%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : CAT009-1 : 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 : n009.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 0.13s 0.57s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 13:55:42 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.57 % Refutation found
% 0.13/0.57 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.57 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.57 fof(f1,axiom,(
% 0.13/0.57 (![X,Y]: (( ~ defined(X,Y)| product(X,Y,compose(X,Y)) ) ))),
% 0.13/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.57 fof(f2,axiom,(
% 0.13/0.57 (![X,Y,Z]: (( ~ product(X,Y,Z)| defined(X,Y) ) ))),
% 0.13/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.57 fof(f3,axiom,(
% 0.13/0.57 (![X,Y,Xy,Z]: (( ~ product(X,Y,Xy)| ~ defined(Xy,Z)| defined(Y,Z) ) ))),
% 0.13/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.57 fof(f7,axiom,(
% 0.13/0.57 (![Y,Z,Yz,X,Xy]: (( ~ product(Y,Z,Yz)| ~ product(X,Y,Xy)| ~ defined(X,Yz)| defined(Xy,Z) ) ))),
% 0.13/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.57 fof(f10,axiom,(
% 0.13/0.57 (![X]: (identity_map(domain(X)) ))),
% 0.13/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.57 fof(f14,axiom,(
% 0.13/0.57 (![X]: (product(X,domain(X),X) ))),
% 0.13/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.57 fof(f16,axiom,(
% 0.13/0.57 (![X,Y]: (( ~ defined(X,Y)| ~ identity_map(X)| product(X,Y,Y) ) ))),
% 0.13/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.57 fof(f17,axiom,(
% 0.13/0.57 (![X,Y]: (( ~ defined(X,Y)| ~ identity_map(Y)| product(X,Y,X) ) ))),
% 0.13/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.57 fof(f18,axiom,(
% 0.13/0.57 (![X,Y,Z,W]: (( ~ product(X,Y,Z)| ~ product(X,Y,W)| Z = W ) ))),
% 0.13/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.57 fof(f19,hypothesis,(
% 0.13/0.57 defined(b,a) ),
% 0.13/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.57 fof(f20,negated_conjecture,(
% 0.13/0.57 domain(compose(b,a)) != domain(a) ),
% 0.13/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.57 fof(f21,plain,(
% 0.13/0.57 ![X0,X1]: (~defined(X0,X1)|product(X0,X1,compose(X0,X1)))),
% 0.13/0.57 inference(cnf_transformation,[status(thm)],[f1])).
% 0.13/0.57 fof(f22,plain,(
% 0.13/0.57 ![X,Y]: ((![Z]: ~product(X,Y,Z))|defined(X,Y))),
% 0.13/0.57 inference(miniscoping,[status(thm)],[f2])).
% 0.13/0.57 fof(f23,plain,(
% 0.13/0.57 ![X0,X1,X2]: (~product(X0,X1,X2)|defined(X0,X1))),
% 0.13/0.57 inference(cnf_transformation,[status(thm)],[f22])).
% 0.13/0.57 fof(f24,plain,(
% 0.13/0.57 ![Y,Z]: ((![Xy]: ((![X]: ~product(X,Y,Xy))|~defined(Xy,Z)))|defined(Y,Z))),
% 0.13/0.57 inference(miniscoping,[status(thm)],[f3])).
% 0.13/0.57 fof(f25,plain,(
% 0.13/0.57 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~defined(X2,X3)|defined(X1,X3))),
% 0.13/0.57 inference(cnf_transformation,[status(thm)],[f24])).
% 0.13/0.57 fof(f32,plain,(
% 0.13/0.57 ![Z,Xy]: ((![Yz,X]: ((![Y]: (~product(Y,Z,Yz)|~product(X,Y,Xy)))|~defined(X,Yz)))|defined(Xy,Z))),
% 0.13/0.57 inference(miniscoping,[status(thm)],[f7])).
% 0.13/0.57 fof(f33,plain,(
% 0.13/0.57 ![X0,X1,X2,X3,X4]: (~product(X0,X1,X2)|~product(X3,X0,X4)|~defined(X3,X2)|defined(X4,X1))),
% 0.13/0.57 inference(cnf_transformation,[status(thm)],[f32])).
% 0.13/0.57 fof(f38,plain,(
% 0.13/0.57 ![X0]: (identity_map(domain(X0)))),
% 0.13/0.57 inference(cnf_transformation,[status(thm)],[f10])).
% 0.13/0.57 fof(f42,plain,(
% 0.13/0.57 ![X0]: (product(X0,domain(X0),X0))),
% 0.13/0.57 inference(cnf_transformation,[status(thm)],[f14])).
% 0.13/0.57 fof(f44,plain,(
% 0.13/0.57 ![X0,X1]: (~defined(X0,X1)|~identity_map(X0)|product(X0,X1,X1))),
% 0.13/0.57 inference(cnf_transformation,[status(thm)],[f16])).
% 0.13/0.57 fof(f45,plain,(
% 0.13/0.57 ![X0,X1]: (~defined(X0,X1)|~identity_map(X1)|product(X0,X1,X0))),
% 0.13/0.57 inference(cnf_transformation,[status(thm)],[f17])).
% 0.13/0.57 fof(f46,plain,(
% 0.13/0.57 ![Z,W]: ((![X,Y]: (~product(X,Y,Z)|~product(X,Y,W)))|Z=W)),
% 0.13/0.57 inference(miniscoping,[status(thm)],[f18])).
% 0.13/0.57 fof(f47,plain,(
% 0.13/0.57 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X1,X3)|X2=X3)),
% 0.13/0.57 inference(cnf_transformation,[status(thm)],[f46])).
% 0.13/0.57 fof(f48,plain,(
% 0.13/0.57 defined(b,a)),
% 0.13/0.57 inference(cnf_transformation,[status(thm)],[f19])).
% 0.13/0.57 fof(f49,plain,(
% 0.13/0.57 ~domain(compose(b,a))=domain(a)),
% 0.13/0.57 inference(cnf_transformation,[status(thm)],[f20])).
% 0.13/0.57 fof(f51,plain,(
% 0.13/0.57 product(b,a,compose(b,a))),
% 0.13/0.57 inference(resolution,[status(thm)],[f48,f21])).
% 0.13/0.57 fof(f70,plain,(
% 0.13/0.57 ![X0,X1]: (~defined(X0,X1)|defined(domain(X0),X1))),
% 0.13/0.57 inference(resolution,[status(thm)],[f25,f42])).
% 0.13/0.57 fof(f143,plain,(
% 0.13/0.57 ![X0,X1,X2]: (~product(X0,X1,X2)|~defined(X0,X1)|defined(X2,domain(X1)))),
% 0.13/0.57 inference(resolution,[status(thm)],[f33,f42])).
% 0.13/0.57 fof(f144,plain,(
% 0.13/0.57 ![X0,X1,X2]: (~product(X0,X1,X2)|defined(X2,domain(X1)))),
% 0.13/0.57 inference(forward_subsumption_resolution,[status(thm)],[f143,f23])).
% 0.13/0.57 fof(f181,plain,(
% 0.13/0.58 defined(compose(b,a),domain(a))),
% 0.13/0.58 inference(resolution,[status(thm)],[f144,f51])).
% 0.13/0.58 fof(f987,plain,(
% 0.13/0.58 defined(domain(compose(b,a)),domain(a))),
% 0.13/0.58 inference(resolution,[status(thm)],[f181,f70])).
% 0.13/0.58 fof(f1817,plain,(
% 0.13/0.58 ~identity_map(domain(a))|product(domain(compose(b,a)),domain(a),domain(compose(b,a)))),
% 0.13/0.58 inference(resolution,[status(thm)],[f987,f45])).
% 0.13/0.58 fof(f1818,plain,(
% 0.13/0.58 ~identity_map(domain(compose(b,a)))|product(domain(compose(b,a)),domain(a),domain(a))),
% 0.13/0.58 inference(resolution,[status(thm)],[f987,f44])).
% 0.13/0.58 fof(f1824,plain,(
% 0.13/0.58 product(domain(compose(b,a)),domain(a),domain(compose(b,a)))),
% 0.13/0.58 inference(forward_subsumption_resolution,[status(thm)],[f1817,f38])).
% 0.13/0.58 fof(f1825,plain,(
% 0.13/0.58 product(domain(compose(b,a)),domain(a),domain(a))),
% 0.13/0.58 inference(forward_subsumption_resolution,[status(thm)],[f1818,f38])).
% 0.13/0.58 fof(f2866,plain,(
% 0.13/0.58 ![X0]: (~product(domain(compose(b,a)),domain(a),X0)|domain(a)=X0)),
% 0.13/0.58 inference(resolution,[status(thm)],[f1825,f47])).
% 0.13/0.58 fof(f3284,plain,(
% 0.13/0.58 domain(a)=domain(compose(b,a))),
% 0.13/0.58 inference(resolution,[status(thm)],[f2866,f1824])).
% 0.13/0.58 fof(f3286,plain,(
% 0.13/0.58 $false),
% 0.13/0.58 inference(forward_subsumption_resolution,[status(thm)],[f3284,f49])).
% 0.13/0.58 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.58 % Elapsed time: 0.214190 seconds
% 0.13/0.58 % CPU time: 1.547305 seconds
% 0.13/0.58 % Total memory used: 61.446 MB
% 0.13/0.58 % Net memory used: 57.879 MB
%------------------------------------------------------------------------------