%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : CAT003-1 : 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 : n007.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 12:07:41 PM UTC 2026
% Result : Unsatisfiable 0.16s 6.10s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/5.38 % Computer : n007.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Mon Sep 21 13:53:27 UTC 2026
% 0.12/5.38 % CPUTime :
% 0.12/5.39 % Drodi V4.1.1
% 0.16/6.10 % Refutation found
% 0.16/6.10 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/6.10 % SZS output start CNFRefutation for theBenchmark
% 0.16/6.10 fof(f1,axiom,(
% 0.16/6.10 (![X,Y]: (( ~ defined(X,Y)| product(X,Y,compose(X,Y)) ) ))),
% 0.16/6.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/6.10 fof(f2,axiom,(
% 0.16/6.10 (![X,Y,Z]: (( ~ product(X,Y,Z)| defined(X,Y) ) ))),
% 0.16/6.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/6.10 fof(f4,axiom,(
% 0.16/6.10 (![X,Y,Xy,Z,Yz]: (( ~ product(X,Y,Xy)| ~ product(Y,Z,Yz)| ~ defined(Xy,Z)| defined(X,Yz) ) ))),
% 0.16/6.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/6.10 fof(f5,axiom,(
% 0.16/6.10 (![X,Y,Xy,Z,Xyz,Yz]: (( ~ product(X,Y,Xy)| ~ product(Xy,Z,Xyz)| ~ product(Y,Z,Yz)| product(X,Yz,Xyz) ) ))),
% 0.16/6.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/6.10 fof(f6,axiom,(
% 0.16/6.10 (![Y,Z,Yz,X]: (( ~ product(Y,Z,Yz)| ~ defined(X,Yz)| defined(X,Y) ) ))),
% 0.16/6.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/6.10 fof(f7,axiom,(
% 0.16/6.10 (![Y,Z,Yz,X,Xy]: (( ~ product(Y,Z,Yz)| ~ product(X,Y,Xy)| ~ defined(X,Yz)| defined(Xy,Z) ) ))),
% 0.16/6.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/6.10 fof(f9,axiom,(
% 0.16/6.10 (![X,Y,Z]: (( ~ defined(X,Y)| ~ defined(Y,Z)| ~ identity_map(Y)| defined(X,Z) ) ))),
% 0.16/6.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/6.10 fof(f11,axiom,(
% 0.16/6.10 (![X]: (identity_map(codomain(X)) ))),
% 0.16/6.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/6.10 fof(f15,axiom,(
% 0.16/6.10 (![X]: (product(codomain(X),X,X) ))),
% 0.16/6.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/6.10 fof(f18,axiom,(
% 0.16/6.10 (![X,Y,Z,W]: (( ~ product(X,Y,Z)| ~ product(X,Y,W)| Z = W ) ))),
% 0.16/6.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/6.10 fof(f19,hypothesis,(
% 0.16/6.10 product(a,b,c) ),
% 0.16/6.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/6.10 fof(f20,hypothesis,(
% 0.16/6.10 (![X,W,Y]: (( ~ product(X,c,W)| ~ product(Y,c,W)| X = Y ) ))),
% 0.16/6.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/6.10 fof(f21,hypothesis,(
% 0.16/6.10 product(h,a,d) ),
% 0.16/6.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/6.10 fof(f22,hypothesis,(
% 0.16/6.10 product(g,a,d) ),
% 0.16/6.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/6.11 fof(f23,negated_conjecture,(
% 0.16/6.11 h != g ),
% 0.16/6.11 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.16/6.11 fof(f24,plain,(
% 0.16/6.11 ![X0,X1]: (~defined(X0,X1)|product(X0,X1,compose(X0,X1)))),
% 0.16/6.11 inference(cnf_transformation,[status(thm)],[f1])).
% 0.16/6.11 fof(f25,plain,(
% 0.16/6.11 ![X,Y]: ((![Z]: ~product(X,Y,Z))|defined(X,Y))),
% 0.16/6.11 inference(miniscoping,[status(thm)],[f2])).
% 0.16/6.11 fof(f26,plain,(
% 0.16/6.11 ![X0,X1,X2]: (~product(X0,X1,X2)|defined(X0,X1))),
% 0.16/6.11 inference(cnf_transformation,[status(thm)],[f25])).
% 0.16/6.11 fof(f29,plain,(
% 0.16/6.11 ![X,Yz]: ((![Xy,Z]: ((![Y]: (~product(X,Y,Xy)|~product(Y,Z,Yz)))|~defined(Xy,Z)))|defined(X,Yz))),
% 0.16/6.11 inference(miniscoping,[status(thm)],[f4])).
% 0.16/6.11 fof(f30,plain,(
% 0.16/6.11 ![X0,X1,X2,X3,X4]: (~product(X0,X1,X2)|~product(X1,X3,X4)|~defined(X2,X3)|defined(X0,X4))),
% 0.16/6.11 inference(cnf_transformation,[status(thm)],[f29])).
% 0.16/6.11 fof(f31,plain,(
% 0.16/6.11 ![X,Xyz,Yz]: ((![Y,Z]: ((![Xy]: (~product(X,Y,Xy)|~product(Xy,Z,Xyz)))|~product(Y,Z,Yz)))|product(X,Yz,Xyz))),
% 0.16/6.11 inference(miniscoping,[status(thm)],[f5])).
% 0.16/6.11 fof(f32,plain,(
% 0.16/6.11 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~product(X2,X3,X4)|~product(X1,X3,X5)|product(X0,X5,X4))),
% 0.16/6.11 inference(cnf_transformation,[status(thm)],[f31])).
% 0.16/6.11 fof(f33,plain,(
% 0.16/6.11 ![Y,X]: ((![Yz]: ((![Z]: ~product(Y,Z,Yz))|~defined(X,Yz)))|defined(X,Y))),
% 0.16/6.11 inference(miniscoping,[status(thm)],[f6])).
% 0.16/6.11 fof(f34,plain,(
% 0.16/6.11 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~defined(X3,X2)|defined(X3,X0))),
% 0.16/6.11 inference(cnf_transformation,[status(thm)],[f33])).
% 0.16/6.11 fof(f35,plain,(
% 0.16/6.11 ![Z,Xy]: ((![Yz,X]: ((![Y]: (~product(Y,Z,Yz)|~product(X,Y,Xy)))|~defined(X,Yz)))|defined(Xy,Z))),
% 0.16/6.11 inference(miniscoping,[status(thm)],[f7])).
% 0.16/6.11 fof(f36,plain,(
% 0.16/6.11 ![X0,X1,X2,X3,X4]: (~product(X0,X1,X2)|~product(X3,X0,X4)|~defined(X3,X2)|defined(X4,X1))),
% 0.16/6.11 inference(cnf_transformation,[status(thm)],[f35])).
% 0.16/6.11 fof(f39,plain,(
% 0.16/6.11 ![X,Z]: ((![Y]: ((~defined(X,Y)|~defined(Y,Z))|~identity_map(Y)))|defined(X,Z))),
% 0.16/6.11 inference(miniscoping,[status(thm)],[f9])).
% 0.16/6.11 fof(f40,plain,(
% 0.16/6.11 ![X0,X1,X2]: (~defined(X0,X1)|~defined(X1,X2)|~identity_map(X1)|defined(X0,X2))),
% 0.16/6.11 inference(cnf_transformation,[status(thm)],[f39])).
% 0.16/6.11 fof(f42,plain,(
% 0.16/6.11 ![X0]: (identity_map(codomain(X0)))),
% 0.16/6.11 inference(cnf_transformation,[status(thm)],[f11])).
% 0.16/6.11 fof(f46,plain,(
% 0.16/6.11 ![X0]: (product(codomain(X0),X0,X0))),
% 0.16/6.11 inference(cnf_transformation,[status(thm)],[f15])).
% 0.16/6.11 fof(f49,plain,(
% 0.16/6.11 ![Z,W]: ((![X,Y]: (~product(X,Y,Z)|~product(X,Y,W)))|Z=W)),
% 0.16/6.11 inference(miniscoping,[status(thm)],[f18])).
% 0.16/6.11 fof(f50,plain,(
% 0.16/6.11 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X1,X3)|X2=X3)),
% 0.16/6.11 inference(cnf_transformation,[status(thm)],[f49])).
% 0.16/6.11 fof(f51,plain,(
% 0.16/6.11 product(a,b,c)),
% 0.16/6.11 inference(cnf_transformation,[status(thm)],[f19])).
% 0.16/6.11 fof(f52,plain,(
% 0.16/6.11 ![X,Y]: ((![W]: (~product(X,c,W)|~product(Y,c,W)))|X=Y)),
% 0.16/6.11 inference(miniscoping,[status(thm)],[f20])).
% 0.16/6.11 fof(f53,plain,(
% 0.16/6.11 ![X0,X1,X2]: (~product(X0,c,X1)|~product(X2,c,X1)|X0=X2)),
% 0.16/6.11 inference(cnf_transformation,[status(thm)],[f52])).
% 0.16/6.11 fof(f54,plain,(
% 0.16/6.11 product(h,a,d)),
% 0.16/6.11 inference(cnf_transformation,[status(thm)],[f21])).
% 0.16/6.11 fof(f55,plain,(
% 0.16/6.11 product(g,a,d)),
% 0.16/6.11 inference(cnf_transformation,[status(thm)],[f22])).
% 0.16/6.11 fof(f56,plain,(
% 0.16/6.11 ~h=g),
% 0.16/6.11 inference(cnf_transformation,[status(thm)],[f23])).
% 0.16/6.11 fof(f60,plain,(
% 0.16/6.11 defined(h,a)),
% 0.16/6.11 inference(resolution,[status(thm)],[f26,f54])).
% 0.16/6.11 fof(f73,plain,(
% 0.16/6.11 ![X0,X1,X2]: (~product(X0,X1,X2)|~defined(X0,X1)|defined(codomain(X0),X2))),
% 0.16/6.11 inference(resolution,[status(thm)],[f30,f46])).
% 0.16/6.11 fof(f77,plain,(
% 0.16/6.11 ![X0,X1,X2]: (~product(X0,X1,X2)|defined(codomain(X0),X2))),
% 0.16/6.11 inference(forward_subsumption_resolution,[status(thm)],[f73,f26])).
% 0.16/6.11 fof(f80,plain,(
% 0.16/6.11 ![X0,X1,X2]: (~product(d,X0,X1)|~product(a,X0,X2)|product(g,X2,X1))),
% 0.16/6.11 inference(resolution,[status(thm)],[f32,f55])).
% 0.16/6.11 fof(f81,plain,(
% 0.16/6.11 ![X0,X1,X2]: (~product(d,X0,X1)|~product(a,X0,X2)|product(h,X2,X1))),
% 0.16/6.11 inference(resolution,[status(thm)],[f32,f54])).
% 0.16/6.11 fof(f116,plain,(
% 0.16/6.11 ![X0,X1]: (~defined(X0,X1)|defined(X0,codomain(X1)))),
% 0.16/6.11 inference(resolution,[status(thm)],[f34,f46])).
% 0.16/6.11 fof(f122,plain,(
% 0.16/6.11 ![X0,X1]: (~product(X0,a,X1)|~defined(X0,c)|defined(X1,b))),
% 0.16/6.11 inference(resolution,[status(thm)],[f36,f51])).
% 0.16/6.11 fof(f313,plain,(
% 0.16/6.11 defined(h,codomain(a))),
% 0.16/6.11 inference(resolution,[status(thm)],[f116,f60])).
% 0.16/6.11 fof(f331,plain,(
% 0.16/6.11 ![X0]: (~defined(codomain(a),X0)|~identity_map(codomain(a))|defined(h,X0))),
% 0.16/6.11 inference(resolution,[status(thm)],[f313,f40])).
% 0.16/6.11 fof(f335,plain,(
% 0.16/6.11 ![X0]: (~defined(codomain(a),X0)|defined(h,X0))),
% 0.16/6.11 inference(forward_subsumption_resolution,[status(thm)],[f331,f42])).
% 0.16/6.11 fof(f467,plain,(
% 0.16/6.11 defined(codomain(a),c)),
% 0.16/6.11 inference(resolution,[status(thm)],[f77,f51])).
% 0.16/6.11 fof(f764,plain,(
% 0.16/6.11 ~defined(h,c)|defined(d,b)),
% 0.16/6.11 inference(resolution,[status(thm)],[f122,f54])).
% 0.16/6.11 fof(f2324,plain,(
% 0.16/6.11 defined(h,c)),
% 0.16/6.11 inference(resolution,[status(thm)],[f335,f467])).
% 0.16/6.11 fof(f2353,plain,(
% 0.16/6.11 defined(d,b)),
% 0.16/6.11 inference(backward_subsumption_resolution,[status(thm)],[f764,f2324])).
% 0.16/6.11 fof(f2361,plain,(
% 0.16/6.11 product(h,c,compose(h,c))),
% 0.16/6.11 inference(resolution,[status(thm)],[f2324,f24])).
% 0.16/6.11 fof(f2371,plain,(
% 0.16/6.11 product(d,b,compose(d,b))),
% 0.16/6.11 inference(resolution,[status(thm)],[f2353,f24])).
% 0.16/6.11 fof(f4262,plain,(
% 0.16/6.11 ![X0]: (~product(a,b,X0)|product(h,X0,compose(d,b)))),
% 0.16/6.11 inference(resolution,[status(thm)],[f2371,f81])).
% 0.16/6.11 fof(f4263,plain,(
% 0.16/6.11 ![X0]: (~product(a,b,X0)|product(g,X0,compose(d,b)))),
% 0.16/6.11 inference(resolution,[status(thm)],[f2371,f80])).
% 0.16/6.11 fof(f5158,plain,(
% 0.16/6.11 ![X0]: (~product(X0,c,compose(h,c))|h=X0)),
% 0.16/6.11 inference(resolution,[status(thm)],[f2361,f53])).
% 0.16/6.11 fof(f5165,plain,(
% 0.16/6.11 ![X0]: (~product(h,c,X0)|compose(h,c)=X0)),
% 0.16/6.11 inference(resolution,[status(thm)],[f2361,f50])).
% 0.16/6.11 fof(f10730,plain,(
% 0.16/6.11 product(h,c,compose(d,b))),
% 0.16/6.11 inference(resolution,[status(thm)],[f4262,f51])).
% 0.16/6.11 fof(f10731,plain,(
% 0.16/6.11 compose(h,c)=compose(d,b)),
% 0.16/6.11 inference(resolution,[status(thm)],[f10730,f5165])).
% 0.16/6.11 fof(f10839,plain,(
% 0.16/6.11 ![X0]: (~product(a,b,X0)|product(g,X0,compose(h,c)))),
% 0.16/6.11 inference(forward_demodulation,[status(thm)],[f10731,f4263])).
% 0.16/6.11 fof(f10840,plain,(
% 0.16/6.11 product(g,c,compose(h,c))),
% 0.16/6.11 inference(resolution,[status(thm)],[f10839,f51])).
% 0.16/6.11 fof(f10844,plain,(
% 0.16/6.11 h=g),
% 0.16/6.11 inference(resolution,[status(thm)],[f10840,f5158])).
% 0.16/6.11 fof(f10864,plain,(
% 0.16/6.11 $false),
% 0.16/6.11 inference(forward_subsumption_resolution,[status(thm)],[f10844,f56])).
% 0.16/6.11 % SZS output end CNFRefutation for theBenchmark.p
% 0.16/6.12 % Elapsed time: 0.729391 seconds
% 0.16/6.12 % CPU time: 5.571886 seconds
% 0.16/6.12 % Total memory used: 79.960 MB
% 0.16/6.12 % Net memory used: 72.816 MB
%------------------------------------------------------------------------------