%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : ALG002-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 11:49:26 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.42s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 12:57:45 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.42 % Refutation found
% 0.13/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.42 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.42 fof(f1,axiom,(
% 0.13/0.42 (![X]: (product(X,multiplicative_identity,X) ))),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f2,axiom,(
% 0.13/0.42 ~ product(multiplicative_identity,multiplicative_identity,additive_identity) ),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f4,axiom,(
% 0.13/0.42 (![X,Y,Z]: (( product(X,Y,Z)| ~ product(additive_inverse(X),additive_inverse(Y),Z) ) ))),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f5,axiom,(
% 0.13/0.42 (![X,Y,Z]: (( ~ product(X,Y,Z)| product(X,additive_inverse(Y),additive_inverse(Z)) ) ))),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f6,axiom,(
% 0.13/0.42 (![X]: (( product(X,multiplicative_inverse(X),multiplicative_identity)| product(X,X,additive_identity) ) ))),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f7,axiom,(
% 0.13/0.42 (![X]: (( ~ greater_than_0(X)| ~ greater_than_0(additive_inverse(X)) ) ))),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f8,axiom,(
% 0.13/0.42 (![X]: (( ~ greater_than_0(X)| ~ product(X,X,additive_identity) ) ))),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f9,axiom,(
% 0.13/0.42 (![X,Y,Z]: (( ~ product(X,Y,Z)| product(Y,X,Z) ) ))),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f10,axiom,(
% 0.13/0.42 (![X]: (( greater_than_0(X)| product(X,X,additive_identity)| greater_than_0(additive_inverse(X)) ) ))),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f11,axiom,(
% 0.13/0.42 (![Y,Z,X]: (( ~ product(Y,Z,X)| ~ product(Y,Y,additive_identity)| product(X,X,additive_identity) ) ))),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f12,axiom,(
% 0.13/0.42 (![Y,Z,X]: (( ~ product(Y,Z,X)| ~ greater_than_0(Y)| ~ greater_than_0(Z)| greater_than_0(X) ) ))),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f13,hypothesis,(
% 0.13/0.42 greater_than_0(a) ),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f14,negated_conjecture,(
% 0.13/0.42 ~ greater_than_0(multiplicative_inverse(a)) ),
% 0.13/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f15,plain,(
% 0.13/0.42 ![X0]: (product(X0,multiplicative_identity,X0))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f1])).
% 0.13/0.42 fof(f16,plain,(
% 0.13/0.42 ~product(multiplicative_identity,multiplicative_identity,additive_identity)),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f2])).
% 0.13/0.42 fof(f18,plain,(
% 0.13/0.42 ![X0,X1,X2]: (product(X0,X1,X2)|~product(additive_inverse(X0),additive_inverse(X1),X2))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f4])).
% 0.13/0.42 fof(f19,plain,(
% 0.13/0.42 ![X0,X1,X2]: (~product(X0,X1,X2)|product(X0,additive_inverse(X1),additive_inverse(X2)))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f5])).
% 0.13/0.42 fof(f20,plain,(
% 0.13/0.42 ![X0]: (product(X0,multiplicative_inverse(X0),multiplicative_identity)|product(X0,X0,additive_identity))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f6])).
% 0.13/0.42 fof(f21,plain,(
% 0.13/0.42 ![X0]: (~greater_than_0(X0)|~greater_than_0(additive_inverse(X0)))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f7])).
% 0.13/0.42 fof(f22,plain,(
% 0.13/0.42 ![X0]: (~greater_than_0(X0)|~product(X0,X0,additive_identity))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f8])).
% 0.13/0.42 fof(f23,plain,(
% 0.13/0.42 ![X0,X1,X2]: (~product(X0,X1,X2)|product(X1,X0,X2))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f9])).
% 0.13/0.42 fof(f24,plain,(
% 0.13/0.42 ![X0]: (greater_than_0(X0)|product(X0,X0,additive_identity)|greater_than_0(additive_inverse(X0)))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f10])).
% 0.13/0.42 fof(f25,plain,(
% 0.13/0.42 ![X]: ((![Y]: ((![Z]: ~product(Y,Z,X))|~product(Y,Y,additive_identity)))|product(X,X,additive_identity))),
% 0.13/0.42 inference(miniscoping,[status(thm)],[f11])).
% 0.13/0.42 fof(f26,plain,(
% 0.13/0.42 ![X0,X1,X2]: (~product(X0,X1,X2)|~product(X0,X0,additive_identity)|product(X2,X2,additive_identity))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f25])).
% 0.13/0.42 fof(f27,plain,(
% 0.13/0.42 ![X]: ((![Z]: ((![Y]: (~product(Y,Z,X)|~greater_than_0(Y)))|~greater_than_0(Z)))|greater_than_0(X))),
% 0.13/0.42 inference(miniscoping,[status(thm)],[f12])).
% 0.13/0.42 fof(f28,plain,(
% 0.13/0.42 ![X0,X1,X2]: (~product(X0,X1,X2)|~greater_than_0(X0)|~greater_than_0(X1)|greater_than_0(X2))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f27])).
% 0.13/0.42 fof(f29,plain,(
% 0.13/0.42 greater_than_0(a)),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f13])).
% 0.13/0.42 fof(f30,plain,(
% 0.13/0.42 ~greater_than_0(multiplicative_inverse(a))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f14])).
% 0.13/0.42 fof(f31,plain,(
% 0.13/0.42 ![X0,X1]: (~product(X0,a,X1)|~greater_than_0(X0)|greater_than_0(X1))),
% 0.13/0.42 inference(resolution,[status(thm)],[f28,f29])).
% 0.13/0.42 fof(f33,plain,(
% 0.13/0.42 ~product(a,a,additive_identity)),
% 0.13/0.42 inference(resolution,[status(thm)],[f22,f29])).
% 0.13/0.42 fof(f36,plain,(
% 0.13/0.42 ![X0]: (product(multiplicative_inverse(X0),X0,multiplicative_identity)|product(X0,X0,additive_identity))),
% 0.13/0.42 inference(resolution,[status(thm)],[f23,f20])).
% 0.13/0.42 fof(f39,plain,(
% 0.13/0.42 ![X0,X1,X2]: (~product(additive_inverse(X0),X1,X2)|product(X0,X1,additive_inverse(X2)))),
% 0.13/0.42 inference(resolution,[status(thm)],[f19,f18])).
% 0.13/0.42 fof(f40,plain,(
% 0.13/0.42 ![X0,X1,X2]: (~product(X0,X1,X2)|product(additive_inverse(X1),X0,additive_inverse(X2)))),
% 0.13/0.42 inference(resolution,[status(thm)],[f19,f23])).
% 0.13/0.42 fof(f43,plain,(
% 0.13/0.42 greater_than_0(multiplicative_identity)|greater_than_0(additive_inverse(multiplicative_identity))),
% 0.13/0.42 inference(resolution,[status(thm)],[f24,f16])).
% 0.13/0.42 fof(f47,plain,(
% 0.13/0.42 ![X0,X1,X2]: (~product(X0,X1,X2)|product(X2,X2,additive_identity)|greater_than_0(X0)|greater_than_0(additive_inverse(X0)))),
% 0.13/0.42 inference(resolution,[status(thm)],[f26,f24])).
% 0.13/0.42 fof(f55,plain,(
% 0.13/0.42 ![X0,X1]: (greater_than_0(multiplicative_identity)|~product(X0,additive_inverse(multiplicative_identity),X1)|~greater_than_0(X0)|greater_than_0(X1))),
% 0.13/0.42 inference(resolution,[status(thm)],[f43,f28])).
% 0.13/0.42 fof(f57,plain,(
% 0.13/0.42 ![X0]: (greater_than_0(multiplicative_identity)|~product(a,additive_inverse(multiplicative_identity),X0)|greater_than_0(X0))),
% 0.13/0.42 inference(resolution,[status(thm)],[f55,f29])).
% 0.13/0.42 fof(f59,plain,(
% 0.13/0.42 ![X0]: (greater_than_0(multiplicative_identity)|greater_than_0(additive_inverse(X0))|~product(a,multiplicative_identity,X0))),
% 0.13/0.42 inference(resolution,[status(thm)],[f57,f19])).
% 0.13/0.42 fof(f60,plain,(
% 0.13/0.42 greater_than_0(multiplicative_identity)|greater_than_0(additive_inverse(a))),
% 0.13/0.42 inference(resolution,[status(thm)],[f59,f15])).
% 0.13/0.42 fof(f61,plain,(
% 0.13/0.42 greater_than_0(multiplicative_identity)|~greater_than_0(a)),
% 0.13/0.42 inference(resolution,[status(thm)],[f60,f21])).
% 0.13/0.42 fof(f65,plain,(
% 0.13/0.42 greater_than_0(multiplicative_identity)),
% 0.13/0.42 inference(forward_subsumption_resolution,[status(thm)],[f61,f29])).
% 0.13/0.42 fof(f68,plain,(
% 0.13/0.42 ![X0,X1]: (~product(X0,multiplicative_identity,X1)|~greater_than_0(X0)|greater_than_0(X1))),
% 0.13/0.42 inference(resolution,[status(thm)],[f65,f28])).
% 0.13/0.42 fof(f69,plain,(
% 0.13/0.42 ![X0]: (~product(multiplicative_identity,multiplicative_identity,X0)|greater_than_0(X0))),
% 0.13/0.42 inference(resolution,[status(thm)],[f68,f65])).
% 0.13/0.42 fof(f78,plain,(
% 0.13/0.42 ![X0]: (product(X0,multiplicative_identity,additive_inverse(additive_inverse(X0))))),
% 0.13/0.42 inference(resolution,[status(thm)],[f39,f15])).
% 0.13/0.42 fof(f83,plain,(
% 0.13/0.42 greater_than_0(additive_inverse(additive_inverse(multiplicative_identity)))),
% 0.13/0.42 inference(resolution,[status(thm)],[f78,f69])).
% 0.13/0.42 fof(f91,plain,(
% 0.13/0.42 ![X0,X1]: (~product(a,X0,X1)|~greater_than_0(additive_inverse(X0))|greater_than_0(additive_inverse(X1)))),
% 0.13/0.42 inference(resolution,[status(thm)],[f40,f31])).
% 0.13/0.42 fof(f105,plain,(
% 0.13/0.42 ~greater_than_0(additive_inverse(multiplicative_identity))),
% 0.13/0.42 inference(resolution,[status(thm)],[f83,f21])).
% 0.13/0.42 fof(f149,plain,(
% 0.13/0.42 ![X0,X1]: (~product(X0,X1,multiplicative_identity)|greater_than_0(X0)|greater_than_0(additive_inverse(X0)))),
% 0.13/0.42 inference(resolution,[status(thm)],[f47,f16])).
% 0.13/0.42 fof(f224,plain,(
% 0.13/0.42 ![X0]: (greater_than_0(multiplicative_inverse(X0))|greater_than_0(additive_inverse(multiplicative_inverse(X0)))|product(X0,X0,additive_identity))),
% 0.13/0.42 inference(resolution,[status(thm)],[f149,f36])).
% 0.13/0.42 fof(f370,plain,(
% 0.13/0.42 greater_than_0(multiplicative_inverse(a))|greater_than_0(additive_inverse(multiplicative_inverse(a)))),
% 0.13/0.42 inference(resolution,[status(thm)],[f224,f33])).
% 0.13/0.42 fof(f382,plain,(
% 0.13/0.42 greater_than_0(additive_inverse(multiplicative_inverse(a)))),
% 0.13/0.42 inference(forward_subsumption_resolution,[status(thm)],[f370,f30])).
% 0.13/0.42 fof(f392,plain,(
% 0.13/0.42 ![X0]: (~product(a,multiplicative_inverse(a),X0)|greater_than_0(additive_inverse(X0)))),
% 0.13/0.42 inference(resolution,[status(thm)],[f382,f91])).
% 0.13/0.42 fof(f443,plain,(
% 0.13/0.42 greater_than_0(additive_inverse(multiplicative_identity))|product(a,a,additive_identity)),
% 0.13/0.42 inference(resolution,[status(thm)],[f392,f20])).
% 0.13/0.42 fof(f448,plain,(
% 0.13/0.42 product(a,a,additive_identity)),
% 0.13/0.42 inference(forward_subsumption_resolution,[status(thm)],[f443,f105])).
% 0.13/0.42 fof(f449,plain,(
% 0.13/0.42 $false),
% 0.13/0.42 inference(forward_subsumption_resolution,[status(thm)],[f448,f33])).
% 0.13/0.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.44 % Elapsed time: 0.078546 seconds
% 0.13/0.44 % CPU time: 0.425822 seconds
% 0.13/0.44 % Total memory used: 22.905 MB
% 0.13/0.44 % Net memory used: 21.792 MB
%------------------------------------------------------------------------------