%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : RNG006-3 : 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 : n013.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 02:05:06 PM UTC 2026
% Result : Unsatisfiable 32.29s 4.62s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG006-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n013.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Mon Sep 21 04:09:50 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.19/0.44 % Drodi V4.1.1
% 32.29/4.62 % Refutation found
% 32.29/4.62 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 32.29/4.62 % SZS output start CNFRefutation for theBenchmark
% 32.29/4.62 fof(f1,axiom,(
% 32.29/4.62 (![X]: (sum(additive_identity,X,X) ))),
% 32.29/4.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 32.29/4.62 fof(f2,axiom,(
% 32.29/4.62 (![X]: (sum(X,additive_identity,X) ))),
% 32.29/4.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 32.29/4.62 fof(f3,axiom,(
% 32.29/4.62 (![X,Y]: (product(X,Y,multiply(X,Y)) ))),
% 32.29/4.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 32.29/4.62 fof(f4,axiom,(
% 32.29/4.62 (![X,Y]: (sum(X,Y,add(X,Y)) ))),
% 32.29/4.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 32.29/4.62 fof(f5,axiom,(
% 32.29/4.62 (![X]: (sum(additive_inverse(X),X,additive_identity) ))),
% 32.29/4.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 32.29/4.62 fof(f7,axiom,(
% 32.29/4.62 (![X,Y,U,Z,V,W]: (( ~ sum(X,Y,U)| ~ sum(Y,Z,V)| ~ sum(U,Z,W)| sum(X,V,W) ) ))),
% 32.29/4.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 32.29/4.62 fof(f9,axiom,(
% 32.29/4.62 (![X,Y,Z]: (( ~ sum(X,Y,Z)| sum(Y,X,Z) ) ))),
% 32.29/4.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 32.29/4.62 fof(f12,axiom,(
% 32.29/4.62 (![X,Y,V1,Z,V2,V3,V4]: (( ~ product(X,Y,V1)| ~ product(X,Z,V2)| ~ sum(Y,Z,V3)| ~ product(X,V3,V4)| sum(V1,V2,V4) ) ))),
% 32.29/4.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 32.29/4.62 fof(f16,axiom,(
% 32.29/4.62 (![X,Y,U,V]: (( ~ sum(X,Y,U)| ~ sum(X,Y,V)| U = V ) ))),
% 32.29/4.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 32.29/4.62 fof(f17,axiom,(
% 32.29/4.62 (![X,Y,U,V]: (( ~ product(X,Y,U)| ~ product(X,Y,V)| U = V ) ))),
% 32.29/4.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 32.29/4.62 fof(f18,hypothesis,(
% 32.29/4.62 sum(b,additive_inverse(c),bS_Ic) ),
% 32.29/4.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 32.29/4.62 fof(f19,hypothesis,(
% 32.29/4.62 product(a,b,aPb) ),
% 32.29/4.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 32.29/4.62 fof(f20,hypothesis,(
% 32.29/4.62 product(a,c,aPc) ),
% 32.29/4.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 32.29/4.62 fof(f21,hypothesis,(
% 32.29/4.62 sum(aPb,additive_inverse(aPc),aPb_S_IaPc) ),
% 32.29/4.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 32.29/4.62 fof(f22,negated_conjecture,(
% 32.29/4.62 ~ product(a,bS_Ic,aPb_S_IaPc) ),
% 32.29/4.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 32.29/4.62 fof(f23,plain,(
% 32.29/4.62 ![X0]: (sum(additive_identity,X0,X0))),
% 32.29/4.62 inference(cnf_transformation,[status(thm)],[f1])).
% 32.29/4.62 fof(f24,plain,(
% 32.29/4.62 ![X0]: (sum(X0,additive_identity,X0))),
% 32.29/4.62 inference(cnf_transformation,[status(thm)],[f2])).
% 32.29/4.62 fof(f25,plain,(
% 32.29/4.62 ![X0,X1]: (product(X0,X1,multiply(X0,X1)))),
% 32.29/4.62 inference(cnf_transformation,[status(thm)],[f3])).
% 32.29/4.62 fof(f26,plain,(
% 32.29/4.62 ![X0,X1]: (sum(X0,X1,add(X0,X1)))),
% 32.29/4.62 inference(cnf_transformation,[status(thm)],[f4])).
% 32.29/4.62 fof(f27,plain,(
% 32.29/4.62 ![X0]: (sum(additive_inverse(X0),X0,additive_identity))),
% 32.29/4.62 inference(cnf_transformation,[status(thm)],[f5])).
% 32.29/4.62 fof(f29,plain,(
% 32.29/4.62 ![X,V,W]: ((![U,Z]: ((![Y]: (~sum(X,Y,U)|~sum(Y,Z,V)))|~sum(U,Z,W)))|sum(X,V,W))),
% 32.29/4.62 inference(miniscoping,[status(thm)],[f7])).
% 32.29/4.62 fof(f30,plain,(
% 32.29/4.62 ![X0,X1,X2,X3,X4,X5]: (~sum(X0,X1,X2)|~sum(X1,X3,X4)|~sum(X2,X3,X5)|sum(X0,X4,X5))),
% 32.29/4.62 inference(cnf_transformation,[status(thm)],[f29])).
% 32.29/4.62 fof(f33,plain,(
% 32.29/4.62 ![X0,X1,X2]: (~sum(X0,X1,X2)|sum(X1,X0,X2))),
% 32.29/4.62 inference(cnf_transformation,[status(thm)],[f9])).
% 32.29/4.62 fof(f38,plain,(
% 32.29/4.62 ![V1,V2,V4]: ((![X,V3]: ((![Y,Z]: ((~product(X,Y,V1)|~product(X,Z,V2))|~sum(Y,Z,V3)))|~product(X,V3,V4)))|sum(V1,V2,V4))),
% 32.29/4.62 inference(miniscoping,[status(thm)],[f12])).
% 32.29/4.62 fof(f39,plain,(
% 32.29/4.62 ![X0,X1,X2,X3,X4,X5,X6]: (~product(X0,X1,X2)|~product(X0,X3,X4)|~sum(X1,X3,X5)|~product(X0,X5,X6)|sum(X2,X4,X6))),
% 32.29/4.62 inference(cnf_transformation,[status(thm)],[f38])).
% 32.29/4.62 fof(f46,plain,(
% 32.29/4.62 ![U,V]: ((![X,Y]: (~sum(X,Y,U)|~sum(X,Y,V)))|U=V)),
% 32.29/4.62 inference(miniscoping,[status(thm)],[f16])).
% 32.29/4.62 fof(f47,plain,(
% 32.29/4.62 ![X0,X1,X2,X3]: (~sum(X0,X1,X2)|~sum(X0,X1,X3)|X2=X3)),
% 32.29/4.62 inference(cnf_transformation,[status(thm)],[f46])).
% 32.29/4.62 fof(f48,plain,(
% 32.29/4.62 ![U,V]: ((![X,Y]: (~product(X,Y,U)|~product(X,Y,V)))|U=V)),
% 32.29/4.62 inference(miniscoping,[status(thm)],[f17])).
% 32.29/4.62 fof(f49,plain,(
% 32.29/4.62 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X1,X3)|X2=X3)),
% 32.29/4.62 inference(cnf_transformation,[status(thm)],[f48])).
% 32.29/4.62 fof(f50,plain,(
% 32.29/4.62 sum(b,additive_inverse(c),bS_Ic)),
% 32.29/4.62 inference(cnf_transformation,[status(thm)],[f18])).
% 32.29/4.62 fof(f51,plain,(
% 32.29/4.62 product(a,b,aPb)),
% 32.29/4.62 inference(cnf_transformation,[status(thm)],[f19])).
% 32.29/4.62 fof(f52,plain,(
% 32.29/4.62 product(a,c,aPc)),
% 32.29/4.62 inference(cnf_transformation,[status(thm)],[f20])).
% 32.29/4.62 fof(f53,plain,(
% 32.29/4.62 sum(aPb,additive_inverse(aPc),aPb_S_IaPc)),
% 32.29/4.62 inference(cnf_transformation,[status(thm)],[f21])).
% 32.29/4.62 fof(f54,plain,(
% 32.29/4.62 ~product(a,bS_Ic,aPb_S_IaPc)),
% 32.29/4.62 inference(cnf_transformation,[status(thm)],[f22])).
% 32.29/4.62 fof(f57,plain,(
% 32.29/4.62 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~sum(X3,X1,X4)|~product(X0,X4,X5)|sum(multiply(X0,X3),X2,X5))),
% 32.29/4.62 inference(resolution,[status(thm)],[f25,f39])).
% 32.29/4.62 fof(f59,plain,(
% 32.29/4.62 ![X0,X1,X2]: (~product(X0,X1,X2)|multiply(X0,X1)=X2)),
% 32.29/4.62 inference(resolution,[status(thm)],[f25,f49])).
% 32.29/4.62 fof(f61,plain,(
% 32.29/4.62 ![X0,X1,X2,X3]: (~sum(X0,X1,X2)|~sum(additive_identity,X1,X3)|sum(additive_inverse(X0),X2,X3))),
% 32.29/4.62 inference(resolution,[status(thm)],[f30,f27])).
% 32.29/4.62 fof(f77,plain,(
% 32.29/4.62 sum(additive_inverse(aPc),aPb,aPb_S_IaPc)),
% 32.29/4.62 inference(resolution,[status(thm)],[f33,f53])).
% 32.29/4.62 fof(f78,plain,(
% 32.29/4.62 sum(additive_inverse(c),b,bS_Ic)),
% 32.29/4.62 inference(resolution,[status(thm)],[f33,f50])).
% 32.29/4.62 fof(f81,plain,(
% 32.29/4.62 ![X0,X1]: (sum(X0,X1,add(X1,X0)))),
% 32.29/4.62 inference(resolution,[status(thm)],[f33,f26])).
% 32.29/4.62 fof(f121,plain,(
% 32.29/4.62 multiply(a,c)=aPc),
% 32.29/4.62 inference(resolution,[status(thm)],[f52,f59])).
% 32.29/4.62 fof(f142,plain,(
% 32.29/4.62 ![X0]: (~sum(additive_inverse(aPc),aPb,X0)|aPb_S_IaPc=X0)),
% 32.29/4.62 inference(resolution,[status(thm)],[f47,f77])).
% 32.29/4.62 fof(f148,plain,(
% 32.29/4.62 ![X0,X1]: (~sum(X0,additive_identity,X1)|X0=X1)),
% 32.29/4.62 inference(resolution,[status(thm)],[f47,f24])).
% 32.29/4.62 fof(f149,plain,(
% 32.29/4.62 ![X0,X1,X2]: (~sum(X0,X1,X2)|add(X1,X0)=X2)),
% 32.29/4.62 inference(resolution,[status(thm)],[f47,f81])).
% 32.29/4.62 fof(f150,plain,(
% 32.29/4.62 ![X0,X1,X2]: (~sum(X0,X1,X2)|add(X0,X1)=X2)),
% 32.29/4.62 inference(resolution,[status(thm)],[f47,f26])).
% 32.29/4.62 fof(f154,plain,(
% 32.29/4.62 ![X0,X1,X2,X3,X4]: (~sum(X0,X1,X2)|~product(X3,X2,X4)|sum(multiply(X3,X0),multiply(X3,X1),X4))),
% 32.29/4.62 inference(resolution,[status(thm)],[f57,f25])).
% 32.29/4.62 fof(f175,plain,(
% 32.29/4.62 aPb_S_IaPc=add(aPb,additive_inverse(aPc))),
% 32.29/4.62 inference(resolution,[status(thm)],[f142,f81])).
% 32.29/4.62 fof(f214,plain,(
% 32.29/4.62 ![X0]: (~sum(additive_identity,b,X0)|sum(additive_inverse(additive_inverse(c)),bS_Ic,X0))),
% 32.29/4.62 inference(resolution,[status(thm)],[f61,f78])).
% 32.29/4.62 fof(f216,plain,(
% 32.29/4.62 ![X0,X1]: (~sum(additive_identity,X0,X1)|sum(additive_inverse(additive_inverse(X0)),additive_identity,X1))),
% 32.29/4.62 inference(resolution,[status(thm)],[f61,f27])).
% 32.29/4.62 fof(f223,plain,(
% 32.29/4.62 ![X0,X1,X2]: (~sum(additive_identity,X0,X1)|sum(additive_inverse(X2),add(X2,X0),X1))),
% 32.29/4.62 inference(resolution,[status(thm)],[f61,f26])).
% 32.29/4.62 fof(f1524,plain,(
% 32.29/4.62 sum(additive_inverse(additive_inverse(c)),bS_Ic,b)),
% 32.29/4.62 inference(resolution,[status(thm)],[f214,f23])).
% 32.29/4.62 fof(f1535,plain,(
% 32.29/4.62 ![X0]: (sum(additive_inverse(additive_inverse(X0)),additive_identity,X0))),
% 32.29/4.62 inference(resolution,[status(thm)],[f216,f23])).
% 32.29/4.62 fof(f1551,plain,(
% 32.29/4.62 ![X0,X1]: (~product(X0,b,X1)|sum(multiply(X0,additive_inverse(additive_inverse(c))),multiply(X0,bS_Ic),X1))),
% 32.29/4.62 inference(resolution,[status(thm)],[f1524,f154])).
% 32.29/4.62 fof(f1651,plain,(
% 32.29/4.62 ![X0]: (additive_inverse(additive_inverse(X0))=X0)),
% 32.29/4.62 inference(resolution,[status(thm)],[f1535,f148])).
% 32.29/4.62 fof(f1724,plain,(
% 32.29/4.62 ![X0,X1]: (sum(additive_inverse(X0),add(X0,X1),X1))),
% 32.29/4.62 inference(resolution,[status(thm)],[f223,f23])).
% 32.29/4.62 fof(f2029,plain,(
% 32.29/4.62 ![X0,X1]: (add(add(X0,X1),additive_inverse(X0))=X1)),
% 32.29/4.62 inference(resolution,[status(thm)],[f1724,f149])).
% 32.29/4.62 fof(f21554,plain,(
% 32.29/4.62 ![X0,X1]: (~product(X0,b,X1)|sum(multiply(X0,c),multiply(X0,bS_Ic),X1))),
% 32.29/4.62 inference(forward_demodulation,[status(thm)],[f1651,f1551])).
% 32.29/4.62 fof(f21556,plain,(
% 32.29/4.62 sum(multiply(a,c),multiply(a,bS_Ic),aPb)),
% 32.29/4.62 inference(resolution,[status(thm)],[f21554,f51])).
% 32.29/4.62 fof(f21564,plain,(
% 32.29/4.62 sum(aPc,multiply(a,bS_Ic),aPb)),
% 32.29/4.62 inference(forward_demodulation,[status(thm)],[f121,f21556])).
% 32.29/4.62 fof(f21827,plain,(
% 32.29/4.62 add(aPc,multiply(a,bS_Ic))=aPb),
% 32.29/4.62 inference(resolution,[status(thm)],[f21564,f150])).
% 32.29/4.62 fof(f21935,plain,(
% 32.29/4.62 add(aPb,additive_inverse(aPc))=multiply(a,bS_Ic)),
% 32.29/4.62 inference(paramodulation,[status(thm)],[f21827,f2029])).
% 32.29/4.62 fof(f21958,plain,(
% 32.29/4.62 aPb_S_IaPc=multiply(a,bS_Ic)),
% 32.29/4.62 inference(forward_demodulation,[status(thm)],[f175,f21935])).
% 32.29/4.64 fof(f22005,plain,(
% 32.29/4.64 product(a,bS_Ic,aPb_S_IaPc)),
% 32.29/4.64 inference(paramodulation,[status(thm)],[f21958,f25])).
% 32.29/4.64 fof(f22017,plain,(
% 32.29/4.64 $false),
% 32.29/4.64 inference(forward_subsumption_resolution,[status(thm)],[f22005,f54])).
% 32.29/4.64 % SZS output end CNFRefutation for theBenchmark.p
% 1.81/4.65 % Elapsed time: 4.210506 seconds
% 1.81/4.65 % CPU time: 32.923041 seconds
% 1.81/4.65 % Total memory used: 87.084 MB
% 1.81/4.65 % Net memory used: 79.240 MB
%------------------------------------------------------------------------------