%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM423+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 01:42:51 PM UTC 2026
% Result : Theorem 0.32s 0.84s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM423+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n008.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 02:28:53 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.46 % Drodi V4.1.1
% 0.32/0.84 % Refutation found
% 0.32/0.84 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.32/0.84 % SZS output start CNFRefutation for theBenchmark
% 0.32/0.84 fof(f2,axiom,(
% 0.32/0.84 aInteger0(sz00) ),
% 0.32/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.32/0.84 fof(f6,axiom,(
% 0.32/0.84 (! [W0,W1] :( ( aInteger0(W0)& aInteger0(W1) )=> aInteger0(sdtasdt0(W0,W1)) ) )),
% 0.32/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.32/0.84 fof(f10,axiom,(
% 0.32/0.84 (! [W0] :( aInteger0(W0)=> ( sdtpldt0(W0,smndt0(W0)) = sz00& sz00 = sdtpldt0(smndt0(W0),W0) ) ) )),
% 0.32/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.32/0.84 fof(f15,axiom,(
% 0.32/0.84 (! [W0] :( aInteger0(W0)=> ( sdtasdt0(W0,sz00) = sz00& sz00 = sdtasdt0(sz00,W0) ) ) )),
% 0.32/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.32/0.84 fof(f18,definition,(
% 0.32/0.84 (! [W0] :( aInteger0(W0)=> (! [W1] :( aDivisorOf0(W1,W0)<=> ( aInteger0(W1)& W1 != sz00& (? [W2] :( aInteger0(W2)& sdtasdt0(W1,W2) = W0 ) )) ) )) )),
% 0.32/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.32/0.84 fof(f19,definition,(
% 0.32/0.84 (! [W0,W1,W2] :( ( aInteger0(W0)& aInteger0(W1)& aInteger0(W2)& W2 != sz00 )=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ) )),
% 0.32/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.32/0.84 fof(f20,hypothesis,(
% 0.32/0.84 ( aInteger0(xa)& aInteger0(xq)& xq != sz00 ) ),
% 0.32/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.32/0.84 fof(f21,conjecture,(
% 0.32/0.84 sdteqdtlpzmzozddtrp0(xa,xa,xq) ),
% 0.32/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.32/0.84 fof(f22,negated_conjecture,(
% 0.32/0.84 ~(sdteqdtlpzmzozddtrp0(xa,xa,xq) )),
% 0.32/0.84 inference(negated_conjecture,[status(cth)],[f21])).
% 0.32/0.84 fof(f26,plain,(
% 0.32/0.84 aInteger0(sz00)),
% 0.32/0.84 inference(cnf_transformation,[status(thm)],[f2])).
% 0.32/0.84 fof(f32,plain,(
% 0.32/0.84 ![W0,W1]: ((~aInteger0(W0)|~aInteger0(W1))|aInteger0(sdtasdt0(W0,W1)))),
% 0.32/0.84 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.32/0.84 fof(f33,plain,(
% 0.32/0.84 ![X0,X1]: (~aInteger0(X0)|~aInteger0(X1)|aInteger0(sdtasdt0(X0,X1)))),
% 0.32/0.84 inference(cnf_transformation,[status(thm)],[f32])).
% 0.32/0.84 fof(f41,plain,(
% 0.32/0.84 ![W0]: (~aInteger0(W0)|(sdtpldt0(W0,smndt0(W0))=sz00&sz00=sdtpldt0(smndt0(W0),W0)))),
% 0.32/0.84 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.32/0.84 fof(f42,plain,(
% 0.32/0.84 ![X0]: (~aInteger0(X0)|sdtpldt0(X0,smndt0(X0))=sz00)),
% 0.32/0.84 inference(cnf_transformation,[status(thm)],[f41])).
% 0.32/0.84 fof(f54,plain,(
% 0.32/0.84 ![W0]: (~aInteger0(W0)|(sdtasdt0(W0,sz00)=sz00&sz00=sdtasdt0(sz00,W0)))),
% 0.32/0.84 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.32/0.84 fof(f55,plain,(
% 0.32/0.84 ![X0]: (~aInteger0(X0)|sdtasdt0(X0,sz00)=sz00)),
% 0.32/0.84 inference(cnf_transformation,[status(thm)],[f54])).
% 0.32/0.84 fof(f62,plain,(
% 0.32/0.84 ![W0]: (~aInteger0(W0)|(![W1]: (aDivisorOf0(W1,W0)<=>((aInteger0(W1)&~W1=sz00)&(?[W2]: (aInteger0(W2)&sdtasdt0(W1,W2)=W0))))))),
% 0.32/0.84 inference(pre_NNF_transformation,[status(thm)],[f18])).
% 0.32/0.84 fof(f63,plain,(
% 0.32/0.84 ![W0]: (~aInteger0(W0)|(![W1]: ((~aDivisorOf0(W1,W0)|((aInteger0(W1)&~W1=sz00)&(?[W2]: (aInteger0(W2)&sdtasdt0(W1,W2)=W0))))&(aDivisorOf0(W1,W0)|((~aInteger0(W1)|W1=sz00)|(![W2]: (~aInteger0(W2)|~sdtasdt0(W1,W2)=W0)))))))),
% 0.32/0.84 inference(NNF_transformation,[status(thm)],[f62])).
% 0.32/0.84 fof(f64,plain,(
% 0.32/0.84 ![W0]: (~aInteger0(W0)|((![W1]: (~aDivisorOf0(W1,W0)|((aInteger0(W1)&~W1=sz00)&(?[W2]: (aInteger0(W2)&sdtasdt0(W1,W2)=W0)))))&(![W1]: (aDivisorOf0(W1,W0)|((~aInteger0(W1)|W1=sz00)|(![W2]: (~aInteger0(W2)|~sdtasdt0(W1,W2)=W0)))))))),
% 0.32/0.84 inference(miniscoping,[status(thm)],[f63])).
% 0.32/0.84 fof(f65,plain,(
% 0.32/0.84 ![W0]: (~aInteger0(W0)|((![W1]: (~aDivisorOf0(W1,W0)|((aInteger0(W1)&~W1=sz00)&(aInteger0(sK0_skl(W1,W0))&sdtasdt0(W1,sK0_skl(W1,W0))=W0))))&(![W1]: (aDivisorOf0(W1,W0)|((~aInteger0(W1)|W1=sz00)|(![W2]: (~aInteger0(W2)|~sdtasdt0(W1,W2)=W0)))))))),
% 0.32/0.84 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(W2,sK0_skl(W1,W0))],[f64])).
% 0.32/0.84 fof(f70,plain,(
% 0.32/0.84 ![X0,X1,X2]: (~aInteger0(X0)|aDivisorOf0(X1,X0)|~aInteger0(X1)|X1=sz00|~aInteger0(X2)|~sdtasdt0(X1,X2)=X0)),
% 0.32/0.84 inference(cnf_transformation,[status(thm)],[f65])).
% 0.32/0.84 fof(f71,plain,(
% 0.32/0.84 ![W0,W1,W2]: ((((~aInteger0(W0)|~aInteger0(W1))|~aInteger0(W2))|W2=sz00)|(sdteqdtlpzmzozddtrp0(W0,W1,W2)<=>aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1)))))),
% 0.32/0.84 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 0.32/0.86 fof(f72,plain,(
% 0.32/0.86 ![W0,W1,W2]: ((((~aInteger0(W0)|~aInteger0(W1))|~aInteger0(W2))|W2=sz00)|((~sdteqdtlpzmzozddtrp0(W0,W1,W2)|aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))))&(sdteqdtlpzmzozddtrp0(W0,W1,W2)|~aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))))))),
% 0.32/0.86 inference(NNF_transformation,[status(thm)],[f71])).
% 0.32/0.86 fof(f74,plain,(
% 0.32/0.86 ![X0,X1,X2]: (~aInteger0(X0)|~aInteger0(X1)|~aInteger0(X2)|X2=sz00|sdteqdtlpzmzozddtrp0(X0,X1,X2)|~aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))))),
% 0.32/0.86 inference(cnf_transformation,[status(thm)],[f72])).
% 0.32/0.86 fof(f75,plain,(
% 0.32/0.86 aInteger0(xa)),
% 0.32/0.86 inference(cnf_transformation,[status(thm)],[f20])).
% 0.32/0.86 fof(f76,plain,(
% 0.32/0.86 aInteger0(xq)),
% 0.32/0.86 inference(cnf_transformation,[status(thm)],[f20])).
% 0.32/0.86 fof(f77,plain,(
% 0.32/0.86 ~xq=sz00),
% 0.32/0.86 inference(cnf_transformation,[status(thm)],[f20])).
% 0.32/0.86 fof(f78,plain,(
% 0.32/0.86 ~sdteqdtlpzmzozddtrp0(xa,xa,xq)),
% 0.32/0.86 inference(cnf_transformation,[status(thm)],[f22])).
% 0.32/0.86 fof(f80,plain,(
% 0.32/0.86 ![X1,X2]: (~aInteger0(sdtasdt0(X1,X2))|aDivisorOf0(X1,sdtasdt0(X1,X2))|~aInteger0(X1)|X1=sz00|~aInteger0(X2))),
% 0.32/0.86 inference(destructive_equality_resolution,[status(thm)],[f70])).
% 0.32/0.86 fof(f81,plain,(
% 0.32/0.86 ![X0,X1]: (aDivisorOf0(X0,sdtasdt0(X0,X1))|~aInteger0(X0)|X0=sz00|~aInteger0(X1))),
% 0.32/0.86 inference(forward_subsumption_resolution,[status(thm)],[f80,f33])).
% 0.32/0.86 fof(f89,plain,(
% 0.32/0.86 sdtasdt0(xq,sz00)=sz00),
% 0.32/0.86 inference(resolution,[status(thm)],[f55,f76])).
% 0.32/0.86 fof(f96,plain,(
% 0.32/0.86 sdtpldt0(xa,smndt0(xa))=sz00),
% 0.32/0.86 inference(resolution,[status(thm)],[f42,f75])).
% 0.32/0.86 fof(f519,plain,(
% 0.32/0.86 ![X0]: (~aInteger0(xa)|~aInteger0(xa)|~aInteger0(X0)|X0=sz00|sdteqdtlpzmzozddtrp0(xa,xa,X0)|~aDivisorOf0(X0,sz00))),
% 0.32/0.86 inference(paramodulation,[status(thm)],[f96,f74])).
% 0.32/0.86 fof(f520,plain,(
% 0.32/0.86 ![X0]: (~aInteger0(xa)|~aInteger0(X0)|X0=sz00|sdteqdtlpzmzozddtrp0(xa,xa,X0)|~aDivisorOf0(X0,sz00))),
% 0.32/0.86 inference(duplicate_literals_removal,[status(thm)],[f519])).
% 0.32/0.86 fof(f521,plain,(
% 0.32/0.86 ![X0]: (~aInteger0(X0)|X0=sz00|sdteqdtlpzmzozddtrp0(xa,xa,X0)|~aDivisorOf0(X0,sz00))),
% 0.32/0.86 inference(forward_subsumption_resolution,[status(thm)],[f520,f75])).
% 0.32/0.86 fof(f531,plain,(
% 0.32/0.86 aDivisorOf0(xq,sz00)|~aInteger0(xq)|xq=sz00|~aInteger0(sz00)),
% 0.32/0.86 inference(paramodulation,[status(thm)],[f89,f81])).
% 0.32/0.86 fof(f535,plain,(
% 0.32/0.86 aDivisorOf0(xq,sz00)|xq=sz00|~aInteger0(sz00)),
% 0.32/0.86 inference(forward_subsumption_resolution,[status(thm)],[f531,f76])).
% 0.32/0.86 fof(f544,plain,(
% 0.32/0.86 aDivisorOf0(xq,sz00)|xq=sz00),
% 0.32/0.86 inference(resolution,[status(thm)],[f535,f26])).
% 0.32/0.86 fof(f545,plain,(
% 0.32/0.86 aDivisorOf0(xq,sz00)),
% 0.32/0.86 inference(forward_subsumption_resolution,[status(thm)],[f544,f77])).
% 0.32/0.86 fof(f552,plain,(
% 0.32/0.86 ~aInteger0(xq)|xq=sz00|sdteqdtlpzmzozddtrp0(xa,xa,xq)),
% 0.32/0.86 inference(resolution,[status(thm)],[f521,f545])).
% 0.32/0.86 fof(f554,plain,(
% 0.32/0.86 xq=sz00|sdteqdtlpzmzozddtrp0(xa,xa,xq)),
% 0.32/0.86 inference(forward_subsumption_resolution,[status(thm)],[f552,f76])).
% 0.32/0.86 fof(f557,plain,(
% 0.32/0.86 xq=sz00),
% 0.32/0.86 inference(resolution,[status(thm)],[f554,f78])).
% 0.32/0.86 fof(f559,plain,(
% 0.32/0.86 $false),
% 0.32/0.86 inference(forward_subsumption_resolution,[status(thm)],[f557,f77])).
% 0.32/0.86 % SZS output end CNFRefutation for theBenchmark.p
% 0.32/0.87 % Elapsed time: 0.410097 seconds
% 0.32/0.87 % CPU time: 2.870963 seconds
% 0.32/0.87 % Total memory used: 109.280 MB
% 0.32/0.87 % Net memory used: 106.699 MB
%------------------------------------------------------------------------------