%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : RNG008-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 02:05:07 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.42s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG008-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n004.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 04:10:19 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.42 % Refutation found
% 0.10/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.42 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.42 fof(f1,axiom,(
% 0.10/0.42 (![X]: (add(additive_identity,X) = X ))),
% 0.10/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.42 fof(f2,axiom,(
% 0.10/0.42 (![X]: (add(additive_inverse(X),X) = additive_identity ))),
% 0.10/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.42 fof(f3,axiom,(
% 0.10/0.42 (![X,Y,Z]: (multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ))),
% 0.10/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.42 fof(f4,axiom,(
% 0.10/0.42 (![X,Y,Z]: (multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ))),
% 0.10/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.42 fof(f6,axiom,(
% 0.10/0.42 (![X]: (additive_inverse(additive_inverse(X)) = X ))),
% 0.10/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.42 fof(f10,axiom,(
% 0.10/0.42 (![X,Y]: (multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) ))),
% 0.10/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.42 fof(f11,axiom,(
% 0.10/0.42 (![X,Y]: (multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ))),
% 0.10/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.42 fof(f12,axiom,(
% 0.10/0.42 (![X,Y,Z]: (add(add(X,Y),Z) = add(X,add(Y,Z)) ))),
% 0.10/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.42 fof(f13,axiom,(
% 0.10/0.42 (![X,Y]: (add(X,Y) = add(Y,X) ))),
% 0.10/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.42 fof(f14,axiom,(
% 0.10/0.42 (![X,Y,Z]: (multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ))),
% 0.10/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.42 fof(f15,hypothesis,(
% 0.10/0.42 (![X]: (multiply(X,X) = X ))),
% 0.10/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.42 fof(f16,negated_conjecture,(
% 0.10/0.42 multiply(a,b) = c ),
% 0.10/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.42 fof(f17,negated_conjecture,(
% 0.10/0.42 multiply(b,a) != c ),
% 0.10/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.42 fof(f18,plain,(
% 0.10/0.42 ![X0]: (add(additive_identity,X0)=X0)),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f1])).
% 0.10/0.42 fof(f19,plain,(
% 0.10/0.42 ![X0]: (add(additive_inverse(X0),X0)=additive_identity)),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f2])).
% 0.10/0.42 fof(f20,plain,(
% 0.10/0.42 ![X0,X1,X2]: (multiply(X0,add(X1,X2))=add(multiply(X0,X1),multiply(X0,X2)))),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f3])).
% 0.10/0.42 fof(f21,plain,(
% 0.10/0.42 ![X0,X1,X2]: (multiply(add(X0,X1),X2)=add(multiply(X0,X2),multiply(X1,X2)))),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f4])).
% 0.10/0.42 fof(f23,plain,(
% 0.10/0.42 ![X0]: (additive_inverse(additive_inverse(X0))=X0)),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f6])).
% 0.10/0.42 fof(f27,plain,(
% 0.10/0.42 ![X0,X1]: (multiply(X0,additive_inverse(X1))=additive_inverse(multiply(X0,X1)))),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f10])).
% 0.10/0.42 fof(f28,plain,(
% 0.10/0.42 ![X0,X1]: (multiply(additive_inverse(X0),X1)=additive_inverse(multiply(X0,X1)))),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f11])).
% 0.10/0.42 fof(f29,plain,(
% 0.10/0.42 ![X0,X1,X2]: (add(add(X0,X1),X2)=add(X0,add(X1,X2)))),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f12])).
% 0.10/0.42 fof(f30,plain,(
% 0.10/0.42 ![X0,X1]: (add(X0,X1)=add(X1,X0))),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f13])).
% 0.10/0.42 fof(f31,plain,(
% 0.10/0.42 ![X0,X1,X2]: (multiply(multiply(X0,X1),X2)=multiply(X0,multiply(X1,X2)))),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f14])).
% 0.10/0.42 fof(f32,plain,(
% 0.10/0.42 ![X0]: (multiply(X0,X0)=X0)),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f15])).
% 0.10/0.42 fof(f33,plain,(
% 0.10/0.42 multiply(a,b)=c),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f16])).
% 0.10/0.42 fof(f34,plain,(
% 0.10/0.42 ~multiply(b,a)=c),
% 0.10/0.42 inference(cnf_transformation,[status(thm)],[f17])).
% 0.10/0.42 fof(f35,definition,(
% 0.10/0.42 sF0_fnc=multiply(b,a)),
% 0.10/0.42 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 0.10/0.42 fof(f36,plain,(
% 0.10/0.42 ~sF0_fnc=c),
% 0.10/0.42 inference(definition_folding,[],[f34,f35])).
% 0.10/0.42 fof(f37,plain,(
% 0.10/0.42 ![X0]: (add(X0,additive_inverse(X0))=additive_identity)),
% 0.10/0.42 inference(backward_demodulation,[status(thm)],[f30,f19])).
% 0.10/0.42 fof(f39,plain,(
% 0.10/0.42 ![X0,X1]: (multiply(X0,add(X1,X0))=add(multiply(X0,X1),X0))),
% 0.10/0.42 inference(paramodulation,[status(thm)],[f32,f20])).
% 0.10/0.42 fof(f40,plain,(
% 0.10/0.42 ![X0,X1]: (multiply(X0,add(X1,X0))=add(X0,multiply(X0,X1)))),
% 0.10/0.42 inference(forward_demodulation,[status(thm)],[f30,f39])).
% 0.10/0.42 fof(f68,plain,(
% 0.10/0.42 ![X0,X1]: (multiply(add(X0,X1),X0)=add(X0,multiply(X1,X0)))),
% 0.10/0.42 inference(paramodulation,[status(thm)],[f32,f21])).
% 0.10/0.42 fof(f72,plain,(
% 0.10/0.42 ![X0,X1]: (multiply(add(X0,X1),X1)=add(multiply(X0,X1),X1))),
% 0.10/0.42 inference(paramodulation,[status(thm)],[f32,f21])).
% 0.10/0.42 fof(f83,plain,(
% 0.10/0.42 ![X0,X1]: (multiply(add(X0,X1),X1)=add(X1,multiply(X0,X1)))),
% 0.10/0.42 inference(forward_demodulation,[status(thm)],[f30,f72])).
% 0.10/0.42 fof(f135,plain,(
% 0.10/0.42 ![X0]: (additive_inverse(X0)=additive_inverse(multiply(additive_inverse(X0),X0)))),
% 0.10/0.42 inference(paramodulation,[status(thm)],[f32,f27])).
% 0.10/0.42 fof(f145,plain,(
% 0.10/0.42 ![X0]: (additive_inverse(X0)=additive_inverse(additive_inverse(multiply(X0,X0))))),
% 0.10/0.42 inference(forward_demodulation,[status(thm)],[f28,f135])).
% 0.10/0.42 fof(f146,plain,(
% 0.10/0.42 ![X0]: (additive_inverse(X0)=multiply(X0,X0))),
% 0.10/0.42 inference(forward_demodulation,[status(thm)],[f23,f145])).
% 0.10/0.42 fof(f151,plain,(
% 0.10/0.42 ![X0]: (add(X0,X0)=additive_identity)),
% 0.10/0.42 inference(backward_demodulation,[status(thm)],[f156,f37])).
% 0.10/0.42 fof(f156,plain,(
% 0.10/0.42 ![X0]: (additive_inverse(X0)=X0)),
% 0.10/0.42 inference(forward_demodulation,[status(thm)],[f32,f146])).
% 0.10/0.42 fof(f202,plain,(
% 0.10/0.42 ![X0]: (multiply(sF0_fnc,X0)=multiply(b,multiply(a,X0)))),
% 0.10/0.42 inference(paramodulation,[status(thm)],[f35,f31])).
% 0.10/0.42 fof(f203,plain,(
% 0.10/0.42 ![X0]: (multiply(c,X0)=multiply(a,multiply(b,X0)))),
% 0.10/0.42 inference(paramodulation,[status(thm)],[f33,f31])).
% 0.10/0.42 fof(f206,plain,(
% 0.10/0.42 ![X0,X1]: (multiply(X0,X1)=multiply(X0,multiply(X0,X1)))),
% 0.10/0.42 inference(paramodulation,[status(thm)],[f32,f31])).
% 0.10/0.42 fof(f235,plain,(
% 0.10/0.42 ![X0,X1]: (add(additive_identity,X0)=add(X1,add(X1,X0)))),
% 0.10/0.42 inference(paramodulation,[status(thm)],[f151,f29])).
% 0.10/0.42 fof(f244,plain,(
% 0.10/0.42 ![X0,X1]: (X0=add(X1,add(X1,X0)))),
% 0.10/0.42 inference(forward_demodulation,[status(thm)],[f18,f235])).
% 0.10/0.42 fof(f254,plain,(
% 0.10/0.42 ![X0,X1]: (X0=add(X1,add(X0,X1)))),
% 0.10/0.42 inference(paramodulation,[status(thm)],[f30,f244])).
% 0.10/0.42 fof(f296,plain,(
% 0.10/0.42 multiply(b,a)=multiply(b,sF0_fnc)),
% 0.10/0.42 inference(paramodulation,[status(thm)],[f35,f206])).
% 0.10/0.42 fof(f313,plain,(
% 0.10/0.42 sF0_fnc=multiply(b,sF0_fnc)),
% 0.10/0.42 inference(forward_demodulation,[status(thm)],[f35,f296])).
% 0.10/0.42 fof(f394,plain,(
% 0.10/0.42 multiply(sF0_fnc,b)=multiply(b,c)),
% 0.10/0.42 inference(paramodulation,[status(thm)],[f33,f202])).
% 0.10/0.42 fof(f443,plain,(
% 0.10/0.42 ![X0,X1]: (multiply(add(X0,X1),X0)=add(add(X0,X1),multiply(add(X0,X1),X1)))),
% 0.10/0.42 inference(paramodulation,[status(thm)],[f254,f40])).
% 0.10/0.42 fof(f471,plain,(
% 0.10/0.42 ![X0,X1]: (add(X0,multiply(X1,X0))=add(add(X0,X1),multiply(add(X0,X1),X1)))),
% 0.10/0.42 inference(forward_demodulation,[status(thm)],[f68,f443])).
% 0.10/0.42 fof(f472,plain,(
% 0.10/0.42 ![X0,X1]: (add(X0,multiply(X1,X0))=add(X0,add(X1,multiply(add(X0,X1),X1))))),
% 0.10/0.42 inference(forward_demodulation,[status(thm)],[f29,f471])).
% 0.10/0.42 fof(f473,plain,(
% 0.10/0.42 ![X0,X1]: (add(X0,multiply(X1,X0))=add(X0,add(X1,add(X1,multiply(X0,X1)))))),
% 0.10/0.42 inference(forward_demodulation,[status(thm)],[f83,f472])).
% 0.10/0.42 fof(f474,plain,(
% 0.10/0.42 ![X0,X1]: (add(X0,multiply(X1,X0))=add(X0,multiply(X0,X1)))),
% 0.10/0.42 inference(forward_demodulation,[status(thm)],[f244,f473])).
% 0.10/0.42 fof(f519,plain,(
% 0.10/0.42 multiply(c,b)=multiply(a,b)),
% 0.10/0.42 inference(paramodulation,[status(thm)],[f32,f203])).
% 0.10/0.42 fof(f533,plain,(
% 0.10/0.42 multiply(c,b)=c),
% 0.10/0.42 inference(forward_demodulation,[status(thm)],[f33,f519])).
% 0.10/0.42 fof(f612,plain,(
% 0.10/0.42 ![X0,X1]: (multiply(X0,X1)=add(X1,multiply(add(X0,X1),X1)))),
% 0.10/0.42 inference(paramodulation,[status(thm)],[f254,f68])).
% 0.10/0.42 fof(f636,plain,(
% 0.10/0.42 ![X0,X1]: (multiply(X0,X1)=add(X1,multiply(X1,add(X0,X1))))),
% 0.10/0.42 inference(forward_demodulation,[status(thm)],[f474,f612])).
% 0.10/0.42 fof(f637,plain,(
% 0.10/0.42 ![X0,X1]: (multiply(X0,X1)=add(X1,add(X1,multiply(X1,X0))))),
% 0.10/0.42 inference(forward_demodulation,[status(thm)],[f40,f636])).
% 0.10/0.42 fof(f639,plain,(
% 0.10/0.42 multiply(b,c)=c),
% 0.10/0.42 inference(backward_demodulation,[status(thm)],[f670,f533])).
% 0.10/0.42 fof(f640,plain,(
% 0.10/0.42 multiply(b,sF0_fnc)=multiply(b,c)),
% 0.10/0.42 inference(backward_demodulation,[status(thm)],[f670,f394])).
% 0.10/0.42 fof(f670,plain,(
% 0.10/0.42 ![X0,X1]: (multiply(X0,X1)=multiply(X1,X0))),
% 0.10/0.42 inference(forward_demodulation,[status(thm)],[f244,f637])).
% 0.10/0.42 fof(f700,plain,(
% 0.10/0.42 sF0_fnc=multiply(b,c)),
% 0.10/0.42 inference(forward_demodulation,[status(thm)],[f313,f640])).
% 0.10/0.42 fof(f701,plain,(
% 0.10/0.42 sF0_fnc=c),
% 0.10/0.42 inference(forward_demodulation,[status(thm)],[f639,f700])).
% 0.10/0.42 fof(f702,plain,(
% 0.10/0.42 $false),
% 0.10/0.42 inference(forward_subsumption_resolution,[status(thm)],[f701,f36])).
% 0.10/0.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.44 % Elapsed time: 0.055478 seconds
% 0.10/0.44 % CPU time: 0.322067 seconds
% 0.10/0.44 % Total memory used: 15.245 MB
% 0.10/0.44 % Net memory used: 15.058 MB
%------------------------------------------------------------------------------