%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : GRP037-3 : 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 : 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 06:26:42 PM UTC 2025
% Result : Unsatisfiable 5.97s 1.09s
% Output : CNFRefutation 5.97s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named prove_two_inverses_are_equal)
% Comments :
%------------------------------------------------------------------------------
cnf(18,plain,
inverse(a) != another_inverse(a),
inference(cnf,[status(esa)],[prove_two_inverses_are_equal]) ).
cnf(l0,plain,
inverse(a) != another_inverse(a),
inference(instantiation,[status(thm)],[18]) ).
cnf(14,plain,
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| X3 = X1 ),
inference(cnf,[status(esa)],[product_right_cancellation]) ).
cnf(l1,plain,
( ~ product(a,another_inverse(a),another_identity)
| ~ product(a,inverse(a),another_identity)
| inverse(a) = another_inverse(a) ),
inference(instantiation,[status(thm)],[14]) ).
cnf(11,plain,
( ~ subgroup_member(X0)
| product(X0,another_inverse(X0),another_identity) ),
inference(cnf,[status(esa)],[another_right_inverse]) ).
cnf(l2,plain,
( ~ subgroup_member(a)
| product(a,another_inverse(a),another_identity) ),
inference(instantiation,[status(thm)],[11]) ).
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(l4,plain,
( ~ product(another_identity,a,a)
| ~ product(another_identity,multiply(identity,identity),another_identity)
| ~ product(a,inverse(a),multiply(identity,identity))
| product(a,inverse(a),another_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(l8,plain,
( ~ product(another_identity,identity,another_identity)
| ~ product(identity,identity,multiply(identity,identity))
| ~ product(another_identity,identity,another_identity)
| product(another_identity,multiply(identity,identity),another_identity) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(16,plain,
subgroup_member(a),
inference(cnf,[status(esa)],[a_is_in_subgroup]) ).
cnf(l3,plain,
subgroup_member(a),
inference(instantiation,[status(thm)],[16]) ).
cnf(1,plain,
product(X0,identity,X0),
inference(cnf,[status(esa)],[right_identity]) ).
cnf(l19,plain,
product(another_identity,identity,another_identity),
inference(instantiation,[status(thm)],[1]) ).
cnf(l23,plain,
product(another_identity,identity,another_identity),
inference(instantiation,[status(thm)],[1]) ).
cnf(l6,plain,
( ~ product(a,inverse(a),identity)
| ~ product(inverse(a),identity,inverse(a))
| ~ product(identity,identity,multiply(identity,identity))
| product(a,inverse(a),multiply(identity,identity)) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(9,plain,
( ~ subgroup_member(X0)
| product(another_identity,X0,X0) ),
inference(cnf,[status(esa)],[another_left_identity]) ).
cnf(l10,plain,
( ~ subgroup_member(a)
| product(another_identity,a,a) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(l15,plain,
subgroup_member(a),
inference(instantiation,[status(thm)],[16]) ).
cnf(4,plain,
product(X0,X1,multiply(X0,X1)),
inference(cnf,[status(esa)],[total_function1]) ).
cnf(l13,plain,
product(identity,identity,multiply(identity,identity)),
inference(instantiation,[status(thm)],[4]) ).
cnf(3,plain,
product(X0,inverse(X0),identity),
inference(cnf,[status(esa)],[right_inverse]) ).
cnf(l16,plain,
product(a,inverse(a),identity),
inference(instantiation,[status(thm)],[3]) ).
cnf(l9,plain,
product(inverse(a),identity,inverse(a)),
inference(instantiation,[status(thm)],[1]) ).
cnf(l20,plain,
product(identity,identity,multiply(identity,identity)),
inference(instantiation,[status(thm)],[4]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l4,l8,l3,l19,l23,l6,l10,l15,l13,l16,l9,l20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP037-3 : TPTP v9.0.0. Released v1.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Jul 20 13:31:04 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.19/0.34 % launching worker at depth: 1
% 0.19/0.34 % launching worker at depth: 8
% 0.19/0.34 % launching worker at depth: 3
% 0.19/0.34 % launching worker at depth: 4
% 0.19/0.34 % launching worker at depth: 5
% 0.19/0.34 % launching worker at depth: 6
% 0.19/0.34 % launching worker at depth: 7
% 0.19/0.34 % launching worker at depth: 2
% 0.19/0.35 % launching worker at depth: 9
% 0.19/0.35 % launching worker at depth: 10
% 3.51/0.79 % launching worker at depth: 11
% 5.97/1.09 % SZS status Theorem for theBenchmark
% 5.97/1.09 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------