%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : GRP012-2 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n025.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 : Thu Jul 24 06:26:37 PM UTC 2025
% Result : Unsatisfiable 3.07s 0.72s
% Output : CNFRefutation 3.07s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named prove_c_inverse_equals_d)
% Comments :
%------------------------------------------------------------------------------
cnf(10,plain,
inverse(c) != d,
inference(cnf,[status(esa)],[prove_c_inverse_equals_d]) ).
cnf(l0,plain,
inverse(c) != d,
inference(instantiation,[status(thm)],[10]) ).
cnf(5,plain,
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| X2 = X3 ),
inference(cnf,[status(esa)],[total_function2]) ).
cnf(l1,plain,
( ~ product(identity,d,inverse(c))
| ~ product(identity,d,d)
| inverse(c) = d ),
inference(instantiation,[status(thm)],[5]) ).
cnf(0,plain,
product(identity,X0,X0),
inference(cnf,[status(esa)],[left_identity]) ).
cnf(l4,plain,
product(identity,d,d),
inference(instantiation,[status(thm)],[0]) ).
cnf(7,plain,
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X4)
| ~ product(X1,X5,X3)
| product(X2,X5,X4) ),
inference(cnf,[status(esa)],[associativity2]) ).
cnf(l2,plain,
( ~ product(multiply(inverse(c),a),b,identity)
| ~ product(multiply(inverse(c),a),inverse(a),inverse(c))
| ~ product(b,d,inverse(a))
| product(identity,d,inverse(c)) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l3,plain,
( ~ product(inverse(c),a,multiply(inverse(c),a))
| ~ product(inverse(c),c,identity)
| ~ product(a,b,c)
| product(multiply(inverse(c),a),b,identity) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(6,plain,
( ~ product(X0,X1,X2)
| ~ product(X1,X3,X4)
| ~ product(X2,X3,X5)
| product(X0,X4,X5) ),
inference(cnf,[status(esa)],[associativity1]) ).
cnf(l7,plain,
( ~ product(b,inverse(b),identity)
| ~ product(inverse(b),inverse(a),d)
| ~ product(identity,inverse(a),inverse(a))
| product(b,d,inverse(a)) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(9,plain,
product(inverse(b),inverse(a),d),
inference(cnf,[status(esa)],[inverse_b_multiply_inverse_a_is_d]) ).
cnf(l17,plain,
product(inverse(b),inverse(a),d),
inference(instantiation,[status(thm)],[9]) ).
cnf(l5,plain,
( ~ product(inverse(c),a,multiply(inverse(c),a))
| ~ product(inverse(c),identity,inverse(c))
| ~ product(a,inverse(a),identity)
| product(multiply(inverse(c),a),inverse(a),inverse(c)) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(4,plain,
product(X0,X1,multiply(X0,X1)),
inference(cnf,[status(esa)],[total_function1]) ).
cnf(l16,plain,
product(inverse(c),a,multiply(inverse(c),a)),
inference(instantiation,[status(thm)],[4]) ).
cnf(3,plain,
product(X0,inverse(X0),identity),
inference(cnf,[status(esa)],[right_inverse]) ).
cnf(l15,plain,
product(a,inverse(a),identity),
inference(instantiation,[status(thm)],[3]) ).
cnf(l32,plain,
product(inverse(c),a,multiply(inverse(c),a)),
inference(instantiation,[status(thm)],[4]) ).
cnf(1,plain,
product(X0,identity,X0),
inference(cnf,[status(esa)],[right_identity]) ).
cnf(l9,plain,
product(inverse(c),identity,inverse(c)),
inference(instantiation,[status(thm)],[1]) ).
cnf(l13,plain,
product(identity,inverse(a),inverse(a)),
inference(instantiation,[status(thm)],[0]) ).
cnf(8,plain,
product(a,b,c),
inference(cnf,[status(esa)],[a_multiply_b_is_c]) ).
cnf(l31,plain,
product(a,b,c),
inference(instantiation,[status(thm)],[8]) ).
cnf(2,plain,
product(inverse(X0),X0,identity),
inference(cnf,[status(esa)],[left_inverse]) ).
cnf(l33,plain,
product(inverse(c),c,identity),
inference(instantiation,[status(thm)],[2]) ).
cnf(l12,plain,
product(b,inverse(b),identity),
inference(instantiation,[status(thm)],[3]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l4,l2,l3,l7,l17,l5,l16,l15,l32,l9,l13,l31,l33,l12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP012-2 : TPTP v9.0.0. Released v1.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Jul 20 13:24:49 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % launching worker at depth: 1
% 0.14/0.35 % launching worker at depth: 2
% 0.14/0.35 % launching worker at depth: 7
% 0.14/0.35 % launching worker at depth: 4
% 0.14/0.35 % launching worker at depth: 8
% 0.14/0.35 % launching worker at depth: 5
% 0.14/0.35 % launching worker at depth: 6
% 0.14/0.35 % launching worker at depth: 3
% 0.14/0.35 % launching worker at depth: 9
% 0.14/0.35 % launching worker at depth: 10
% 0.20/0.47 % launching worker at depth: 11
% 3.07/0.72 % SZS status Theorem for theBenchmark
% 3.07/0.72 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------