%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP002-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 92.43s 17.91s
% Output : CNFRefutation 92.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 16
% Syntax : Number of clauses : 110 ( 72 unt; 0 nHn; 77 RR)
% Number of literals : 165 ( 21 equ; 58 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 162 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(x_cubed_is_identity_1,hypothesis,
( product(X0,X1,identity)
| ~ product(X0,X0,X1) ) ).
cnf(x_cubed_is_identity_2,hypothesis,
( product(X1,X0,identity)
| ~ product(X0,X0,X1) ) ).
cnf(a_times_b_is_c,negated_conjecture,
product(a,b,c) ).
cnf(c_times_inverse_a_is_d,negated_conjecture,
product(c,inverse(a),d) ).
cnf(d_times_inverse_b_is_h,negated_conjecture,
product(d,inverse(b),h) ).
cnf(h_times_b_is_j,negated_conjecture,
product(h,b,j) ).
cnf(j_times_inverse_h_is_k,negated_conjecture,
product(j,inverse(h),k) ).
cnf(prove_k_times_inverse_b_is_e,negated_conjecture,
~ product(k,inverse(b),identity) ).
cnf(left_identity,axiom,
product(identity,X0,X0) ).
cnf(right_identity,axiom,
product(X0,identity,X0) ).
cnf(left_inverse,axiom,
product(inverse(X0),X0,identity) ).
cnf(right_inverse,axiom,
product(X0,inverse(X0),identity) ).
cnf(total_function1,axiom,
product(X0,X1,multiply(X0,X1)) ).
cnf(total_function2,axiom,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
cnf(associativity1,axiom,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(associativity2,axiom,
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(c0,plain,
( product(X0,X1,identity)
| ~ product(X0,X0,X1) ),
inference(clausification,[status(esa)],[x_cubed_is_identity_1]) ).
cnf(c1,plain,
( product(X1,X0,identity)
| ~ product(X0,X0,X1) ),
inference(clausification,[status(esa)],[x_cubed_is_identity_2]) ).
cnf(c2,plain,
product(a,b,c),
inference(clausification,[status(esa)],[a_times_b_is_c]) ).
cnf(c3,plain,
product(c,inverse(a),d),
inference(clausification,[status(esa)],[c_times_inverse_a_is_d]) ).
cnf(c4,plain,
product(d,inverse(b),h),
inference(clausification,[status(esa)],[d_times_inverse_b_is_h]) ).
cnf(c5,plain,
product(h,b,j),
inference(clausification,[status(esa)],[h_times_b_is_j]) ).
cnf(c6,plain,
product(j,inverse(h),k),
inference(clausification,[status(esa)],[j_times_inverse_h_is_k]) ).
cnf(c7,plain,
~ product(k,inverse(b),identity),
inference(clausification,[status(esa)],[prove_k_times_inverse_b_is_e]) ).
cnf(c8,plain,
product(identity,X0,X0),
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c9,plain,
product(X0,identity,X0),
inference(clausification,[status(esa)],[right_identity]) ).
cnf(c10,plain,
product(inverse(X0),X0,identity),
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c11,plain,
product(X0,inverse(X0),identity),
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c12,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[total_function1]) ).
cnf(c13,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[total_function2]) ).
cnf(c14,plain,
( product(X3,X5,X2)
| ~ product(X4,X1,X5)
| ~ product(X3,X4,X0)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity1]) ).
cnf(c15,plain,
( product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity2]) ).
cnf(d0,plain,
( ~ product(X3,X1,X0)
| ~ product(X3,identity,X2)
| product(X0,inverse(X1),X2) ),
inference(resolution,[status(thm)],[c15,c11]) ).
cnf(d1,plain,
( product(multiply(X0,X2),inverse(X2),X1)
| ~ product(X0,identity,X1) ),
inference(resolution,[status(thm)],[d0,c12]) ).
cnf(d2,plain,
product(multiply(X0,X1),inverse(X1),X0),
inference(resolution,[status(thm)],[d1,c9]) ).
cnf(d3,plain,
( ~ product(multiply(X1,X2),inverse(X2),X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[d2,c13]) ).
cnf(d4,plain,
( ~ product(X2,c,X0)
| ~ product(X2,d,X1)
| product(X0,inverse(a),X1) ),
inference(resolution,[status(thm)],[c15,c3]) ).
cnf(d5,plain,
( product(multiply(X0,c),inverse(a),X1)
| ~ product(X0,d,X1) ),
inference(resolution,[status(thm)],[d4,c12]) ).
cnf(d6,plain,
product(multiply(X0,c),inverse(a),multiply(X0,d)),
inference(resolution,[status(thm)],[d5,c12]) ).
cnf(d7,plain,
( ~ product(multiply(X1,c),inverse(a),X0)
| X0 = multiply(X1,d) ),
inference(resolution,[status(thm)],[d6,c13]) ).
cnf(d8,plain,
( ~ product(X1,X2,X0)
| X0 = multiply(X1,X2) ),
inference(resolution,[status(thm)],[c13,c12]) ).
cnf(d9,plain,
( ~ product(X3,X0,X4)
| product(X3,X2,multiply(X4,X1))
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c14,c12]) ).
cnf(d10,plain,
( ~ product(X3,inverse(X1),X0)
| ~ product(X3,identity,X2)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c15,c10]) ).
cnf(d11,plain,
( product(X2,X1,X0)
| ~ product(X0,inverse(X1),X2) ),
inference(resolution,[status(thm)],[d10,c9]) ).
cnf(d12,plain,
product(d,a,c),
inference(resolution,[status(thm)],[d11,c3]) ).
cnf(d13,plain,
( ~ product(a,X1,X0)
| product(d,X0,multiply(c,X1)) ),
inference(resolution,[status(thm)],[d12,d9]) ).
cnf(d14,plain,
X0 = multiply(identity,X0),
inference(resolution,[status(thm)],[d8,c8]) ).
cnf(d15,plain,
( ~ product(X2,X3,X1)
| product(X0,X1,multiply(multiply(X0,X2),X3)) ),
inference(resolution,[status(thm)],[d9,c12]) ).
cnf(d16,plain,
product(X0,multiply(X1,X2),multiply(multiply(X0,X1),X2)),
inference(resolution,[status(thm)],[d15,c12]) ).
cnf(d17,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(resolution,[status(thm)],[d16,d8]) ).
cnf(d18,plain,
product(X0,multiply(X0,X0),identity),
inference(resolution,[status(thm)],[c12,c0]) ).
cnf(d19,plain,
( ~ product(X1,multiply(X1,X1),X0)
| X0 = identity ),
inference(resolution,[status(thm)],[d18,c13]) ).
cnf(d20,plain,
multiply(X0,multiply(X0,X0)) = identity,
inference(resolution,[status(thm)],[d19,c12]) ).
cnf(d21,plain,
product(X0,multiply(multiply(X0,X0),X1),multiply(identity,X1)),
inference(superposition,[status(thm)],[d20,d16]) ).
cnf(d22,plain,
product(X0,multiply(X0,multiply(X0,X1)),multiply(identity,X1)),
inference(demodulation,[status(thm)],[d21,d17]) ).
cnf(d23,plain,
product(X1,multiply(X1,multiply(X1,X0)),X0),
inference(demodulation,[status(thm)],[d22,d14]) ).
cnf(d24,plain,
( ~ product(a,b,X0)
| X0 = c ),
inference(resolution,[status(thm)],[c13,c2]) ).
cnf(d25,plain,
multiply(a,b) = c,
inference(resolution,[status(thm)],[d24,c12]) ).
cnf(d26,plain,
product(a,multiply(a,c),b),
inference(superposition,[status(thm)],[d25,d23]) ).
cnf(d27,plain,
product(d,b,multiply(c,multiply(a,c))),
inference(resolution,[status(thm)],[d26,d13]) ).
cnf(d28,plain,
multiply(c,multiply(a,c)) = multiply(d,b),
inference(resolution,[status(thm)],[d27,d8]) ).
cnf(d29,plain,
( ~ product(inverse(X0),X2,X1)
| product(X0,X1,multiply(identity,X2)) ),
inference(resolution,[status(thm)],[d9,c11]) ).
cnf(d30,plain,
( ~ product(inverse(X1),X0,X2)
| product(X1,X2,X0) ),
inference(demodulation,[status(thm)],[d29,d14]) ).
cnf(d31,plain,
( ~ product(X1,identity,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c13,c9]) ).
cnf(d32,plain,
product(X0,identity,inverse(inverse(X0))),
inference(resolution,[status(thm)],[d30,c11]) ).
cnf(d33,plain,
inverse(inverse(X0)) = X0,
inference(resolution,[status(thm)],[d32,d31]) ).
cnf(d34,plain,
( product(X2,inverse(X0),X1)
| ~ product(X1,X0,X2) ),
inference(superposition,[status(thm)],[d33,d11]) ).
cnf(d35,plain,
( ~ product(b,X1,X0)
| product(a,X0,multiply(c,X1)) ),
inference(resolution,[status(thm)],[d9,c2]) ).
cnf(d36,plain,
product(a,multiply(b,X0),multiply(c,X0)),
inference(resolution,[status(thm)],[d35,c12]) ).
cnf(d37,plain,
( ~ product(X0,X2,X1)
| product(inverse(X0),X1,multiply(identity,X2)) ),
inference(resolution,[status(thm)],[d9,c10]) ).
cnf(d38,plain,
( product(inverse(X1),X2,X0)
| ~ product(X1,X0,X2) ),
inference(demodulation,[status(thm)],[d37,d14]) ).
cnf(d39,plain,
product(inverse(X0),identity,multiply(X0,X0)),
inference(resolution,[status(thm)],[d38,d18]) ).
cnf(d40,plain,
multiply(X0,X0) = inverse(X0),
inference(resolution,[status(thm)],[d39,d31]) ).
cnf(d41,plain,
product(a,multiply(b,c),inverse(c)),
inference(superposition,[status(thm)],[d40,d36]) ).
cnf(d42,plain,
product(inverse(c),inverse(multiply(b,c)),a),
inference(resolution,[status(thm)],[d41,d34]) ).
cnf(d43,plain,
product(c,a,inverse(multiply(b,c))),
inference(resolution,[status(thm)],[d42,d30]) ).
cnf(d44,plain,
inverse(multiply(b,c)) = multiply(c,a),
inference(resolution,[status(thm)],[d43,d8]) ).
cnf(d45,plain,
product(multiply(X0,X0),X0,identity),
inference(resolution,[status(thm)],[c12,c1]) ).
cnf(d46,plain,
( ~ product(X3,multiply(X1,X1),X0)
| ~ product(X3,identity,X2)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c15,d45]) ).
cnf(d47,plain,
( product(X2,X1,X0)
| ~ product(X0,multiply(X1,X1),X2) ),
inference(resolution,[status(thm)],[d46,c9]) ).
cnf(d48,plain,
product(multiply(multiply(X0,X1),X1),X1,X0),
inference(resolution,[status(thm)],[d16,d47]) ).
cnf(d49,plain,
product(inverse(a),c,b),
inference(resolution,[status(thm)],[d38,c2]) ).
cnf(d50,plain,
b = multiply(inverse(a),c),
inference(resolution,[status(thm)],[d49,d8]) ).
cnf(d51,plain,
product(multiply(b,c),c,inverse(a)),
inference(superposition,[status(thm)],[d50,d48]) ).
cnf(d52,plain,
product(inverse(X0),multiply(X0,X1),X1),
inference(resolution,[status(thm)],[d38,c12]) ).
cnf(d53,plain,
product(X0,X0,inverse(X0)),
inference(resolution,[status(thm)],[d52,d47]) ).
cnf(d54,plain,
( ~ product(X0,X2,X1)
| product(X0,X1,multiply(inverse(X0),X2)) ),
inference(resolution,[status(thm)],[d53,d9]) ).
cnf(d55,plain,
product(multiply(b,c),inverse(a),multiply(inverse(multiply(b,c)),c)),
inference(resolution,[status(thm)],[d54,d51]) ).
cnf(d56,plain,
product(multiply(b,c),inverse(a),multiply(multiply(c,a),c)),
inference(demodulation,[status(thm)],[d55,d44]) ).
cnf(d57,plain,
product(multiply(b,c),inverse(a),multiply(c,multiply(a,c))),
inference(demodulation,[status(thm)],[d56,d17]) ).
cnf(d58,plain,
product(multiply(b,c),inverse(a),multiply(d,b)),
inference(demodulation,[status(thm)],[d57,d28]) ).
cnf(d59,plain,
multiply(d,b) = multiply(b,d),
inference(resolution,[status(thm)],[d58,d7]) ).
cnf(d60,plain,
( ~ product(X2,X0,h)
| product(X2,X1,j)
| ~ product(X0,b,X1) ),
inference(resolution,[status(thm)],[c14,c5]) ).
cnf(d61,plain,
( ~ product(inverse(b),b,X0)
| product(d,X0,j) ),
inference(resolution,[status(thm)],[d60,c4]) ).
cnf(d62,plain,
product(d,identity,j),
inference(resolution,[status(thm)],[d61,c10]) ).
cnf(d63,plain,
j = d,
inference(resolution,[status(thm)],[d62,d31]) ).
cnf(d64,plain,
product(X0,j,multiply(multiply(X0,h),b)),
inference(resolution,[status(thm)],[d15,c5]) ).
cnf(d65,plain,
product(X0,d,multiply(multiply(X0,h),b)),
inference(demodulation,[status(thm)],[d64,d63]) ).
cnf(d66,plain,
( ~ product(X2,X0,X3)
| product(X2,X1,X3)
| ~ product(X0,identity,X1) ),
inference(resolution,[status(thm)],[c14,c9]) ).
cnf(d67,plain,
( ~ product(inverse(h),identity,X0)
| product(j,X0,k) ),
inference(resolution,[status(thm)],[d66,c6]) ).
cnf(d68,plain,
product(j,inverse(h),k),
inference(resolution,[status(thm)],[d67,c9]) ).
cnf(d69,plain,
product(d,inverse(h),k),
inference(demodulation,[status(thm)],[d68,d63]) ).
cnf(d70,plain,
product(k,h,d),
inference(resolution,[status(thm)],[d11,d69]) ).
cnf(d71,plain,
d = multiply(k,h),
inference(resolution,[status(thm)],[d70,d8]) ).
cnf(d72,plain,
product(k,d,multiply(d,b)),
inference(superposition,[status(thm)],[d71,d65]) ).
cnf(d73,plain,
product(multiply(d,b),inverse(d),k),
inference(resolution,[status(thm)],[d34,d72]) ).
cnf(d74,plain,
product(multiply(b,d),inverse(d),k),
inference(demodulation,[status(thm)],[d73,d59]) ).
cnf(d75,plain,
k = b,
inference(resolution,[status(thm)],[d74,d3]) ).
cnf(d76,plain,
~ product(b,inverse(b),identity),
inference(demodulation,[status(thm)],[c7,d75]) ).
cnf(d77,plain,
$false,
inference(resolution,[status(thm)],[c11,d76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 14:10:48 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 92.43/17.91 % SZS status Unsatisfiable for theBenchmark.p
% 92.43/17.91 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------