%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL372+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 01:09:54 PM UTC 2026
% Result : Theorem 58.68s 7.93s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL372+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n017.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 00:19:57 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 58.68/7.93 % Refutation found
% 58.68/7.93 % SZS status Theorem for theBenchmark: Theorem is valid
% 58.68/7.93 % SZS output start CNFRefutation for theBenchmark
% 58.68/7.93 fof(f1,axiom,(
% 58.68/7.93 (! [X,Y] :( ( is_a_theorem(implies(X,Y))& is_a_theorem(X) )=> is_a_theorem(Y) ) )),
% 58.68/7.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 58.68/7.93 fof(f2,axiom,(
% 58.68/7.93 (! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )),
% 58.68/7.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 58.68/7.93 fof(f3,axiom,(
% 58.68/7.93 (! [X] : is_a_theorem(implies(implies(not(X),X),X)) )),
% 58.68/7.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 58.68/7.93 fof(f4,axiom,(
% 58.68/7.93 (! [X,Y] : is_a_theorem(implies(X,implies(not(X),Y))) )),
% 58.68/7.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 58.68/7.93 fof(f5,conjecture,(
% 58.68/7.93 is_a_theorem(implies(implies(implies(implies(x,y),y),z),implies(implies(implies(y,u),x),z))) ),
% 58.68/7.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 58.68/7.93 fof(f6,negated_conjecture,(
% 58.68/7.93 ~(is_a_theorem(implies(implies(implies(implies(x,y),y),z),implies(implies(implies(y,u),x),z))) )),
% 58.68/7.93 inference(negated_conjecture,[status(cth)],[f5])).
% 58.68/7.93 fof(f7,plain,(
% 58.68/7.93 ![X,Y]: ((~is_a_theorem(implies(X,Y))|~is_a_theorem(X))|is_a_theorem(Y))),
% 58.68/7.93 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 58.68/7.93 fof(f8,plain,(
% 58.68/7.93 ![Y]: ((![X]: (~is_a_theorem(implies(X,Y))|~is_a_theorem(X)))|is_a_theorem(Y))),
% 58.68/7.93 inference(miniscoping,[status(thm)],[f7])).
% 58.68/7.93 fof(f9,plain,(
% 58.68/7.93 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(X0)|is_a_theorem(X1))),
% 58.68/7.93 inference(cnf_transformation,[status(thm)],[f8])).
% 58.68/7.93 fof(f10,plain,(
% 58.68/7.93 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))))),
% 58.68/7.93 inference(cnf_transformation,[status(thm)],[f2])).
% 58.68/7.93 fof(f11,plain,(
% 58.68/7.93 ![X0]: (is_a_theorem(implies(implies(not(X0),X0),X0)))),
% 58.68/7.93 inference(cnf_transformation,[status(thm)],[f3])).
% 58.68/7.93 fof(f12,plain,(
% 58.68/7.93 ![X0,X1]: (is_a_theorem(implies(X0,implies(not(X0),X1))))),
% 58.68/7.93 inference(cnf_transformation,[status(thm)],[f4])).
% 58.68/7.93 fof(f13,plain,(
% 58.68/7.93 ~is_a_theorem(implies(implies(implies(implies(x,y),y),z),implies(implies(implies(y,u),x),z)))),
% 58.68/7.93 inference(cnf_transformation,[status(thm)],[f6])).
% 58.68/7.93 fof(f14,plain,(
% 58.68/7.93 ![X0,X1,X2]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(implies(X1,X2),implies(X0,X2))))),
% 58.68/7.93 inference(resolution,[status(thm)],[f10,f9])).
% 58.68/7.93 fof(f15,plain,(
% 58.68/7.93 ![X0,X1,X2,X3]: (is_a_theorem(implies(implies(implies(implies(X0,X1),implies(X2,X1)),X3),implies(implies(X2,X0),X3))))),
% 58.68/7.93 inference(resolution,[status(thm)],[f14,f10])).
% 58.68/7.93 fof(f17,plain,(
% 58.68/7.93 ![X0,X1,X2,X3]: (~is_a_theorem(implies(implies(implies(X0,X1),implies(X2,X1)),X3))|is_a_theorem(implies(implies(X2,X0),X3)))),
% 58.68/7.93 inference(resolution,[status(thm)],[f15,f9])).
% 58.68/7.93 fof(f22,plain,(
% 58.68/7.93 ![X0,X1,X2,X3]: (is_a_theorem(implies(implies(X0,X1),implies(implies(implies(X0,X2),X3),implies(implies(X1,X2),X3)))))),
% 58.68/7.93 inference(resolution,[status(thm)],[f17,f10])).
% 58.68/7.93 fof(f27,plain,(
% 58.68/7.93 ![X0,X1,X2,X3,X4]: (is_a_theorem(implies(implies(implies(implies(implies(X0,X1),X2),implies(implies(X3,X1),X2)),X4),implies(implies(X0,X3),X4))))),
% 58.68/7.93 inference(resolution,[status(thm)],[f22,f14])).
% 58.68/7.93 fof(f28,plain,(
% 58.68/7.93 ![X0,X1,X2,X3]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(implies(implies(X0,X2),X3),implies(implies(X1,X2),X3))))),
% 58.68/7.93 inference(resolution,[status(thm)],[f22,f9])).
% 58.68/7.93 fof(f37,plain,(
% 58.68/7.93 ![X0,X1,X2,X3]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(implies(X0,X2),X3))|is_a_theorem(implies(implies(X1,X2),X3)))),
% 58.68/7.93 inference(resolution,[status(thm)],[f28,f9])).
% 58.68/7.93 fof(f45,plain,(
% 58.68/7.93 ![X0]: (~is_a_theorem(implies(X0,implies(implies(x,y),y)))|~is_a_theorem(implies(implies(X0,z),implies(implies(implies(y,u),x),z))))),
% 58.68/7.93 inference(resolution,[status(thm)],[f37,f13])).
% 58.68/7.93 fof(f55,plain,(
% 58.68/7.93 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),implies(implies(not(X0),X0),X1))))),
% 58.68/7.93 inference(resolution,[status(thm)],[f11,f14])).
% 58.68/7.93 fof(f58,plain,(
% 58.68/7.93 ![X0,X1,X2]: (is_a_theorem(implies(implies(implies(not(X0),X1),X2),implies(X0,X2))))),
% 58.68/7.93 inference(resolution,[status(thm)],[f12,f14])).
% 58.68/7.93 fof(f59,plain,(
% 58.68/7.93 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(implies(not(X0),X1)))),
% 58.68/7.93 inference(resolution,[status(thm)],[f12,f9])).
% 58.68/7.93 fof(f62,plain,(
% 58.68/7.93 ![X0,X1,X2]: (~is_a_theorem(X0)|is_a_theorem(implies(implies(X1,X2),implies(not(X0),X2))))),
% 58.68/7.93 inference(resolution,[status(thm)],[f59,f14])).
% 58.68/7.93 fof(f65,plain,(
% 58.68/7.93 ![X0,X1,X2]: (is_a_theorem(implies(implies(implies(implies(not(X0),X0),X1),X2),implies(implies(X0,X1),X2))))),
% 58.68/7.93 inference(resolution,[status(thm)],[f55,f14])).
% 58.68/7.93 fof(f66,plain,(
% 58.68/7.93 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|is_a_theorem(implies(implies(not(X0),X0),X1)))),
% 58.68/7.93 inference(resolution,[status(thm)],[f55,f9])).
% 58.68/7.93 fof(f67,plain,(
% 58.68/7.93 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,not(X1)),implies(X1,implies(X0,X2)))))),
% 58.68/7.93 inference(resolution,[status(thm)],[f58,f17])).
% 58.68/7.93 fof(f68,plain,(
% 58.68/7.93 ![X0,X1,X2,X3]: (is_a_theorem(implies(implies(implies(X0,X1),X2),implies(implies(implies(not(X0),X3),X1),X2))))),
% 58.68/7.93 inference(resolution,[status(thm)],[f58,f14])).
% 58.68/7.93 fof(f69,plain,(
% 58.68/7.93 ![X0,X1,X2]: (~is_a_theorem(implies(implies(not(X0),X1),X2))|is_a_theorem(implies(X0,X2)))),
% 58.68/7.93 inference(resolution,[status(thm)],[f58,f9])).
% 58.68/7.93 fof(f71,plain,(
% 58.68/7.93 ![X0,X1,X2,X3]: (~is_a_theorem(X0)|is_a_theorem(implies(implies(implies(not(X0),X1),X2),implies(implies(X3,X1),X2))))),
% 58.68/7.93 inference(resolution,[status(thm)],[f62,f14])).
% 58.68/7.93 fof(f74,plain,(
% 58.68/7.93 ![X0,X1]: (~is_a_theorem(implies(X0,X1))|~is_a_theorem(implies(not(X0),X0))|is_a_theorem(X1))),
% 58.68/7.93 inference(resolution,[status(thm)],[f66,f9])).
% 58.68/7.93 fof(f78,plain,(
% 58.68/7.93 ![X0]: (is_a_theorem(implies(X0,X0)))),
% 58.68/7.93 inference(resolution,[status(thm)],[f69,f11])).
% 58.68/7.93 fof(f79,plain,(
% 58.68/7.93 ![X0,X1,X2]: (is_a_theorem(implies(X0,implies(X1,implies(not(X0),X2)))))),
% 58.68/7.93 inference(resolution,[status(thm)],[f69,f67])).
% 58.68/7.93 fof(f97,plain,(
% 58.68/7.93 ![X0,X1,X2,X3]: (is_a_theorem(implies(implies(implies(X0,implies(not(X1),X2)),X3),implies(X1,X3))))),
% 58.68/7.93 inference(resolution,[status(thm)],[f79,f14])).
% 58.68/7.93 fof(f104,plain,(
% 58.68/7.93 ![X0,X1,X2]: (is_a_theorem(implies(implies(X0,implies(not(X1),X1)),implies(implies(X1,X2),implies(X0,X2)))))),
% 58.68/7.93 inference(resolution,[status(thm)],[f65,f17])).
% 58.68/7.93 fof(f106,plain,(
% 58.68/7.93 ![X0,X1,X2]: (~is_a_theorem(implies(implies(implies(not(X0),X0),X1),X2))|is_a_theorem(implies(implies(X0,X1),X2)))),
% 58.68/7.93 inference(resolution,[status(thm)],[f65,f9])).
% 58.68/7.93 fof(f109,plain,(
% 58.68/7.93 ![X0,X1,X2,X3]: (~is_a_theorem(implies(implies(X0,X1),X2))|is_a_theorem(implies(implies(implies(not(X0),X3),X1),X2)))),
% 58.68/7.93 inference(resolution,[status(thm)],[f68,f9])).
% 58.68/7.93 fof(f112,plain,(
% 58.68/7.93 ![X0,X1,X2,X3]: (~is_a_theorem(X0)|~is_a_theorem(implies(implies(not(X0),X1),X2))|is_a_theorem(implies(implies(X3,X1),X2)))),
% 58.68/7.93 inference(resolution,[status(thm)],[f71,f9])).
% 58.68/7.93 fof(f213,plain,(
% 58.68/7.93 ![X0,X1,X2,X3]: (~is_a_theorem(implies(implies(X0,implies(not(X1),X2)),X3))|is_a_theorem(implies(X1,X3)))),
% 58.68/7.93 inference(resolution,[status(thm)],[f97,f9])).
% 58.68/7.93 fof(f286,plain,(
% 58.68/7.93 ![X0,X1,X2]: (is_a_theorem(implies(X0,implies(implies(X0,X1),implies(X2,X1)))))),
% 58.68/7.93 inference(resolution,[status(thm)],[f104,f213])).
% 58.68/7.93 fof(f317,plain,(
% 58.68/7.93 ![X0,X1,X2]: (~is_a_theorem(X0)|is_a_theorem(implies(implies(X0,X1),implies(X2,X1))))),
% 58.68/7.93 inference(resolution,[status(thm)],[f286,f9])).
% 58.68/7.93 fof(f497,plain,(
% 58.68/7.93 ![X0,X1,X2,X3]: (~is_a_theorem(implies(implies(X0,implies(X1,X2)),X3))|is_a_theorem(implies(implies(X1,not(X0)),X3)))),
% 58.68/7.93 inference(resolution,[status(thm)],[f109,f17])).
% 58.68/7.93 fof(f707,plain,(
% 58.68/7.93 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(implies(implies(X1,X0),X0)))),
% 58.68/7.93 inference(resolution,[status(thm)],[f112,f11])).
% 58.68/7.93 fof(f798,plain,(
% 58.68/7.93 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(implies(X1,X0)))),
% 58.68/7.93 inference(resolution,[status(thm)],[f707,f69])).
% 58.68/7.93 fof(f824,plain,(
% 58.68/7.93 ![X0,X1]: (is_a_theorem(implies(X0,implies(implies(not(X1),X1),X1))))),
% 58.68/7.93 inference(resolution,[status(thm)],[f798,f11])).
% 58.68/7.93 fof(f870,plain,(
% 58.68/7.93 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X1))))),
% 58.68/7.93 inference(resolution,[status(thm)],[f798,f78])).
% 58.68/7.93 fof(f886,plain,(
% 58.68/7.93 ![X0,X1,X2]: (is_a_theorem(implies(implies(implies(X0,X0),X1),implies(X2,X1))))),
% 58.68/7.93 inference(resolution,[status(thm)],[f870,f14])).
% 58.68/7.93 fof(f966,plain,(
% 58.68/7.93 ![X0,X1]: (~is_a_theorem(implies(implies(implies(implies(implies(y,u),X0),X1),implies(implies(x,X0),X1)),implies(implies(x,y),y))))),
% 58.68/7.93 inference(resolution,[status(thm)],[f27,f45])).
% 57.60/7.96 fof(f1014,plain,(
% 57.60/7.96 ![X0,X1]: (~is_a_theorem(implies(implies(implies(not(X0),X0),X0),X1))|is_a_theorem(X1))),
% 57.60/7.96 inference(resolution,[status(thm)],[f824,f74])).
% 57.60/7.96 fof(f1223,plain,(
% 57.60/7.96 ![X0,X1,X2]: (~is_a_theorem(implies(implies(X0,X0),X1))|is_a_theorem(implies(X2,X1)))),
% 57.60/7.96 inference(resolution,[status(thm)],[f886,f9])).
% 57.60/7.96 fof(f1451,plain,(
% 57.60/7.96 ![X0,X1,X2]: (is_a_theorem(implies(X0,implies(X1,X2)))|~is_a_theorem(X2))),
% 57.60/7.96 inference(resolution,[status(thm)],[f1223,f317])).
% 57.60/7.96 fof(f2175,plain,(
% 57.60/7.96 ![X0,X1]: (is_a_theorem(implies(implies(X0,X1),X1))|~is_a_theorem(implies(not(X1),X0)))),
% 57.60/7.96 inference(resolution,[status(thm)],[f1014,f28])).
% 57.60/7.96 fof(f2780,plain,(
% 57.60/7.96 ![X0,X1]: (is_a_theorem(implies(implies(implies(implies(not(X0),X0),X0),X1),X1)))),
% 57.60/7.96 inference(resolution,[status(thm)],[f2175,f824])).
% 57.60/7.96 fof(f2803,plain,(
% 57.60/7.96 ![X0,X1,X2]: (is_a_theorem(implies(implies(implies(X0,X1),X2),X2))|~is_a_theorem(X1))),
% 57.60/7.96 inference(resolution,[status(thm)],[f2175,f1451])).
% 57.60/7.96 fof(f3099,plain,(
% 57.60/7.96 ![X0,X1]: (~is_a_theorem(X0)|is_a_theorem(implies(implies(X0,X1),X1)))),
% 57.60/7.96 inference(resolution,[status(thm)],[f2803,f106])).
% 57.60/7.96 fof(f4683,plain,(
% 57.60/7.96 ![X0,X1]: (is_a_theorem(implies(implies(X0,implies(not(X1),X1)),implies(X0,X1))))),
% 57.60/7.96 inference(resolution,[status(thm)],[f2780,f17])).
% 57.60/7.96 fof(f5951,plain,(
% 57.60/7.96 ![X0,X1]: (is_a_theorem(implies(X0,implies(X1,X0))))),
% 57.60/7.96 inference(resolution,[status(thm)],[f4683,f213])).
% 57.60/7.96 fof(f5952,plain,(
% 57.60/7.96 ![X0,X1]: (is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))))),
% 57.60/7.96 inference(resolution,[status(thm)],[f4683,f497])).
% 57.60/7.96 fof(f6012,plain,(
% 57.60/7.96 ![X0,X1,X2]: (is_a_theorem(implies(implies(implies(X0,X1),X2),implies(X1,X2))))),
% 57.60/7.96 inference(resolution,[status(thm)],[f5951,f14])).
% 57.60/7.96 fof(f6742,plain,(
% 57.60/7.96 ![X0,X1,X2]: (~is_a_theorem(implies(implies(X0,X1),X2))|is_a_theorem(implies(X1,X2)))),
% 57.60/7.96 inference(resolution,[status(thm)],[f6012,f9])).
% 57.60/7.96 fof(f7597,plain,(
% 57.60/7.96 ![X0,X1]: (is_a_theorem(implies(not(X0),implies(X0,X1))))),
% 57.60/7.96 inference(resolution,[status(thm)],[f5952,f6742])).
% 57.60/7.96 fof(f7623,plain,(
% 57.60/7.96 ![X0,X1]: (is_a_theorem(implies(implies(implies(X0,X1),X0),X0)))),
% 57.60/7.96 inference(resolution,[status(thm)],[f7597,f2175])).
% 57.60/7.96 fof(f13688,plain,(
% 57.60/7.96 ~is_a_theorem(implies(implies(implies(y,u),y),y))),
% 57.60/7.96 inference(resolution,[status(thm)],[f966,f3099])).
% 57.60/7.96 fof(f13695,plain,(
% 57.60/7.96 $false),
% 57.60/7.96 inference(forward_subsumption_resolution,[status(thm)],[f13688,f7623])).
% 57.60/7.96 % SZS output end CNFRefutation for theBenchmark.p
% 8.97/8.03 % Elapsed time: 7.627182 seconds
% 8.97/8.03 % CPU time: 59.868367 seconds
% 8.97/8.03 % Total memory used: 336.653 MB
% 8.97/8.03 % Net memory used: 288.548 MB
%------------------------------------------------------------------------------