%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL163-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 01:09:28 PM UTC 2026
% Result : Unsatisfiable 0.22s 0.56s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL163-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.48 % Computer : n019.cluster.edu
% 0.18/0.48 % Model : x86_64 x86_64
% 0.18/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.48 % Memory : 8046.5625MB
% 0.18/0.48 % OS : Linux 6.8.0-71-generic
% 0.18/0.49 % CPULimit : 300
% 0.18/0.49 % WCLimit : 300
% 0.18/0.49 % DateTime : Mon Sep 21 00:08:34 UTC 2026
% 0.18/0.49 % CPUTime :
% 0.18/0.52 % Drodi V4.1.1
% 0.22/0.56 % Refutation found
% 0.22/0.56 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.22/0.56 % SZS output start CNFRefutation for theBenchmark
% 0.22/0.56 fof(f1,axiom,(
% 0.22/0.56 (![X]: (not(X) = xor(X,truth) ))),
% 0.22/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/0.56 fof(f2,axiom,(
% 0.22/0.56 (![X]: (xor(X,falsehood) = X ))),
% 0.22/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/0.56 fof(f4,axiom,(
% 0.22/0.56 (![X]: (and_star(X,truth) = X ))),
% 0.22/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/0.56 fof(f5,axiom,(
% 0.22/0.56 (![X]: (and_star(X,falsehood) = falsehood ))),
% 0.22/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/0.56 fof(f7,axiom,(
% 0.22/0.56 (![X,Y]: (xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ))),
% 0.22/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/0.56 fof(f8,axiom,(
% 0.22/0.56 (![X,Y]: (and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(xor(and_star(xor(truth,Y),X),truth),X) ))),
% 0.22/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/0.56 fof(f9,axiom,(
% 0.22/0.56 (![X,Y]: (xor(X,Y) = xor(Y,X) ))),
% 0.22/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/0.56 fof(f11,axiom,(
% 0.22/0.56 (![X,Y]: (and_star(X,Y) = and_star(Y,X) ))),
% 0.22/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/0.56 fof(f12,axiom,(
% 0.22/0.56 not(truth) = falsehood ),
% 0.22/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/0.56 fof(f13,axiom,(
% 0.22/0.56 (![X,Y]: (implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ))),
% 0.22/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/0.56 fof(f14,negated_conjecture,(
% 0.22/0.56 implies(implies(x,y),y) != implies(implies(y,x),x) ),
% 0.22/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/0.56 fof(f15,plain,(
% 0.22/0.56 ![X0]: (not(X0)=xor(X0,truth))),
% 0.22/0.56 inference(cnf_transformation,[status(thm)],[f1])).
% 0.22/0.56 fof(f16,plain,(
% 0.22/0.56 ![X0]: (xor(X0,falsehood)=X0)),
% 0.22/0.56 inference(cnf_transformation,[status(thm)],[f2])).
% 0.22/0.56 fof(f18,plain,(
% 0.22/0.56 ![X0]: (and_star(X0,truth)=X0)),
% 0.22/0.56 inference(cnf_transformation,[status(thm)],[f4])).
% 0.22/0.56 fof(f19,plain,(
% 0.22/0.56 ![X0]: (and_star(X0,falsehood)=falsehood)),
% 0.22/0.56 inference(cnf_transformation,[status(thm)],[f5])).
% 0.22/0.56 fof(f21,plain,(
% 0.22/0.56 ![X0,X1]: (xor(X0,xor(truth,X1))=xor(xor(X0,truth),X1))),
% 0.22/0.56 inference(cnf_transformation,[status(thm)],[f7])).
% 0.22/0.56 fof(f22,plain,(
% 0.22/0.56 ![X0,X1]: (and_star(xor(and_star(xor(truth,X0),X1),truth),X1)=and_star(xor(and_star(xor(truth,X1),X0),truth),X0))),
% 0.22/0.56 inference(cnf_transformation,[status(thm)],[f8])).
% 0.22/0.56 fof(f23,plain,(
% 0.22/0.56 ![X0,X1]: (xor(X0,X1)=xor(X1,X0))),
% 0.22/0.56 inference(cnf_transformation,[status(thm)],[f9])).
% 0.22/0.56 fof(f25,plain,(
% 0.22/0.56 ![X0,X1]: (and_star(X0,X1)=and_star(X1,X0))),
% 0.22/0.56 inference(cnf_transformation,[status(thm)],[f11])).
% 0.22/0.56 fof(f26,plain,(
% 0.22/0.56 not(truth)=falsehood),
% 0.22/0.56 inference(cnf_transformation,[status(thm)],[f12])).
% 0.22/0.56 fof(f27,plain,(
% 0.22/0.56 ![X0,X1]: (implies(X0,X1)=xor(truth,and_star(X0,xor(truth,X1))))),
% 0.22/0.56 inference(cnf_transformation,[status(thm)],[f13])).
% 0.22/0.56 fof(f28,plain,(
% 0.22/0.56 ~implies(implies(x,y),y)=implies(implies(y,x),x)),
% 0.22/0.56 inference(cnf_transformation,[status(thm)],[f14])).
% 0.22/0.56 fof(f34,plain,(
% 0.22/0.56 ![X0,X1]: (xor(X0,xor(truth,X1))=xor(not(X0),X1))),
% 0.22/0.56 inference(forward_demodulation,[status(thm)],[f15,f21])).
% 0.22/0.56 fof(f35,plain,(
% 0.22/0.56 ![X0,X1]: (and_star(not(and_star(xor(truth,X0),X1)),X1)=and_star(xor(and_star(xor(truth,X1),X0),truth),X0))),
% 0.22/0.56 inference(forward_demodulation,[status(thm)],[f15,f22])).
% 0.22/0.56 fof(f36,plain,(
% 0.22/0.56 ![X0,X1]: (and_star(not(and_star(xor(truth,X0),X1)),X1)=and_star(not(and_star(xor(truth,X1),X0)),X0))),
% 0.22/0.56 inference(forward_demodulation,[status(thm)],[f15,f35])).
% 0.22/0.56 fof(f37,plain,(
% 0.22/0.56 ![X0,X1,X2]: (implies(X0,and_star(X1,xor(truth,X2)))=xor(truth,and_star(X0,implies(X1,X2))))),
% 0.22/0.56 inference(paramodulation,[status(thm)],[f27,f27])).
% 0.22/0.56 fof(f40,plain,(
% 0.22/0.56 ![X0]: (implies(X0,truth)=xor(truth,and_star(X0,not(truth))))),
% 0.22/0.56 inference(paramodulation,[status(thm)],[f15,f27])).
% 0.22/0.56 fof(f41,plain,(
% 0.22/0.56 ![X0]: (implies(X0,truth)=xor(truth,and_star(X0,falsehood)))),
% 0.22/0.56 inference(forward_demodulation,[status(thm)],[f26,f40])).
% 0.22/0.56 fof(f42,plain,(
% 0.22/0.56 ![X0]: (implies(X0,truth)=xor(truth,falsehood))),
% 0.22/0.56 inference(forward_demodulation,[status(thm)],[f19,f41])).
% 0.22/0.56 fof(f43,plain,(
% 0.22/0.56 ![X0]: (implies(X0,truth)=truth)),
% 0.22/0.56 inference(forward_demodulation,[status(thm)],[f16,f42])).
% 0.22/0.56 fof(f44,plain,(
% 0.22/0.56 ![X0,X1]: (implies(X0,and_star(X1,xor(truth,truth)))=xor(truth,and_star(X0,truth)))),
% 0.22/0.56 inference(paramodulation,[status(thm)],[f43,f37])).
% 0.22/0.56 fof(f45,plain,(
% 0.22/0.56 ![X0,X1]: (implies(X0,and_star(X1,not(truth)))=xor(truth,and_star(X0,truth)))),
% 0.22/0.56 inference(forward_demodulation,[status(thm)],[f15,f44])).
% 0.22/0.56 fof(f46,plain,(
% 0.22/0.56 ![X0,X1]: (implies(X0,and_star(X1,falsehood))=xor(truth,and_star(X0,truth)))),
% 0.22/0.56 inference(forward_demodulation,[status(thm)],[f26,f45])).
% 0.22/0.56 fof(f47,plain,(
% 0.22/0.56 ![X0]: (implies(X0,falsehood)=xor(truth,and_star(X0,truth)))),
% 0.22/0.56 inference(forward_demodulation,[status(thm)],[f19,f46])).
% 0.22/0.56 fof(f48,plain,(
% 0.22/0.56 ![X0,X1,X2]: (implies(X0,and_star(X1,xor(truth,X2)))=implies(and_star(X0,implies(X1,X2)),falsehood))),
% 0.22/0.56 inference(backward_demodulation,[status(thm)],[f53,f37])).
% 0.22/0.56 fof(f49,plain,(
% 0.22/0.56 ![X0,X1]: (implies(X0,X1)=implies(and_star(X0,xor(truth,X1)),falsehood))),
% 0.22/0.56 inference(backward_demodulation,[status(thm)],[f53,f27])).
% 0.22/0.56 fof(f50,plain,(
% 0.22/0.56 ![X0,X1]: (and_star(not(and_star(xor(truth,X0),X1)),X1)=and_star(not(and_star(implies(X1,falsehood),X0)),X0))),
% 0.22/0.56 inference(backward_demodulation,[status(thm)],[f53,f36])).
% 0.22/0.56 fof(f51,plain,(
% 0.22/0.56 ![X0,X1]: (xor(X0,implies(X1,falsehood))=xor(not(X0),X1))),
% 0.22/0.56 inference(backward_demodulation,[status(thm)],[f53,f34])).
% 0.22/0.56 fof(f53,plain,(
% 0.22/0.56 ![X0]: (implies(X0,falsehood)=xor(truth,X0))),
% 0.22/0.56 inference(forward_demodulation,[status(thm)],[f18,f47])).
% 0.22/0.56 fof(f54,plain,(
% 0.22/0.56 ![X0,X1,X2]: (implies(X0,and_star(X1,implies(X2,falsehood)))=implies(and_star(X0,implies(X1,X2)),falsehood))),
% 0.22/0.56 inference(forward_demodulation,[status(thm)],[f53,f48])).
% 0.22/0.56 fof(f55,plain,(
% 0.22/0.56 ![X0,X1]: (implies(X0,X1)=implies(and_star(X0,implies(X1,falsehood)),falsehood))),
% 0.22/0.56 inference(forward_demodulation,[status(thm)],[f53,f49])).
% 0.22/0.56 fof(f56,plain,(
% 0.22/0.56 ![X0,X1]: (implies(X0,X1)=implies(X0,and_star(X1,implies(falsehood,falsehood))))),
% 0.22/0.56 inference(forward_demodulation,[status(thm)],[f54,f55])).
% 0.22/0.56 fof(f57,plain,(
% 0.22/0.56 ![X0,X1]: (and_star(not(and_star(implies(X0,falsehood),X1)),X1)=and_star(not(and_star(implies(X1,falsehood),X0)),X0))),
% 0.22/0.56 inference(forward_demodulation,[status(thm)],[f53,f50])).
% 0.22/0.56 fof(f89,plain,(
% 0.22/0.56 ![X0]: (not(X0)=xor(truth,X0))),
% 0.22/0.56 inference(paramodulation,[status(thm)],[f15,f23])).
% 0.22/0.56 fof(f100,plain,(
% 0.22/0.56 ![X0]: (implies(X0,falsehood)=not(X0))),
% 0.22/0.56 inference(backward_demodulation,[status(thm)],[f89,f53])).
% 0.22/0.56 fof(f101,plain,(
% 0.22/0.56 ![X0,X1]: (implies(X0,X1)=implies(X0,and_star(X1,not(falsehood))))),
% 0.22/0.56 inference(backward_demodulation,[status(thm)],[f100,f56])).
% 0.22/0.56 fof(f102,plain,(
% 0.22/0.56 ![X0,X1]: (and_star(not(and_star(implies(X0,falsehood),X1)),X1)=and_star(not(and_star(not(X1),X0)),X0))),
% 0.22/0.56 inference(backward_demodulation,[status(thm)],[f100,f57])).
% 0.22/0.56 fof(f106,plain,(
% 0.22/0.56 ![X0,X1,X2]: (implies(X0,and_star(X1,implies(X2,falsehood)))=not(and_star(X0,implies(X1,X2))))),
% 0.22/0.56 inference(backward_demodulation,[status(thm)],[f100,f54])).
% 0.22/0.56 fof(f108,plain,(
% 0.22/0.56 ![X0,X1]: (xor(X0,not(X1))=xor(not(X0),X1))),
% 0.22/0.56 inference(backward_demodulation,[status(thm)],[f100,f51])).
% 0.22/0.56 fof(f109,plain,(
% 0.22/0.56 ![X0,X1]: (and_star(not(and_star(not(X0),X1)),X1)=and_star(not(and_star(not(X1),X0)),X0))),
% 0.22/0.56 inference(forward_demodulation,[status(thm)],[f100,f102])).
% 0.22/0.56 fof(f115,plain,(
% 0.22/0.56 ![X0,X1]: (implies(X0,X1)=not(and_star(X0,implies(X1,falsehood))))),
% 0.22/0.56 inference(backward_demodulation,[status(thm)],[f116,f101])).
% 0.22/0.56 fof(f116,plain,(
% 0.22/0.56 ![X0,X1,X2]: (implies(X0,and_star(X1,not(X2)))=not(and_star(X0,implies(X1,X2))))),
% 0.22/0.56 inference(forward_demodulation,[status(thm)],[f100,f106])).
% 0.22/0.56 fof(f118,plain,(
% 0.22/0.56 ![X0,X1]: (implies(X0,X1)=not(and_star(X0,not(X1))))),
% 0.22/0.56 inference(forward_demodulation,[status(thm)],[f100,f115])).
% 0.22/0.56 fof(f236,plain,(
% 0.22/0.56 ![X0]: (xor(X0,not(truth))=not(not(X0)))),
% 0.22/0.56 inference(paramodulation,[status(thm)],[f15,f108])).
% 0.22/0.56 fof(f246,plain,(
% 0.22/0.56 ![X0]: (xor(X0,falsehood)=not(not(X0)))),
% 0.22/0.56 inference(forward_demodulation,[status(thm)],[f26,f236])).
% 0.22/0.56 fof(f250,plain,(
% 0.22/0.56 ![X0]: (X0=not(not(X0)))),
% 0.22/0.56 inference(forward_demodulation,[status(thm)],[f16,f246])).
% 0.22/0.56 fof(f271,plain,(
% 0.22/0.56 ![X0,X1]: (implies(not(and_star(not(X0),not(X1))),X1)=not(and_star(not(and_star(not(not(X1)),X0)),X0)))),
% 0.22/0.56 inference(paramodulation,[status(thm)],[f109,f118])).
% 0.22/0.58 fof(f275,plain,(
% 0.22/0.58 ![X0,X1]: (implies(X0,X1)=not(and_star(not(X1),X0)))),
% 0.22/0.58 inference(paramodulation,[status(thm)],[f25,f118])).
% 0.22/0.58 fof(f282,plain,(
% 0.22/0.58 ![X0,X1]: (and_star(X0,not(X1))=not(implies(X0,X1)))),
% 0.22/0.58 inference(paramodulation,[status(thm)],[f118,f250])).
% 0.22/0.58 fof(f287,plain,(
% 0.22/0.58 ![X0,X1]: (implies(implies(not(X0),X1),X1)=not(and_star(not(and_star(not(not(X1)),X0)),X0)))),
% 0.22/0.58 inference(forward_demodulation,[status(thm)],[f118,f271])).
% 0.22/0.58 fof(f288,plain,(
% 0.22/0.58 ![X0,X1]: (implies(implies(not(X0),X1),X1)=not(and_star(not(and_star(X1,X0)),X0)))),
% 0.22/0.58 inference(forward_demodulation,[status(thm)],[f250,f287])).
% 0.22/0.58 fof(f294,plain,(
% 0.22/0.58 ![X0,X1]: (implies(implies(not(X0),X1),X1)=implies(X0,and_star(X1,X0)))),
% 0.22/0.58 inference(backward_demodulation,[status(thm)],[f275,f288])).
% 0.22/0.58 fof(f448,plain,(
% 0.22/0.58 ![X0,X1]: (implies(X0,not(X1))=not(and_star(X1,X0)))),
% 0.22/0.58 inference(paramodulation,[status(thm)],[f250,f275])).
% 0.22/0.58 fof(f510,plain,(
% 0.22/0.58 ![X0,X1]: (implies(implies(X0,X1),X1)=implies(not(X0),and_star(X1,not(X0))))),
% 0.22/0.58 inference(paramodulation,[status(thm)],[f250,f294])).
% 0.22/0.58 fof(f538,plain,(
% 0.22/0.58 ![X0,X1]: (implies(implies(X0,X1),X1)=implies(not(X0),not(implies(X1,X0))))),
% 0.22/0.58 inference(forward_demodulation,[status(thm)],[f282,f510])).
% 0.22/0.58 fof(f539,plain,(
% 0.22/0.58 ![X0,X1]: (implies(implies(X0,X1),X1)=not(and_star(implies(X1,X0),not(X0))))),
% 0.22/0.58 inference(forward_demodulation,[status(thm)],[f448,f538])).
% 0.22/0.58 fof(f540,plain,(
% 0.22/0.58 ![X0,X1]: (implies(implies(X0,X1),X1)=not(not(implies(implies(X1,X0),X0))))),
% 0.22/0.58 inference(forward_demodulation,[status(thm)],[f282,f539])).
% 0.22/0.58 fof(f542,plain,(
% 0.22/0.58 ![X0,X1]: (implies(implies(X0,X1),X1)=implies(implies(X1,X0),X0))),
% 0.22/0.58 inference(forward_demodulation,[status(thm)],[f250,f540])).
% 0.22/0.58 fof(f543,plain,(
% 0.22/0.58 $false),
% 0.22/0.58 inference(backward_subsumption_resolution,[status(thm)],[f28,f542])).
% 0.22/0.58 % SZS output end CNFRefutation for theBenchmark.p
% 8.55/1.83 % Elapsed time: 1.102497 seconds
% 8.55/1.83 % CPU time: 0.179275 seconds
% 8.55/1.83 % Total memory used: 3.440 MB
% 8.55/1.83 % Net memory used: 3.326 MB
%------------------------------------------------------------------------------