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Drodi-SAT---4.1.1.THM-Ass.s

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%------------------------------------------------------------------------------
% File     : Drodi-SAT---4.1.1
% Problem  : ALG210+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n018.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 11:49:48 AM UTC 2026

% Result   : Theorem 0.14s 0.51s
% Output   : Assurance 0s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : ALG210+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04  % Command  : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37  % Computer : n018.cluster.edu
% 0.10/0.37  % Model    : x86_64 x86_64
% 0.10/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37  % Memory   : 8046.5625MB
% 0.10/0.37  % OS       : Linux 6.8.0-71-generic
% 0.10/0.37  % CPULimit : 300
% 0.10/0.37  % WCLimit  : 300
% 0.10/0.37  % DateTime : Mon Sep 21 13:03:59 UTC 2026
% 0.10/0.37  % CPUTime  : 
% 0.14/0.38  % Drodi V4.1.1
% 0.14/0.51  % Refutation found
% 0.14/0.51  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.51  % SZS output start CNFRefutation for theBenchmark
% 0.14/0.51  fof(f1,axiom,(
% 0.14/0.51    (! [A,B,C] : times(times(A,B),C) = times(B,times(C,A)) )),
% 0.14/0.51    file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.51  fof(f2,axiom,(
% 0.14/0.51    (! [B] :( element(B)<=> (? [C] :( times(B,C) = B& times(B,B) = C ) )) )),
% 0.14/0.51    file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.51  fof(f3,conjecture,(
% 0.14/0.51    (! [A,B] :( ( element(A)& element(B) )=> element(times(A,B)) ) )),
% 0.14/0.51    file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.51  fof(f4,negated_conjecture,(
% 0.14/0.51    ~((! [A,B] :( ( element(A)& element(B) )=> element(times(A,B)) ) ))),
% 0.14/0.51    inference(negated_conjecture,[status(cth)],[f3])).
% 0.14/0.51  fof(f5,plain,(
% 0.14/0.51    ![X0,X1,X2]: (times(times(X0,X1),X2)=times(X1,times(X2,X0)))),
% 0.14/0.51    inference(cnf_transformation,[status(thm)],[f1])).
% 0.14/0.51  fof(f6,plain,(
% 0.14/0.51    ![B]: ((~element(B)|(?[C]: (times(B,C)=B&times(B,B)=C)))&(element(B)|(![C]: (~times(B,C)=B|~times(B,B)=C))))),
% 0.14/0.51    inference(NNF_transformation,[status(thm)],[f2])).
% 0.14/0.51  fof(f7,plain,(
% 0.14/0.51    (![B]: (~element(B)|(?[C]: (times(B,C)=B&times(B,B)=C))))&(![B]: (element(B)|(![C]: (~times(B,C)=B|~times(B,B)=C))))),
% 0.14/0.51    inference(miniscoping,[status(thm)],[f6])).
% 0.14/0.51  fof(f8,plain,(
% 0.14/0.51    (![B]: (~element(B)|(times(B,sK0_skl(B))=B&times(B,B)=sK0_skl(B))))&(![B]: (element(B)|(![C]: (~times(B,C)=B|~times(B,B)=C))))),
% 0.14/0.51    inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B))],[f7])).
% 0.14/0.51  fof(f9,plain,(
% 0.14/0.51    ![X0]: (~element(X0)|times(X0,sK0_skl(X0))=X0)),
% 0.14/0.51    inference(cnf_transformation,[status(thm)],[f8])).
% 0.14/0.51  fof(f10,plain,(
% 0.14/0.51    ![X0]: (~element(X0)|times(X0,X0)=sK0_skl(X0))),
% 0.14/0.51    inference(cnf_transformation,[status(thm)],[f8])).
% 0.14/0.51  fof(f11,plain,(
% 0.14/0.51    ![X0,X1]: (element(X0)|~times(X0,X1)=X0|~times(X0,X0)=X1)),
% 0.14/0.51    inference(cnf_transformation,[status(thm)],[f8])).
% 0.14/0.51  fof(f12,plain,(
% 0.14/0.51    (?[A,B]: ((element(A)&element(B))&~element(times(A,B))))),
% 0.14/0.51    inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.14/0.51  fof(f13,plain,(
% 0.14/0.51    ((element(sK1_skl)&element(sK2_skl))&~element(times(sK1_skl,sK2_skl)))),
% 0.14/0.51    inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(A,sK1_skl),skolemize(B,sK2_skl)],[f12])).
% 0.14/0.51  fof(f14,plain,(
% 0.14/0.51    element(sK1_skl)),
% 0.14/0.51    inference(cnf_transformation,[status(thm)],[f13])).
% 0.14/0.51  fof(f15,plain,(
% 0.14/0.51    element(sK2_skl)),
% 0.14/0.51    inference(cnf_transformation,[status(thm)],[f13])).
% 0.14/0.51  fof(f16,plain,(
% 0.14/0.51    ~element(times(sK1_skl,sK2_skl))),
% 0.14/0.51    inference(cnf_transformation,[status(thm)],[f13])).
% 0.14/0.51  fof(f17,plain,(
% 0.14/0.51    ![X0]: (element(X0)|~times(X0,times(X0,X0))=X0)),
% 0.14/0.51    inference(destructive_equality_resolution,[status(thm)],[f11])).
% 0.14/0.51  fof(f18,plain,(
% 0.14/0.51    times(sK2_skl,sK0_skl(sK2_skl))=sK2_skl),
% 0.14/0.51    inference(resolution,[status(thm)],[f9,f15])).
% 0.14/0.51  fof(f19,plain,(
% 0.14/0.51    times(sK1_skl,sK0_skl(sK1_skl))=sK1_skl),
% 0.14/0.51    inference(resolution,[status(thm)],[f9,f14])).
% 0.14/0.51  fof(f20,plain,(
% 0.14/0.51    ![X0,X1,X2,X3]: (times(times(X0,times(X1,X2)),X3)=times(X1,times(X3,times(X2,X0))))),
% 0.14/0.51    inference(paramodulation,[status(thm)],[f5,f5])).
% 0.14/0.51  fof(f21,plain,(
% 0.14/0.51    ![X0,X1,X2,X3]: (times(times(X0,X1),times(X2,X3))=times(X0,times(X2,times(X1,X3))))),
% 0.14/0.51    inference(forward_demodulation,[status(thm)],[f5,f20])).
% 0.14/0.51  fof(f22,plain,(
% 0.14/0.51    ![X0,X1,X2,X3]: (times(X0,times(times(X1,X2),X3))=times(X3,times(X1,times(X0,X2))))),
% 0.14/0.51    inference(forward_demodulation,[status(thm)],[f5,f21])).
% 0.14/0.51  fof(f23,plain,(
% 0.14/0.51    ![X0,X1,X2,X3]: (times(X0,times(X1,times(X2,X3)))=times(X2,times(X3,times(X0,X1))))),
% 0.14/0.51    inference(forward_demodulation,[status(thm)],[f5,f22])).
% 0.14/0.51  fof(f24,plain,(
% 0.14/0.51    times(sK2_skl,sK2_skl)=sK0_skl(sK2_skl)),
% 0.14/0.51    inference(resolution,[status(thm)],[f10,f15])).
% 0.14/0.51  fof(f25,plain,(
% 0.14/0.51    times(sK1_skl,sK1_skl)=sK0_skl(sK1_skl)),
% 0.14/0.51    inference(resolution,[status(thm)],[f10,f14])).
% 0.14/0.51  fof(f26,plain,(
% 0.14/0.51    ![X0]: (times(sK2_skl,X0)=times(sK0_skl(sK2_skl),times(X0,sK2_skl)))),
% 0.14/0.51    inference(paramodulation,[status(thm)],[f18,f5])).
% 0.14/0.51  fof(f28,plain,(
% 0.14/0.51    ![X0]: (times(sK0_skl(sK2_skl),X0)=times(sK2_skl,times(X0,sK2_skl)))),
% 0.14/0.51    inference(paramodulation,[status(thm)],[f24,f5])).
% 0.14/0.51  fof(f29,plain,(
% 0.14/0.51    ~times(times(sK1_skl,sK2_skl),times(times(sK1_skl,sK2_skl),times(sK1_skl,sK2_skl)))=times(sK1_skl,sK2_skl)),
% 0.14/0.51    inference(resolution,[status(thm)],[f17,f16])).
% 0.14/0.51  fof(f32,plain,(
% 0.14/0.51    ~times(sK2_skl,times(times(times(sK1_skl,sK2_skl),times(sK1_skl,sK2_skl)),sK1_skl))=times(sK1_skl,sK2_skl)),
% 0.14/0.51    inference(forward_demodulation,[status(thm)],[f5,f29])).
% 0.14/0.51  fof(f33,plain,(
% 0.14/0.51    ~times(sK2_skl,times(times(sK1_skl,sK2_skl),times(sK1_skl,times(sK1_skl,sK2_skl))))=times(sK1_skl,sK2_skl)),
% 0.14/0.51    inference(forward_demodulation,[status(thm)],[f5,f32])).
% 0.14/0.51  fof(f34,plain,(
% 0.14/0.51    ~times(sK2_skl,times(sK2_skl,times(times(sK1_skl,times(sK1_skl,sK2_skl)),sK1_skl)))=times(sK1_skl,sK2_skl)),
% 0.14/0.51    inference(forward_demodulation,[status(thm)],[f5,f33])).
% 0.14/0.51  fof(f35,plain,(
% 0.14/0.51    ~times(sK2_skl,times(sK2_skl,times(times(sK1_skl,sK2_skl),times(sK1_skl,sK1_skl))))=times(sK1_skl,sK2_skl)),
% 0.14/0.51    inference(forward_demodulation,[status(thm)],[f5,f34])).
% 0.14/0.51  fof(f36,plain,(
% 0.14/0.51    ~times(sK2_skl,times(sK2_skl,times(sK2_skl,times(times(sK1_skl,sK1_skl),sK1_skl))))=times(sK1_skl,sK2_skl)),
% 0.14/0.51    inference(forward_demodulation,[status(thm)],[f5,f35])).
% 0.14/0.51  fof(f37,plain,(
% 0.14/0.51    ~times(sK2_skl,times(sK2_skl,times(sK2_skl,times(sK1_skl,times(sK1_skl,sK1_skl)))))=times(sK1_skl,sK2_skl)),
% 0.14/0.51    inference(forward_demodulation,[status(thm)],[f5,f36])).
% 0.14/0.51  fof(f38,plain,(
% 0.14/0.51    ~times(sK2_skl,times(sK2_skl,times(sK2_skl,times(sK1_skl,sK0_skl(sK1_skl)))))=times(sK1_skl,sK2_skl)),
% 0.14/0.51    inference(forward_demodulation,[status(thm)],[f25,f37])).
% 0.14/0.51  fof(f39,plain,(
% 0.14/0.51    ~times(sK2_skl,times(sK2_skl,times(sK2_skl,sK1_skl)))=times(sK1_skl,sK2_skl)),
% 0.14/0.51    inference(forward_demodulation,[status(thm)],[f19,f38])).
% 0.14/0.51  fof(f87,plain,(
% 0.14/0.51    ![X0,X1]: (times(X0,times(sK2_skl,X1))=times(X1,times(sK2_skl,times(X0,sK0_skl(sK2_skl)))))),
% 0.14/0.51    inference(paramodulation,[status(thm)],[f26,f23])).
% 0.14/0.51  fof(f94,plain,(
% 0.14/0.51    ![X0,X1]: (times(X0,times(X1,sK0_skl(sK2_skl)))=times(sK2_skl,times(sK2_skl,times(X0,X1))))),
% 0.14/0.51    inference(paramodulation,[status(thm)],[f24,f23])).
% 0.14/0.51  fof(f137,plain,(
% 0.14/0.51    ~times(sK2_skl,times(sK1_skl,sK0_skl(sK2_skl)))=times(sK1_skl,sK2_skl)),
% 0.14/0.51    inference(backward_demodulation,[status(thm)],[f94,f39])).
% 0.14/0.51  fof(f278,plain,(
% 0.14/0.51    times(sK0_skl(sK2_skl),sK2_skl)=times(sK2_skl,sK0_skl(sK2_skl))),
% 0.14/0.51    inference(paramodulation,[status(thm)],[f24,f28])).
% 0.14/0.51  fof(f287,plain,(
% 0.14/0.51    times(sK0_skl(sK2_skl),sK2_skl)=sK2_skl),
% 0.14/0.51    inference(forward_demodulation,[status(thm)],[f18,f278])).
% 0.14/0.51  fof(f305,plain,(
% 0.14/0.51    ![X0,X1]: (times(sK0_skl(sK2_skl),times(sK2_skl,times(X0,X1)))=times(X0,times(X1,sK2_skl)))),
% 0.14/0.51    inference(paramodulation,[status(thm)],[f287,f23])).
% 0.14/0.51  fof(f307,plain,(
% 0.14/0.51    ![X0]: (times(sK2_skl,X0)=times(sK2_skl,times(X0,sK0_skl(sK2_skl))))),
% 0.14/0.51    inference(paramodulation,[status(thm)],[f287,f5])).
% 0.14/0.51  fof(f311,plain,(
% 0.14/0.51    ~times(sK2_skl,sK1_skl)=times(sK1_skl,sK2_skl)),
% 0.14/0.51    inference(backward_demodulation,[status(thm)],[f307,f137])).
% 0.14/0.51  fof(f312,plain,(
% 0.14/0.51    ![X0,X1]: (times(X0,times(sK2_skl,X1))=times(X1,times(sK2_skl,X0)))),
% 0.14/0.51    inference(backward_demodulation,[status(thm)],[f307,f87])).
% 0.14/0.51  fof(f380,plain,(
% 0.14/0.51    ![X0]: (times(X0,sK2_skl)=times(sK0_skl(sK2_skl),times(sK2_skl,X0)))),
% 0.14/0.51    inference(paramodulation,[status(thm)],[f18,f312])).
% 0.14/0.51  fof(f436,plain,(
% 0.14/0.51    ![X0,X1]: (times(times(X0,X1),sK2_skl)=times(X0,times(X1,sK2_skl)))),
% 0.14/0.51    inference(backward_demodulation,[status(thm)],[f380,f305])).
% 0.14/0.51  fof(f543,plain,(
% 0.14/0.51    ![X0,X1]: (times(X0,times(sK2_skl,X1))=times(X1,times(X0,sK2_skl)))),
% 0.14/0.51    inference(forward_demodulation,[status(thm)],[f5,f436])).
% 0.14/0.51  fof(f1190,plain,(
% 0.14/0.51    ![X0]: (times(X0,times(sK2_skl,sK0_skl(sK2_skl)))=times(sK2_skl,X0))),
% 0.14/0.51    inference(paramodulation,[status(thm)],[f26,f543])).
% 0.14/0.51  fof(f1296,plain,(
% 0.14/0.51    ![X0]: (times(X0,sK2_skl)=times(sK2_skl,X0))),
% 0.14/0.51    inference(forward_demodulation,[status(thm)],[f18,f1190])).
% 0.14/0.51  fof(f1297,plain,(
% 0.14/0.51    $false),
% 0.14/0.51    inference(backward_subsumption_resolution,[status(thm)],[f311,f1296])).
% 0.14/0.51  % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.52  % Elapsed time: 0.146097 seconds
% 0.14/0.52  % CPU time: 0.932683 seconds
% 0.14/0.52  % Total memory used: 79.956 MB
% 0.14/0.52  % Net memory used: 79.454 MB
%------------------------------------------------------------------------------