%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP002-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 07:22:02 AM UTC 2026
% Result : Unsatisfiable 13.58s 11.49s
% Output : CNFRefutation 13.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 18
% Syntax : Number of clauses : 212 ( 212 unt; 0 nHn; 76 RR)
% Number of literals : 212 ( 211 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-4 aty)
% Number of variables : 290 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ifeq_axiom,axiom,
ifeq2(X0,X0,X1,X2) = X1 ).
cnf(ifeq_axiom_001,axiom,
ifeq(X0,X0,X1,X2) = X1 ).
cnf(left_identity,axiom,
product(identity,X0,X0) = true ).
cnf(right_identity,axiom,
product(X0,identity,X0) = true ).
cnf(left_inverse,axiom,
product(inverse(X0),X0,identity) = true ).
cnf(right_inverse,axiom,
product(X0,inverse(X0),identity) = true ).
cnf(total_function1,axiom,
product(X0,X1,multiply(X0,X1)) = true ).
cnf(total_function2,axiom,
ifeq2(product(X0,X1,X2),true,ifeq2(product(X0,X1,X3),true,X3,X2),X2) = X2 ).
cnf(associativity1,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(product(X5,X3,X0),true,product(X5,X4,X2),true),true),true) = true ).
cnf(associativity2,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X3,X2,X4),true,ifeq(product(X3,X0,X5),true,product(X5,X1,X4),true),true),true) = true ).
cnf(x_cubed_is_identity_1,hypothesis,
ifeq(product(X0,X0,X1),true,product(X0,X1,identity),true) = true ).
cnf(x_cubed_is_identity_2,hypothesis,
ifeq(product(X0,X0,X1),true,product(X1,X0,identity),true) = true ).
cnf(a_times_b_is_c,negated_conjecture,
product(a,b,c) = true ).
cnf(c_times_inverse_a_is_d,negated_conjecture,
product(c,inverse(a),d) = true ).
cnf(d_times_inverse_b_is_h,negated_conjecture,
product(d,inverse(b),h) = true ).
cnf(h_times_b_is_j,negated_conjecture,
product(h,b,j) = true ).
cnf(j_times_inverse_h_is_k,negated_conjecture,
product(j,inverse(h),k) = true ).
cnf(prove_k_times_inverse_b_is_e,negated_conjecture,
product(k,inverse(b),identity) != true ).
cnf(c0,plain,
ifeq2(X0,X0,X1,X2) = X1,
inference(clausification,[status(esa)],[ifeq_axiom]) ).
cnf(c1,plain,
ifeq(X0,X0,X1,X2) = X1,
inference(clausification,[status(esa)],[ifeq_axiom_001]) ).
cnf(c2,plain,
product(identity,X0,X0) = true,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c3,plain,
product(X0,identity,X0) = true,
inference(clausification,[status(esa)],[right_identity]) ).
cnf(c4,plain,
product(inverse(X0),X0,identity) = true,
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c5,plain,
product(X0,inverse(X0),identity) = true,
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c6,plain,
product(X0,X1,multiply(X0,X1)) = true,
inference(clausification,[status(esa)],[total_function1]) ).
cnf(c7,plain,
ifeq2(product(X0,X1,X2),true,ifeq2(product(X0,X1,X3),true,X3,X2),X2) = X2,
inference(clausification,[status(esa)],[total_function2]) ).
cnf(c8,plain,
ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(product(X5,X3,X0),true,product(X5,X4,X2),true),true),true) = true,
inference(clausification,[status(esa)],[associativity1]) ).
cnf(c9,plain,
ifeq(product(X0,X1,X2),true,ifeq(product(X3,X2,X4),true,ifeq(product(X3,X0,X5),true,product(X5,X1,X4),true),true),true) = true,
inference(clausification,[status(esa)],[associativity2]) ).
cnf(c10,plain,
ifeq(product(X0,X0,X1),true,product(X0,X1,identity),true) = true,
inference(clausification,[status(esa)],[x_cubed_is_identity_1]) ).
cnf(c11,plain,
ifeq(product(X0,X0,X1),true,product(X1,X0,identity),true) = true,
inference(clausification,[status(esa)],[x_cubed_is_identity_2]) ).
cnf(c12,plain,
product(a,b,c) = true,
inference(clausification,[status(esa)],[a_times_b_is_c]) ).
cnf(c13,plain,
product(c,inverse(a),d) = true,
inference(clausification,[status(esa)],[c_times_inverse_a_is_d]) ).
cnf(c14,plain,
product(d,inverse(b),h) = true,
inference(clausification,[status(esa)],[d_times_inverse_b_is_h]) ).
cnf(c15,plain,
product(h,b,j) = true,
inference(clausification,[status(esa)],[h_times_b_is_j]) ).
cnf(c16,plain,
product(j,inverse(h),k) = true,
inference(clausification,[status(esa)],[j_times_inverse_h_is_k]) ).
cnf(c17,plain,
product(k,inverse(b),identity) != true,
inference(clausification,[status(esa)],[prove_k_times_inverse_b_is_e]) ).
cnf(d0,plain,
ifeq2(product(X0,X1,X2),true,ifeq2(true,true,multiply(X0,X1),X2),X2) = X2,
inference(superposition,[status(thm)],[c6,c7]) ).
cnf(d1,plain,
ifeq2(product(X0,X1,X2),true,multiply(X0,X1),X2) = X2,
inference(demodulation,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
ifeq(true,true,ifeq(product(X2,X1,X3),true,ifeq(product(X4,X2,X0),true,product(X4,X3,multiply(X0,X1)),true),true),true) = true,
inference(superposition,[status(thm)],[c6,c8]) ).
cnf(d3,plain,
ifeq(product(X0,X1,X2),true,ifeq(product(X3,X0,X4),true,product(X3,X2,multiply(X4,X1)),true),true) = true,
inference(demodulation,[status(thm)],[d2,c1]) ).
cnf(d4,plain,
ifeq(true,true,ifeq(product(X2,X0,X3),true,product(X2,multiply(X0,X1),multiply(X3,X1)),true),true) = true,
inference(superposition,[status(thm)],[c6,d3]) ).
cnf(d5,plain,
ifeq(product(X0,X1,X2),true,product(X0,multiply(X1,X3),multiply(X2,X3)),true) = true,
inference(demodulation,[status(thm)],[d4,c1]) ).
cnf(d6,plain,
ifeq(true,true,product(X0,multiply(X1,X2),multiply(multiply(X0,X1),X2)),true) = true,
inference(superposition,[status(thm)],[c6,d5]) ).
cnf(d7,plain,
product(X0,multiply(X1,X2),multiply(multiply(X0,X1),X2)) = true,
inference(demodulation,[status(thm)],[d6,c1]) ).
cnf(d8,plain,
ifeq2(true,true,multiply(X0,multiply(X1,X2)),multiply(multiply(X0,X1),X2)) = multiply(multiply(X0,X1),X2),
inference(superposition,[status(thm)],[d7,d1]) ).
cnf(d9,plain,
multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(demodulation,[status(thm)],[d8,c0]) ).
cnf(d10,plain,
ifeq(true,true,ifeq(product(X1,identity,X2),true,ifeq(product(X1,inverse(X0),X3),true,product(X3,X0,X2),true),true),true) = true,
inference(superposition,[status(thm)],[c4,c9]) ).
cnf(d11,plain,
ifeq(product(X0,identity,X1),true,ifeq(product(X0,inverse(X2),X3),true,product(X3,X2,X1),true),true) = true,
inference(demodulation,[status(thm)],[d10,c1]) ).
cnf(d12,plain,
ifeq(true,true,ifeq(product(X0,inverse(X1),X2),true,product(X2,X1,X0),true),true) = true,
inference(superposition,[status(thm)],[c3,d11]) ).
cnf(d13,plain,
ifeq(product(X0,inverse(X1),X2),true,product(X2,X1,X0),true) = true,
inference(demodulation,[status(thm)],[d12,c1]) ).
cnf(d14,plain,
ifeq(true,true,product(d,a,c),true) = true,
inference(superposition,[status(thm)],[c13,d13]) ).
cnf(d15,plain,
product(d,a,c) = true,
inference(demodulation,[status(thm)],[d14,c1]) ).
cnf(d16,plain,
ifeq2(true,true,multiply(d,a),c) = c,
inference(superposition,[status(thm)],[d15,d1]) ).
cnf(d17,plain,
multiply(d,a) = c,
inference(demodulation,[status(thm)],[d16,c0]) ).
cnf(d18,plain,
multiply(d,multiply(a,X0)) = multiply(c,X0),
inference(superposition,[status(thm)],[d17,d9]) ).
cnf(d19,plain,
ifeq2(true,true,ifeq2(product(X0,identity,X1),true,X1,X0),X0) = X0,
inference(superposition,[status(thm)],[c3,c7]) ).
cnf(d20,plain,
ifeq2(product(X0,identity,X1),true,X1,X0) = X0,
inference(demodulation,[status(thm)],[d19,c0]) ).
cnf(d21,plain,
ifeq2(true,true,ifeq2(product(identity,X0,X1),true,X1,X0),X0) = X0,
inference(superposition,[status(thm)],[c2,c7]) ).
cnf(d22,plain,
ifeq2(product(identity,X0,X1),true,X1,X0) = X0,
inference(demodulation,[status(thm)],[d21,c0]) ).
cnf(d23,plain,
ifeq2(true,true,multiply(identity,X0),X0) = X0,
inference(superposition,[status(thm)],[c6,d22]) ).
cnf(d24,plain,
multiply(identity,X0) = X0,
inference(demodulation,[status(thm)],[d23,c0]) ).
cnf(d25,plain,
ifeq(true,true,product(X0,multiply(inverse(X0),X1),multiply(identity,X1)),true) = true,
inference(superposition,[status(thm)],[c5,d5]) ).
cnf(d26,plain,
product(X0,multiply(inverse(X0),X1),multiply(identity,X1)) = true,
inference(demodulation,[status(thm)],[d25,c1]) ).
cnf(d27,plain,
product(X1,multiply(inverse(X1),X0),X0) = true,
inference(demodulation,[status(thm)],[d26,d24]) ).
cnf(d28,plain,
ifeq2(true,true,ifeq2(product(X0,X1,X2),true,X2,multiply(X0,X1)),multiply(X0,X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c6,c7]) ).
cnf(d29,plain,
ifeq2(product(X0,X1,X2),true,X2,multiply(X0,X1)) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d28,c0]) ).
cnf(d30,plain,
ifeq2(true,true,identity,multiply(X0,inverse(X0))) = multiply(X0,inverse(X0)),
inference(superposition,[status(thm)],[c5,d29]) ).
cnf(d31,plain,
identity = multiply(X0,inverse(X0)),
inference(demodulation,[status(thm)],[d30,c0]) ).
cnf(d32,plain,
product(X0,identity,inverse(inverse(X0))) = true,
inference(superposition,[status(thm)],[d31,d27]) ).
cnf(d33,plain,
ifeq2(true,true,inverse(inverse(X0)),X0) = X0,
inference(superposition,[status(thm)],[d32,d20]) ).
cnf(d34,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d33,c0]) ).
cnf(d35,plain,
ifeq2(true,true,multiply(X0,multiply(inverse(X0),X1)),X1) = X1,
inference(superposition,[status(thm)],[d27,d1]) ).
cnf(d36,plain,
multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[d35,c0]) ).
cnf(d37,plain,
ifeq(true,true,ifeq(product(X1,X0,X2),true,product(X1,identity,multiply(X2,inverse(X0))),true),true) = true,
inference(superposition,[status(thm)],[c5,d3]) ).
cnf(d38,plain,
ifeq(product(X0,X1,X2),true,product(X0,identity,multiply(X2,inverse(X1))),true) = true,
inference(demodulation,[status(thm)],[d37,c1]) ).
cnf(d39,plain,
ifeq(true,true,product(X0,identity,multiply(multiply(X0,X1),inverse(X1))),true) = true,
inference(superposition,[status(thm)],[c6,d38]) ).
cnf(d40,plain,
product(X0,identity,multiply(multiply(X0,X1),inverse(X1))) = true,
inference(demodulation,[status(thm)],[d39,c1]) ).
cnf(d41,plain,
ifeq2(true,true,multiply(multiply(X0,X1),inverse(X1)),X0) = X0,
inference(superposition,[status(thm)],[d40,d20]) ).
cnf(d42,plain,
multiply(multiply(X0,X1),inverse(X1)) = X0,
inference(demodulation,[status(thm)],[d41,c0]) ).
cnf(d43,plain,
ifeq2(product(X0,identity,X1),true,ifeq2(true,true,X0,X1),X1) = X1,
inference(superposition,[status(thm)],[c3,c7]) ).
cnf(d44,plain,
ifeq2(product(X0,identity,X1),true,X0,X1) = X1,
inference(demodulation,[status(thm)],[d43,c0]) ).
cnf(d45,plain,
ifeq2(true,true,X0,inverse(inverse(X0))) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d32,d44]) ).
cnf(d46,plain,
X0 = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d45,c0]) ).
cnf(d47,plain,
multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(superposition,[status(thm)],[d46,d36]) ).
cnf(d48,plain,
multiply(X1,inverse(multiply(X0,X1))) = inverse(X0),
inference(superposition,[status(thm)],[d47,d42]) ).
cnf(d49,plain,
multiply(X0,inverse(X1)) = inverse(multiply(X1,inverse(X0))),
inference(superposition,[status(thm)],[d48,d36]) ).
cnf(d50,plain,
inverse(multiply(X1,inverse(X0))) = multiply(X0,inverse(X1)),
inference(superposition,[status(thm)],[d49,d34]) ).
cnf(d51,plain,
inverse(X0) = multiply(X1,inverse(multiply(X0,X1))),
inference(superposition,[status(thm)],[d42,d50]) ).
cnf(d52,plain,
multiply(d,inverse(X0)) = multiply(c,inverse(multiply(X0,a))),
inference(superposition,[status(thm)],[d51,d18]) ).
cnf(d53,plain,
multiply(multiply(X1,inverse(X0)),X0) = X1,
inference(superposition,[status(thm)],[d46,d42]) ).
cnf(d54,plain,
multiply(inverse(multiply(X0,X1)),X0) = inverse(X1),
inference(superposition,[status(thm)],[d42,d47]) ).
cnf(d55,plain,
multiply(inverse(X1),X0) = inverse(multiply(inverse(X0),X1)),
inference(superposition,[status(thm)],[d54,d53]) ).
cnf(d56,plain,
inverse(multiply(inverse(X1),X0)) = multiply(inverse(X0),X1),
inference(superposition,[status(thm)],[d55,d34]) ).
cnf(d57,plain,
inverse(X1) = multiply(inverse(multiply(X0,X1)),X0),
inference(superposition,[status(thm)],[d47,d56]) ).
cnf(d58,plain,
ifeq2(true,true,multiply(X0,identity),X0) = X0,
inference(superposition,[status(thm)],[c6,d20]) ).
cnf(d59,plain,
multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[d58,c0]) ).
cnf(d60,plain,
ifeq(true,true,product(multiply(X0,X0),X0,identity),true) = true,
inference(superposition,[status(thm)],[c6,c11]) ).
cnf(d61,plain,
product(multiply(X0,X0),X0,identity) = true,
inference(demodulation,[status(thm)],[d60,c1]) ).
cnf(d62,plain,
ifeq(true,true,product(multiply(X0,X0),identity,multiply(identity,inverse(X0))),true) = true,
inference(superposition,[status(thm)],[d61,d38]) ).
cnf(d63,plain,
product(multiply(X0,X0),identity,multiply(identity,inverse(X0))) = true,
inference(demodulation,[status(thm)],[d62,c1]) ).
cnf(d64,plain,
product(multiply(X0,X0),identity,inverse(X0)) = true,
inference(demodulation,[status(thm)],[d63,d24]) ).
cnf(d65,plain,
ifeq2(true,true,multiply(X0,X0),inverse(X0)) = inverse(X0),
inference(superposition,[status(thm)],[d64,d44]) ).
cnf(d66,plain,
multiply(X0,X0) = inverse(X0),
inference(demodulation,[status(thm)],[d65,c0]) ).
cnf(d67,plain,
multiply(X0,multiply(X0,X1)) = multiply(inverse(X0),X1),
inference(superposition,[status(thm)],[d66,d9]) ).
cnf(d68,plain,
ifeq(product(X2,X3,X1),true,ifeq(true,true,ifeq(product(X0,X2,X4),true,product(X4,X3,multiply(X0,X1)),true),true),true) = true,
inference(superposition,[status(thm)],[c6,c9]) ).
cnf(d69,plain,
ifeq(product(X1,X3,X4),true,ifeq(product(X0,X1,X2),true,product(X2,X3,multiply(X0,X4)),true),true) = true,
inference(demodulation,[status(thm)],[d68,c1]) ).
cnf(d70,plain,
ifeq(true,true,ifeq(product(X1,multiply(X0,X0),X2),true,product(X2,X0,multiply(X1,identity)),true),true) = true,
inference(superposition,[status(thm)],[d61,d69]) ).
cnf(d71,plain,
ifeq(product(X0,multiply(X1,X1),X2),true,product(X2,X1,multiply(X0,identity)),true) = true,
inference(demodulation,[status(thm)],[d70,c1]) ).
cnf(d72,plain,
ifeq(product(X0,multiply(X1,X1),X2),true,product(X2,X1,X0),true) = true,
inference(demodulation,[status(thm)],[d71,d59]) ).
cnf(d73,plain,
ifeq(true,true,product(a,multiply(b,X0),multiply(c,X0)),true) = true,
inference(superposition,[status(thm)],[c12,d5]) ).
cnf(d74,plain,
product(a,multiply(b,X0),multiply(c,X0)) = true,
inference(demodulation,[status(thm)],[d73,c1]) ).
cnf(d75,plain,
ifeq(true,true,product(multiply(c,b),b,a),true) = true,
inference(superposition,[status(thm)],[d74,d72]) ).
cnf(d76,plain,
product(multiply(c,b),b,a) = true,
inference(demodulation,[status(thm)],[d75,c1]) ).
cnf(d77,plain,
ifeq2(true,true,multiply(multiply(c,b),b),a) = a,
inference(superposition,[status(thm)],[d76,d1]) ).
cnf(d78,plain,
multiply(multiply(c,b),b) = a,
inference(demodulation,[status(thm)],[d77,c0]) ).
cnf(d79,plain,
multiply(a,inverse(b)) = multiply(c,b),
inference(superposition,[status(thm)],[d78,d42]) ).
cnf(d80,plain,
product(d,multiply(a,X0),multiply(c,X0)) = true,
inference(superposition,[status(thm)],[d17,d7]) ).
cnf(d81,plain,
ifeq(true,true,product(a,identity,multiply(c,inverse(b))),true) = true,
inference(superposition,[status(thm)],[c12,d38]) ).
cnf(d82,plain,
product(a,identity,multiply(c,inverse(b))) = true,
inference(demodulation,[status(thm)],[d81,c1]) ).
cnf(d83,plain,
ifeq2(true,true,multiply(c,inverse(b)),a) = a,
inference(superposition,[status(thm)],[d82,d20]) ).
cnf(d84,plain,
multiply(c,inverse(b)) = a,
inference(demodulation,[status(thm)],[d83,c0]) ).
cnf(d85,plain,
product(d,multiply(a,inverse(b)),a) = true,
inference(superposition,[status(thm)],[d84,d80]) ).
cnf(d86,plain,
product(d,multiply(c,b),a) = true,
inference(demodulation,[status(thm)],[d85,d79]) ).
cnf(d87,plain,
ifeq2(true,true,multiply(d,multiply(c,b)),a) = a,
inference(superposition,[status(thm)],[d86,d1]) ).
cnf(d88,plain,
multiply(d,multiply(c,b)) = a,
inference(demodulation,[status(thm)],[d87,c0]) ).
cnf(d89,plain,
multiply(inverse(d),a) = multiply(c,b),
inference(superposition,[status(thm)],[d88,d47]) ).
cnf(d90,plain,
ifeq(true,true,product(X0,multiply(X0,X0),identity),true) = true,
inference(superposition,[status(thm)],[c6,c10]) ).
cnf(d91,plain,
product(X0,multiply(X0,X0),identity) = true,
inference(demodulation,[status(thm)],[d90,c1]) ).
cnf(d92,plain,
ifeq(true,true,product(X0,identity,multiply(identity,inverse(multiply(X0,X0)))),true) = true,
inference(superposition,[status(thm)],[d91,d38]) ).
cnf(d93,plain,
product(X0,identity,multiply(identity,inverse(multiply(X0,X0)))) = true,
inference(demodulation,[status(thm)],[d92,c1]) ).
cnf(d94,plain,
product(X0,identity,inverse(multiply(X0,X0))) = true,
inference(demodulation,[status(thm)],[d93,d24]) ).
cnf(d95,plain,
ifeq2(true,true,inverse(multiply(X0,X0)),X0) = X0,
inference(superposition,[status(thm)],[d94,d20]) ).
cnf(d96,plain,
inverse(multiply(X0,X0)) = X0,
inference(demodulation,[status(thm)],[d95,c0]) ).
cnf(d97,plain,
inverse(X0) = multiply(X0,X0),
inference(superposition,[status(thm)],[d96,d34]) ).
cnf(d98,plain,
product(X0,multiply(X0,X1),multiply(inverse(X0),X1)) = true,
inference(superposition,[status(thm)],[d97,d7]) ).
cnf(d99,plain,
ifeq(true,true,product(inverse(X0),multiply(X0,X1),multiply(identity,X1)),true) = true,
inference(superposition,[status(thm)],[c4,d5]) ).
cnf(d100,plain,
product(inverse(X0),multiply(X0,X1),multiply(identity,X1)) = true,
inference(demodulation,[status(thm)],[d99,c1]) ).
cnf(d101,plain,
product(inverse(X1),multiply(X1,X0),X0) = true,
inference(demodulation,[status(thm)],[d100,d24]) ).
cnf(d102,plain,
product(inverse(d),c,a) = true,
inference(superposition,[status(thm)],[d17,d101]) ).
cnf(d103,plain,
ifeq2(true,true,multiply(inverse(d),c),a) = a,
inference(superposition,[status(thm)],[d102,d1]) ).
cnf(d104,plain,
multiply(inverse(d),c) = a,
inference(demodulation,[status(thm)],[d103,c0]) ).
cnf(d105,plain,
product(d,multiply(d,c),a) = true,
inference(superposition,[status(thm)],[d104,d98]) ).
cnf(d106,plain,
ifeq2(true,true,multiply(d,multiply(d,c)),a) = a,
inference(superposition,[status(thm)],[d105,d1]) ).
cnf(d107,plain,
multiply(d,multiply(d,c)) = a,
inference(demodulation,[status(thm)],[d106,c0]) ).
cnf(d108,plain,
multiply(inverse(d),a) = multiply(d,c),
inference(superposition,[status(thm)],[d107,d47]) ).
cnf(d109,plain,
multiply(c,b) = multiply(d,c),
inference(demodulation,[status(thm)],[d108,d89]) ).
cnf(d110,plain,
multiply(d,multiply(c,X0)) = multiply(multiply(c,b),X0),
inference(superposition,[status(thm)],[d109,d9]) ).
cnf(d111,plain,
multiply(d,multiply(c,X0)) = multiply(c,multiply(b,X0)),
inference(demodulation,[status(thm)],[d110,d9]) ).
cnf(d112,plain,
ifeq2(product(multiply(X0,X0),X0,X1),true,ifeq2(true,true,identity,X1),X1) = X1,
inference(superposition,[status(thm)],[d61,c7]) ).
cnf(d113,plain,
ifeq2(product(multiply(X1,X1),X1,X0),true,identity,X0) = X0,
inference(demodulation,[status(thm)],[d112,c0]) ).
cnf(d114,plain,
ifeq2(true,true,identity,multiply(multiply(multiply(multiply(X0,X1),multiply(X0,X1)),X0),X1)) = multiply(multiply(multiply(multiply(X0,X1),multiply(X0,X1)),X0),X1),
inference(superposition,[status(thm)],[d7,d113]) ).
cnf(d115,plain,
identity = multiply(multiply(multiply(multiply(X0,X1),multiply(X0,X1)),X0),X1),
inference(demodulation,[status(thm)],[d114,c0]) ).
cnf(d116,plain,
identity = multiply(multiply(multiply(X0,X1),multiply(X0,X1)),multiply(X0,X1)),
inference(demodulation,[status(thm)],[d115,d9]) ).
cnf(d117,plain,
identity = multiply(multiply(X0,X1),multiply(multiply(X0,X1),multiply(X0,X1))),
inference(demodulation,[status(thm)],[d116,d9]) ).
cnf(d118,plain,
identity = multiply(X0,multiply(X1,multiply(multiply(X0,X1),multiply(X0,X1)))),
inference(demodulation,[status(thm)],[d117,d9]) ).
cnf(d119,plain,
identity = multiply(X0,multiply(X1,multiply(X0,multiply(X1,multiply(X0,X1))))),
inference(demodulation,[status(thm)],[d118,d9]) ).
cnf(d120,plain,
ifeq2(true,true,multiply(multiply(X0,X1),X2),multiply(X0,multiply(X1,X2))) = multiply(X0,multiply(X1,X2)),
inference(superposition,[status(thm)],[d7,d29]) ).
cnf(d121,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(demodulation,[status(thm)],[d120,c0]) ).
cnf(d122,plain,
ifeq(true,true,ifeq(product(X0,b,X1),true,ifeq(product(X2,X0,h),true,product(X2,X1,j),true),true),true) = true,
inference(superposition,[status(thm)],[c15,c8]) ).
cnf(d123,plain,
ifeq(product(X0,b,X1),true,ifeq(product(X2,X0,h),true,product(X2,X1,j),true),true) = true,
inference(demodulation,[status(thm)],[d122,c1]) ).
cnf(d124,plain,
ifeq(true,true,ifeq(product(X0,inverse(b),h),true,product(X0,identity,j),true),true) = true,
inference(superposition,[status(thm)],[c4,d123]) ).
cnf(d125,plain,
ifeq(product(X0,inverse(b),h),true,product(X0,identity,j),true) = true,
inference(demodulation,[status(thm)],[d124,c1]) ).
cnf(d126,plain,
ifeq(true,true,product(d,identity,j),true) = true,
inference(superposition,[status(thm)],[c14,d125]) ).
cnf(d127,plain,
product(d,identity,j) = true,
inference(demodulation,[status(thm)],[d126,c1]) ).
cnf(d128,plain,
ifeq2(true,true,d,j) = j,
inference(superposition,[status(thm)],[d127,d44]) ).
cnf(d129,plain,
d = j,
inference(demodulation,[status(thm)],[d128,c0]) ).
cnf(d130,plain,
ifeq2(true,true,ifeq2(product(h,b,X0),true,X0,j),j) = j,
inference(superposition,[status(thm)],[c15,c7]) ).
cnf(d131,plain,
ifeq2(product(h,b,X0),true,X0,j) = j,
inference(demodulation,[status(thm)],[d130,c0]) ).
cnf(d132,plain,
ifeq2(true,true,multiply(h,b),j) = j,
inference(superposition,[status(thm)],[c6,d131]) ).
cnf(d133,plain,
multiply(h,b) = j,
inference(demodulation,[status(thm)],[d132,c0]) ).
cnf(d134,plain,
multiply(h,b) = d,
inference(demodulation,[status(thm)],[d133,d129]) ).
cnf(d135,plain,
multiply(d,X0) = multiply(h,multiply(b,X0)),
inference(superposition,[status(thm)],[d134,d121]) ).
cnf(d136,plain,
multiply(inverse(X1),inverse(X0)) = inverse(multiply(X0,X1)),
inference(superposition,[status(thm)],[d54,d42]) ).
cnf(d137,plain,
ifeq2(true,true,d,multiply(c,inverse(a))) = multiply(c,inverse(a)),
inference(superposition,[status(thm)],[c13,d29]) ).
cnf(d138,plain,
d = multiply(c,inverse(a)),
inference(demodulation,[status(thm)],[d137,c0]) ).
cnf(d139,plain,
multiply(c,d) = multiply(inverse(c),inverse(a)),
inference(superposition,[status(thm)],[d138,d67]) ).
cnf(d140,plain,
multiply(c,d) = inverse(multiply(a,c)),
inference(demodulation,[status(thm)],[d139,d136]) ).
cnf(d141,plain,
inverse(inverse(X1)) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[status(thm)],[d54,d56]) ).
cnf(d142,plain,
X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(demodulation,[status(thm)],[d141,d34]) ).
cnf(d143,plain,
X1 = multiply(X0,multiply(inverse(X0),X1)),
inference(superposition,[status(thm)],[d46,d142]) ).
cnf(d144,plain,
ifeq(product(X0,X1,X2),true,ifeq(true,true,product(inverse(X0),X2,multiply(identity,X1)),true),true) = true,
inference(superposition,[status(thm)],[c4,d3]) ).
cnf(d145,plain,
ifeq(product(X0,X2,X1),true,product(inverse(X0),X1,multiply(identity,X2)),true) = true,
inference(demodulation,[status(thm)],[d144,c1]) ).
cnf(d146,plain,
ifeq(product(X1,X0,X2),true,product(inverse(X1),X2,X0),true) = true,
inference(demodulation,[status(thm)],[d145,d24]) ).
cnf(d147,plain,
ifeq(true,true,product(inverse(a),c,b),true) = true,
inference(superposition,[status(thm)],[c12,d146]) ).
cnf(d148,plain,
product(inverse(a),c,b) = true,
inference(demodulation,[status(thm)],[d147,c1]) ).
cnf(d149,plain,
ifeq2(true,true,multiply(inverse(a),c),b) = b,
inference(superposition,[status(thm)],[d148,d1]) ).
cnf(d150,plain,
multiply(inverse(a),c) = b,
inference(demodulation,[status(thm)],[d149,c0]) ).
cnf(d151,plain,
product(a,multiply(a,c),b) = true,
inference(superposition,[status(thm)],[d150,d98]) ).
cnf(d152,plain,
ifeq2(true,true,multiply(a,multiply(a,c)),b) = b,
inference(superposition,[status(thm)],[d151,d1]) ).
cnf(d153,plain,
multiply(a,multiply(a,c)) = b,
inference(demodulation,[status(thm)],[d152,c0]) ).
cnf(d154,plain,
multiply(inverse(a),b) = multiply(a,c),
inference(superposition,[status(thm)],[d153,d47]) ).
cnf(d155,plain,
inverse(multiply(a,c)) = multiply(inverse(b),a),
inference(superposition,[status(thm)],[d154,d56]) ).
cnf(d156,plain,
a = multiply(b,inverse(multiply(a,c))),
inference(superposition,[status(thm)],[d155,d143]) ).
cnf(d157,plain,
a = multiply(b,multiply(c,d)),
inference(demodulation,[status(thm)],[d156,d140]) ).
cnf(d158,plain,
multiply(d,multiply(c,d)) = multiply(h,a),
inference(superposition,[status(thm)],[d157,d135]) ).
cnf(d159,plain,
identity = multiply(c,multiply(d,multiply(c,multiply(h,a)))),
inference(superposition,[status(thm)],[d158,d119]) ).
cnf(d160,plain,
identity = multiply(c,multiply(c,multiply(b,multiply(h,a)))),
inference(demodulation,[status(thm)],[d159,d111]) ).
cnf(d161,plain,
identity = multiply(inverse(c),multiply(b,multiply(h,a))),
inference(demodulation,[status(thm)],[d160,d67]) ).
cnf(d162,plain,
multiply(c,identity) = multiply(b,multiply(h,a)),
inference(superposition,[status(thm)],[d161,d36]) ).
cnf(d163,plain,
c = multiply(b,multiply(h,a)),
inference(demodulation,[status(thm)],[d162,d59]) ).
cnf(d164,plain,
inverse(multiply(h,a)) = multiply(inverse(c),b),
inference(superposition,[status(thm)],[d163,d57]) ).
cnf(d165,plain,
multiply(c,inverse(multiply(h,a))) = b,
inference(superposition,[status(thm)],[d164,d36]) ).
cnf(d166,plain,
multiply(d,inverse(h)) = b,
inference(demodulation,[status(thm)],[d165,d52]) ).
cnf(d167,plain,
ifeq2(true,true,k,multiply(j,inverse(h))) = multiply(j,inverse(h)),
inference(superposition,[status(thm)],[c16,d29]) ).
cnf(d168,plain,
k = multiply(j,inverse(h)),
inference(demodulation,[status(thm)],[d167,c0]) ).
cnf(d169,plain,
k = multiply(d,inverse(h)),
inference(demodulation,[status(thm)],[d168,d129]) ).
cnf(d170,plain,
k = b,
inference(demodulation,[status(thm)],[d169,d166]) ).
cnf(d171,plain,
product(b,inverse(b),identity) != true,
inference(demodulation,[status(thm)],[c17,d170]) ).
cnf(d172,plain,
true != true,
inference(demodulation,[status(thm)],[d171,c5]) ).
cnf(d173,plain,
ifeq2(true,true,X0,X0) = X0,
inference(superposition,[status(thm)],[c3,d20]) ).
cnf(d174,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d173,c0]) ).
cnf(d175,plain,
$false,
inference(resolution,[status(thm)],[d174,d172]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP002-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n016.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 14:20:16 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.58/11.49 % SZS status Unsatisfiable for theBenchmark.p
% 13.58/11.49 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------