%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL154-1 : 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 : n001.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 01:09:27 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL154-1 : 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 : n001.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 00:13:13 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.39 % Refutation found
% 0.10/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.39 fof(f1,axiom,(
% 0.10/0.39 (![X]: (implies(truth,X) = X ))),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f2,axiom,(
% 0.10/0.39 (![X,Y,Z]: (implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ))),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f3,axiom,(
% 0.10/0.39 (![X,Y]: (implies(implies(X,Y),Y) = implies(implies(Y,X),X) ))),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f4,axiom,(
% 0.10/0.39 (![X,Y]: (implies(implies(not(X),not(Y)),implies(Y,X)) = truth ))),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f5,axiom,(
% 0.10/0.39 (![X,Y]: (or(X,Y) = implies(not(X),Y) ))),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f7,axiom,(
% 0.10/0.39 (![X,Y]: (or(X,Y) = or(Y,X) ))),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f8,axiom,(
% 0.10/0.39 (![X,Y]: (and(X,Y) = not(or(not(X),not(Y))) ))),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f11,axiom,(
% 0.10/0.39 (![X,Y]: (xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) ))),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f12,axiom,(
% 0.10/0.39 (![X,Y]: (xor(X,Y) = xor(Y,X) ))),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f16,axiom,(
% 0.10/0.39 not(truth) = falsehood ),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f17,negated_conjecture,(
% 0.10/0.39 xor(x,falsehood) != x ),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f18,plain,(
% 0.10/0.39 ![X0]: (implies(truth,X0)=X0)),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f1])).
% 0.10/0.39 fof(f19,plain,(
% 0.10/0.39 ![X0,X1,X2]: (implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))=truth)),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f2])).
% 0.10/0.39 fof(f20,plain,(
% 0.10/0.39 ![X0,X1]: (implies(implies(X0,X1),X1)=implies(implies(X1,X0),X0))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f3])).
% 0.10/0.39 fof(f21,plain,(
% 0.10/0.39 ![X0,X1]: (implies(implies(not(X0),not(X1)),implies(X1,X0))=truth)),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f4])).
% 0.10/0.39 fof(f22,plain,(
% 0.10/0.39 ![X0,X1]: (or(X0,X1)=implies(not(X0),X1))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f5])).
% 0.10/0.39 fof(f24,plain,(
% 0.10/0.39 ![X0,X1]: (or(X0,X1)=or(X1,X0))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f7])).
% 0.10/0.39 fof(f25,plain,(
% 0.10/0.39 ![X0,X1]: (and(X0,X1)=not(or(not(X0),not(X1))))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f8])).
% 0.10/0.39 fof(f28,plain,(
% 0.10/0.39 ![X0,X1]: (xor(X0,X1)=or(and(X0,not(X1)),and(not(X0),X1)))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f11])).
% 0.10/0.39 fof(f29,plain,(
% 0.10/0.39 ![X0,X1]: (xor(X0,X1)=xor(X1,X0))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f12])).
% 0.10/0.39 fof(f33,plain,(
% 0.10/0.39 not(truth)=falsehood),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f16])).
% 0.10/0.39 fof(f34,plain,(
% 0.10/0.39 ~xor(x,falsehood)=x),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f17])).
% 0.10/0.39 fof(f35,definition,(
% 0.10/0.39 sF0_fnc=xor(x,falsehood)),
% 0.10/0.39 introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition])).
% 0.10/0.39 fof(f36,plain,(
% 0.10/0.39 ~sF0_fnc=x),
% 0.10/0.39 inference(definition_folding,[],[f34,f35])).
% 0.10/0.39 fof(f37,plain,(
% 0.10/0.39 ![X0,X1]: (implies(or(X0,not(X1)),implies(X1,X0))=truth)),
% 0.10/0.39 inference(backward_demodulation,[status(thm)],[f22,f21])).
% 0.10/0.39 fof(f57,plain,(
% 0.10/0.39 ![X0,X1]: (implies(X0,implies(implies(X0,X1),implies(truth,X1)))=truth)),
% 0.10/0.39 inference(paramodulation,[status(thm)],[f18,f19])).
% 0.10/0.39 fof(f64,plain,(
% 0.10/0.39 ![X0,X1]: (implies(X0,implies(implies(X0,X1),X1))=truth)),
% 0.10/0.39 inference(forward_demodulation,[status(thm)],[f18,f57])).
% 0.10/0.39 fof(f69,plain,(
% 0.10/0.39 sF0_fnc=xor(falsehood,x)),
% 0.10/0.39 inference(paramodulation,[status(thm)],[f29,f35])).
% 0.10/0.39 fof(f73,plain,(
% 0.10/0.39 ![X0]: (or(truth,X0)=implies(falsehood,X0))),
% 0.10/0.39 inference(paramodulation,[status(thm)],[f33,f22])).
% 0.10/0.39 fof(f79,plain,(
% 0.10/0.39 ![X0]: (or(X0,truth)=implies(falsehood,X0))),
% 0.10/0.39 inference(paramodulation,[status(thm)],[f24,f73])).
% 0.10/0.39 fof(f87,plain,(
% 0.10/0.39 ![X0]: (implies(X0,X0)=implies(implies(X0,truth),truth))),
% 0.10/0.39 inference(paramodulation,[status(thm)],[f18,f20])).
% 0.10/0.39 fof(f108,plain,(
% 0.10/0.39 ![X0]: (implies(implies(truth,X0),X0)=truth)),
% 0.10/0.39 inference(paramodulation,[status(thm)],[f18,f64])).
% 0.10/0.39 fof(f126,plain,(
% 0.10/0.39 ![X0]: (truth=implies(implies(X0,truth),truth))),
% 0.10/0.39 inference(backward_demodulation,[status(thm)],[f127,f87])).
% 0.10/0.39 fof(f127,plain,(
% 0.10/0.39 ![X0]: (implies(X0,X0)=truth)),
% 0.10/0.39 inference(forward_demodulation,[status(thm)],[f18,f108])).
% 0.10/0.39 fof(f138,plain,(
% 0.10/0.39 ![X0]: (or(X0,not(X0))=truth)),
% 0.10/0.39 inference(paramodulation,[status(thm)],[f22,f127])).
% 0.10/0.39 fof(f165,plain,(
% 0.10/0.39 ![X0]: (implies(X0,truth)=truth)),
% 0.10/0.39 inference(paramodulation,[status(thm)],[f126,f64])).
% 0.10/0.39 fof(f198,plain,(
% 0.10/0.39 ![X0]: (or(X0,truth)=truth)),
% 0.10/0.39 inference(paramodulation,[status(thm)],[f22,f165])).
% 0.10/0.39 fof(f215,plain,(
% 0.10/0.39 ![X0]: (truth=implies(falsehood,X0))),
% 0.10/0.39 inference(backward_demodulation,[status(thm)],[f198,f79])).
% 0.10/0.39 fof(f272,plain,(
% 0.10/0.39 ![X0]: (implies(implies(X0,falsehood),falsehood)=implies(truth,X0))),
% 0.10/0.39 inference(paramodulation,[status(thm)],[f215,f20])).
% 0.10/0.39 fof(f277,plain,(
% 0.10/0.39 ![X0]: (implies(implies(X0,falsehood),falsehood)=X0)),
% 0.10/0.39 inference(forward_demodulation,[status(thm)],[f18,f272])).
% 0.10/0.39 fof(f373,plain,(
% 0.10/0.39 ![X0]: (and(truth,X0)=not(or(falsehood,not(X0))))),
% 0.10/0.39 inference(paramodulation,[status(thm)],[f33,f25])).
% 0.10/0.39 fof(f389,plain,(
% 0.10/0.39 ![X0]: (implies(or(X0,falsehood),falsehood)=not(X0))),
% 0.10/0.39 inference(paramodulation,[status(thm)],[f22,f277])).
% 0.10/0.39 fof(f486,plain,(
% 0.10/0.39 ![X0]: (implies(or(falsehood,X0),falsehood)=not(X0))),
% 0.10/0.39 inference(paramodulation,[status(thm)],[f24,f389])).
% 0.10/0.39 fof(f505,plain,(
% 0.10/0.39 implies(truth,falsehood)=not(not(falsehood))),
% 0.10/0.39 inference(paramodulation,[status(thm)],[f138,f486])).
% 0.10/0.39 fof(f519,plain,(
% 0.10/0.39 falsehood=not(not(falsehood))),
% 0.10/0.39 inference(forward_demodulation,[status(thm)],[f18,f505])).
% 0.10/0.39 fof(f531,plain,(
% 0.10/0.39 ![X0]: (and(not(falsehood),X0)=not(or(falsehood,not(X0))))),
% 0.10/0.39 inference(paramodulation,[status(thm)],[f519,f25])).
% 0.10/0.39 fof(f533,plain,(
% 0.10/0.39 ![X0]: (or(not(falsehood),X0)=implies(falsehood,X0))),
% 0.10/0.39 inference(paramodulation,[status(thm)],[f519,f22])).
% 0.10/0.39 fof(f536,plain,(
% 0.10/0.39 ![X0]: (and(not(falsehood),X0)=and(truth,X0))),
% 0.10/0.39 inference(forward_demodulation,[status(thm)],[f373,f531])).
% 0.10/0.39 fof(f542,plain,(
% 0.10/0.39 ![X0]: (or(not(falsehood),X0)=truth)),
% 0.10/0.39 inference(forward_demodulation,[status(thm)],[f215,f533])).
% 0.10/0.39 fof(f550,plain,(
% 0.10/0.39 ![X0]: (and(falsehood,X0)=not(truth))),
% 0.10/0.39 inference(paramodulation,[status(thm)],[f542,f25])).
% 0.10/0.39 fof(f567,plain,(
% 0.10/0.39 ![X0]: (and(falsehood,X0)=falsehood)),
% 0.10/0.39 inference(forward_demodulation,[status(thm)],[f33,f550])).
% 0.10/0.39 fof(f594,plain,(
% 0.10/0.39 ![X0]: (xor(falsehood,X0)=or(falsehood,and(not(falsehood),X0)))),
% 0.10/0.39 inference(paramodulation,[status(thm)],[f567,f28])).
% 0.10/0.39 fof(f612,plain,(
% 0.10/0.39 ![X0]: (xor(falsehood,X0)=or(falsehood,and(truth,X0)))),
% 0.10/0.39 inference(forward_demodulation,[status(thm)],[f536,f594])).
% 0.10/0.39 fof(f745,plain,(
% 0.10/0.39 ![X0]: (implies(truth,implies(X0,not(falsehood)))=truth)),
% 0.10/0.39 inference(paramodulation,[status(thm)],[f542,f37])).
% 0.10/0.39 fof(f783,plain,(
% 0.10/0.39 ![X0]: (implies(X0,not(falsehood))=truth)),
% 0.10/0.39 inference(forward_demodulation,[status(thm)],[f18,f745])).
% 0.10/0.39 fof(f800,plain,(
% 0.10/0.39 not(falsehood)=truth),
% 0.10/0.39 inference(paramodulation,[status(thm)],[f18,f783])).
% 0.10/0.39 fof(f860,plain,(
% 0.10/0.39 ![X0]: (or(falsehood,X0)=implies(truth,X0))),
% 0.10/0.39 inference(paramodulation,[status(thm)],[f800,f22])).
% 0.10/0.39 fof(f872,plain,(
% 0.10/0.39 ![X0]: (implies(X0,falsehood)=not(X0))),
% 0.10/0.39 inference(backward_demodulation,[status(thm)],[f887,f486])).
% 0.10/0.39 fof(f875,plain,(
% 0.10/0.39 ![X0]: (xor(falsehood,X0)=and(truth,X0))),
% 0.10/0.39 inference(backward_demodulation,[status(thm)],[f887,f612])).
% 0.10/0.39 fof(f879,plain,(
% 0.10/0.39 ![X0]: (and(truth,X0)=not(not(X0)))),
% 0.10/0.39 inference(backward_demodulation,[status(thm)],[f887,f373])).
% 0.10/0.39 fof(f887,plain,(
% 0.10/0.39 ![X0]: (or(falsehood,X0)=X0)),
% 0.10/0.39 inference(forward_demodulation,[status(thm)],[f18,f860])).
% 0.10/0.39 fof(f889,plain,(
% 0.10/0.39 ![X0]: (not(implies(X0,falsehood))=X0)),
% 0.10/0.39 inference(backward_demodulation,[status(thm)],[f872,f277])).
% 0.10/0.39 fof(f897,plain,(
% 0.10/0.39 sF0_fnc=and(truth,x)),
% 0.10/0.39 inference(backward_demodulation,[status(thm)],[f875,f69])).
% 0.10/0.39 fof(f918,plain,(
% 0.10/0.39 ![X0]: (not(not(X0))=X0)),
% 0.10/0.39 inference(forward_demodulation,[status(thm)],[f872,f889])).
% 0.10/0.39 fof(f926,plain,(
% 0.10/0.39 sF0_fnc=not(not(x))),
% 0.10/0.39 inference(forward_demodulation,[status(thm)],[f879,f897])).
% 0.10/0.39 fof(f927,plain,(
% 0.10/0.39 sF0_fnc=x),
% 0.10/0.39 inference(forward_demodulation,[status(thm)],[f918,f926])).
% 0.10/0.39 fof(f928,plain,(
% 0.10/0.39 $false),
% 0.10/0.39 inference(forward_subsumption_resolution,[status(thm)],[f927,f36])).
% 0.10/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.41 % Elapsed time: 0.038958 seconds
% 0.10/0.41 % CPU time: 0.159640 seconds
% 0.10/0.41 % Total memory used: 7.051 MB
% 0.10/0.41 % Net memory used: 6.995 MB
%------------------------------------------------------------------------------