%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL164-1 : 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 : n003.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 0.14s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL164-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 00:10:00 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.39 fof(f1,axiom,(
% 0.14/0.39 (![X]: (not(X) = xor(X,truth) ))),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.39 fof(f2,axiom,(
% 0.14/0.39 (![X]: (xor(X,falsehood) = X ))),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.39 fof(f4,axiom,(
% 0.14/0.39 (![X]: (and_star(X,truth) = X ))),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.39 fof(f5,axiom,(
% 0.14/0.39 (![X]: (and_star(X,falsehood) = falsehood ))),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.39 fof(f6,axiom,(
% 0.14/0.39 (![X]: (and_star(xor(truth,X),X) = falsehood ))),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.39 fof(f7,axiom,(
% 0.14/0.39 (![X,Y]: (xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ))),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.39 fof(f8,axiom,(
% 0.14/0.39 (![X,Y]: (and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(xor(and_star(xor(truth,Y),X),truth),X) ))),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.39 fof(f9,axiom,(
% 0.14/0.39 (![X,Y]: (xor(X,Y) = xor(Y,X) ))),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.39 fof(f11,axiom,(
% 0.14/0.39 (![X,Y]: (and_star(X,Y) = and_star(Y,X) ))),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.39 fof(f12,axiom,(
% 0.14/0.39 not(truth) = falsehood ),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.39 fof(f13,axiom,(
% 0.14/0.39 (![X,Y]: (implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ))),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.39 fof(f14,negated_conjecture,(
% 0.14/0.39 implies(implies(not(x),not(y)),implies(y,x)) != truth ),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.39 fof(f15,plain,(
% 0.14/0.39 ![X0]: (not(X0)=xor(X0,truth))),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f1])).
% 0.14/0.39 fof(f16,plain,(
% 0.14/0.39 ![X0]: (xor(X0,falsehood)=X0)),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f2])).
% 0.14/0.39 fof(f18,plain,(
% 0.14/0.39 ![X0]: (and_star(X0,truth)=X0)),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f4])).
% 0.14/0.39 fof(f19,plain,(
% 0.14/0.39 ![X0]: (and_star(X0,falsehood)=falsehood)),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f5])).
% 0.14/0.39 fof(f20,plain,(
% 0.14/0.39 ![X0]: (and_star(xor(truth,X0),X0)=falsehood)),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f6])).
% 0.14/0.39 fof(f21,plain,(
% 0.14/0.39 ![X0,X1]: (xor(X0,xor(truth,X1))=xor(xor(X0,truth),X1))),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f7])).
% 0.14/0.39 fof(f22,plain,(
% 0.14/0.39 ![X0,X1]: (and_star(xor(and_star(xor(truth,X0),X1),truth),X1)=and_star(xor(and_star(xor(truth,X1),X0),truth),X0))),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f8])).
% 0.14/0.39 fof(f23,plain,(
% 0.14/0.39 ![X0,X1]: (xor(X0,X1)=xor(X1,X0))),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f9])).
% 0.14/0.39 fof(f25,plain,(
% 0.14/0.39 ![X0,X1]: (and_star(X0,X1)=and_star(X1,X0))),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f11])).
% 0.14/0.39 fof(f26,plain,(
% 0.14/0.39 not(truth)=falsehood),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f12])).
% 0.14/0.39 fof(f27,plain,(
% 0.14/0.39 ![X0,X1]: (implies(X0,X1)=xor(truth,and_star(X0,xor(truth,X1))))),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f13])).
% 0.14/0.39 fof(f28,plain,(
% 0.14/0.39 ~implies(implies(not(x),not(y)),implies(y,x))=truth),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f14])).
% 0.14/0.39 fof(f35,plain,(
% 0.14/0.39 ![X0,X1]: (xor(X0,xor(truth,X1))=xor(not(X0),X1))),
% 0.14/0.39 inference(forward_demodulation,[status(thm)],[f15,f21])).
% 0.14/0.39 fof(f36,plain,(
% 0.14/0.39 ![X0,X1]: (and_star(not(and_star(xor(truth,X0),X1)),X1)=and_star(xor(and_star(xor(truth,X1),X0),truth),X0))),
% 0.14/0.39 inference(forward_demodulation,[status(thm)],[f15,f22])).
% 0.14/0.39 fof(f37,plain,(
% 0.14/0.39 ![X0,X1]: (and_star(not(and_star(xor(truth,X0),X1)),X1)=and_star(not(and_star(xor(truth,X1),X0)),X0))),
% 0.14/0.39 inference(forward_demodulation,[status(thm)],[f15,f36])).
% 0.14/0.39 fof(f39,plain,(
% 0.14/0.39 ![X0]: (xor(X0,not(truth))=xor(not(X0),truth))),
% 0.14/0.39 inference(paramodulation,[status(thm)],[f15,f35])).
% 0.14/0.39 fof(f42,plain,(
% 0.14/0.39 ![X0]: (xor(X0,falsehood)=xor(not(X0),truth))),
% 0.14/0.39 inference(forward_demodulation,[status(thm)],[f26,f39])).
% 0.14/0.39 fof(f43,plain,(
% 0.14/0.39 ![X0]: (X0=xor(not(X0),truth))),
% 0.14/0.39 inference(forward_demodulation,[status(thm)],[f16,f42])).
% 0.14/0.39 fof(f45,plain,(
% 0.14/0.39 ![X0]: (X0=not(not(X0)))),
% 0.14/0.39 inference(forward_demodulation,[status(thm)],[f15,f43])).
% 0.14/0.39 fof(f89,plain,(
% 0.14/0.39 ![X0,X1]: (implies(X0,xor(truth,X1))=xor(truth,and_star(X0,xor(not(truth),X1))))),
% 0.14/0.39 inference(paramodulation,[status(thm)],[f35,f27])).
% 0.14/0.39 fof(f91,plain,(
% 0.14/0.39 ![X0,X1,X2]: (and_star(not(and_star(xor(truth,X0),and_star(X1,xor(truth,X2)))),and_star(X1,xor(truth,X2)))=and_star(not(and_star(implies(X1,X2),X0)),X0))),
% 0.14/0.39 inference(paramodulation,[status(thm)],[f27,f37])).
% 0.14/0.39 fof(f98,plain,(
% 0.14/0.39 ![X0,X1]: (implies(X0,xor(truth,X1))=xor(truth,and_star(X0,xor(falsehood,X1))))),
% 0.14/0.39 inference(forward_demodulation,[status(thm)],[f26,f89])).
% 0.14/0.39 fof(f103,plain,(
% 0.14/0.39 truth=not(falsehood)),
% 0.14/0.39 inference(paramodulation,[status(thm)],[f26,f45])).
% 0.14/0.39 fof(f115,plain,(
% 0.14/0.39 ![X0]: (implies(X0,falsehood)=xor(truth,and_star(X0,truth)))),
% 0.14/0.39 inference(paramodulation,[status(thm)],[f16,f27])).
% 0.14/0.39 fof(f123,plain,(
% 0.14/0.39 ![X0,X1]: (implies(X0,xor(truth,X1))=implies(and_star(X0,xor(falsehood,X1)),falsehood))),
% 0.14/0.39 inference(backward_demodulation,[status(thm)],[f131,f98])).
% 0.14/0.39 fof(f127,plain,(
% 0.14/0.39 ![X0,X1,X2]: (and_star(not(and_star(xor(truth,X0),and_star(X1,xor(truth,X2)))),and_star(X1,implies(X2,falsehood)))=and_star(not(and_star(implies(X1,X2),X0)),X0))),
% 0.14/0.39 inference(backward_demodulation,[status(thm)],[f131,f91])).
% 0.14/0.39 fof(f130,plain,(
% 0.14/0.39 ![X0]: (and_star(implies(X0,falsehood),X0)=falsehood)),
% 0.14/0.39 inference(backward_demodulation,[status(thm)],[f131,f20])).
% 0.14/0.39 fof(f131,plain,(
% 0.14/0.39 ![X0]: (implies(X0,falsehood)=xor(truth,X0))),
% 0.14/0.39 inference(forward_demodulation,[status(thm)],[f18,f115])).
% 0.14/0.39 fof(f139,plain,(
% 0.14/0.39 ![X0,X1]: (implies(X0,implies(X1,falsehood))=implies(and_star(X0,xor(falsehood,X1)),falsehood))),
% 0.14/0.39 inference(forward_demodulation,[status(thm)],[f131,f123])).
% 0.14/0.39 fof(f143,plain,(
% 0.14/0.39 ![X0,X1,X2]: (and_star(not(and_star(implies(X0,falsehood),and_star(X1,xor(truth,X2)))),and_star(X1,implies(X2,falsehood)))=and_star(not(and_star(implies(X1,X2),X0)),X0))),
% 0.14/0.39 inference(forward_demodulation,[status(thm)],[f131,f127])).
% 0.14/0.39 fof(f144,plain,(
% 0.14/0.39 ![X0,X1,X2]: (and_star(not(and_star(implies(X0,falsehood),and_star(X1,implies(X2,falsehood)))),and_star(X1,implies(X2,falsehood)))=and_star(not(and_star(implies(X1,X2),X0)),X0))),
% 0.14/0.39 inference(forward_demodulation,[status(thm)],[f131,f143])).
% 0.14/0.39 fof(f154,plain,(
% 0.14/0.39 ![X0]: (X0=xor(falsehood,X0))),
% 0.14/0.39 inference(paramodulation,[status(thm)],[f16,f23])).
% 0.14/0.39 fof(f156,plain,(
% 0.14/0.39 ![X0]: (not(X0)=xor(truth,X0))),
% 0.14/0.39 inference(paramodulation,[status(thm)],[f15,f23])).
% 0.14/0.39 fof(f176,plain,(
% 0.14/0.39 ![X0,X1]: (implies(X0,implies(X1,falsehood))=implies(and_star(X0,X1),falsehood))),
% 0.14/0.39 inference(backward_demodulation,[status(thm)],[f154,f139])).
% 0.14/0.39 fof(f180,plain,(
% 0.14/0.39 ![X0]: (implies(X0,falsehood)=not(X0))),
% 0.14/0.39 inference(backward_demodulation,[status(thm)],[f156,f131])).
% 0.14/0.39 fof(f188,plain,(
% 0.14/0.39 ![X0,X1]: (implies(X0,implies(X1,falsehood))=not(and_star(X0,X1)))),
% 0.14/0.39 inference(backward_demodulation,[status(thm)],[f180,f176])).
% 0.14/0.39 fof(f191,plain,(
% 0.14/0.39 ![X0]: (and_star(not(X0),X0)=falsehood)),
% 0.14/0.39 inference(backward_demodulation,[status(thm)],[f180,f130])).
% 0.14/0.39 fof(f193,plain,(
% 0.14/0.39 ![X0,X1,X2]: (and_star(not(and_star(implies(X0,falsehood),and_star(X1,implies(X2,falsehood)))),and_star(X1,not(X2)))=and_star(not(and_star(implies(X1,X2),X0)),X0))),
% 0.14/0.39 inference(backward_demodulation,[status(thm)],[f180,f144])).
% 0.14/0.39 fof(f201,plain,(
% 0.14/0.39 ~implies(not(and_star(not(x),y)),implies(y,x))=truth),
% 0.14/0.39 inference(backward_demodulation,[status(thm)],[f203,f28])).
% 0.14/0.39 fof(f203,plain,(
% 0.14/0.39 ![X0,X1]: (implies(X0,not(X1))=not(and_star(X0,X1)))),
% 0.14/0.39 inference(forward_demodulation,[status(thm)],[f180,f188])).
% 0.14/0.39 fof(f210,plain,(
% 0.14/0.39 ![X0,X1,X2]: (and_star(not(and_star(not(X0),and_star(X1,implies(X2,falsehood)))),and_star(X1,not(X2)))=and_star(not(and_star(implies(X1,X2),X0)),X0))),
% 0.14/0.39 inference(forward_demodulation,[status(thm)],[f180,f193])).
% 0.14/0.39 fof(f211,plain,(
% 0.14/0.39 ![X0,X1,X2]: (and_star(not(and_star(not(X0),and_star(X1,not(X2)))),and_star(X1,not(X2)))=and_star(not(and_star(implies(X1,X2),X0)),X0))),
% 0.14/0.39 inference(forward_demodulation,[status(thm)],[f180,f210])).
% 0.14/0.39 fof(f226,plain,(
% 0.14/0.39 ![X0]: (falsehood=and_star(falsehood,X0))),
% 0.14/0.39 inference(paramodulation,[status(thm)],[f19,f25])).
% 0.14/0.39 fof(f227,plain,(
% 0.14/0.39 ![X0]: (X0=and_star(truth,X0))),
% 0.14/0.39 inference(paramodulation,[status(thm)],[f18,f25])).
% 0.14/0.39 fof(f251,plain,(
% 0.14/0.39 ![X0]: (and_star(X0,not(X0))=falsehood)),
% 0.14/0.39 inference(paramodulation,[status(thm)],[f25,f191])).
% 0.14/0.39 fof(f287,plain,(
% 0.14/0.39 ~implies(not(and_star(y,not(x))),implies(y,x))=truth),
% 0.14/0.39 inference(paramodulation,[status(thm)],[f25,f201])).
% 0.14/0.39 fof(f405,plain,(
% 0.14/0.39 ![X0,X1]: (implies(X0,X1)=not(and_star(X0,not(X1))))),
% 0.14/0.39 inference(paramodulation,[status(thm)],[f45,f203])).
% 0.14/0.39 fof(f409,plain,(
% 0.14/0.39 ~implies(implies(y,x),implies(y,x))=truth),
% 0.14/0.39 inference(backward_demodulation,[status(thm)],[f405,f287])).
% 0.14/0.39 fof(f425,plain,(
% 0.14/0.39 ![X0,X1]: (and_star(not(and_star(falsehood,and_star(X0,not(X1)))),and_star(X0,not(X1)))=and_star(not(and_star(implies(X0,X1),truth)),truth))),
% 0.14/0.39 inference(paramodulation,[status(thm)],[f26,f211])).
% 0.14/0.39 fof(f473,plain,(
% 0.14/0.39 ![X0,X1]: (and_star(not(falsehood),and_star(X0,not(X1)))=and_star(not(and_star(implies(X0,X1),truth)),truth))),
% 0.14/0.39 inference(forward_demodulation,[status(thm)],[f226,f425])).
% 0.14/0.39 fof(f474,plain,(
% 0.14/0.39 ![X0,X1]: (and_star(truth,and_star(X0,not(X1)))=and_star(not(and_star(implies(X0,X1),truth)),truth))),
% 0.14/0.39 inference(forward_demodulation,[status(thm)],[f103,f473])).
% 0.14/0.39 fof(f475,plain,(
% 0.14/0.39 ![X0,X1]: (and_star(X0,not(X1))=and_star(not(and_star(implies(X0,X1),truth)),truth))),
% 0.14/0.39 inference(forward_demodulation,[status(thm)],[f227,f474])).
% 0.14/0.39 fof(f476,plain,(
% 0.14/0.39 ![X0,X1]: (and_star(X0,not(X1))=not(and_star(implies(X0,X1),truth)))),
% 0.14/0.39 inference(forward_demodulation,[status(thm)],[f18,f475])).
% 0.14/0.39 fof(f485,plain,(
% 0.14/0.39 ![X0]: (not(implies(X0,X0))=falsehood)),
% 0.14/0.39 inference(backward_demodulation,[status(thm)],[f487,f251])).
% 0.14/0.39 fof(f487,plain,(
% 0.14/0.39 ![X0,X1]: (and_star(X0,not(X1))=not(implies(X0,X1)))),
% 0.14/0.39 inference(forward_demodulation,[status(thm)],[f18,f476])).
% 0.14/0.39 fof(f727,plain,(
% 0.14/0.39 ![X0]: (implies(X0,X0)=not(falsehood))),
% 0.14/0.39 inference(paramodulation,[status(thm)],[f485,f45])).
% 0.14/0.39 fof(f743,plain,(
% 0.14/0.39 ~truth=truth),
% 0.14/0.39 inference(backward_demodulation,[status(thm)],[f748,f409])).
% 0.14/0.39 fof(f748,plain,(
% 0.14/0.39 ![X0]: (implies(X0,X0)=truth)),
% 0.14/0.39 inference(forward_demodulation,[status(thm)],[f103,f727])).
% 0.14/0.39 fof(f749,plain,(
% 0.14/0.39 $false),
% 0.14/0.39 inference(trivial_equality_resolution,[status(thm)],[f743])).
% 0.14/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 6.18/1.63 % Elapsed time: 1.044521 seconds
% 6.18/1.63 % CPU time: 0.073877 seconds
% 6.18/1.63 % Total memory used: 2.066 MB
% 6.18/1.63 % Net memory used: 1.972 MB
%------------------------------------------------------------------------------