%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : CAT010-1 : 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 : n026.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 12:07:42 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.51s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n026.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 13:58:36 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.12/0.51 % Refutation found
% 0.12/0.51 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.51 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.51 fof(f1,axiom,(
% 0.12/0.51 (![X,Y]: (( ~ defined(X,Y)| product(X,Y,compose(X,Y)) ) ))),
% 0.12/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.51 fof(f2,axiom,(
% 0.12/0.51 (![X,Y,Z]: (( ~ product(X,Y,Z)| defined(X,Y) ) ))),
% 0.12/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.51 fof(f4,axiom,(
% 0.12/0.51 (![X,Y,Xy,Z,Yz]: (( ~ product(X,Y,Xy)| ~ product(Y,Z,Yz)| ~ defined(Xy,Z)| defined(X,Yz) ) ))),
% 0.12/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.51 fof(f6,axiom,(
% 0.12/0.51 (![Y,Z,Yz,X]: (( ~ product(Y,Z,Yz)| ~ defined(X,Yz)| defined(X,Y) ) ))),
% 0.12/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.51 fof(f11,axiom,(
% 0.12/0.51 (![X]: (identity_map(codomain(X)) ))),
% 0.12/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.51 fof(f15,axiom,(
% 0.12/0.51 (![X]: (product(codomain(X),X,X) ))),
% 0.12/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.51 fof(f16,axiom,(
% 0.12/0.51 (![X,Y]: (( ~ defined(X,Y)| ~ identity_map(X)| product(X,Y,Y) ) ))),
% 0.12/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.51 fof(f17,axiom,(
% 0.12/0.51 (![X,Y]: (( ~ defined(X,Y)| ~ identity_map(Y)| product(X,Y,X) ) ))),
% 0.12/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.51 fof(f18,axiom,(
% 0.12/0.51 (![X,Y,Z,W]: (( ~ product(X,Y,Z)| ~ product(X,Y,W)| Z = W ) ))),
% 0.12/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.51 fof(f19,hypothesis,(
% 0.12/0.51 defined(b,a) ),
% 0.12/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.51 fof(f20,negated_conjecture,(
% 0.12/0.51 codomain(compose(b,a)) != codomain(b) ),
% 0.12/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.51 fof(f21,plain,(
% 0.12/0.51 ![X0,X1]: (~defined(X0,X1)|product(X0,X1,compose(X0,X1)))),
% 0.12/0.51 inference(cnf_transformation,[status(thm)],[f1])).
% 0.12/0.51 fof(f22,plain,(
% 0.12/0.51 ![X,Y]: ((![Z]: ~product(X,Y,Z))|defined(X,Y))),
% 0.12/0.51 inference(miniscoping,[status(thm)],[f2])).
% 0.12/0.51 fof(f23,plain,(
% 0.12/0.51 ![X0,X1,X2]: (~product(X0,X1,X2)|defined(X0,X1))),
% 0.12/0.51 inference(cnf_transformation,[status(thm)],[f22])).
% 0.12/0.51 fof(f26,plain,(
% 0.12/0.51 ![X,Yz]: ((![Xy,Z]: ((![Y]: (~product(X,Y,Xy)|~product(Y,Z,Yz)))|~defined(Xy,Z)))|defined(X,Yz))),
% 0.12/0.51 inference(miniscoping,[status(thm)],[f4])).
% 0.12/0.51 fof(f27,plain,(
% 0.12/0.51 ![X0,X1,X2,X3,X4]: (~product(X0,X1,X2)|~product(X1,X3,X4)|~defined(X2,X3)|defined(X0,X4))),
% 0.12/0.51 inference(cnf_transformation,[status(thm)],[f26])).
% 0.12/0.51 fof(f30,plain,(
% 0.12/0.51 ![Y,X]: ((![Yz]: ((![Z]: ~product(Y,Z,Yz))|~defined(X,Yz)))|defined(X,Y))),
% 0.12/0.51 inference(miniscoping,[status(thm)],[f6])).
% 0.12/0.51 fof(f31,plain,(
% 0.12/0.51 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~defined(X3,X2)|defined(X3,X0))),
% 0.12/0.51 inference(cnf_transformation,[status(thm)],[f30])).
% 0.12/0.51 fof(f39,plain,(
% 0.12/0.51 ![X0]: (identity_map(codomain(X0)))),
% 0.12/0.51 inference(cnf_transformation,[status(thm)],[f11])).
% 0.12/0.51 fof(f43,plain,(
% 0.12/0.51 ![X0]: (product(codomain(X0),X0,X0))),
% 0.12/0.51 inference(cnf_transformation,[status(thm)],[f15])).
% 0.12/0.51 fof(f44,plain,(
% 0.12/0.51 ![X0,X1]: (~defined(X0,X1)|~identity_map(X0)|product(X0,X1,X1))),
% 0.12/0.51 inference(cnf_transformation,[status(thm)],[f16])).
% 0.12/0.51 fof(f45,plain,(
% 0.12/0.51 ![X0,X1]: (~defined(X0,X1)|~identity_map(X1)|product(X0,X1,X0))),
% 0.12/0.51 inference(cnf_transformation,[status(thm)],[f17])).
% 0.12/0.51 fof(f46,plain,(
% 0.12/0.51 ![Z,W]: ((![X,Y]: (~product(X,Y,Z)|~product(X,Y,W)))|Z=W)),
% 0.12/0.51 inference(miniscoping,[status(thm)],[f18])).
% 0.12/0.51 fof(f47,plain,(
% 0.12/0.51 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X1,X3)|X2=X3)),
% 0.12/0.51 inference(cnf_transformation,[status(thm)],[f46])).
% 0.12/0.51 fof(f48,plain,(
% 0.12/0.51 defined(b,a)),
% 0.12/0.51 inference(cnf_transformation,[status(thm)],[f19])).
% 0.12/0.51 fof(f49,plain,(
% 0.12/0.51 ~codomain(compose(b,a))=codomain(b)),
% 0.12/0.51 inference(cnf_transformation,[status(thm)],[f20])).
% 0.12/0.51 fof(f51,plain,(
% 0.12/0.51 product(b,a,compose(b,a))),
% 0.12/0.51 inference(resolution,[status(thm)],[f48,f21])).
% 0.12/0.51 fof(f73,plain,(
% 0.12/0.51 ![X0,X1,X2]: (~product(X0,X1,X2)|~defined(X0,X1)|defined(codomain(X0),X2))),
% 0.12/0.51 inference(resolution,[status(thm)],[f27,f43])).
% 0.12/0.51 fof(f75,plain,(
% 0.12/0.51 ![X0,X1,X2]: (~product(X0,X1,X2)|defined(codomain(X0),X2))),
% 0.12/0.51 inference(forward_subsumption_resolution,[status(thm)],[f73,f23])).
% 0.12/0.51 fof(f88,plain,(
% 0.12/0.51 defined(codomain(b),compose(b,a))),
% 0.12/0.51 inference(resolution,[status(thm)],[f75,f51])).
% 0.12/0.51 fof(f133,plain,(
% 0.12/0.51 ![X0,X1]: (~defined(X0,X1)|defined(X0,codomain(X1)))),
% 0.12/0.52 inference(resolution,[status(thm)],[f31,f43])).
% 0.12/0.52 fof(f674,plain,(
% 0.12/0.52 defined(codomain(b),codomain(compose(b,a)))),
% 0.12/0.52 inference(resolution,[status(thm)],[f88,f133])).
% 0.12/0.52 fof(f1553,plain,(
% 0.12/0.52 ~identity_map(codomain(compose(b,a)))|product(codomain(b),codomain(compose(b,a)),codomain(b))),
% 0.12/0.52 inference(resolution,[status(thm)],[f674,f45])).
% 0.12/0.52 fof(f1554,plain,(
% 0.12/0.52 ~identity_map(codomain(b))|product(codomain(b),codomain(compose(b,a)),codomain(compose(b,a)))),
% 0.12/0.52 inference(resolution,[status(thm)],[f674,f44])).
% 0.12/0.52 fof(f1560,plain,(
% 0.12/0.52 product(codomain(b),codomain(compose(b,a)),codomain(b))),
% 0.12/0.52 inference(forward_subsumption_resolution,[status(thm)],[f1553,f39])).
% 0.12/0.52 fof(f1561,plain,(
% 0.12/0.52 product(codomain(b),codomain(compose(b,a)),codomain(compose(b,a)))),
% 0.12/0.52 inference(forward_subsumption_resolution,[status(thm)],[f1554,f39])).
% 0.12/0.52 fof(f2923,plain,(
% 0.12/0.52 ![X0]: (~product(codomain(b),codomain(compose(b,a)),X0)|codomain(b)=X0)),
% 0.12/0.52 inference(resolution,[status(thm)],[f1560,f47])).
% 0.12/0.52 fof(f3384,plain,(
% 0.12/0.52 codomain(b)=codomain(compose(b,a))),
% 0.12/0.52 inference(resolution,[status(thm)],[f2923,f1561])).
% 0.12/0.52 fof(f3386,plain,(
% 0.12/0.52 $false),
% 0.12/0.52 inference(forward_subsumption_resolution,[status(thm)],[f3384,f49])).
% 0.12/0.52 % SZS output end CNFRefutation for theBenchmark.p
% 0.87/0.54 % Elapsed time: 0.172898 seconds
% 0.87/0.54 % CPU time: 1.123649 seconds
% 0.87/0.54 % Total memory used: 54.810 MB
% 0.87/0.54 % Net memory used: 52.850 MB
%------------------------------------------------------------------------------