%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE027+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 12:58:12 PM UTC 2026
% Result : Theorem 45.26s 6.13s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE027+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n005.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 : Sun Sep 20 22:39:17 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 45.26/6.13 % Refutation found
% 45.26/6.13 % SZS status Theorem for theBenchmark: Theorem is valid
% 45.26/6.13 % SZS output start CNFRefutation for theBenchmark
% 45.26/6.13 fof(f1,axiom,(
% 45.26/6.13 (! [A,B] : addition(A,B) = addition(B,A) )),
% 45.26/6.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 45.26/6.13 fof(f2,axiom,(
% 45.26/6.13 (! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) )),
% 45.26/6.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 45.26/6.13 fof(f3,axiom,(
% 45.26/6.13 (! [A] : addition(A,zero) = A )),
% 45.26/6.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 45.26/6.13 fof(f4,axiom,(
% 45.26/6.13 (! [A] : addition(A,A) = A )),
% 45.26/6.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 45.26/6.13 fof(f5,axiom,(
% 45.26/6.13 (! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )),
% 45.26/6.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 45.26/6.13 fof(f6,axiom,(
% 45.26/6.13 (! [A] : multiplication(A,one) = A )),
% 45.26/6.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 45.26/6.13 fof(f8,axiom,(
% 45.26/6.13 (! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )),
% 45.26/6.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 45.26/6.13 fof(f11,axiom,(
% 45.26/6.13 (! [A] : multiplication(zero,A) = zero )),
% 45.26/6.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 45.26/6.13 fof(f13,axiom,(
% 45.26/6.13 (! [X0] :( test(X0)<=> (? [X1] : complement(X1,X0) )) )),
% 45.26/6.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 45.26/6.13 fof(f14,axiom,(
% 45.26/6.13 (! [X0,X1] :( complement(X1,X0)<=> ( multiplication(X0,X1) = zero& multiplication(X1,X0) = zero& addition(X0,X1) = one ) ) )),
% 45.26/6.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 45.26/6.13 fof(f15,axiom,(
% 45.26/6.13 (! [X0,X1] :( test(X0)=> ( c(X0) = X1<=> complement(X0,X1) ) ) )),
% 45.26/6.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 45.26/6.13 fof(f19,conjecture,(
% 45.26/6.13 (! [X0,X1,X2,X3,X4] :( ( test(X3)& test(X4) )=> addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) = addition(multiplication(X3,X0),multiplication(c(X3),X2)) ) )),
% 45.26/6.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 45.26/6.13 fof(f20,negated_conjecture,(
% 45.26/6.13 ~((! [X0,X1,X2,X3,X4] :( ( test(X3)& test(X4) )=> addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) = addition(multiplication(X3,X0),multiplication(c(X3),X2)) ) ))),
% 45.26/6.13 inference(negated_conjecture,[status(cth)],[f19])).
% 45.26/6.13 fof(f21,plain,(
% 45.26/6.13 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 45.26/6.13 inference(cnf_transformation,[status(thm)],[f1])).
% 45.26/6.13 fof(f22,plain,(
% 45.26/6.13 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(addition(X0,X1),X2))),
% 45.26/6.13 inference(cnf_transformation,[status(thm)],[f2])).
% 45.26/6.13 fof(f23,plain,(
% 45.26/6.13 ![X0]: (addition(X0,zero)=X0)),
% 45.26/6.13 inference(cnf_transformation,[status(thm)],[f3])).
% 45.26/6.13 fof(f24,plain,(
% 45.26/6.13 ![X0]: (addition(X0,X0)=X0)),
% 45.26/6.13 inference(cnf_transformation,[status(thm)],[f4])).
% 45.26/6.13 fof(f25,plain,(
% 45.26/6.13 ![X0,X1,X2]: (multiplication(X0,multiplication(X1,X2))=multiplication(multiplication(X0,X1),X2))),
% 45.26/6.13 inference(cnf_transformation,[status(thm)],[f5])).
% 45.26/6.13 fof(f26,plain,(
% 45.26/6.13 ![X0]: (multiplication(X0,one)=X0)),
% 45.26/6.13 inference(cnf_transformation,[status(thm)],[f6])).
% 45.26/6.13 fof(f28,plain,(
% 45.26/6.13 ![X0,X1,X2]: (multiplication(X0,addition(X1,X2))=addition(multiplication(X0,X1),multiplication(X0,X2)))),
% 45.26/6.13 inference(cnf_transformation,[status(thm)],[f8])).
% 45.26/6.13 fof(f31,plain,(
% 45.26/6.13 ![X0]: (multiplication(zero,X0)=zero)),
% 45.26/6.13 inference(cnf_transformation,[status(thm)],[f11])).
% 45.26/6.13 fof(f36,plain,(
% 45.26/6.13 ![X0]: ((~test(X0)|(?[X1]: complement(X1,X0)))&(test(X0)|(![X1]: ~complement(X1,X0))))),
% 45.26/6.13 inference(NNF_transformation,[status(thm)],[f13])).
% 45.26/6.13 fof(f37,plain,(
% 45.26/6.13 (![X0]: (~test(X0)|(?[X1]: complement(X1,X0))))&(![X0]: (test(X0)|(![X1]: ~complement(X1,X0))))),
% 45.26/6.13 inference(miniscoping,[status(thm)],[f36])).
% 45.26/6.13 fof(f38,plain,(
% 45.26/6.13 (![X0]: (~test(X0)|complement(sK0_skl(X0),X0)))&(![X0]: (test(X0)|(![X1]: ~complement(X1,X0))))),
% 45.26/6.13 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X1,sK0_skl(X0))],[f37])).
% 45.26/6.13 fof(f39,plain,(
% 45.26/6.13 ![X0]: (~test(X0)|complement(sK0_skl(X0),X0))),
% 45.26/6.13 inference(cnf_transformation,[status(thm)],[f38])).
% 45.26/6.13 fof(f41,plain,(
% 45.26/6.13 ![X0,X1]: ((~complement(X1,X0)|((multiplication(X0,X1)=zero&multiplication(X1,X0)=zero)&addition(X0,X1)=one))&(complement(X1,X0)|((~multiplication(X0,X1)=zero|~multiplication(X1,X0)=zero)|~addition(X0,X1)=one)))),
% 45.26/6.13 inference(NNF_transformation,[status(thm)],[f14])).
% 45.26/6.13 fof(f42,plain,(
% 45.26/6.13 (![X0,X1]: (~complement(X1,X0)|((multiplication(X0,X1)=zero&multiplication(X1,X0)=zero)&addition(X0,X1)=one)))&(![X0,X1]: (complement(X1,X0)|((~multiplication(X0,X1)=zero|~multiplication(X1,X0)=zero)|~addition(X0,X1)=one)))),
% 45.26/6.13 inference(miniscoping,[status(thm)],[f41])).
% 45.26/6.13 fof(f43,plain,(
% 45.26/6.13 ![X0,X1]: (~complement(X0,X1)|multiplication(X1,X0)=zero)),
% 45.26/6.13 inference(cnf_transformation,[status(thm)],[f42])).
% 45.26/6.13 fof(f44,plain,(
% 45.26/6.13 ![X0,X1]: (~complement(X0,X1)|multiplication(X0,X1)=zero)),
% 45.26/6.13 inference(cnf_transformation,[status(thm)],[f42])).
% 45.26/6.13 fof(f45,plain,(
% 45.26/6.13 ![X0,X1]: (~complement(X0,X1)|addition(X1,X0)=one)),
% 45.26/6.13 inference(cnf_transformation,[status(thm)],[f42])).
% 45.26/6.13 fof(f47,plain,(
% 45.26/6.13 ![X0,X1]: (~test(X0)|(c(X0)=X1<=>complement(X0,X1)))),
% 45.26/6.13 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 45.26/6.13 fof(f48,plain,(
% 45.26/6.13 ![X0,X1]: (~test(X0)|((~c(X0)=X1|complement(X0,X1))&(c(X0)=X1|~complement(X0,X1))))),
% 45.26/6.13 inference(NNF_transformation,[status(thm)],[f47])).
% 45.26/6.13 fof(f49,plain,(
% 45.26/6.13 ![X0]: (~test(X0)|((![X1]: (~c(X0)=X1|complement(X0,X1)))&(![X1]: (c(X0)=X1|~complement(X0,X1)))))),
% 45.26/6.13 inference(miniscoping,[status(thm)],[f48])).
% 45.26/6.13 fof(f50,plain,(
% 45.26/6.13 ![X0,X1]: (~test(X0)|~c(X0)=X1|complement(X0,X1))),
% 45.26/6.13 inference(cnf_transformation,[status(thm)],[f49])).
% 45.26/6.13 fof(f58,plain,(
% 45.26/6.13 (?[X0,X1,X2,X3,X4]: ((test(X3)&test(X4))&~addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2))=addition(multiplication(X3,X0),multiplication(c(X3),X2))))),
% 45.26/6.13 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 45.26/6.13 fof(f59,plain,(
% 45.26/6.13 ?[X3]: ((test(X3)&(?[X4]: test(X4)))&(?[X0,X1,X2]: ~addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2))=addition(multiplication(X3,X0),multiplication(c(X3),X2))))),
% 45.26/6.13 inference(miniscoping,[status(thm)],[f58])).
% 45.26/6.13 fof(f60,plain,(
% 45.26/6.13 ((test(sK1_skl)&test(sK2_skl))&~addition(multiplication(sK1_skl,addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK4_skl))),multiplication(c(sK1_skl),sK5_skl))=addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK5_skl)))),
% 45.26/6.13 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(X3,sK1_skl),skolemize(X4,sK2_skl),skolemize(X0,sK3_skl),skolemize(X1,sK4_skl),skolemize(X2,sK5_skl)],[f59])).
% 45.26/6.13 fof(f61,plain,(
% 45.26/6.13 test(sK1_skl)),
% 45.26/6.13 inference(cnf_transformation,[status(thm)],[f60])).
% 45.26/6.13 fof(f63,plain,(
% 45.26/6.13 ~addition(multiplication(sK1_skl,addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK4_skl))),multiplication(c(sK1_skl),sK5_skl))=addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK5_skl))),
% 45.26/6.13 inference(cnf_transformation,[status(thm)],[f60])).
% 45.26/6.13 fof(f64,plain,(
% 45.26/6.13 ![X0]: (~test(X0)|complement(X0,c(X0)))),
% 45.26/6.13 inference(destructive_equality_resolution,[status(thm)],[f50])).
% 45.26/6.13 fof(f69,plain,(
% 45.26/6.13 ~addition(multiplication(c(sK1_skl),sK5_skl),multiplication(sK1_skl,addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK4_skl))))=addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK5_skl))),
% 45.26/6.13 inference(paramodulation,[status(thm)],[f21,f63])).
% 45.26/6.13 fof(f71,plain,(
% 45.26/6.13 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(X2,addition(X0,X1)))),
% 45.26/6.13 inference(paramodulation,[status(thm)],[f21,f22])).
% 45.26/6.13 fof(f77,plain,(
% 45.26/6.13 ![X0,X1]: (addition(X0,addition(X0,X1))=addition(X0,X1))),
% 45.26/6.13 inference(paramodulation,[status(thm)],[f24,f22])).
% 45.26/6.13 fof(f86,plain,(
% 45.26/6.13 ![X0,X1]: (addition(X0,addition(X1,X0))=addition(X0,X1))),
% 45.26/6.13 inference(paramodulation,[status(thm)],[f21,f77])).
% 45.26/6.13 fof(f145,plain,(
% 45.26/6.13 ![X0,X1]: (addition(X0,X1)=addition(X1,addition(X0,X1)))),
% 45.26/6.13 inference(paramodulation,[status(thm)],[f24,f71])).
% 45.26/6.13 fof(f428,plain,(
% 45.26/6.13 ![X0,X1,X2]: (multiplication(X0,addition(X1,X2))=addition(multiplication(X0,X2),multiplication(X0,X1)))),
% 45.26/6.13 inference(paramodulation,[status(thm)],[f21,f28])).
% 45.26/6.13 fof(f488,plain,(
% 45.26/6.13 ![X0]: (addition(zero,X0)=X0)),
% 45.26/6.17 inference(paramodulation,[status(thm)],[f21,f23])).
% 45.26/6.17 fof(f605,plain,(
% 45.26/6.17 ![X0]: (multiplication(X0,sK0_skl(X0))=zero|~test(X0))),
% 45.26/6.17 inference(resolution,[status(thm)],[f43,f39])).
% 45.26/6.17 fof(f608,plain,(
% 45.26/6.17 ![X0]: (multiplication(X0,c(X0))=zero|~test(X0))),
% 45.26/6.17 inference(resolution,[status(thm)],[f44,f64])).
% 45.26/6.17 fof(f609,plain,(
% 45.26/6.17 ![X0]: (addition(X0,sK0_skl(X0))=one|~test(X0))),
% 45.26/6.17 inference(resolution,[status(thm)],[f45,f39])).
% 45.26/6.17 fof(f2478,plain,(
% 45.26/6.17 multiplication(sK1_skl,sK0_skl(sK1_skl))=zero),
% 45.26/6.17 inference(resolution,[status(thm)],[f605,f61])).
% 45.26/6.17 fof(f2509,plain,(
% 45.26/6.17 ![X0]: (multiplication(sK1_skl,addition(sK0_skl(sK1_skl),X0))=addition(multiplication(sK1_skl,X0),zero))),
% 45.26/6.17 inference(paramodulation,[status(thm)],[f2478,f428])).
% 45.26/6.17 fof(f2521,plain,(
% 45.26/6.17 ![X0]: (multiplication(sK1_skl,addition(sK0_skl(sK1_skl),X0))=multiplication(sK1_skl,X0))),
% 45.26/6.17 inference(forward_demodulation,[status(thm)],[f23,f2509])).
% 45.26/6.17 fof(f2664,plain,(
% 45.26/6.17 multiplication(sK1_skl,c(sK1_skl))=zero),
% 45.26/6.17 inference(resolution,[status(thm)],[f608,f61])).
% 45.26/6.17 fof(f3094,plain,(
% 45.26/6.17 ![X0]: (multiplication(sK1_skl,multiplication(c(sK1_skl),X0))=multiplication(zero,X0))),
% 45.26/6.17 inference(paramodulation,[status(thm)],[f2664,f25])).
% 45.26/6.17 fof(f3117,plain,(
% 45.26/6.17 ![X0]: (multiplication(sK1_skl,multiplication(c(sK1_skl),X0))=zero)),
% 45.26/6.17 inference(forward_demodulation,[status(thm)],[f31,f3094])).
% 45.26/6.17 fof(f3448,plain,(
% 45.26/6.17 ![X0,X1]: (multiplication(sK1_skl,addition(X0,multiplication(c(sK1_skl),X1)))=addition(zero,multiplication(sK1_skl,X0)))),
% 45.26/6.17 inference(paramodulation,[status(thm)],[f3117,f428])).
% 45.26/6.17 fof(f3466,plain,(
% 45.26/6.17 ~addition(multiplication(c(sK1_skl),sK5_skl),multiplication(sK1_skl,multiplication(sK1_skl,sK3_skl)))=addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK5_skl))),
% 45.26/6.17 inference(backward_demodulation,[status(thm)],[f3468,f69])).
% 45.26/6.17 fof(f3468,plain,(
% 45.26/6.17 ![X0,X1]: (multiplication(sK1_skl,addition(X0,multiplication(c(sK1_skl),X1)))=multiplication(sK1_skl,X0))),
% 45.26/6.17 inference(forward_demodulation,[status(thm)],[f488,f3448])).
% 45.26/6.17 fof(f4128,plain,(
% 45.26/6.17 addition(sK1_skl,sK0_skl(sK1_skl))=one),
% 45.26/6.17 inference(resolution,[status(thm)],[f609,f61])).
% 45.26/6.17 fof(f4219,plain,(
% 45.26/6.17 addition(sK1_skl,sK0_skl(sK1_skl))=addition(sK0_skl(sK1_skl),one)),
% 45.26/6.17 inference(paramodulation,[status(thm)],[f4128,f145])).
% 45.26/6.17 fof(f4222,plain,(
% 45.26/6.17 addition(sK0_skl(sK1_skl),one)=addition(sK0_skl(sK1_skl),sK1_skl)),
% 45.26/6.17 inference(paramodulation,[status(thm)],[f4128,f86])).
% 45.26/6.17 fof(f4227,plain,(
% 45.26/6.17 one=addition(sK0_skl(sK1_skl),one)),
% 45.26/6.17 inference(forward_demodulation,[status(thm)],[f4128,f4219])).
% 45.26/6.17 fof(f4229,plain,(
% 45.26/6.17 one=addition(sK0_skl(sK1_skl),sK1_skl)),
% 45.26/6.17 inference(forward_demodulation,[status(thm)],[f4227,f4222])).
% 45.26/6.17 fof(f18822,plain,(
% 45.26/6.17 multiplication(sK1_skl,one)=multiplication(sK1_skl,sK1_skl)),
% 45.26/6.17 inference(paramodulation,[status(thm)],[f4229,f2521])).
% 45.26/6.17 fof(f18896,plain,(
% 45.26/6.17 sK1_skl=multiplication(sK1_skl,sK1_skl)),
% 45.26/6.17 inference(forward_demodulation,[status(thm)],[f26,f18822])).
% 45.26/6.17 fof(f18975,plain,(
% 45.26/6.17 ![X0]: (multiplication(sK1_skl,multiplication(sK1_skl,X0))=multiplication(sK1_skl,X0))),
% 45.26/6.17 inference(paramodulation,[status(thm)],[f18896,f25])).
% 45.26/6.17 fof(f19017,plain,(
% 45.26/6.17 ~addition(multiplication(c(sK1_skl),sK5_skl),multiplication(sK1_skl,sK3_skl))=addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK5_skl))),
% 45.26/6.17 inference(backward_demodulation,[status(thm)],[f18975,f3466])).
% 45.26/6.17 fof(f19020,plain,(
% 45.26/6.17 $false),
% 45.26/6.17 inference(forward_subsumption_resolution,[status(thm)],[f19017,f21])).
% 45.26/6.17 % SZS output end CNFRefutation for theBenchmark.p
% 1.58/6.20 % Elapsed time: 5.828931 seconds
% 1.58/6.20 % CPU time: 45.955944 seconds
% 1.58/6.20 % Total memory used: 450.196 MB
% 1.58/6.20 % Net memory used: 436.927 MB
%------------------------------------------------------------------------------