%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : BOO010-1 : 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 : n015.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 12:06:44 PM UTC 2026
% Result : Unsatisfiable 2.97s 0.86s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 13:50:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 2.97/0.86 % Refutation found
% 2.97/0.86 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.97/0.86 % SZS output start CNFRefutation for theBenchmark
% 2.97/0.86 fof(f1,axiom,(
% 2.97/0.86 (![X,Y]: (sum(X,Y,add(X,Y)) ))),
% 2.97/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.97/0.86 fof(f2,axiom,(
% 2.97/0.86 (![X,Y]: (product(X,Y,multiply(X,Y)) ))),
% 2.97/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.97/0.86 fof(f3,axiom,(
% 2.97/0.86 (![X,Y,Z]: (( ~ sum(X,Y,Z)| sum(Y,X,Z) ) ))),
% 2.97/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.97/0.86 fof(f4,axiom,(
% 2.97/0.86 (![X,Y,Z]: (( ~ product(X,Y,Z)| product(Y,X,Z) ) ))),
% 2.97/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.97/0.86 fof(f5,axiom,(
% 2.97/0.86 (![X]: (sum(additive_identity,X,X) ))),
% 2.97/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.97/0.86 fof(f7,axiom,(
% 2.97/0.86 (![X]: (product(multiplicative_identity,X,X) ))),
% 2.97/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.97/0.86 fof(f8,axiom,(
% 2.97/0.86 (![X]: (product(X,multiplicative_identity,X) ))),
% 2.97/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.97/0.86 fof(f9,axiom,(
% 2.97/0.86 (![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) ) ))),
% 2.97/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.97/0.86 fof(f11,axiom,(
% 2.97/0.86 (![Y,X,V1,Z,V2,V3,V4]: (( ~ product(Y,X,V1)| ~ product(Z,X,V2)| ~ sum(Y,Z,V3)| ~ product(V3,X,V4)| sum(V1,V2,V4) ) ))),
% 2.97/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.97/0.86 fof(f15,axiom,(
% 2.97/0.86 (![Y,X,V1,Z,V2,V3,V4]: (( ~ sum(Y,X,V1)| ~ sum(Z,X,V2)| ~ product(Y,Z,V3)| ~ sum(V3,X,V4)| product(V1,V2,V4) ) ))),
% 2.97/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.97/0.86 fof(f20,axiom,(
% 2.97/0.86 (![X]: (product(X,inverse(X),additive_identity) ))),
% 2.97/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.97/0.86 fof(f21,axiom,(
% 2.97/0.86 (![X,Y,U,V]: (( ~ sum(X,Y,U)| ~ sum(X,Y,V)| U = V ) ))),
% 2.97/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.97/0.86 fof(f22,axiom,(
% 2.97/0.86 (![X,Y,U,V]: (( ~ product(X,Y,U)| ~ product(X,Y,V)| U = V ) ))),
% 2.97/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.97/0.86 fof(f23,negated_conjecture,(
% 2.97/0.86 ~ sum(x,multiply(x,y),x) ),
% 2.97/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.97/0.86 fof(f24,plain,(
% 2.97/0.86 ![X0,X1]: (sum(X0,X1,add(X0,X1)))),
% 2.97/0.86 inference(cnf_transformation,[status(thm)],[f1])).
% 2.97/0.86 fof(f25,plain,(
% 2.97/0.86 ![X0,X1]: (product(X0,X1,multiply(X0,X1)))),
% 2.97/0.86 inference(cnf_transformation,[status(thm)],[f2])).
% 2.97/0.86 fof(f26,plain,(
% 2.97/0.86 ![X0,X1,X2]: (~sum(X0,X1,X2)|sum(X1,X0,X2))),
% 2.97/0.86 inference(cnf_transformation,[status(thm)],[f3])).
% 2.97/0.86 fof(f27,plain,(
% 2.97/0.86 ![X0,X1,X2]: (~product(X0,X1,X2)|product(X1,X0,X2))),
% 2.97/0.86 inference(cnf_transformation,[status(thm)],[f4])).
% 2.97/0.86 fof(f28,plain,(
% 2.97/0.86 ![X0]: (sum(additive_identity,X0,X0))),
% 2.97/0.86 inference(cnf_transformation,[status(thm)],[f5])).
% 2.97/0.86 fof(f30,plain,(
% 2.97/0.86 ![X0]: (product(multiplicative_identity,X0,X0))),
% 2.97/0.86 inference(cnf_transformation,[status(thm)],[f7])).
% 2.97/0.86 fof(f31,plain,(
% 2.97/0.86 ![X0]: (product(X0,multiplicative_identity,X0))),
% 2.97/0.86 inference(cnf_transformation,[status(thm)],[f8])).
% 2.97/0.86 fof(f32,plain,(
% 2.97/0.86 ![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))),
% 2.97/0.86 inference(miniscoping,[status(thm)],[f9])).
% 2.97/0.86 fof(f33,plain,(
% 2.97/0.86 ![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))),
% 2.97/0.86 inference(cnf_transformation,[status(thm)],[f32])).
% 2.97/0.86 fof(f36,plain,(
% 2.97/0.86 ![V1,V2,V4]: ((![X,V3]: ((![Y,Z]: ((~product(Y,X,V1)|~product(Z,X,V2))|~sum(Y,Z,V3)))|~product(V3,X,V4)))|sum(V1,V2,V4))),
% 2.97/0.86 inference(miniscoping,[status(thm)],[f11])).
% 2.97/0.86 fof(f37,plain,(
% 2.97/0.86 ![X0,X1,X2,X3,X4,X5,X6]: (~product(X0,X1,X2)|~product(X3,X1,X4)|~sum(X0,X3,X5)|~product(X5,X1,X6)|sum(X2,X4,X6))),
% 2.97/0.86 inference(cnf_transformation,[status(thm)],[f36])).
% 2.97/0.86 fof(f44,plain,(
% 2.97/0.86 ![V1,V2,V4]: ((![X,V3]: ((![Y,Z]: ((~sum(Y,X,V1)|~sum(Z,X,V2))|~product(Y,Z,V3)))|~sum(V3,X,V4)))|product(V1,V2,V4))),
% 2.97/0.86 inference(miniscoping,[status(thm)],[f15])).
% 2.97/0.86 fof(f45,plain,(
% 2.97/0.86 ![X0,X1,X2,X3,X4,X5,X6]: (~sum(X0,X1,X2)|~sum(X3,X1,X4)|~product(X0,X3,X5)|~sum(X5,X1,X6)|product(X2,X4,X6))),
% 2.97/0.86 inference(cnf_transformation,[status(thm)],[f44])).
% 2.97/0.86 fof(f51,plain,(
% 2.97/0.86 ![X0]: (product(X0,inverse(X0),additive_identity))),
% 2.97/0.86 inference(cnf_transformation,[status(thm)],[f20])).
% 2.97/0.86 fof(f52,plain,(
% 2.97/0.86 ![U,V]: ((![X,Y]: (~sum(X,Y,U)|~sum(X,Y,V)))|U=V)),
% 2.97/0.86 inference(miniscoping,[status(thm)],[f21])).
% 2.97/0.86 fof(f53,plain,(
% 2.97/0.86 ![X0,X1,X2,X3]: (~sum(X0,X1,X2)|~sum(X0,X1,X3)|X2=X3)),
% 2.97/0.86 inference(cnf_transformation,[status(thm)],[f52])).
% 2.97/0.86 fof(f54,plain,(
% 2.97/0.86 ![U,V]: ((![X,Y]: (~product(X,Y,U)|~product(X,Y,V)))|U=V)),
% 2.97/0.86 inference(miniscoping,[status(thm)],[f22])).
% 2.97/0.86 fof(f55,plain,(
% 2.97/0.86 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X1,X3)|X2=X3)),
% 2.97/0.86 inference(cnf_transformation,[status(thm)],[f54])).
% 2.97/0.86 fof(f56,plain,(
% 2.97/0.86 ~sum(x,multiply(x,y),x)),
% 2.97/0.86 inference(cnf_transformation,[status(thm)],[f23])).
% 2.97/0.86 fof(f58,plain,(
% 2.97/0.86 ![X0]: (sum(X0,additive_identity,X0))),
% 2.97/0.86 inference(resolution,[status(thm)],[f28,f26])).
% 2.97/0.86 fof(f61,plain,(
% 2.97/0.86 ![X0,X1]: (~sum(X0,additive_identity,X1)|X1=X0)),
% 2.97/0.86 inference(resolution,[status(thm)],[f58,f53])).
% 2.97/0.86 fof(f66,plain,(
% 2.97/0.86 ![X0]: (add(X0,additive_identity)=X0)),
% 2.97/0.86 inference(resolution,[status(thm)],[f24,f61])).
% 2.97/0.86 fof(f67,plain,(
% 2.97/0.86 ![X0,X1,X2]: (~sum(X0,X1,X2)|X2=add(X0,X1))),
% 2.97/0.86 inference(resolution,[status(thm)],[f24,f53])).
% 2.97/0.86 fof(f68,plain,(
% 2.97/0.86 ![X0,X1]: (sum(X0,X1,add(X1,X0)))),
% 2.97/0.86 inference(resolution,[status(thm)],[f24,f26])).
% 2.97/0.86 fof(f128,plain,(
% 2.97/0.86 ![X0,X1]: (product(X0,X1,multiply(X1,X0)))),
% 2.97/0.86 inference(resolution,[status(thm)],[f27,f25])).
% 2.97/0.86 fof(f150,plain,(
% 2.97/0.86 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~sum(X1,X3,X3)|sum(X2,multiply(X3,X0),multiply(X3,X0)))),
% 2.97/0.86 inference(resolution,[status(thm)],[f33,f128])).
% 2.97/0.86 fof(f244,plain,(
% 2.97/0.86 ![X0,X1,X2,X3]: (~product(X0,X1,x)|~product(X2,X1,multiply(x,y))|~sum(X0,X2,X3)|~product(X3,X1,x))),
% 2.97/0.86 inference(resolution,[status(thm)],[f37,f56])).
% 2.97/0.86 fof(f272,plain,(
% 2.97/0.86 ![X0,X1]: (~product(X0,x,x)|~sum(X0,y,X1)|~product(X1,x,x))),
% 2.97/0.86 inference(resolution,[status(thm)],[f244,f128])).
% 2.97/0.86 fof(f275,plain,(
% 2.97/0.86 ![X0]: (~product(X0,x,x)|~sum(X0,y,multiplicative_identity))),
% 2.97/0.86 inference(resolution,[status(thm)],[f272,f30])).
% 2.97/0.86 fof(f283,plain,(
% 2.97/0.86 ![X0,X1,X2]: (~product(X0,additive_identity,X1)|sum(X1,multiply(X2,X0),multiply(X2,X0)))),
% 2.97/0.86 inference(resolution,[status(thm)],[f150,f28])).
% 2.97/0.86 fof(f289,plain,(
% 2.97/0.86 ![X0,X1]: (sum(multiply(additive_identity,X0),multiply(X1,X0),multiply(X1,X0)))),
% 2.97/0.86 inference(resolution,[status(thm)],[f283,f128])).
% 2.97/0.86 fof(f302,plain,(
% 2.97/0.86 ![X0,X1]: (multiply(X0,X1)=add(multiply(additive_identity,X1),multiply(X0,X1)))),
% 2.97/0.86 inference(resolution,[status(thm)],[f289,f67])).
% 2.97/0.86 fof(f357,plain,(
% 2.97/0.86 ![X0,X1]: (~product(X0,multiplicative_identity,X1)|X1=X0)),
% 2.97/0.86 inference(resolution,[status(thm)],[f55,f31])).
% 2.97/0.86 fof(f358,plain,(
% 2.97/0.86 ![X0,X1,X2]: (~product(X0,X1,X2)|X2=multiply(X1,X0))),
% 2.97/0.86 inference(resolution,[status(thm)],[f55,f128])).
% 2.97/0.86 fof(f743,plain,(
% 2.97/0.86 ![X0]: (additive_identity=multiply(inverse(X0),X0))),
% 2.97/0.86 inference(resolution,[status(thm)],[f358,f51])).
% 2.97/0.86 fof(f901,plain,(
% 2.97/0.86 ![X0]: (multiply(inverse(X0),X0)=add(multiply(additive_identity,X0),additive_identity))),
% 2.97/0.86 inference(paramodulation,[status(thm)],[f743,f302])).
% 2.97/0.86 fof(f919,plain,(
% 2.97/0.86 ![X0]: (additive_identity=add(multiply(additive_identity,X0),additive_identity))),
% 2.97/0.86 inference(forward_demodulation,[status(thm)],[f743,f901])).
% 2.97/0.86 fof(f920,plain,(
% 2.97/0.86 ![X0]: (additive_identity=multiply(additive_identity,X0))),
% 2.97/0.86 inference(forward_demodulation,[status(thm)],[f66,f919])).
% 2.97/0.86 fof(f944,plain,(
% 2.97/0.86 ![X0]: (product(X0,additive_identity,additive_identity))),
% 2.97/0.86 inference(paramodulation,[status(thm)],[f920,f128])).
% 2.97/0.86 fof(f1086,plain,(
% 2.97/0.86 ![X0,X1,X2]: (~sum(X0,X1,X2)|~product(X0,additive_identity,additive_identity)|product(X2,X1,X1))),
% 2.97/0.86 inference(resolution,[status(thm)],[f45,f28])).
% 2.97/0.86 fof(f1112,plain,(
% 2.97/0.86 ![X0,X1,X2]: (~sum(X0,X1,X2)|product(X2,X1,X1))),
% 2.97/0.86 inference(forward_subsumption_resolution,[status(thm)],[f1086,f944])).
% 2.97/0.86 fof(f1194,plain,(
% 2.97/0.86 ![X0,X1]: (product(add(X0,X1),X0,X0))),
% 2.97/0.86 inference(resolution,[status(thm)],[f1112,f68])).
% 2.97/0.86 fof(f1249,plain,(
% 2.97/0.86 ![X0]: (multiplicative_identity=add(multiplicative_identity,X0))),
% 2.97/0.86 inference(resolution,[status(thm)],[f1194,f357])).
% 2.97/0.86 fof(f1292,plain,(
% 2.97/0.86 ![X0]: (sum(multiplicative_identity,X0,multiplicative_identity))),
% 2.97/0.86 inference(paramodulation,[status(thm)],[f1249,f24])).
% 3.39/0.87 fof(f1457,plain,(
% 3.39/0.87 ~product(multiplicative_identity,x,x)),
% 3.39/0.87 inference(resolution,[status(thm)],[f1292,f275])).
% 3.39/0.87 fof(f1495,plain,(
% 3.39/0.87 $false),
% 3.39/0.87 inference(forward_subsumption_resolution,[status(thm)],[f1457,f30])).
% 3.39/0.87 % SZS output end CNFRefutation for theBenchmark.p
% 3.39/0.88 % Elapsed time: 0.504786 seconds
% 3.39/0.88 % CPU time: 3.760373 seconds
% 3.39/0.88 % Total memory used: 62.571 MB
% 3.39/0.88 % Net memory used: 58.252 MB
%------------------------------------------------------------------------------