%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM494+1 : 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 : n006.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 01:43:02 PM UTC 2026
% Result : Theorem 34.68s 10.11s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM494+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.59 % Computer : n006.cluster.edu
% 0.11/5.59 % Model : x86_64 x86_64
% 0.11/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.59 % Memory : 8046.5625MB
% 0.11/5.59 % OS : Linux 6.8.0-71-generic
% 0.11/5.59 % CPULimit : 300
% 0.11/5.59 % WCLimit : 300
% 0.11/5.59 % DateTime : Mon Sep 21 02:35:03 UTC 2026
% 0.16/5.60 % CPUTime :
% 0.16/5.62 % Drodi V4.1.1
% 34.68/10.11 % Refutation found
% 34.68/10.11 % SZS status Theorem for theBenchmark: Theorem is valid
% 34.68/10.11 % SZS output start CNFRefutation for theBenchmark
% 34.68/10.11 fof(f4,axiom,(
% 34.68/10.11 (! [W0,W1] :( ( aNaturalNumber0(W0)& aNaturalNumber0(W1) )=> aNaturalNumber0(sdtpldt0(W0,W1)) ) )),
% 34.68/10.11 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 34.68/10.11 fof(f14,axiom,(
% 34.68/10.11 (! [W0,W1,W2] :( ( aNaturalNumber0(W0)& aNaturalNumber0(W1)& aNaturalNumber0(W2) )=> ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2)| sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )=> W1 = W2 ) ) )),
% 34.68/10.11 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 34.68/10.11 fof(f19,definition,(
% 34.68/10.11 (! [W0,W1] :( ( aNaturalNumber0(W0)& aNaturalNumber0(W1) )=> ( sdtlseqdt0(W0,W1)=> (! [W2] :( W2 = sdtmndt0(W1,W0)<=> ( aNaturalNumber0(W2)& sdtpldt0(W0,W2) = W1 ) ) )) ) )),
% 34.68/10.11 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 34.68/10.11 fof(f24,axiom,(
% 34.68/10.11 (! [W0,W1] :( ( aNaturalNumber0(W0)& aNaturalNumber0(W1) )=> ( ( W0 != W1& sdtlseqdt0(W0,W1) )=> (! [W2] :( aNaturalNumber0(W2)=> ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1)& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))& sdtpldt0(W0,W2) != sdtpldt0(W1,W2)& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) )) ) )),
% 34.68/10.11 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 34.68/10.11 fof(f39,hypothesis,(
% 34.68/10.11 ( aNaturalNumber0(xn)& aNaturalNumber0(xm)& aNaturalNumber0(xp) ) ),
% 34.68/10.11 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 34.68/10.11 fof(f42,hypothesis,(
% 34.68/10.11 sdtlseqdt0(xp,xn) ),
% 34.68/10.11 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 34.68/10.11 fof(f43,hypothesis,(
% 34.68/10.11 xr = sdtmndt0(xn,xp) ),
% 34.68/10.11 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 34.68/10.11 fof(f44,hypothesis,(
% 34.68/10.11 ( xr != xn& sdtlseqdt0(xr,xn) ) ),
% 34.68/10.11 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 34.68/10.11 fof(f46,conjecture,(
% 34.68/10.11 ( sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp)& sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ) ),
% 34.68/10.11 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 34.68/10.11 fof(f47,negated_conjecture,(
% 34.68/10.11 ~(( sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp)& sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ) )),
% 34.68/10.11 inference(negated_conjecture,[status(cth)],[f46])).
% 34.68/10.11 fof(f54,plain,(
% 34.68/10.11 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|aNaturalNumber0(sdtpldt0(W0,W1)))),
% 34.68/10.11 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 34.68/10.11 fof(f55,plain,(
% 34.68/10.11 ![X0,X1]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|aNaturalNumber0(sdtpldt0(X0,X1)))),
% 34.68/10.11 inference(cnf_transformation,[status(thm)],[f54])).
% 34.68/10.11 fof(f78,plain,(
% 34.68/10.11 ![W0,W1,W2]: (((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|~aNaturalNumber0(W2))|((~sdtpldt0(W0,W1)=sdtpldt0(W0,W2)&~sdtpldt0(W1,W0)=sdtpldt0(W2,W0))|W1=W2))),
% 34.68/10.11 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 34.68/10.11 fof(f80,plain,(
% 34.68/10.11 ![X0,X1,X2]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|~aNaturalNumber0(X2)|~sdtpldt0(X1,X0)=sdtpldt0(X2,X0)|X1=X2)),
% 34.68/10.11 inference(cnf_transformation,[status(thm)],[f78])).
% 34.68/10.11 fof(f95,plain,(
% 34.68/10.11 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|(~sdtlseqdt0(W0,W1)|(![W2]: (W2=sdtmndt0(W1,W0)<=>(aNaturalNumber0(W2)&sdtpldt0(W0,W2)=W1)))))),
% 34.68/10.11 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 34.68/10.11 fof(f96,plain,(
% 34.68/10.11 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|(~sdtlseqdt0(W0,W1)|(![W2]: ((~W2=sdtmndt0(W1,W0)|(aNaturalNumber0(W2)&sdtpldt0(W0,W2)=W1))&(W2=sdtmndt0(W1,W0)|(~aNaturalNumber0(W2)|~sdtpldt0(W0,W2)=W1))))))),
% 34.68/10.11 inference(NNF_transformation,[status(thm)],[f95])).
% 34.68/10.11 fof(f97,plain,(
% 34.68/10.11 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|(~sdtlseqdt0(W0,W1)|((![W2]: (~W2=sdtmndt0(W1,W0)|(aNaturalNumber0(W2)&sdtpldt0(W0,W2)=W1)))&(![W2]: (W2=sdtmndt0(W1,W0)|(~aNaturalNumber0(W2)|~sdtpldt0(W0,W2)=W1))))))),
% 34.68/10.11 inference(miniscoping,[status(thm)],[f96])).
% 34.68/10.11 fof(f98,plain,(
% 34.68/10.11 ![X0,X1,X2]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|~sdtlseqdt0(X0,X1)|~X2=sdtmndt0(X1,X0)|aNaturalNumber0(X2))),
% 34.68/10.11 inference(cnf_transformation,[status(thm)],[f97])).
% 34.68/10.11 fof(f110,plain,(
% 34.68/10.11 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|((W0=W1|~sdtlseqdt0(W0,W1))|(![W2]: (~aNaturalNumber0(W2)|(((~sdtpldt0(W2,W0)=sdtpldt0(W2,W1)&sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1)))&~sdtpldt0(W0,W2)=sdtpldt0(W1,W2))&sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)))))))),
% 34.68/10.11 inference(pre_NNF_transformation,[status(thm)],[f24])).
% 34.68/10.11 fof(f114,plain,(
% 34.68/10.11 ![X0,X1,X2]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|X0=X1|~sdtlseqdt0(X0,X1)|~aNaturalNumber0(X2)|sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2)))),
% 34.68/10.11 inference(cnf_transformation,[status(thm)],[f110])).
% 34.68/10.11 fof(f166,plain,(
% 34.68/10.11 aNaturalNumber0(xn)),
% 34.68/10.11 inference(cnf_transformation,[status(thm)],[f39])).
% 34.68/10.11 fof(f167,plain,(
% 34.68/10.11 aNaturalNumber0(xm)),
% 34.68/10.11 inference(cnf_transformation,[status(thm)],[f39])).
% 34.68/10.11 fof(f168,plain,(
% 34.68/10.11 aNaturalNumber0(xp)),
% 34.68/10.11 inference(cnf_transformation,[status(thm)],[f39])).
% 34.68/10.11 fof(f173,plain,(
% 34.68/10.11 sdtlseqdt0(xp,xn)),
% 34.68/10.11 inference(cnf_transformation,[status(thm)],[f42])).
% 34.68/10.11 fof(f174,plain,(
% 34.68/10.11 xr=sdtmndt0(xn,xp)),
% 34.68/10.11 inference(cnf_transformation,[status(thm)],[f43])).
% 34.68/10.11 fof(f175,plain,(
% 34.68/10.11 ~xr=xn),
% 34.68/10.11 inference(cnf_transformation,[status(thm)],[f44])).
% 34.68/10.11 fof(f176,plain,(
% 34.68/10.11 sdtlseqdt0(xr,xn)),
% 34.68/10.11 inference(cnf_transformation,[status(thm)],[f44])).
% 34.68/10.11 fof(f178,plain,(
% 34.68/10.11 (sdtpldt0(sdtpldt0(xr,xm),xp)=sdtpldt0(sdtpldt0(xn,xm),xp)|~sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)))),
% 34.68/10.11 inference(pre_NNF_transformation,[status(thm)],[f47])).
% 34.68/10.11 fof(f179,plain,(
% 34.68/10.11 sdtpldt0(sdtpldt0(xr,xm),xp)=sdtpldt0(sdtpldt0(xn,xm),xp)|~sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))),
% 34.68/10.11 inference(cnf_transformation,[status(thm)],[f178])).
% 34.68/10.11 fof(f181,plain,(
% 34.68/10.11 ![X0,X1]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|~sdtlseqdt0(X0,X1)|aNaturalNumber0(sdtmndt0(X1,X0)))),
% 34.68/10.11 inference(destructive_equality_resolution,[status(thm)],[f98])).
% 34.68/10.11 fof(f400,plain,(
% 34.68/10.11 ~aNaturalNumber0(sdtpldt0(xr,xm))|~aNaturalNumber0(sdtpldt0(xn,xm))|sdtpldt0(xr,xm)=sdtpldt0(xn,xm)|~sdtlseqdt0(sdtpldt0(xr,xm),sdtpldt0(xn,xm))|~aNaturalNumber0(xp)|sdtpldt0(sdtpldt0(xr,xm),xp)=sdtpldt0(sdtpldt0(xn,xm),xp)),
% 34.68/10.11 inference(resolution,[status(thm)],[f114,f179])).
% 34.68/10.11 fof(f406,plain,(
% 34.68/10.11 ~aNaturalNumber0(sdtpldt0(xr,xm))|~aNaturalNumber0(sdtpldt0(xn,xm))|sdtpldt0(xr,xm)=sdtpldt0(xn,xm)|~sdtlseqdt0(sdtpldt0(xr,xm),sdtpldt0(xn,xm))|~aNaturalNumber0(xp)),
% 34.68/10.11 inference(forward_subsumption_resolution,[status(thm)],[f400,f80])).
% 34.68/10.11 fof(f455,plain,(
% 34.68/10.11 ~aNaturalNumber0(sdtpldt0(xr,xm))|~aNaturalNumber0(sdtpldt0(xn,xm))|sdtpldt0(xr,xm)=sdtpldt0(xn,xm)|~sdtlseqdt0(sdtpldt0(xr,xm),sdtpldt0(xn,xm))),
% 34.68/10.11 inference(forward_subsumption_resolution,[status(thm)],[f406,f168])).
% 34.68/10.11 fof(f456,plain,(
% 34.68/10.11 ~aNaturalNumber0(sdtpldt0(xn,xm))|sdtpldt0(xr,xm)=sdtpldt0(xn,xm)|~sdtlseqdt0(sdtpldt0(xr,xm),sdtpldt0(xn,xm))|~aNaturalNumber0(xr)|~aNaturalNumber0(xm)),
% 34.68/10.11 inference(resolution,[status(thm)],[f455,f55])).
% 34.68/10.11 fof(f457,plain,(
% 34.68/10.11 ~aNaturalNumber0(sdtpldt0(xn,xm))|sdtpldt0(xr,xm)=sdtpldt0(xn,xm)|~sdtlseqdt0(sdtpldt0(xr,xm),sdtpldt0(xn,xm))|~aNaturalNumber0(xr)),
% 34.68/10.11 inference(forward_subsumption_resolution,[status(thm)],[f456,f167])).
% 34.68/10.11 fof(f516,plain,(
% 34.68/10.11 ![X0]: (~aNaturalNumber0(X0)|~sdtlseqdt0(X0,xn)|aNaturalNumber0(sdtmndt0(xn,X0)))),
% 34.68/10.11 inference(resolution,[status(thm)],[f181,f166])).
% 34.68/10.11 fof(f8840,plain,(
% 34.68/10.11 ~aNaturalNumber0(xp)|aNaturalNumber0(sdtmndt0(xn,xp))),
% 34.68/10.11 inference(resolution,[status(thm)],[f516,f173])).
% 34.68/10.11 fof(f8846,plain,(
% 34.68/10.11 ~aNaturalNumber0(xp)|aNaturalNumber0(xr)),
% 34.68/10.11 inference(forward_demodulation,[status(thm)],[f174,f8840])).
% 34.68/10.11 fof(f8847,plain,(
% 34.68/10.11 aNaturalNumber0(xr)),
% 34.68/10.11 inference(forward_subsumption_resolution,[status(thm)],[f8846,f168])).
% 34.68/10.11 fof(f8910,plain,(
% 34.68/10.11 ~aNaturalNumber0(sdtpldt0(xn,xm))|sdtpldt0(xr,xm)=sdtpldt0(xn,xm)|~sdtlseqdt0(sdtpldt0(xr,xm),sdtpldt0(xn,xm))),
% 34.68/10.11 inference(backward_subsumption_resolution,[status(thm)],[f457,f8847])).
% 34.68/10.11 fof(f9519,plain,(
% 34.68/10.11 sdtpldt0(xr,xm)=sdtpldt0(xn,xm)|~sdtlseqdt0(sdtpldt0(xr,xm),sdtpldt0(xn,xm))|~aNaturalNumber0(xn)|~aNaturalNumber0(xm)),
% 34.68/10.11 inference(resolution,[status(thm)],[f8910,f55])).
% 34.68/10.11 fof(f9520,plain,(
% 34.68/10.11 sdtpldt0(xr,xm)=sdtpldt0(xn,xm)|~sdtlseqdt0(sdtpldt0(xr,xm),sdtpldt0(xn,xm))|~aNaturalNumber0(xm)),
% 34.68/10.11 inference(forward_subsumption_resolution,[status(thm)],[f9519,f166])).
% 34.68/10.11 fof(f9523,plain,(
% 34.68/10.11 sdtpldt0(xr,xm)=sdtpldt0(xn,xm)|~sdtlseqdt0(sdtpldt0(xr,xm),sdtpldt0(xn,xm))),
% 34.68/10.13 inference(forward_subsumption_resolution,[status(thm)],[f9520,f167])).
% 34.68/10.13 fof(f9524,plain,(
% 34.68/10.13 sdtpldt0(xr,xm)=sdtpldt0(xn,xm)|~aNaturalNumber0(xr)|~aNaturalNumber0(xn)|xr=xn|~sdtlseqdt0(xr,xn)|~aNaturalNumber0(xm)),
% 34.68/10.13 inference(resolution,[status(thm)],[f9523,f114])).
% 34.68/10.13 fof(f9526,plain,(
% 34.68/10.13 ~aNaturalNumber0(xr)|~aNaturalNumber0(xn)|xr=xn|~sdtlseqdt0(xr,xn)|~aNaturalNumber0(xm)),
% 34.68/10.13 inference(forward_subsumption_resolution,[status(thm)],[f9524,f80])).
% 34.68/10.13 fof(f10808,plain,(
% 34.68/10.13 ~aNaturalNumber0(xn)|xr=xn|~sdtlseqdt0(xr,xn)|~aNaturalNumber0(xm)),
% 34.68/10.13 inference(forward_subsumption_resolution,[status(thm)],[f9526,f8847])).
% 34.68/10.13 fof(f10809,plain,(
% 34.68/10.13 ~aNaturalNumber0(xn)|xr=xn|~sdtlseqdt0(xr,xn)),
% 34.68/10.13 inference(resolution,[status(thm)],[f10808,f167])).
% 34.68/10.13 fof(f10810,plain,(
% 34.68/10.13 xr=xn|~sdtlseqdt0(xr,xn)),
% 34.68/10.13 inference(forward_subsumption_resolution,[status(thm)],[f10809,f166])).
% 34.68/10.13 fof(f12256,plain,(
% 34.68/10.13 ~sdtlseqdt0(xr,xn)),
% 34.68/10.13 inference(forward_subsumption_resolution,[status(thm)],[f10810,f175])).
% 34.68/10.13 fof(f12257,plain,(
% 34.68/10.13 $false),
% 34.68/10.13 inference(backward_subsumption_resolution,[status(thm)],[f176,f12256])).
% 34.68/10.13 % SZS output end CNFRefutation for theBenchmark.p
% 31.22/10.17 % Elapsed time: 4.554559 seconds
% 31.22/10.17 % CPU time: 35.509958 seconds
% 31.22/10.17 % Total memory used: 265.486 MB
% 31.22/10.17 % Net memory used: 249.165 MB
%------------------------------------------------------------------------------