubed_is_identity]) ).
cnf(c3,plain,
multiply(a,b) = c,
inference(clausification,[status(esa)],[a_times_b_is_c]) ).
cnf(c4,plain,
multiply(c,inverse(a)) = d,
inference(clausification,[status(esa)],[c_times_inverse_a_is_d]) ).
cnf(c5,plain,
multiply(d,inverse(b)) = h,
inference(clausification,[status(esa)],[d_times_inverse_b_is_h]) ).
cnf(c6,plain,
multiply(h,b) = j,
inference(clausification,[status(esa)],[h_times_b_is_j]) ).
cnf(c7,plain,
multiply(j,inverse(h)) = k,
inference(clausification,[status(esa)],[j_times_inverse_h_is_k]) ).
cnf(c8,plain,
multiply(k,inverse(b)) != identity,
inference(clausification,[status(esa)],[prove_k_times_inverse_b_is_e]) ).
cnf(c9,plain,
multiply(identity,X0) = X0,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c10,plain,
multiply(inverse(X0),X0) = identity,
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c11,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(clausification,[status(esa)],[associativity]) ).
cnf(d0,plain,
multiply(X0,multiply(X1,identity)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c11,c0]) ).
cnf(d1,plain,
multiply(X1,X0) = multiply(X1,X0),
inference(demodulation,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
multiply(identity,X1) = multiply(X0,multiply(inverse(X0),X1)),
inference(superposition,[status(thm)],[c1,c11]) ).
cnf(d3,plain,
X0 = multiply(X1,multiply(inverse(X1),X0)),
inference(demodulation,[status(thm)],[d2,c9]) ).
cnf(d4,plain,
multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
multiply(identity,X1) = multiply(X0,multiply(multiply(X0,X0),X1)),
inference(superposition,[status(thm)],[c2,c11]) ).
cnf(d6,plain,
X0 = multiply(X1,multiply(multiply(X1,X1),X0)),
inference(demodulation,[status(thm)],[d5,c9]) ).
cnf(d7,plain,
X1 = multiply(X0,multiply(X0,multiply(X0,X1))),
inference(demodulation,[status(thm)],[d6,c11]) ).
cnf(d8,plain,
multiply(inverse(X0),X1) = multiply(X0,multiply(X0,X1)),
inference(superposition,[status(thm)],[d3,d7]) ).
cnf(d9,plain,
multiply(d,X0) = multiply(c,multiply(inverse(a),X0)),
inference(superposition,[status(thm)],[c4,c11]) ).
cnf(d10,plain,
multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[status(thm)],[c10,c11]) ).
cnf(d11,plain,
X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(demodulation,[status(thm)],[d10,c9]) ).
cnf(d12,plain,
c = multiply(a,b),
inference(superposition,[status(thm)],[c3,d1]) ).
cnf(d13,plain,
b = multiply(inverse(a),c),
inference(superposition,[status(thm)],[d12,d11]) ).
cnf(d14,plain,
multiply(d,c) = multiply(c,b),
inference(superposition,[status(thm)],[d13,d9]) ).
cnf(d15,plain,
multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(superposition,[status(thm)],[c11,d1]) ).
cnf(d16,plain,
inverse(X0) = multiply(X0,multiply(X0,identity)),
inference(superposition,[status(thm)],[c1,d7]) ).
cnf(d17,plain,
inverse(X0) = multiply(X0,X0),
inference(demodulation,[status(thm)],[d16,c0]) ).
cnf(d18,plain,
multiply(X0,multiply(X1,multiply(X0,X1))) = inverse(multiply(X0,X1)),
inference(superposition,[status(thm)],[d17,d15]) ).
cnf(d19,plain,
multiply(multiply(X0,X1),multiply(X0,multiply(X1,multiply(X0,X1)))) = identity,
inference(superposition,[status(thm)],[c11,c2]) ).
cnf(d20,plain,
multiply(X0,multiply(X1,multiply(X0,multiply(X1,multiply(X0,X1))))) = identity,
inference(demodulation,[status(thm)],[d19,c11]) ).
cnf(d21,plain,
multiply(X1,multiply(inverse(X0),multiply(X1,multiply(inverse(X0),X1)))) = multiply(X0,identity),
inference(superposition,[status(thm)],[d20,d3]) ).
cnf(d22,plain,
multiply(X1,multiply(inverse(X0),multiply(X1,multiply(inverse(X0),X1)))) = X0,
inference(demodulation,[status(thm)],[d21,c0]) ).
cnf(d23,plain,
multiply(inverse(X1),multiply(X0,multiply(inverse(X1),X0))) = multiply(inverse(X0),X1),
inference(superposition,[status(thm)],[d22,d11]) ).
cnf(d24,plain,
inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0),
inference(demodulation,[status(thm)],[d23,d18]) ).
cnf(d25,plain,
multiply(h,X0) = multiply(d,multiply(inverse(b),X0)),
inference(superposition,[status(thm)],[c5,c11]) ).
cnf(d26,plain,
multiply(h,b) = multiply(d,identity),
inference(superposition,[status(thm)],[c10,d25]) ).
cnf(d27,plain,
j = multiply(d,identity),
inference(demodulation,[status(thm)],[d26,c6]) ).
cnf(d28,plain,
j = d,
inference(demodulation,[status(thm)],[d27,c0]) ).
cnf(d29,plain,
multiply(k,X0) = multiply(j,multiply(inverse(h),X0)),
inference(superposition,[status(thm)],[c7,c11]) ).
cnf(d30,plain,
multiply(k,h) = multiply(j,identity),
inference(superposition,[status(thm)],[c10,d29]) ).
cnf(d31,plain,
multiply(k,h) = j,
inference(demodulation,[status(thm)],[d30,c0]) ).
cnf(d32,plain,
h = multiply(inverse(k),j),
inference(superposition,[status(thm)],[d31,d11]) ).
cnf(d33,plain,
multiply(inverse(k),multiply(j,X0)) = multiply(h,X0),
inference(superposition,[status(thm)],[d32,d15]) ).
cnf(d34,plain,
multiply(inverse(k),multiply(d,X0)) = multiply(h,X0),
inference(demodulation,[status(thm)],[d33,d28]) ).
cnf(d35,plain,
multiply(d,a) = multiply(c,identity),
inference(superposition,[status(thm)],[c10,d9]) ).
cnf(d36,plain,
multiply(d,a) = c,
inference(demodulation,[status(thm)],[d35,c0]) ).
cnf(d37,plain,
c = multiply(d,a),
inference(superposition,[status(thm)],[d36,d1]) ).
cnf(d38,plain,
multiply(inverse(k),c) = multiply(h,a),
inference(superposition,[status(thm)],[d37,d34]) ).
cnf(d39,plain,
inverse(multiply(h,a)) = multiply(inverse(c),k),
inference(superposition,[status(thm)],[d38,d24]) ).
cnf(d40,plain,
multiply(identity,X2) = multiply(X0,multiply(multiply(X1,multiply(X0,multiply(X1,multiply(X0,X1)))),X2)),
inference(superposition,[status(thm)],[d20,c11]) ).
cnf(d41,plain,
X0 = multiply(X1,multiply(multiply(X2,multiply(X1,multiply(X2,multiply(X1,X2)))),X0)),
inference(demodulation,[status(thm)],[d40,c9]) ).
cnf(d42,plain,
X2 = multiply(X1,multiply(X0,multiply(multiply(X1,multiply(X0,multiply(X1,X0))),X2))),
inference(demodulation,[status(thm)],[d41,c11]) ).
cnf(d43,plain,
X2 = multiply(X0,multiply(X1,multiply(X0,multiply(multiply(X1,multiply(X0,X1)),X2)))),
inference(demodulation,[status(thm)],[d42,c11]) ).
cnf(d44,plain,
X2 = multiply(X1,multiply(X0,multiply(X1,multiply(X0,multiply(multiply(X1,X0),X2))))),
inference(demodulation,[status(thm)],[d43,c11]) ).
cnf(d45,plain,
X2 = multiply(X0,multiply(X1,multiply(X0,multiply(X1,multiply(X0,multiply(X1,X2)))))),
inference(demodulation,[status(thm)],[d44,c11]) ).
cnf(d46,plain,
multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = identity,
inference(superposition,[status(thm)],[c11,c1]) ).
cnf(d47,plain,
identity = multiply(X0,multiply(X1,multiply(X2,inverse(multiply(multiply(X0,X1),X2))))),
inference(superposition,[status(thm)],[d46,c11]) ).
cnf(d48,plain,
identity = multiply(X0,multiply(X1,multiply(X2,inverse(multiply(X0,multiply(X1,X2)))))),
inference(demodulation,[status(thm)],[d47,c11]) ).
cnf(d49,plain,
inverse(multiply(X0,multiply(X1,X0))) = multiply(X1,multiply(X0,multiply(X1,identity))),
inference(superposition,[status(thm)],[d48,d45]) ).
cnf(d50,plain,
inverse(multiply(X1,multiply(X0,X1))) = multiply(X0,multiply(X1,X0)),
inference(demodulation,[status(thm)],[d49,c0]) ).
cnf(d51,plain,
multiply(j,X0) = multiply(h,multiply(b,X0)),
inference(superposition,[status(thm)],[c6,c11]) ).
cnf(d52,plain,
multiply(j,X0) = multiply(h,multiply(b,X0)),
inference(superposition,[status(thm)],[d51,d1]) ).
cnf(d53,plain,
multiply(d,X0) = multiply(h,multiply(b,X0)),
inference(demodulation,[status(thm)],[d52,d28]) ).
cnf(d54,plain,
inverse(a) = multiply(c,multiply(c,d)),
inference(superposition,[status(thm)],[c4,d7]) ).
cnf(d55,plain,
multiply(c,d) = multiply(inverse(c),inverse(a)),
inference(superposition,[status(thm)],[d54,d11]) ).
cnf(d56,plain,
multiply(c,X0) = multiply(a,multiply(b,X0)),
inference(superposition,[status(thm)],[c3,c11]) ).
cnf(d57,plain,
X0 = multiply(b,multiply(c,multiply(a,multiply(b,multiply(a,X0))))),
inference(superposition,[status(thm)],[d56,d45]) ).
cnf(d58,plain,
X0 = multiply(b,multiply(c,multiply(c,multiply(a,X0)))),
inference(demodulation,[status(thm)],[d57,d56]) ).
cnf(d59,plain,
X0 = multiply(b,multiply(inverse(c),multiply(a,X0))),
inference(demodulation,[status(thm)],[d58,d8]) ).
cnf(d60,plain,
inverse(X0) = multiply(inverse(X0),identity),
inference(superposition,[status(thm)],[c1,d11]) ).
cnf(d61,plain,
inverse(X0) = inverse(X0),
inference(demodulation,[status(thm)],[d60,c0]) ).
cnf(d62,plain,
inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[status(thm)],[c1,d3]) ).
cnf(d63,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d62,c0]) ).
cnf(d64,plain,
X0 = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d63,d61]) ).
cnf(d65,plain,
inverse(multiply(X0,X0)) = multiply(X0,identity),
inference(superposition,[status(thm)],[d46,d7]) ).
cnf(d66,plain,
inverse(multiply(X0,X0)) = X0,
inference(demodulation,[status(thm)],[d65,c0]) ).
cnf(d67,plain,
multiply(X0,X0) = inverse(X0),
inference(superposition,[status(thm)],[d66,d64]) ).
cnf(d68,plain,
a = multiply(b,multiply(inverse(c),inverse(a))),
inference(superposition,[status(thm)],[d67,d59]) ).
cnf(d69,plain,
a = multiply(b,multiply(c,d)),
inference(demodulation,[status(thm)],[d68,d55]) ).
cnf(d70,plain,
multiply(d,multiply(c,d)) = multiply(h,a),
inference(superposition,[status(thm)],[d69,d53]) ).
cnf(d71,plain,
inverse(multiply(h,a)) = multiply(c,multiply(d,c)),
inference(superposition,[status(thm)],[d70,d50]) ).
cnf(d72,plain,
multiply(inverse(c),k) = multiply(c,multiply(d,c)),
inference(demodulation,[status(thm)],[d71,d39]) ).
cnf(d73,plain,
multiply(inverse(c),k) = multiply(c,multiply(c,b)),
inference(demodulation,[status(thm)],[d72,d14]) ).
cnf(d74,plain,
multiply(inverse(c),k) = multiply(inverse(c),b),
inference(demodulation,[status(thm)],[d73,d8]) ).
cnf(d75,plain,
k = multiply(c,multiply(inverse(c),b)),
inference(superposition,[status(thm)],[d74,d3]) ).
cnf(d76,plain,
k = b,
inference(demodulation,[status(thm)],[d75,d4]) ).
cnf(d77,plain,
multiply(b,inverse(b)) != identity,
inference(demodulation,[status(thm)],[c8,d76]) ).
cnf(d78,plain,
identity != identity,
inference(demodulation,[status(thm)],[d77,c1]) ).
cnf(d79,plain,
multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(superposition,[status(thm)],[d11,d1]) ).
cnf(d80,plain,
multiply(d,multiply(c,multiply(inverse(a),multiply(c,multiply(inverse(a),X0))))) = X0,
inference(superposition,[status(thm)],[d45,d9]) ).
cnf(d81,plain,
multiply(d,multiply(d,multiply(c,multiply(inverse(a),X0)))) = X0,
inference(demodulation,[status(thm)],[d80,d9]) ).
cnf(d82,plain,
multiply(inverse(d),multiply(c,multiply(inverse(a),X0))) = X0,
inference(demodulation,[status(thm)],[d81,d8]) ).
cnf(d83,plain,
multiply(inverse(d),multiply(d,X0)) = X0,
inference(demodulation,[status(thm)],[d82,d9]) ).
cnf(d84,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d83,d79]) ).
cnf(d85,plain,
$false,
inference(resolution,[status(thm)],[d84,d78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP002-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n018.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 : Fri Sep 25 14:17:35 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.57/4.11 % SZS status Unsatisfiable for theBenchmark.p
% 25.57/4.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------