%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : RNG038-2 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Jul 25 03:02:42 PM UTC 2025
% Result : Unsatisfiable 4.12s 0.89s
% Output : CNFRefutation 4.12s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named a_not_additive_identity)
% Comments :
%------------------------------------------------------------------------------
cnf(28,plain,
~ equalish(a,additive_identity),
inference(cnf,[status(esa)],[a_not_additive_identity]) ).
cnf(l0,plain,
~ equalish(a,additive_identity),
inference(instantiation,[status(thm)],[28]) ).
cnf(23,plain,
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| equalish(X2,X3) ),
inference(cnf,[status(esa)],[multiplication_is_well_defined]) ).
cnf(l1,plain,
( ~ product(additive_identity,h(additive_identity,a),a)
| ~ product(additive_identity,h(additive_identity,a),additive_identity)
| equalish(a,additive_identity) ),
inference(instantiation,[status(thm)],[23]) ).
cnf(26,plain,
( ~ equalish(X0,additive_identity)
| product(X0,h(X0,X1),X1) ),
inference(cnf,[status(esa)],[some_property]) ).
cnf(l2,plain,
( ~ equalish(additive_identity,additive_identity)
| product(additive_identity,h(additive_identity,a),a) ),
inference(instantiation,[status(thm)],[26]) ).
cnf(19,plain,
( ~ sum(X0,X1,X2)
| ~ sum(X3,X4,X5)
| ~ product(X6,X0,X3)
| ~ product(X6,X1,X4)
| product(X6,X2,X5) ),
inference(cnf,[status(esa)],[distributivity2]) ).
cnf(l4,plain,
( ~ sum(additive_identity,additive_inverse(additive_inverse(h(additive_identity,a))),h(additive_identity,a))
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ product(additive_identity,additive_identity,additive_identity)
| ~ product(additive_identity,additive_inverse(additive_inverse(h(additive_identity,a))),additive_identity)
| product(additive_identity,h(additive_identity,a),additive_identity) ),
inference(instantiation,[status(thm)],[19]) ).
cnf(20,plain,
( ~ sum(X0,X1,X2)
| ~ product(X0,X3,X4)
| ~ product(X1,X3,X5)
| ~ product(X2,X3,X6)
| sum(X4,X5,X6) ),
inference(cnf,[status(esa)],[distributivity3]) ).
cnf(l15,plain,
( ~ sum(a,additive_identity,a)
| ~ product(a,b,additive_identity)
| ~ product(additive_identity,b,additive_identity)
| ~ product(a,b,additive_identity)
| sum(additive_identity,additive_identity,additive_identity) ),
inference(instantiation,[status(thm)],[20]) ).
cnf(25,plain,
product(X0,additive_identity,additive_identity),
inference(cnf,[status(esa)],[multiplicative_identity2]) ).
cnf(l13,plain,
product(additive_identity,additive_identity,additive_identity),
inference(instantiation,[status(thm)],[25]) ).
cnf(22,plain,
( ~ sum(X0,X1,X2)
| ~ sum(X0,X1,X3)
| equalish(X2,X3) ),
inference(cnf,[status(esa)],[addition_is_well_defined]) ).
cnf(l3,plain,
( ~ sum(X0_5,additive_inverse(X0_5),additive_identity)
| ~ sum(X0_5,additive_inverse(X0_5),additive_identity)
| equalish(additive_identity,additive_identity) ),
inference(instantiation,[status(thm)],[22]) ).
cnf(17,plain,
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X4)
| ~ product(X1,X5,X3)
| product(X2,X5,X4) ),
inference(cnf,[status(esa)],[associativity_of_multiplication2]) ).
cnf(l6,plain,
( ~ product(additive_identity,additive_identity,additive_identity)
| ~ product(additive_identity,multiply(additive_identity,additive_inverse(additive_inverse(h(additive_identity,a)))),additive_identity)
| ~ product(additive_identity,additive_inverse(additive_inverse(h(additive_identity,a))),multiply(additive_identity,additive_inverse(additive_inverse(h(additive_identity,a)))))
| product(additive_identity,additive_inverse(additive_inverse(h(additive_identity,a))),additive_identity) ),
inference(instantiation,[status(thm)],[17]) ).
cnf(9,plain,
sum(X0,additive_identity,X0),
inference(cnf,[status(esa)],[additive_identity2]) ).
cnf(l16,plain,
sum(a,additive_identity,a),
inference(instantiation,[status(thm)],[9]) ).
cnf(12,plain,
sum(X0,additive_inverse(X0),additive_identity),
inference(cnf,[status(esa)],[additive_inverse2]) ).
cnf(l10,plain,
sum(X0_5,additive_inverse(X0_5),additive_identity),
inference(instantiation,[status(thm)],[12]) ).
cnf(l9,plain,
product(additive_identity,additive_identity,additive_identity),
inference(instantiation,[status(thm)],[25]) ).
cnf(14,plain,
( ~ sum(X0,X1,X2)
| ~ sum(X0,X3,X4)
| ~ sum(X1,X5,X3)
| sum(X2,X5,X4) ),
inference(cnf,[status(esa)],[associativity_of_addition2]) ).
cnf(l8,plain,
( ~ sum(h(additive_identity,a),additive_inverse(h(additive_identity,a)),additive_identity)
| ~ sum(h(additive_identity,a),additive_identity,h(additive_identity,a))
| ~ sum(additive_inverse(h(additive_identity,a)),additive_inverse(additive_inverse(h(additive_identity,a))),additive_identity)
| sum(additive_identity,additive_inverse(additive_inverse(h(additive_identity,a))),h(additive_identity,a)) ),
inference(instantiation,[status(thm)],[14]) ).
cnf(l37,plain,
sum(h(additive_identity,a),additive_identity,h(additive_identity,a)),
inference(instantiation,[status(thm)],[9]) ).
cnf(24,plain,
product(additive_identity,X0,additive_identity),
inference(cnf,[status(esa)],[multiplicative_identity1]) ).
cnf(l21,plain,
product(additive_identity,multiply(additive_identity,additive_inverse(additive_inverse(h(additive_identity,a)))),additive_identity),
inference(instantiation,[status(thm)],[24]) ).
cnf(27,plain,
product(a,b,additive_identity),
inference(cnf,[status(esa)],[a_times_b]) ).
cnf(l17,plain,
product(a,b,additive_identity),
inference(instantiation,[status(thm)],[27]) ).
cnf(l40,plain,
sum(additive_inverse(h(additive_identity,a)),additive_inverse(additive_inverse(h(additive_identity,a))),additive_identity),
inference(instantiation,[status(thm)],[12]) ).
cnf(l20,plain,
product(additive_identity,b,additive_identity),
inference(instantiation,[status(thm)],[24]) ).
cnf(l5,plain,
sum(X0_5,additive_inverse(X0_5),additive_identity),
inference(instantiation,[status(thm)],[12]) ).
cnf(10,plain,
product(X0,X1,multiply(X0,X1)),
inference(cnf,[status(esa)],[closure_of_multiplication]) ).
cnf(l23,plain,
product(additive_identity,additive_inverse(additive_inverse(h(additive_identity,a))),multiply(additive_identity,additive_inverse(additive_inverse(h(additive_identity,a))))),
inference(instantiation,[status(thm)],[10]) ).
cnf(l33,plain,
sum(h(additive_identity,a),additive_inverse(h(additive_identity,a)),additive_identity),
inference(instantiation,[status(thm)],[12]) ).
cnf(l36,plain,
product(a,b,additive_identity),
inference(instantiation,[status(thm)],[27]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l4,l15,l13,l3,l6,l16,l10,l9,l8,l37,l21,l17,l40,l20,l5,l23,l33,l36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG038-2 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 21 17:40:04 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % launching worker at depth: 5
% 0.12/0.34 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 2
% 0.12/0.34 % launching worker at depth: 3
% 0.12/0.34 % launching worker at depth: 7
% 0.12/0.34 % launching worker at depth: 8
% 0.12/0.34 % launching worker at depth: 6
% 0.12/0.34 % launching worker at depth: 4
% 0.12/0.34 % launching worker at depth: 9
% 0.12/0.36 % launching worker at depth: 10
% 0.18/0.44 % launching worker at depth: 11
% 4.12/0.89 % SZS status Theorem for theBenchmark
% 4.12/0.89 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------