%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUN134-1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/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 01:57:31 PM UTC 2026
% Result : Unsatisfiable 13.87s 2.53s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUN134-1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.42 % Computer : n018.cluster.edu
% 0.18/0.42 % Model : x86_64 x86_64
% 0.18/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.42 % Memory : 8046.5625MB
% 0.18/0.42 % OS : Linux 6.8.0-71-generic
% 0.18/0.42 % CPULimit : 300
% 0.18/0.42 % WCLimit : 300
% 0.18/0.42 % DateTime : Mon Sep 21 03:30:58 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.44 % Drodi V4.1.1
% 13.87/2.53 % Refutation found
% 13.87/2.53 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 13.87/2.53 % SZS output start CNFRefutation for theBenchmark
% 13.87/2.53 fof(f1,axiom,(
% 13.87/2.53 (![X,Y]: ('+'(X,Y) = '+'(Y,X) ))),
% 13.87/2.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 13.87/2.53 fof(f2,axiom,(
% 13.87/2.53 (![X,Y,Z]: ('+'(X,'+'(Y,Z)) = '+'('+'(X,Y),Z) ))),
% 13.87/2.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 13.87/2.53 fof(f3,axiom,(
% 13.87/2.53 (![X,Y]: (times(X,Y) = times(Y,X) ))),
% 13.87/2.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 13.87/2.53 fof(f7,axiom,(
% 13.87/2.53 (![X]: (times(X,one) = X ))),
% 13.87/2.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 13.87/2.53 fof(f8,axiom,(
% 13.87/2.53 (![X,Y,Z]: (times(X,'+'(Y,Z)) = '+'(times(X,Y),times(X,Z)) ))),
% 13.87/2.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 13.87/2.53 fof(f10,axiom,(
% 13.87/2.53 (![X,Y]: ('+'(s(X),Y) = s('+'(X,Y)) ))),
% 13.87/2.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 13.87/2.53 fof(f11,axiom,(
% 13.87/2.53 (![X,Y]: (times(s(X),Y) = '+'(Y,times(X,Y)) ))),
% 13.87/2.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 13.87/2.53 fof(f13,axiom,(
% 13.87/2.53 (![N]: (sum(s(N)) = '+'(s(N),sum(N)) ))),
% 13.87/2.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 13.87/2.53 fof(f14,axiom,(
% 13.87/2.53 '+'(sum(a),sum(a)) = times(a,s(a)) ),
% 13.87/2.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 13.87/2.53 fof(f15,negated_conjecture,(
% 13.87/2.53 '+'(sum(s(a)),sum(s(a))) != times(s(a),s(s(a))) ),
% 13.87/2.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 13.87/2.53 fof(f16,plain,(
% 13.87/2.53 ![X0,X1]: ('+'(X0,X1)='+'(X1,X0))),
% 13.87/2.53 inference(cnf_transformation,[status(thm)],[f1])).
% 13.87/2.53 fof(f17,plain,(
% 13.87/2.53 ![X0,X1,X2]: ('+'(X0,'+'(X1,X2))='+'('+'(X0,X1),X2))),
% 13.87/2.53 inference(cnf_transformation,[status(thm)],[f2])).
% 13.87/2.53 fof(f18,plain,(
% 13.87/2.53 ![X0,X1]: (times(X0,X1)=times(X1,X0))),
% 13.87/2.53 inference(cnf_transformation,[status(thm)],[f3])).
% 13.87/2.53 fof(f22,plain,(
% 13.87/2.53 ![X0]: (times(X0,one)=X0)),
% 13.87/2.53 inference(cnf_transformation,[status(thm)],[f7])).
% 13.87/2.53 fof(f23,plain,(
% 13.87/2.53 ![X0,X1,X2]: (times(X0,'+'(X1,X2))='+'(times(X0,X1),times(X0,X2)))),
% 13.87/2.53 inference(cnf_transformation,[status(thm)],[f8])).
% 13.87/2.53 fof(f25,plain,(
% 13.87/2.53 ![X0,X1]: ('+'(s(X0),X1)=s('+'(X0,X1)))),
% 13.87/2.53 inference(cnf_transformation,[status(thm)],[f10])).
% 13.87/2.53 fof(f26,plain,(
% 13.87/2.53 ![X0,X1]: (times(s(X0),X1)='+'(X1,times(X0,X1)))),
% 13.87/2.53 inference(cnf_transformation,[status(thm)],[f11])).
% 13.87/2.53 fof(f28,plain,(
% 13.87/2.53 ![X0]: (sum(s(X0))='+'(s(X0),sum(X0)))),
% 13.87/2.53 inference(cnf_transformation,[status(thm)],[f13])).
% 13.87/2.53 fof(f29,plain,(
% 13.87/2.53 '+'(sum(a),sum(a))=times(a,s(a))),
% 13.87/2.53 inference(cnf_transformation,[status(thm)],[f14])).
% 13.87/2.53 fof(f30,plain,(
% 13.87/2.53 ~'+'(sum(s(a)),sum(s(a)))=times(s(a),s(s(a)))),
% 13.87/2.53 inference(cnf_transformation,[status(thm)],[f15])).
% 13.87/2.53 fof(f31,definition,(
% 13.87/2.53 sF2_fnc=s(a)),
% 13.87/2.53 introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition])).
% 13.87/2.53 fof(f32,definition,(
% 13.87/2.53 sF1_fnc=sum(sF2_fnc)),
% 13.87/2.53 introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition])).
% 13.87/2.53 fof(f33,definition,(
% 13.87/2.53 sF3_fnc=sum(sF2_fnc)),
% 13.87/2.53 introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition])).
% 13.87/2.53 fof(f34,definition,(
% 13.87/2.53 sF0_fnc='+'(sF1_fnc,sF3_fnc)),
% 13.87/2.53 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 13.87/2.53 fof(f35,definition,(
% 13.87/2.53 sF5_fnc=s(sF2_fnc)),
% 13.87/2.53 introduced(definition,[new_symbols(definition,[sF5_fnc])],[function_definition])).
% 13.87/2.53 fof(f36,definition,(
% 13.87/2.53 sF4_fnc=times(sF2_fnc,sF5_fnc)),
% 13.87/2.53 introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition])).
% 13.87/2.53 fof(f37,plain,(
% 13.87/2.53 ~sF0_fnc=sF4_fnc),
% 13.87/2.53 inference(definition_folding,[],[f30,f36,f35,f34,f33,f32,f31])).
% 13.87/2.53 fof(f38,plain,(
% 13.87/2.53 ![X0]: (sum(s(X0))=s('+'(X0,sum(X0))))),
% 13.87/2.53 inference(forward_demodulation,[status(thm)],[f25,f28])).
% 13.87/2.53 fof(f39,plain,(
% 13.87/2.53 '+'(sum(a),sum(a))=times(a,sF2_fnc)),
% 13.87/2.53 inference(backward_demodulation,[status(thm)],[f31,f29])).
% 13.87/2.53 fof(f40,plain,(
% 13.87/2.53 sF3_fnc=sF1_fnc),
% 13.87/2.53 inference(forward_demodulation,[status(thm)],[f32,f33])).
% 13.87/2.53 fof(f41,plain,(
% 13.87/2.53 sF0_fnc='+'(sF1_fnc,sF1_fnc)),
% 13.87/2.53 inference(forward_demodulation,[status(thm)],[f40,f34])).
% 13.87/2.53 fof(f50,plain,(
% 13.87/2.53 ![X0,X1]: ('+'(X0,s(X1))=s('+'(X1,X0)))),
% 13.87/2.53 inference(paramodulation,[status(thm)],[f16,f25])).
% 13.87/2.53 fof(f107,plain,(
% 13.87/2.53 ![X0]: ('+'(X0,sF2_fnc)=s('+'(a,X0)))),
% 13.87/2.53 inference(paramodulation,[status(thm)],[f31,f50])).
% 16.12/2.56 fof(f197,plain,(
% 16.12/2.56 ![X0,X1,X2]: ('+'(X0,'+'(X1,X2))='+'(X2,'+'(X0,X1)))),
% 16.12/2.56 inference(paramodulation,[status(thm)],[f16,f17])).
% 16.12/2.56 fof(f333,plain,(
% 16.12/2.56 sum(s(a))='+'(sum(a),sF2_fnc)),
% 16.12/2.56 inference(paramodulation,[status(thm)],[f107,f38])).
% 16.12/2.56 fof(f347,plain,(
% 16.12/2.56 ![X0,X1]: ('+'(sum(s(X0)),X1)=s('+'('+'(X0,sum(X0)),X1)))),
% 16.12/2.56 inference(paramodulation,[status(thm)],[f38,f25])).
% 16.12/2.56 fof(f348,plain,(
% 16.12/2.56 sum(sF2_fnc)='+'(sum(a),sF2_fnc)),
% 16.12/2.56 inference(forward_demodulation,[status(thm)],[f31,f333])).
% 16.12/2.56 fof(f349,plain,(
% 16.12/2.56 sF1_fnc='+'(sum(a),sF2_fnc)),
% 16.12/2.56 inference(forward_demodulation,[status(thm)],[f32,f348])).
% 16.12/2.56 fof(f350,plain,(
% 16.12/2.56 sF1_fnc='+'(sF2_fnc,sum(a))),
% 16.12/2.56 inference(forward_demodulation,[status(thm)],[f16,f349])).
% 16.12/2.56 fof(f377,plain,(
% 16.12/2.56 ![X0,X1]: ('+'(sum(s(X0)),X1)=s('+'(X0,'+'(sum(X0),X1))))),
% 16.12/2.56 inference(forward_demodulation,[status(thm)],[f17,f347])).
% 16.12/2.56 fof(f411,plain,(
% 16.12/2.56 ![X0]: (times(s(X0),one)='+'(one,X0))),
% 16.12/2.56 inference(paramodulation,[status(thm)],[f22,f26])).
% 16.12/2.56 fof(f429,plain,(
% 16.12/2.56 ![X0]: (s(X0)='+'(one,X0))),
% 16.12/2.56 inference(forward_demodulation,[status(thm)],[f22,f411])).
% 16.12/2.56 fof(f473,plain,(
% 16.12/2.56 ![X0,X1]: (times(X0,'+'(one,X1))='+'(X0,times(X0,X1)))),
% 16.12/2.56 inference(paramodulation,[status(thm)],[f22,f23])).
% 16.12/2.56 fof(f497,plain,(
% 16.12/2.56 ![X0,X1]: (times(X0,s(X1))='+'(X0,times(X0,X1)))),
% 16.12/2.56 inference(forward_demodulation,[status(thm)],[f429,f473])).
% 16.12/2.56 fof(f1013,plain,(
% 16.12/2.56 ![X0,X1]: (times(X0,s(X1))='+'(X0,times(X1,X0)))),
% 16.12/2.56 inference(paramodulation,[status(thm)],[f18,f497])).
% 16.12/2.56 fof(f1473,plain,(
% 16.12/2.56 ![X0,X1,X2]: ('+'('+'(X0,X1),X2)='+'(X1,'+'(X2,X0)))),
% 16.12/2.56 inference(paramodulation,[status(thm)],[f16,f197])).
% 16.12/2.56 fof(f2314,plain,(
% 16.12/2.56 ![X0,X1,X2]: ('+'('+'(X0,X1),X2)='+'(X0,'+'(X2,X1)))),
% 16.12/2.56 inference(paramodulation,[status(thm)],[f16,f1473])).
% 16.12/2.56 fof(f3698,plain,(
% 16.12/2.56 ![X0]: ('+'(sF1_fnc,X0)='+'(sF2_fnc,'+'(X0,sum(a))))),
% 16.12/2.56 inference(paramodulation,[status(thm)],[f350,f2314])).
% 16.12/2.56 fof(f5000,plain,(
% 16.12/2.56 '+'(sum(s(a)),sum(a))=s('+'(a,times(a,sF2_fnc)))),
% 16.12/2.56 inference(paramodulation,[status(thm)],[f39,f377])).
% 16.12/2.56 fof(f5056,plain,(
% 16.12/2.56 '+'(sum(a),sum(s(a)))=s('+'(a,times(a,sF2_fnc)))),
% 16.12/2.56 inference(forward_demodulation,[status(thm)],[f16,f5000])).
% 16.12/2.56 fof(f5057,plain,(
% 16.12/2.56 '+'(sum(a),sum(sF2_fnc))=s('+'(a,times(a,sF2_fnc)))),
% 16.12/2.56 inference(forward_demodulation,[status(thm)],[f31,f5056])).
% 16.12/2.56 fof(f5058,plain,(
% 16.12/2.56 '+'(sum(a),sF1_fnc)=s('+'(a,times(a,sF2_fnc)))),
% 16.12/2.56 inference(forward_demodulation,[status(thm)],[f32,f5057])).
% 16.12/2.56 fof(f5059,plain,(
% 16.12/2.56 '+'(sF1_fnc,sum(a))=s('+'(a,times(a,sF2_fnc)))),
% 16.12/2.56 inference(forward_demodulation,[status(thm)],[f16,f5058])).
% 16.12/2.56 fof(f5060,plain,(
% 16.12/2.56 '+'(sF1_fnc,sum(a))='+'(times(a,sF2_fnc),sF2_fnc)),
% 16.12/2.56 inference(forward_demodulation,[status(thm)],[f107,f5059])).
% 16.12/2.56 fof(f5061,plain,(
% 16.12/2.56 '+'(sF1_fnc,sum(a))='+'(sF2_fnc,times(a,sF2_fnc))),
% 16.12/2.56 inference(forward_demodulation,[status(thm)],[f16,f5060])).
% 16.12/2.56 fof(f5062,plain,(
% 16.12/2.56 '+'(sF1_fnc,sum(a))=times(sF2_fnc,s(a))),
% 16.12/2.56 inference(forward_demodulation,[status(thm)],[f1013,f5061])).
% 16.12/2.56 fof(f5063,plain,(
% 16.12/2.56 '+'(sF1_fnc,sum(a))=times(sF2_fnc,sF2_fnc)),
% 16.12/2.56 inference(forward_demodulation,[status(thm)],[f31,f5062])).
% 16.12/2.56 fof(f5437,plain,(
% 16.12/2.56 '+'(sF1_fnc,sF1_fnc)='+'(sF2_fnc,times(sF2_fnc,sF2_fnc))),
% 16.12/2.56 inference(paramodulation,[status(thm)],[f5063,f3698])).
% 16.12/2.56 fof(f5478,plain,(
% 16.12/2.56 sF0_fnc='+'(sF2_fnc,times(sF2_fnc,sF2_fnc))),
% 16.12/2.56 inference(forward_demodulation,[status(thm)],[f41,f5437])).
% 16.12/2.56 fof(f5479,plain,(
% 16.12/2.56 sF0_fnc=times(sF2_fnc,s(sF2_fnc))),
% 16.12/2.56 inference(forward_demodulation,[status(thm)],[f1013,f5478])).
% 16.12/2.56 fof(f5480,plain,(
% 16.12/2.56 sF4_fnc=sF0_fnc),
% 16.12/2.56 inference(backward_demodulation,[status(thm)],[f5481,f36])).
% 16.12/2.56 fof(f5481,plain,(
% 16.12/2.56 sF0_fnc=times(sF2_fnc,sF5_fnc)),
% 16.12/2.56 inference(forward_demodulation,[status(thm)],[f35,f5479])).
% 16.12/2.56 fof(f5522,plain,(
% 16.12/2.56 $false),
% 16.12/2.56 inference(forward_subsumption_resolution,[status(thm)],[f5480,f37])).
% 16.12/2.56 % SZS output end CNFRefutation for theBenchmark.p
% 16.12/2.59 % Elapsed time: 2.142552 seconds
% 16.12/2.59 % CPU time: 16.669506 seconds
% 16.12/2.59 % Total memory used: 93.588 MB
% 16.12/2.59 % Net memory used: 90.864 MB
%------------------------------------------------------------------------------