%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL894+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 01:11:19 PM UTC 2026
% Result : Theorem 106.93s 13.92s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL894+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.02 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Mon Sep 21 01:09:51 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.30 % Drodi V4.1.1
% 106.93/13.92 % Refutation found
% 106.93/13.92 % SZS status Theorem for theBenchmark: Theorem is valid
% 106.93/13.92 % SZS output start CNFRefutation for theBenchmark
% 106.93/13.92 fof(f2,axiom,(
% 106.93/13.92 (! [A,B] : '+'(A,B) = '+'(B,A) )),
% 106.93/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.93/13.92 fof(f3,axiom,(
% 106.93/13.92 (! [A] : '+'(A,'0') = A )),
% 106.93/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.93/13.92 fof(f4,axiom,(
% 106.93/13.92 (! [A] : '>='(A,A) )),
% 106.93/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.93/13.92 fof(f5,axiom,(
% 106.93/13.92 (! [X0,X1,X2] :( ( '>='(X0,X1)& '>='(X1,X2) )=> '>='(X0,X2) ) )),
% 106.93/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.93/13.92 fof(f6,axiom,(
% 106.93/13.92 (! [X3,X4] :( ( '>='(X3,X4)& '>='(X4,X3) )=> X3 = X4 ) )),
% 106.93/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.93/13.92 fof(f7,axiom,(
% 106.93/13.92 (! [X5,X6,X7] :( '>='('+'(X5,X6),X7)<=> '>='(X6,'==>'(X5,X7)) ) )),
% 106.93/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.93/13.92 fof(f8,axiom,(
% 106.93/13.92 (! [A] : '>='(A,'0') )),
% 106.93/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.93/13.92 fof(f9,axiom,(
% 106.93/13.92 (! [X8,X9,X10] :( '>='(X8,X9)=> '>='('+'(X8,X10),'+'(X9,X10)) ) )),
% 106.93/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.93/13.92 fof(f11,axiom,(
% 106.93/13.92 (! [X14,X15,X16] :( '>='(X14,X15)=> '>='('==>'(X16,X14),'==>'(X16,X15)) ) )),
% 106.93/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.93/13.92 fof(f12,axiom,(
% 106.93/13.92 (! [A,B] : '+'(A,'==>'(A,B)) = '+'(B,'==>'(B,A)) )),
% 106.93/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.93/13.92 fof(f13,conjecture,(
% 106.93/13.92 ( ( '>='(c,a)& '>='(c,b) )<=> '>='(c,'+'(a,'==>'(a,b))) ) ),
% 106.93/13.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.93/13.92 fof(f14,negated_conjecture,(
% 106.93/13.92 ~(( ( '>='(c,a)& '>='(c,b) )<=> '>='(c,'+'(a,'==>'(a,b))) ) )),
% 106.93/13.92 inference(negated_conjecture,[status(cth)],[f13])).
% 106.93/13.92 fof(f16,plain,(
% 106.93/13.92 ![X0,X1]: ('+'(X0,X1)='+'(X1,X0))),
% 106.93/13.92 inference(cnf_transformation,[status(thm)],[f2])).
% 106.93/13.92 fof(f17,plain,(
% 106.93/13.92 ![X0]: ('+'(X0,'0')=X0)),
% 106.93/13.92 inference(cnf_transformation,[status(thm)],[f3])).
% 106.93/13.92 fof(f18,plain,(
% 106.93/13.92 ![X0]: ('>='(X0,X0))),
% 106.93/13.92 inference(cnf_transformation,[status(thm)],[f4])).
% 106.93/13.92 fof(f19,plain,(
% 106.93/13.92 ![X0,X1,X2]: ((~'>='(X0,X1)|~'>='(X1,X2))|'>='(X0,X2))),
% 106.93/13.92 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 106.93/13.92 fof(f20,plain,(
% 106.93/13.92 ![X0,X2]: ((![X1]: (~'>='(X0,X1)|~'>='(X1,X2)))|'>='(X0,X2))),
% 106.93/13.92 inference(miniscoping,[status(thm)],[f19])).
% 106.93/13.92 fof(f21,plain,(
% 106.93/13.92 ![X0,X1,X2]: (~'>='(X0,X1)|~'>='(X1,X2)|'>='(X0,X2))),
% 106.93/13.92 inference(cnf_transformation,[status(thm)],[f20])).
% 106.93/13.92 fof(f22,plain,(
% 106.93/13.92 ![X3,X4]: ((~'>='(X3,X4)|~'>='(X4,X3))|X3=X4)),
% 106.93/13.92 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 106.93/13.92 fof(f23,plain,(
% 106.93/13.92 ![X0,X1]: (~'>='(X0,X1)|~'>='(X1,X0)|X0=X1)),
% 106.93/13.92 inference(cnf_transformation,[status(thm)],[f22])).
% 106.93/13.92 fof(f24,plain,(
% 106.93/13.92 ![X5,X6,X7]: ((~'>='('+'(X5,X6),X7)|'>='(X6,'==>'(X5,X7)))&('>='('+'(X5,X6),X7)|~'>='(X6,'==>'(X5,X7))))),
% 106.93/13.92 inference(NNF_transformation,[status(thm)],[f7])).
% 106.93/13.92 fof(f25,plain,(
% 106.93/13.92 (![X5,X6,X7]: (~'>='('+'(X5,X6),X7)|'>='(X6,'==>'(X5,X7))))&(![X5,X6,X7]: ('>='('+'(X5,X6),X7)|~'>='(X6,'==>'(X5,X7))))),
% 106.93/13.92 inference(miniscoping,[status(thm)],[f24])).
% 106.93/13.92 fof(f26,plain,(
% 106.93/13.92 ![X0,X1,X2]: (~'>='('+'(X0,X1),X2)|'>='(X1,'==>'(X0,X2)))),
% 106.93/13.92 inference(cnf_transformation,[status(thm)],[f25])).
% 106.93/13.92 fof(f27,plain,(
% 106.93/13.92 ![X0,X1,X2]: ('>='('+'(X0,X1),X2)|~'>='(X1,'==>'(X0,X2)))),
% 106.93/13.92 inference(cnf_transformation,[status(thm)],[f25])).
% 106.93/13.92 fof(f28,plain,(
% 106.93/13.92 ![X0]: ('>='(X0,'0'))),
% 106.93/13.92 inference(cnf_transformation,[status(thm)],[f8])).
% 106.93/13.92 fof(f29,plain,(
% 106.93/13.92 ![X8,X9,X10]: (~'>='(X8,X9)|'>='('+'(X8,X10),'+'(X9,X10)))),
% 106.93/13.92 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 106.93/13.92 fof(f30,plain,(
% 106.93/13.92 ![X8,X9]: (~'>='(X8,X9)|(![X10]: '>='('+'(X8,X10),'+'(X9,X10))))),
% 106.93/13.92 inference(miniscoping,[status(thm)],[f29])).
% 106.93/13.92 fof(f31,plain,(
% 106.93/13.92 ![X0,X1,X2]: (~'>='(X0,X1)|'>='('+'(X0,X2),'+'(X1,X2)))),
% 106.93/13.92 inference(cnf_transformation,[status(thm)],[f30])).
% 106.93/13.92 fof(f35,plain,(
% 106.93/13.92 ![X14,X15,X16]: (~'>='(X14,X15)|'>='('==>'(X16,X14),'==>'(X16,X15)))),
% 106.93/13.92 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 106.93/13.92 fof(f36,plain,(
% 106.93/13.92 ![X14,X15]: (~'>='(X14,X15)|(![X16]: '>='('==>'(X16,X14),'==>'(X16,X15))))),
% 106.93/13.92 inference(miniscoping,[status(thm)],[f35])).
% 106.93/13.92 fof(f37,plain,(
% 106.93/13.92 ![X0,X1,X2]: (~'>='(X0,X1)|'>='('==>'(X2,X0),'==>'(X2,X1)))),
% 106.93/13.92 inference(cnf_transformation,[status(thm)],[f36])).
% 106.93/13.92 fof(f38,plain,(
% 106.93/13.92 ![X0,X1]: ('+'(X0,'==>'(X0,X1))='+'(X1,'==>'(X1,X0)))),
% 106.93/13.92 inference(cnf_transformation,[status(thm)],[f12])).
% 106.93/13.92 fof(f39,plain,(
% 106.93/13.92 (('>='(c,a)&'>='(c,b))<~>'>='(c,'+'(a,'==>'(a,b))))),
% 106.93/13.92 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 106.93/13.92 fof(f40,plain,(
% 106.93/13.92 (('>='(c,a)&'>='(c,b))|'>='(c,'+'(a,'==>'(a,b))))&((~'>='(c,a)|~'>='(c,b))|~'>='(c,'+'(a,'==>'(a,b))))),
% 106.93/13.92 inference(NNF_transformation,[status(thm)],[f39])).
% 106.93/13.92 fof(f41,plain,(
% 106.93/13.92 '>='(c,a)|'>='(c,'+'(a,'==>'(a,b)))),
% 106.93/13.92 inference(cnf_transformation,[status(thm)],[f40])).
% 106.93/13.92 fof(f42,plain,(
% 106.93/13.92 '>='(c,b)|'>='(c,'+'(a,'==>'(a,b)))),
% 106.93/13.92 inference(cnf_transformation,[status(thm)],[f40])).
% 106.93/13.92 fof(f43,plain,(
% 106.93/13.92 ~'>='(c,a)|~'>='(c,b)|~'>='(c,'+'(a,'==>'(a,b)))),
% 106.93/13.92 inference(cnf_transformation,[status(thm)],[f40])).
% 106.93/13.92 fof(f66,plain,(
% 106.93/13.92 ![X0]: (~'>='(c,X0)|~'>='(X0,'+'(a,'==>'(a,b)))|~'>='(c,a)|~'>='(c,b))),
% 106.93/13.92 inference(resolution,[status(thm)],[f21,f43])).
% 106.93/13.92 fof(f70,plain,(
% 106.93/13.92 ![X0,X1]: ('>='(X0,'==>'(X1,'+'(X1,X0))))),
% 106.93/13.92 inference(resolution,[status(thm)],[f26,f18])).
% 106.93/13.92 fof(f72,plain,(
% 106.93/13.92 ![X0,X1,X2]: (~'>='('+'(X0,X1),X2)|'>='(X0,'==>'(X1,X2)))),
% 106.93/13.92 inference(paramodulation,[status(thm)],[f16,f26])).
% 106.93/13.92 fof(f78,plain,(
% 106.93/13.92 ![X0,X1]: ('>='(X0,'==>'(X1,'+'(X0,X1))))),
% 106.93/13.92 inference(paramodulation,[status(thm)],[f16,f70])).
% 106.93/13.92 fof(f87,plain,(
% 106.93/13.92 ![X0,X1]: ('>='('+'(X0,X1),'+'(X1,X0)))),
% 106.93/13.92 inference(resolution,[status(thm)],[f27,f78])).
% 106.93/13.92 fof(f90,plain,(
% 106.93/13.92 ![X0,X1]: ('>='('+'(X0,'==>'(X0,X1)),X1))),
% 106.93/13.92 inference(resolution,[status(thm)],[f27,f18])).
% 106.93/13.92 fof(f109,plain,(
% 106.93/13.92 ![X0]: (~'>='('0',X0)|'0'=X0)),
% 106.93/13.92 inference(resolution,[status(thm)],[f28,f23])).
% 106.93/13.92 fof(f111,plain,(
% 106.93/13.92 ![X0]: ('+'('0',X0)=X0)),
% 106.93/13.92 inference(paramodulation,[status(thm)],[f16,f17])).
% 106.93/13.92 fof(f138,plain,(
% 106.93/13.92 ![X0]: ('0'='==>'(X0,'+'('0',X0)))),
% 106.93/13.92 inference(resolution,[status(thm)],[f109,f78])).
% 106.93/13.92 fof(f142,plain,(
% 106.93/13.92 ![X0]: ('0'='==>'(X0,X0))),
% 106.93/13.92 inference(forward_demodulation,[status(thm)],[f111,f138])).
% 106.93/13.92 fof(f145,plain,(
% 106.93/13.92 ![X0,X1]: ('>='('+'(X0,X1),X0)|~'>='(X1,'0'))),
% 106.93/13.92 inference(paramodulation,[status(thm)],[f142,f27])).
% 106.93/13.92 fof(f146,plain,(
% 106.93/13.92 ![X0,X1]: ('>='('+'(X0,X1),X0))),
% 106.93/13.92 inference(forward_subsumption_resolution,[status(thm)],[f145,f28])).
% 106.93/13.92 fof(f155,plain,(
% 106.93/13.92 ![X0,X1,X2]: (~'>='(X0,'+'(X1,X2))|'>='(X0,X1))),
% 106.93/13.92 inference(resolution,[status(thm)],[f146,f21])).
% 106.93/13.92 fof(f186,plain,(
% 106.93/13.92 '>='(c,b)|'>='(c,'+'(b,'==>'(b,a)))),
% 106.93/13.92 inference(paramodulation,[status(thm)],[f38,f42])).
% 106.93/13.92 fof(f718,plain,(
% 106.93/13.92 '>='(c,b)),
% 106.93/13.92 inference(backward_subsumption_resolution,[status(thm)],[f186,f155])).
% 106.93/13.92 fof(f719,plain,(
% 106.93/13.92 '>='(c,a)),
% 106.93/13.92 inference(backward_subsumption_resolution,[status(thm)],[f41,f155])).
% 106.93/13.92 fof(f750,plain,(
% 106.93/13.92 ![X0]: (~'>='(X0,c)|'>='(X0,b))),
% 106.93/13.92 inference(resolution,[status(thm)],[f718,f21])).
% 106.93/13.92 fof(f754,plain,(
% 106.93/13.92 ![X0]: ('>='('==>'(X0,c),'==>'(X0,a)))),
% 106.93/13.92 inference(resolution,[status(thm)],[f719,f37])).
% 106.93/13.92 fof(f763,plain,(
% 106.93/13.92 ![X0]: ('>='('+'(c,X0),b))),
% 106.93/13.92 inference(resolution,[status(thm)],[f750,f146])).
% 106.93/13.92 fof(f780,plain,(
% 106.93/13.92 ![X0]: ('>='(X0,'==>'(c,b)))),
% 106.93/13.92 inference(resolution,[status(thm)],[f763,f26])).
% 106.93/13.92 fof(f810,plain,(
% 106.93/13.92 ![X0]: (~'>='(c,X0)|~'>='(X0,'+'(a,'==>'(a,b)))|~'>='(c,b))),
% 106.93/13.92 inference(forward_subsumption_resolution,[status(thm)],[f66,f719])).
% 106.93/13.92 fof(f819,plain,(
% 106.93/13.92 ![X0]: (~'>='(c,X0)|~'>='(X0,'+'(b,'==>'(b,a)))|~'>='(c,b))),
% 106.93/13.92 inference(paramodulation,[status(thm)],[f38,f810])).
% 106.93/13.92 fof(f830,plain,(
% 106.93/13.92 ![X0]: (~'>='(c,X0)|~'>='(X0,'+'(b,'==>'(b,a))))),
% 106.93/13.92 inference(forward_subsumption_resolution,[status(thm)],[f819,f718])).
% 106.93/13.92 fof(f832,plain,(
% 106.93/13.92 '0'='==>'(c,b)),
% 106.93/13.92 inference(resolution,[status(thm)],[f780,f109])).
% 106.93/13.92 fof(f852,plain,(
% 106.93/13.92 '+'(b,'==>'(b,c))='+'(c,'0')),
% 106.93/13.92 inference(paramodulation,[status(thm)],[f832,f38])).
% 106.93/13.92 fof(f857,plain,(
% 106.93/13.92 '+'(b,'==>'(b,c))=c),
% 106.93/13.92 inference(forward_demodulation,[status(thm)],[f17,f852])).
% 106.93/13.92 fof(f1244,plain,(
% 106.93/13.92 ![X0,X1]: ('>='(X0,'==>'('==>'(X0,X1),X1)))),
% 106.93/13.92 inference(resolution,[status(thm)],[f72,f90])).
% 106.93/13.92 fof(f1332,plain,(
% 106.93/13.92 ![X0,X1]: ('>='('+'('==>'(X0,X1),X0),X1))),
% 106.93/13.92 inference(resolution,[status(thm)],[f1244,f27])).
% 106.93/13.92 fof(f1604,plain,(
% 106.93/13.92 ![X0,X1]: ('>='('+'('==>'(X0,c),X1),'+'('==>'(X0,a),X1)))),
% 107.74/14.00 inference(resolution,[status(thm)],[f754,f31])).
% 107.74/14.00 fof(f1843,plain,(
% 107.74/14.00 '>='(c,'+'('==>'(b,c),b))),
% 107.74/14.00 inference(paramodulation,[status(thm)],[f857,f87])).
% 107.74/14.00 fof(f27118,plain,(
% 107.74/14.00 ~'>='('+'('==>'(b,c),b),c)|'+'('==>'(b,c),b)=c),
% 107.74/14.00 inference(resolution,[status(thm)],[f1843,f23])).
% 107.74/14.00 fof(f27123,plain,(
% 107.74/14.00 '+'('==>'(b,c),b)=c),
% 107.74/14.00 inference(forward_subsumption_resolution,[status(thm)],[f27118,f1332])).
% 107.74/14.00 fof(f34639,plain,(
% 107.74/14.00 ~'>='(c,'+'('==>'(b,a),b))),
% 107.74/14.00 inference(resolution,[status(thm)],[f830,f87])).
% 107.74/14.00 fof(f55223,plain,(
% 107.74/14.00 '>='(c,'+'('==>'(b,a),b))),
% 107.74/14.00 inference(paramodulation,[status(thm)],[f27123,f1604])).
% 107.74/14.00 fof(f55359,plain,(
% 107.74/14.00 $false),
% 107.74/14.00 inference(forward_subsumption_resolution,[status(thm)],[f55223,f34639])).
% 107.74/14.00 % SZS output end CNFRefutation for theBenchmark.p
% 107.74/14.02 % Elapsed time: 13.714697 seconds
% 107.74/14.02 % CPU time: 108.461413 seconds
% 107.74/14.02 % Total memory used: 598.586 MB
% 107.74/14.02 % Net memory used: 568.066 MB
%------------------------------------------------------------------------------