%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP048-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 : Thu Sep 24 12:35:33 PM UTC 2026
% Result : Unsatisfiable 12.76s 2.04s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP048-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n002.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sun Sep 20 19:58:31 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.36 % Drodi V4.1.1
% 12.76/2.04 % Refutation found
% 12.76/2.04 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 12.76/2.04 % SZS output start CNFRefutation for theBenchmark
% 12.76/2.04 fof(f1,axiom,(
% 12.76/2.04 (![X]: (product(identity,X,X) ))),
% 12.76/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.76/2.04 fof(f2,axiom,(
% 12.76/2.04 (![X]: (product(inverse(X),X,identity) ))),
% 12.76/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.76/2.04 fof(f3,axiom,(
% 12.76/2.04 (![X,Y]: (product(X,Y,multiply(X,Y)) ))),
% 12.76/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.76/2.04 fof(f4,axiom,(
% 12.76/2.04 (![X,Y,Z,W]: (( ~ product(X,Y,Z)| ~ product(X,Y,W)| equalish(Z,W) ) ))),
% 12.76/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.76/2.04 fof(f5,axiom,(
% 12.76/2.04 (![X,Y,U,Z,V,W]: (( ~ product(X,Y,U)| ~ product(Y,Z,V)| ~ product(U,Z,W)| product(X,V,W) ) ))),
% 12.76/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.76/2.04 fof(f7,axiom,(
% 12.76/2.04 (![X,Y,W,Z]: (( ~ equalish(X,Y)| ~ product(W,Z,X)| product(W,Z,Y) ) ))),
% 12.76/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.76/2.04 fof(f8,hypothesis,(
% 12.76/2.04 equalish(a,b) ),
% 12.76/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.76/2.04 fof(f9,negated_conjecture,(
% 12.76/2.04 ~ equalish(inverse(a),inverse(b)) ),
% 12.76/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 12.76/2.04 fof(f10,plain,(
% 12.76/2.04 ![X0]: (product(identity,X0,X0))),
% 12.76/2.04 inference(cnf_transformation,[status(thm)],[f1])).
% 12.76/2.04 fof(f11,plain,(
% 12.76/2.04 ![X0]: (product(inverse(X0),X0,identity))),
% 12.76/2.04 inference(cnf_transformation,[status(thm)],[f2])).
% 12.76/2.04 fof(f12,plain,(
% 12.76/2.04 ![X0,X1]: (product(X0,X1,multiply(X0,X1)))),
% 12.76/2.04 inference(cnf_transformation,[status(thm)],[f3])).
% 12.76/2.04 fof(f13,plain,(
% 12.76/2.04 ![Z,W]: ((![X,Y]: (~product(X,Y,Z)|~product(X,Y,W)))|equalish(Z,W))),
% 12.76/2.04 inference(miniscoping,[status(thm)],[f4])).
% 12.76/2.04 fof(f14,plain,(
% 12.76/2.04 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X1,X3)|equalish(X2,X3))),
% 12.76/2.04 inference(cnf_transformation,[status(thm)],[f13])).
% 12.76/2.04 fof(f15,plain,(
% 12.76/2.04 ![X,V,W]: ((![U,Z]: ((![Y]: (~product(X,Y,U)|~product(Y,Z,V)))|~product(U,Z,W)))|product(X,V,W))),
% 12.76/2.04 inference(miniscoping,[status(thm)],[f5])).
% 12.76/2.04 fof(f16,plain,(
% 12.76/2.04 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~product(X1,X3,X4)|~product(X2,X3,X5)|product(X0,X4,X5))),
% 12.76/2.04 inference(cnf_transformation,[status(thm)],[f15])).
% 12.76/2.04 fof(f19,plain,(
% 12.76/2.04 ![Y,W,Z]: ((![X]: (~equalish(X,Y)|~product(W,Z,X)))|product(W,Z,Y))),
% 12.76/2.04 inference(miniscoping,[status(thm)],[f7])).
% 12.76/2.04 fof(f20,plain,(
% 12.76/2.04 ![X0,X1,X2,X3]: (~equalish(X0,X1)|~product(X2,X3,X0)|product(X2,X3,X1))),
% 12.76/2.04 inference(cnf_transformation,[status(thm)],[f19])).
% 12.76/2.04 fof(f21,plain,(
% 12.76/2.04 equalish(a,b)),
% 12.76/2.04 inference(cnf_transformation,[status(thm)],[f8])).
% 12.76/2.04 fof(f22,plain,(
% 12.76/2.04 ~equalish(inverse(a),inverse(b))),
% 12.76/2.04 inference(cnf_transformation,[status(thm)],[f9])).
% 12.76/2.04 fof(f23,plain,(
% 12.76/2.04 ![X0,X1]: (~equalish(X0,X1)|product(identity,X0,X1))),
% 12.76/2.04 inference(resolution,[status(thm)],[f10,f20])).
% 12.76/2.04 fof(f25,plain,(
% 12.76/2.04 product(identity,a,b)),
% 12.76/2.04 inference(resolution,[status(thm)],[f23,f21])).
% 12.76/2.04 fof(f44,plain,(
% 12.76/2.04 ![X0,X1]: (~product(inverse(X0),X0,X1)|equalish(X1,identity))),
% 12.76/2.04 inference(resolution,[status(thm)],[f11,f14])).
% 12.76/2.04 fof(f48,plain,(
% 12.76/2.04 ![X0,X1,X2]: (~equalish(multiply(X0,X1),X2)|product(X0,X1,X2))),
% 12.76/2.04 inference(resolution,[status(thm)],[f12,f20])).
% 12.76/2.04 fof(f76,plain,(
% 12.76/2.04 ![X0,X1,X2,X3]: (~product(X0,inverse(X1),X2)|~product(X2,X1,X3)|product(X0,identity,X3))),
% 12.76/2.04 inference(resolution,[status(thm)],[f16,f11])).
% 12.76/2.04 fof(f93,plain,(
% 12.76/2.04 ![X0,X1,X2,X3]: (~product(X0,X1,identity)|~product(X1,X2,X3)|product(X0,X3,X2))),
% 12.76/2.04 inference(resolution,[status(thm)],[f16,f10])).
% 12.76/2.04 fof(f105,plain,(
% 12.76/2.04 ![X0,X1,X2,X3,X4,X5,X6]: (~product(X0,X1,X2)|~product(X1,X3,X4)|~product(X2,X3,X5)|~product(X0,X4,X6)|equalish(X6,X5))),
% 12.76/2.04 inference(resolution,[status(thm)],[f16,f14])).
% 12.76/2.04 fof(f272,plain,(
% 12.76/2.04 ![X0,X1,X2,X3,X4]: (~product(X0,X1,X2)|~product(X1,X3,X4)|~product(X2,X3,inverse(b))|~product(X0,X4,inverse(a)))),
% 12.76/2.04 inference(resolution,[status(thm)],[f105,f22])).
% 12.76/2.04 fof(f424,plain,(
% 12.76/2.04 ![X0,X1,X2]: (~product(X0,X1,identity)|~product(X1,inverse(b),X2)|~product(X0,X2,inverse(a)))),
% 12.76/2.04 inference(resolution,[status(thm)],[f272,f10])).
% 12.76/2.04 fof(f974,plain,(
% 12.76/2.04 ![X0,X1,X2]: (~product(X0,X1,X2)|product(inverse(X0),X2,X1))),
% 12.76/2.04 inference(resolution,[status(thm)],[f93,f11])).
% 12.76/2.04 fof(f1169,plain,(
% 12.76/2.04 ![X0,X1]: (~product(X0,X1,X0)|equalish(X1,identity))),
% 12.76/2.04 inference(resolution,[status(thm)],[f974,f44])).
% 12.76/2.04 fof(f1236,plain,(
% 12.76/2.04 ![X0,X1]: (equalish(X0,identity)|~product(X1,inverse(X1),X0))),
% 12.76/2.04 inference(resolution,[status(thm)],[f1169,f974])).
% 12.76/2.04 fof(f1701,plain,(
% 12.76/2.04 ![X0]: (equalish(multiply(X0,inverse(X0)),identity))),
% 12.76/2.04 inference(resolution,[status(thm)],[f1236,f12])).
% 12.76/2.04 fof(f1708,plain,(
% 12.76/2.04 ![X0]: (product(X0,inverse(X0),identity))),
% 12.76/2.04 inference(resolution,[status(thm)],[f1701,f48])).
% 12.76/2.04 fof(f1724,plain,(
% 12.76/2.04 ![X0,X1]: (~product(identity,X0,X1)|product(X0,identity,X1))),
% 12.76/2.04 inference(resolution,[status(thm)],[f1708,f76])).
% 12.76/2.04 fof(f2219,plain,(
% 12.76/2.04 product(a,identity,b)),
% 12.76/2.04 inference(resolution,[status(thm)],[f1724,f25])).
% 12.76/2.04 fof(f2222,plain,(
% 12.76/2.04 ![X0]: (product(X0,identity,X0))),
% 12.76/2.04 inference(resolution,[status(thm)],[f1724,f10])).
% 12.76/2.04 fof(f2250,plain,(
% 12.76/2.04 ![X0]: (~product(inverse(a),X0,identity)|~product(X0,inverse(b),identity))),
% 12.76/2.04 inference(resolution,[status(thm)],[f2222,f424])).
% 12.76/2.04 fof(f2846,plain,(
% 12.76/2.04 ![X0]: (~product(X0,inverse(b),identity)|~product(a,identity,X0))),
% 12.76/2.04 inference(resolution,[status(thm)],[f2250,f974])).
% 12.76/2.04 fof(f4076,plain,(
% 12.76/2.04 ~product(a,identity,b)),
% 12.76/2.04 inference(resolution,[status(thm)],[f2846,f1708])).
% 12.76/2.04 fof(f4079,plain,(
% 12.76/2.04 $false),
% 12.76/2.04 inference(forward_subsumption_resolution,[status(thm)],[f4076,f2219])).
% 12.76/2.04 % SZS output end CNFRefutation for theBenchmark.p
% 12.76/2.07 % Elapsed time: 1.700619 seconds
% 12.76/2.07 % CPU time: 13.160138 seconds
% 12.76/2.07 % Total memory used: 104.677 MB
% 12.76/2.07 % Net memory used: 91.161 MB
%------------------------------------------------------------------------------