%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL531+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 01:10:13 PM UTC 2026
% Result : Theorem 0.13s 0.42s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL531+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 00:37:03 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.42 % Refutation found
% 0.13/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.42 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.42 fof(f1,axiom,(
% 0.13/0.42 ( modus_ponens<=> (! [X,Y] :( ( is_a_theorem(X)& is_a_theorem(implies(X,Y)) )=> is_a_theorem(Y) ) )) ),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f5,axiom,(
% 0.13/0.42 ( implies_2<=> (! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )) ),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f9,axiom,(
% 0.13/0.42 ( and_3<=> (! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) )) ),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f35,axiom,(
% 0.13/0.42 modus_ponens ),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f38,axiom,(
% 0.13/0.42 implies_2 ),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f42,axiom,(
% 0.13/0.42 and_3 ),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f50,axiom,(
% 0.13/0.42 ( necessitation<=> (! [X] :( is_a_theorem(X)=> is_a_theorem(necessarily(X)) ) )) ),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f66,axiom,(
% 0.13/0.42 ( axiom_m4<=> (! [X] : is_a_theorem(strict_implies(X,and(X,X))) )) ),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f75,axiom,(
% 0.13/0.42 ( op_strict_implies=> (! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) )) ),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f78,axiom,(
% 0.13/0.42 necessitation ),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f85,axiom,(
% 0.13/0.42 op_strict_implies ),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f88,conjecture,(
% 0.13/0.42 axiom_m4 ),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f89,negated_conjecture,(
% 0.13/0.42 ~(axiom_m4 )),
% 0.13/0.42 inference(negated_conjecture,[status(cth)],[f88])).
% 0.13/0.42 fof(f90,plain,(
% 0.13/0.42 modus_ponens<=>(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))),
% 0.13/0.42 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.13/0.42 fof(f91,plain,(
% 0.13/0.42 (~modus_ponens|(![X,Y]: ((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y))))&(modus_ponens|(?[X,Y]: ((is_a_theorem(X)&is_a_theorem(implies(X,Y)))&~is_a_theorem(Y))))),
% 0.13/0.42 inference(NNF_transformation,[status(thm)],[f90])).
% 0.13/0.42 fof(f92,plain,(
% 0.13/0.42 (~modus_ponens|(![Y]: ((![X]: (~is_a_theorem(X)|~is_a_theorem(implies(X,Y))))|is_a_theorem(Y))))&(modus_ponens|(?[Y]: ((?[X]: (is_a_theorem(X)&is_a_theorem(implies(X,Y))))&~is_a_theorem(Y))))),
% 0.13/0.42 inference(miniscoping,[status(thm)],[f91])).
% 0.13/0.42 fof(f93,plain,(
% 0.13/0.42 (~modus_ponens|(![Y]: ((![X]: (~is_a_theorem(X)|~is_a_theorem(implies(X,Y))))|is_a_theorem(Y))))&(modus_ponens|((is_a_theorem(sK1_skl)&is_a_theorem(implies(sK1_skl,sK0_skl)))&~is_a_theorem(sK0_skl)))),
% 0.13/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f92])).
% 0.13/0.42 fof(f94,plain,(
% 0.13/0.42 ![X0,X1]: (~modus_ponens|~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f93])).
% 0.13/0.42 fof(f112,plain,(
% 0.13/0.42 (~implies_2|(![X,Y]: is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))))&(implies_2|(?[X,Y]: ~is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))))),
% 0.13/0.42 inference(NNF_transformation,[status(thm)],[f5])).
% 0.13/0.42 fof(f113,plain,(
% 0.13/0.42 (~implies_2|(![X,Y]: is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))))&(implies_2|~is_a_theorem(implies(implies(sK8_skl,implies(sK8_skl,sK9_skl)),implies(sK8_skl,sK9_skl))))),
% 0.13/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(X,sK8_skl),skolemize(Y,sK9_skl)],[f112])).
% 0.13/0.42 fof(f114,plain,(
% 0.13/0.42 ![X0,X1]: (~implies_2|is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f113])).
% 0.13/0.42 fof(f128,plain,(
% 0.13/0.42 (~and_3|(![X,Y]: is_a_theorem(implies(X,implies(Y,and(X,Y))))))&(and_3|(?[X,Y]: ~is_a_theorem(implies(X,implies(Y,and(X,Y))))))),
% 0.13/0.42 inference(NNF_transformation,[status(thm)],[f9])).
% 0.13/0.42 fof(f129,plain,(
% 0.13/0.42 (~and_3|(![X,Y]: is_a_theorem(implies(X,implies(Y,and(X,Y))))))&(and_3|~is_a_theorem(implies(sK17_skl,implies(sK18_skl,and(sK17_skl,sK18_skl)))))),
% 0.13/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl]),skolemize(X,sK17_skl),skolemize(Y,sK18_skl)],[f128])).
% 0.13/0.42 fof(f130,plain,(
% 0.13/0.42 ![X0,X1]: (~and_3|is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f129])).
% 0.13/0.42 fof(f213,plain,(
% 0.13/0.42 modus_ponens),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f35])).
% 0.13/0.42 fof(f216,plain,(
% 0.13/0.42 implies_2),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f38])).
% 0.13/0.42 fof(f220,plain,(
% 0.13/0.42 and_3),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f42])).
% 0.13/0.42 fof(f228,plain,(
% 0.13/0.42 necessitation<=>(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X))))),
% 0.13/0.42 inference(pre_NNF_transformation,[status(thm)],[f50])).
% 0.13/0.42 fof(f229,plain,(
% 0.13/0.42 (~necessitation|(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&(necessitation|(?[X]: (is_a_theorem(X)&~is_a_theorem(necessarily(X)))))),
% 0.13/0.42 inference(NNF_transformation,[status(thm)],[f228])).
% 0.13/0.42 fof(f230,plain,(
% 0.13/0.42 (~necessitation|(![X]: (~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&(necessitation|(is_a_theorem(sK55_skl)&~is_a_theorem(necessarily(sK55_skl))))),
% 0.13/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK55_skl]),skolemize(X,sK55_skl)],[f229])).
% 0.13/0.42 fof(f231,plain,(
% 0.13/0.42 ![X0]: (~necessitation|~is_a_theorem(X0)|is_a_theorem(necessarily(X0)))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f230])).
% 0.13/0.42 fof(f303,plain,(
% 0.13/0.42 (~axiom_m4|(![X]: is_a_theorem(strict_implies(X,and(X,X)))))&(axiom_m4|(?[X]: ~is_a_theorem(strict_implies(X,and(X,X)))))),
% 0.13/0.42 inference(NNF_transformation,[status(thm)],[f66])).
% 0.13/0.42 fof(f304,plain,(
% 0.13/0.42 (~axiom_m4|(![X]: is_a_theorem(strict_implies(X,and(X,X)))))&(axiom_m4|~is_a_theorem(strict_implies(sK83_skl,and(sK83_skl,sK83_skl))))),
% 0.13/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK83_skl]),skolemize(X,sK83_skl)],[f303])).
% 0.13/0.42 fof(f306,plain,(
% 0.13/0.42 axiom_m4|~is_a_theorem(strict_implies(sK83_skl,and(sK83_skl,sK83_skl)))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f304])).
% 0.13/0.42 fof(f335,plain,(
% 0.13/0.42 ~op_strict_implies|(![X,Y]: strict_implies(X,Y)=necessarily(implies(X,Y)))),
% 0.13/0.42 inference(pre_NNF_transformation,[status(thm)],[f75])).
% 0.13/0.42 fof(f336,plain,(
% 0.13/0.42 ![X0,X1]: (~op_strict_implies|strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f335])).
% 0.13/0.42 fof(f340,plain,(
% 0.13/0.42 necessitation),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f78])).
% 0.13/0.42 fof(f347,plain,(
% 0.13/0.42 op_strict_implies),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f85])).
% 0.13/0.42 fof(f350,plain,(
% 0.13/0.42 ~axiom_m4),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f89])).
% 0.13/0.42 fof(f354,plain,(
% 0.13/0.42 ![X0,X1]: (~is_a_theorem(X0)|~is_a_theorem(implies(X0,X1))|is_a_theorem(X1))),
% 0.13/0.42 inference(backward_subsumption_resolution,[status(thm)],[f94,f213])).
% 0.13/0.42 fof(f357,plain,(
% 0.13/0.42 ![X0,X1]: (is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))))),
% 0.13/0.42 inference(backward_subsumption_resolution,[status(thm)],[f114,f216])).
% 0.13/0.42 fof(f361,plain,(
% 0.13/0.42 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,and(X0,X1)))))),
% 0.13/0.42 inference(backward_subsumption_resolution,[status(thm)],[f130,f220])).
% 0.13/0.42 fof(f370,plain,(
% 0.13/0.42 ![X0]: (~is_a_theorem(X0)|is_a_theorem(necessarily(X0)))),
% 0.13/0.42 inference(backward_subsumption_resolution,[status(thm)],[f231,f340])).
% 0.13/0.42 fof(f374,plain,(
% 0.13/0.42 ![X0,X1]: (strict_implies(X0,X1)=necessarily(implies(X0,X1)))),
% 0.13/0.42 inference(backward_subsumption_resolution,[status(thm)],[f336,f347])).
% 0.13/0.42 fof(f376,plain,(
% 0.13/0.42 ~is_a_theorem(strict_implies(sK83_skl,and(sK83_skl,sK83_skl)))),
% 0.13/0.42 inference(backward_subsumption_resolution,[status(thm)],[f306,f350])).
% 0.13/0.42 fof(f399,plain,(
% 0.13/0.42 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(strict_implies(X0,X1)))),
% 0.13/0.42 inference(paramodulation,[status(thm)],[f374,f370])).
% 0.13/0.42 fof(f622,plain,(
% 0.13/0.42 ![X0,X1]: (~is_a_theorem(implies(X0,implies(X0,X1)))|is_a_theorem(implies(X0,X1)))),
% 0.13/0.42 inference(resolution,[status(thm)],[f357,f354])).
% 0.13/0.42 fof(f1074,plain,(
% 0.13/0.42 ![X0]: (is_a_theorem(implies(X0,and(X0,X0))))),
% 0.13/0.42 inference(resolution,[status(thm)],[f622,f361])).
% 0.13/0.42 fof(f1106,plain,(
% 0.13/0.42 ![X0]: (is_a_theorem(strict_implies(X0,and(X0,X0))))),
% 0.13/0.42 inference(resolution,[status(thm)],[f1074,f399])).
% 0.13/0.42 fof(f1113,plain,(
% 0.13/0.42 $false),
% 0.13/0.42 inference(backward_subsumption_resolution,[status(thm)],[f376,f1106])).
% 0.13/0.43 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.48 % Elapsed time: 0.121127 seconds
% 0.13/0.48 % CPU time: 0.452945 seconds
% 0.13/0.48 % Total memory used: 92.313 MB
% 0.13/0.48 % Net memory used: 92.055 MB
%------------------------------------------------------------------------------