%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL414+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 01:10:00 PM UTC 2026
% Result : Theorem 0.23s 5.51s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL414+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/5.47 % Computer : n016.cluster.edu
% 0.19/5.47 % Model : x86_64 x86_64
% 0.19/5.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.47 % Memory : 8046.5625MB
% 0.19/5.47 % OS : Linux 6.8.0-71-generic
% 0.19/5.47 % CPULimit : 300
% 0.19/5.47 % WCLimit : 300
% 0.19/5.47 % DateTime : Mon Sep 21 00:33:57 UTC 2026
% 0.19/5.47 % CPUTime :
% 0.19/5.48 % Drodi V4.1.1
% 0.23/5.51 % Refutation found
% 0.23/5.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.23/5.51 % SZS output start CNFRefutation for theBenchmark
% 0.23/5.51 fof(f1,conjecture,(
% 0.23/5.51 ~ ( (! [P,Q] :( ~ a_truth(implies(P,Q))| ~ a_truth(P)| a_truth(Q) ))& (! [P,Q] : a_truth(implies(P,implies(Q,P))))& (! [P,Q,R] : a_truth(implies(implies(P,implies(Q,R)),implies(implies(P,Q),implies(P,R)))))& (! [P,Q] : a_truth(implies(implies(not(P),not(Q)),implies(Q,P))))& (? [A] : ~ a_truth(implies(A,A)) )) ),
% 0.23/5.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/5.51 fof(f2,negated_conjecture,(
% 0.23/5.51 ~(~ ( (! [P,Q] :( ~ a_truth(implies(P,Q))| ~ a_truth(P)| a_truth(Q) ))& (! [P,Q] : a_truth(implies(P,implies(Q,P))))& (! [P,Q,R] : a_truth(implies(implies(P,implies(Q,R)),implies(implies(P,Q),implies(P,R)))))& (! [P,Q] : a_truth(implies(implies(not(P),not(Q)),implies(Q,P))))& (? [A] : ~ a_truth(implies(A,A)) )) )),
% 0.23/5.51 inference(negated_conjecture,[status(cth)],[f1])).
% 0.23/5.51 fof(f3,plain,(
% 0.23/5.51 ((((![Q]: ((![P]: (~a_truth(implies(P,Q))|~a_truth(P)))|a_truth(Q)))&(![P,Q]: a_truth(implies(P,implies(Q,P)))))&(![P,Q,R]: a_truth(implies(implies(P,implies(Q,R)),implies(implies(P,Q),implies(P,R))))))&(![P,Q]: a_truth(implies(implies(not(P),not(Q)),implies(Q,P)))))&(?[A]: ~a_truth(implies(A,A)))),
% 0.23/5.51 inference(miniscoping,[status(thm)],[f2])).
% 0.23/5.51 fof(f4,plain,(
% 0.23/5.51 ((((![Q]: ((![P]: (~a_truth(implies(P,Q))|~a_truth(P)))|a_truth(Q)))&(![P,Q]: a_truth(implies(P,implies(Q,P)))))&(![P,Q,R]: a_truth(implies(implies(P,implies(Q,R)),implies(implies(P,Q),implies(P,R))))))&(![P,Q]: a_truth(implies(implies(not(P),not(Q)),implies(Q,P)))))&~a_truth(implies(sK0_skl,sK0_skl))),
% 0.23/5.51 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(A,sK0_skl)],[f3])).
% 0.23/5.51 fof(f5,plain,(
% 0.23/5.51 ![X0,X1]: (~a_truth(implies(X0,X1))|~a_truth(X0)|a_truth(X1))),
% 0.23/5.51 inference(cnf_transformation,[status(thm)],[f4])).
% 0.23/5.51 fof(f6,plain,(
% 0.23/5.51 ![X0,X1]: (a_truth(implies(X0,implies(X1,X0))))),
% 0.23/5.51 inference(cnf_transformation,[status(thm)],[f4])).
% 0.23/5.51 fof(f7,plain,(
% 0.23/5.51 ![X0,X1,X2]: (a_truth(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2)))))),
% 0.23/5.51 inference(cnf_transformation,[status(thm)],[f4])).
% 0.23/5.51 fof(f9,plain,(
% 0.23/5.51 ~a_truth(implies(sK0_skl,sK0_skl))),
% 0.23/5.51 inference(cnf_transformation,[status(thm)],[f4])).
% 0.23/5.51 fof(f12,plain,(
% 0.23/5.51 ![X0,X1,X2]: (~a_truth(implies(X0,implies(X1,X2)))|a_truth(implies(implies(X0,X1),implies(X0,X2))))),
% 0.23/5.51 inference(resolution,[status(thm)],[f7,f5])).
% 0.23/5.51 fof(f24,plain,(
% 0.23/5.51 ![X0,X1,X2]: (~a_truth(implies(X0,implies(X1,X2)))|~a_truth(implies(X0,X1))|a_truth(implies(X0,X2)))),
% 0.23/5.51 inference(resolution,[status(thm)],[f12,f5])).
% 0.23/5.51 fof(f39,plain,(
% 0.23/5.51 ![X0,X1,X2]: (~a_truth(implies(X0,implies(implies(X1,X0),X2)))|a_truth(implies(X0,X2)))),
% 0.23/5.51 inference(resolution,[status(thm)],[f24,f6])).
% 0.23/5.51 fof(f46,plain,(
% 0.23/5.51 ![X0]: (a_truth(implies(X0,X0)))),
% 0.23/5.51 inference(resolution,[status(thm)],[f39,f6])).
% 0.23/5.51 fof(f48,plain,(
% 0.23/5.51 $false),
% 0.23/5.51 inference(backward_subsumption_resolution,[status(thm)],[f9,f46])).
% 0.23/5.51 % SZS output end CNFRefutation for theBenchmark.p
% 0.23/5.54 % Elapsed time: 0.059641 seconds
% 0.23/5.54 % CPU time: 0.074575 seconds
% 0.23/5.54 % Total memory used: 1.810 MB
% 0.23/5.54 % Net memory used: 1.801 MB
%------------------------------------------------------------------------------