0.10/0.11	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.10/0.12	% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
0.11/0.33	% Computer : n026.cluster.edu
0.11/0.33	% Model    : x86_64 x86_64
0.11/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.33	% Memory   : 8042.1875MB
0.11/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.11/0.33	% CPULimit : 960
0.11/0.33	% WCLimit  : 120
0.11/0.33	% DateTime : Tue Aug  9 04:27:04 EDT 2022
0.11/0.33	% CPUTime  : 
0.11/0.33	
0.11/0.33	 No.of.Axioms: 4
0.11/0.33	
0.11/0.33	 Length.of.Defs: 5540
0.11/0.33	
0.11/0.33	 Contains.Choice.Funs: false
0.11/0.34	(rf:0,axioms:4,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:6,loop_count:0,foatp_calls:0,translation:fof_full)...
0.17/0.41	
0.17/0.41	********************************
0.17/0.41	*   All subproblems solved!    *
0.17/0.41	********************************
0.17/0.41	% SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:63,loop_count:0,foatp_calls:1,translation:fof_full)
0.17/0.41	
0.17/0.41	%**** Beginning of derivation protocol ****
0.17/0.41	% SZS output start CNFRefutation
0.17/0.41	 thf(tp_mu,type,(mu: $tType)).
0.17/0.41	 thf(tp_exists_in_world,type,(exists_in_world: (mu>($i>$o)))).
0.17/0.41	 thf(tp_mand,type,(mand: (($i>$o)>(($i>$o)>($i>$o))))).
0.17/0.41	 thf(tp_mbox,type,(mbox: (($i>($i>$o))>(($i>$o)>($i>$o))))).
0.17/0.41	 thf(tp_mbox_s4,type,(mbox_s4: (($i>$o)>($i>$o)))).
0.17/0.41	 thf(tp_mcountersatisfiable,type,(mcountersatisfiable: (($i>$o)>$o))).
0.17/0.41	 thf(tp_mdia,type,(mdia: (($i>($i>$o))>(($i>$o)>($i>$o))))).
0.17/0.41	 thf(tp_mdia_s4,type,(mdia_s4: (($i>$o)>($i>$o)))).
0.17/0.41	 thf(tp_meq_prop,type,(meq_prop: (($i>$o)>(($i>$o)>($i>$o))))).
0.17/0.41	 thf(tp_mequiv,type,(mequiv: (($i>$o)>(($i>$o)>($i>$o))))).
0.17/0.41	 thf(tp_meuclidean,type,(meuclidean: (($i>($i>$o))>$o))).
0.17/0.41	 thf(tp_mexists_ind,type,(mexists_ind: ((mu>($i>$o))>($i>$o)))).
0.17/0.41	 thf(tp_mexists_prop,type,(mexists_prop: ((($i>$o)>($i>$o))>($i>$o)))).
0.17/0.41	 thf(tp_mfalse,type,(mfalse: ($i>$o))).
0.17/0.41	 thf(tp_mforall_ind,type,(mforall_ind: ((mu>($i>$o))>($i>$o)))).
0.17/0.41	 thf(tp_mforall_prop,type,(mforall_prop: ((($i>$o)>($i>$o))>($i>$o)))).
0.17/0.41	 thf(tp_mfunctional,type,(mfunctional: (($i>($i>$o))>$o))).
0.17/0.41	 thf(tp_mimplied,type,(mimplied: (($i>$o)>(($i>$o)>($i>$o))))).
0.17/0.41	 thf(tp_mimplies,type,(mimplies: (($i>$o)>(($i>$o)>($i>$o))))).
0.17/0.41	 thf(tp_minvalid,type,(minvalid: (($i>$o)>$o))).
0.17/0.41	 thf(tp_mnot,type,(mnot: (($i>$o)>($i>$o)))).
0.17/0.41	 thf(tp_mor,type,(mor: (($i>$o)>(($i>$o)>($i>$o))))).
0.17/0.41	 thf(tp_mpartially_functional,type,(mpartially_functional: (($i>($i>$o))>$o))).
0.17/0.41	 thf(tp_mreflexive,type,(mreflexive: (($i>($i>$o))>$o))).
0.17/0.41	 thf(tp_msatisfiable,type,(msatisfiable: (($i>$o)>$o))).
0.17/0.41	 thf(tp_mserial,type,(mserial: (($i>($i>$o))>$o))).
0.17/0.41	 thf(tp_msymmetric,type,(msymmetric: (($i>($i>$o))>$o))).
0.17/0.41	 thf(tp_mtransitive,type,(mtransitive: (($i>($i>$o))>$o))).
0.17/0.41	 thf(tp_mtrue,type,(mtrue: ($i>$o))).
0.17/0.41	 thf(tp_mvalid,type,(mvalid: (($i>$o)>$o))).
0.17/0.41	 thf(tp_mweakly_connected,type,(mweakly_connected: (($i>($i>$o))>$o))).
0.17/0.41	 thf(tp_mweakly_dense,type,(mweakly_dense: (($i>($i>$o))>$o))).
0.17/0.41	 thf(tp_mweakly_directed,type,(mweakly_directed: (($i>($i>$o))>$o))).
0.17/0.41	 thf(tp_mxor,type,(mxor: (($i>$o)>(($i>$o)>($i>$o))))).
0.17/0.41	 thf(tp_p,type,(p: ($i>$o))).
0.17/0.41	 thf(tp_q,type,(q: ($i>$o))).
0.17/0.41	 thf(tp_qmltpeq,type,(qmltpeq: (mu>(mu>($i>$o))))).
0.17/0.41	 thf(tp_rel_s4,type,(rel_s4: ($i>($i>$o)))).
0.17/0.41	 thf(tp_sK1_X,type,(sK1_X: ($i>mu))).
0.17/0.41	 thf(tp_sK2_SX0,type,(sK2_SX0: $i)).
0.17/0.41	 thf(tp_sK3_SY5,type,(sK3_SY5: $i)).
0.17/0.41	 thf(mand,definition,(mand = (^[Phi:($i>$o),Psi:($i>$o)]: (mnot@((mor@(mnot@Phi))@(mnot@Psi))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand)).
0.17/0.41	 thf(mbox,definition,(mbox = (^[R:($i>($i>$o)),Phi:($i>$o),W:$i]: (![V:$i]: ((~ ((R@W)@V)) | (Phi@V))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox)).
0.17/0.41	 thf(mbox_s4,definition,(mbox_s4 = (^[Phi:($i>$o),W:$i]: (![V:$i]: ((~ ((rel_s4@W)@V)) | (Phi@V))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s4)).
0.17/0.41	 thf(mcountersatisfiable,definition,(mcountersatisfiable = (^[Phi:($i>$o)]: (?[W:$i]: (~ (Phi@W))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mcountersatisfiable)).
0.17/0.41	 thf(mdia,definition,(mdia = (^[R:($i>($i>$o)),Phi:($i>$o)]: (mnot@((mbox@R)@(mnot@Phi))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia)).
0.17/0.41	 thf(mdia_s4,definition,(mdia_s4 = (^[Phi:($i>$o)]: (mnot@(mbox_s4@(mnot@Phi))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_s4)).
0.17/0.41	 thf(meq_prop,definition,(meq_prop = (^[X:($i>$o),Y:($i>$o),W:$i]: ((X@W) = (Y@W)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meq_prop)).
0.17/0.41	 thf(mequiv,definition,(mequiv = (^[Phi:($i>$o),Psi:($i>$o)]: ((mand@((mimplies@Phi)@Psi))@((mimplies@Psi)@Phi)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv)).
0.17/0.41	 thf(meuclidean,definition,(meuclidean = (^[R:($i>($i>$o))]: (![S:$i,T:$i,U:$i]: ((((R@S)@T) & ((R@S)@U)) => ((R@T)@U))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meuclidean)).
0.17/0.41	 thf(mexists_ind,definition,(mexists_ind = (^[Phi:(mu>($i>$o))]: (mnot@(mforall_ind@(^[X:mu]: (mnot@(Phi@X))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_ind)).
0.17/0.41	 thf(mexists_prop,definition,(mexists_prop = (^[Phi:(($i>$o)>($i>$o))]: (mnot@(mforall_prop@(^[P:($i>$o)]: (mnot@(Phi@P))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_prop)).
0.17/0.41	 thf(mfalse,definition,(mfalse = (mnot@mtrue)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mfalse)).
0.17/0.41	 thf(mforall_ind,definition,(mforall_ind = (^[Phi:(mu>($i>$o)),W:$i]: (![X:mu]: (((exists_in_world@X)@W) => ((Phi@X)@W))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_ind)).
0.17/0.41	 thf(mforall_prop,definition,(mforall_prop = (^[Phi:(($i>$o)>($i>$o)),W:$i]: (![P:($i>$o)]: ((Phi@P)@W)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_prop)).
0.17/0.41	 thf(mfunctional,definition,(mfunctional = (^[R:($i>($i>$o))]: (![S:$i]: (?[T:$i]: (((R@S)@T) & (![U:$i]: (((R@S)@U) => (T = U)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mfunctional)).
0.17/0.41	 thf(mimplied,definition,(mimplied = (^[Phi:($i>$o),Psi:($i>$o)]: ((mor@(mnot@Psi))@Phi))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplied)).
0.17/0.41	 thf(mimplies,definition,(mimplies = (^[Phi:($i>$o),Psi:($i>$o)]: ((mor@(mnot@Phi))@Psi))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
0.17/0.41	 thf(minvalid,definition,(minvalid = (^[Phi:($i>$o)]: (![W:$i]: (~ (Phi@W))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minvalid)).
0.17/0.41	 thf(mnot,definition,(mnot = (^[Phi:($i>$o),W:$i]: (~ (Phi@W)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
0.17/0.41	 thf(mor,definition,(mor = (^[Phi:($i>$o),Psi:($i>$o),W:$i]: ((Phi@W) | (Psi@W)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
0.17/0.41	 thf(mpartially_functional,definition,(mpartially_functional = (^[R:($i>($i>$o))]: (![S:$i,T:$i,U:$i]: ((((R@S)@T) & ((R@S)@U)) => (T = U))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mpartially_functional)).
0.17/0.41	 thf(mreflexive,definition,(mreflexive = (^[R:($i>($i>$o))]: (![S:$i]: ((R@S)@S)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mreflexive)).
0.17/0.41	 thf(msatisfiable,definition,(msatisfiable = (^[Phi:($i>$o)]: (?[W:$i]: (Phi@W)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msatisfiable)).
0.17/0.41	 thf(mserial,definition,(mserial = (^[R:($i>($i>$o))]: (![S:$i]: (?[T:$i]: ((R@S)@T))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mserial)).
0.17/0.41	 thf(msymmetric,definition,(msymmetric = (^[R:($i>($i>$o))]: (![S:$i,T:$i]: (((R@S)@T) => ((R@T)@S))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msymmetric)).
0.17/0.41	 thf(mtransitive,definition,(mtransitive = (^[R:($i>($i>$o))]: (![S:$i,T:$i,U:$i]: ((((R@S)@T) & ((R@T)@U)) => ((R@S)@U))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtransitive)).
0.17/0.41	 thf(mtrue,definition,(mtrue = (^[W:$i]: $true)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtrue)).
0.17/0.41	 thf(mvalid,definition,(mvalid = (^[Phi:($i>$o)]: (![W:$i]: (Phi@W)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
0.17/0.41	 thf(mweakly_connected,definition,(mweakly_connected = (^[R:($i>($i>$o))]: (![S:$i,T:$i,U:$i]: ((((R@S)@T) & ((R@S)@U)) => ((((R@T)@U) | (T = U)) | ((R@U)@T)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_connected)).
0.17/0.41	 thf(mweakly_dense,definition,(mweakly_dense = (^[R:($i>($i>$o))]: (![S:$i,T:$i,U:$i]: (((R@S)@T) => (?[U:$i]: (((R@S)@U) & ((R@U)@T))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_dense)).
0.17/0.41	 thf(mweakly_directed,definition,(mweakly_directed = (^[R:($i>($i>$o))]: (![S:$i,T:$i,U:$i]: ((((R@S)@T) & ((R@S)@U)) => (?[V:$i]: (((R@T)@V) & ((R@U)@V))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_directed)).
0.17/0.41	 thf(mxor,definition,(mxor = (^[Phi:($i>$o),Psi:($i>$o)]: (mnot@((mequiv@Phi)@Psi)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mxor)).
0.17/0.41	 thf(1,axiom,(![X:mu,V:$i,W:$i]: (((exists_in_world@X)@W) <= (((rel_s4@V)@W) & ((exists_in_world@X)@V)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cumulative_ax)).
0.17/0.41	 thf(2,axiom,(mreflexive@rel_s4),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1)).
0.17/0.41	 thf(3,axiom,(mtransitive@rel_s4),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2)).
0.17/0.41	 thf(4,axiom,(![V:$i]: (?[X:mu]: ((exists_in_world@X)@V))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty_ax)).
0.17/0.41	 thf(5,conjecture,(mvalid@((mimplies@(mdia_s4@((mimplies@p)@(mbox_s4@q))))@((mimplies@(mbox_s4@p))@(mdia_s4@q)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con)).
0.17/0.41	 thf(6,negated_conjecture,(((mvalid@((mimplies@(mdia_s4@((mimplies@p)@(mbox_s4@q))))@((mimplies@(mbox_s4@p))@(mdia_s4@q))))=$false)),inference(negate_conjecture,[status(cth)],[5])).
0.17/0.41	 thf(7,plain,(((~ (mvalid@((mimplies@(mdia_s4@((mimplies@p)@(mbox_s4@q))))@((mimplies@(mbox_s4@p))@(mdia_s4@q)))))=$true)),inference(polarity_switch,[status(thm)],[6])).
0.17/0.41	 thf(8,plain,(((![X:mu,V:$i,W:$i]: (((~ ((exists_in_world@X)@V)) | (~ ((rel_s4@V)@W))) | ((exists_in_world@X)@W)))=$true)),inference(extcnf_combined,[status(esa)],[1])).
0.17/0.41	 thf(9,plain,(((![V:$i]: ((exists_in_world@(sK1_X@V))@V))=$true)),inference(extcnf_combined,[status(esa)],[4])).
0.17/0.41	 thf(10,plain,(((![V:$i]: ((exists_in_world@(sK1_X@V))@V))=$true)),inference(copy,[status(thm)],[9])).
0.17/0.41	 thf(11,plain,(((mtransitive@rel_s4)=$true)),inference(copy,[status(thm)],[3])).
0.17/0.41	 thf(12,plain,(((mreflexive@rel_s4)=$true)),inference(copy,[status(thm)],[2])).
0.17/0.41	 thf(13,plain,(((![X:mu,V:$i,W:$i]: (((~ ((exists_in_world@X)@V)) | (~ ((rel_s4@V)@W))) | ((exists_in_world@X)@W)))=$true)),inference(copy,[status(thm)],[8])).
0.17/0.41	 thf(14,plain,(((~ (mvalid@((mimplies@(mdia_s4@((mimplies@p)@(mbox_s4@q))))@((mimplies@(mbox_s4@p))@(mdia_s4@q)))))=$true)),inference(copy,[status(thm)],[7])).
0.17/0.41	 thf(15,plain,(((~ (![SX0:$i]: ((~ (~ (![SX1:$i]: ((~ ((rel_s4@SX0)@SX1)) | (~ ((~ (p@SX1)) | (![SX2:$i]: ((~ ((rel_s4@SX1)@SX2)) | (q@SX2))))))))) | ((~ (![SX1:$i]: ((~ ((rel_s4@SX0)@SX1)) | (p@SX1)))) | (~ (![SX1:$i]: ((~ ((rel_s4@SX0)@SX1)) | (~ (q@SX1)))))))))=$true)),inference(unfold_def,[status(thm)],[14,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor])).
0.17/0.41	 thf(16,plain,(((![SX0:$i]: ((rel_s4@SX0)@SX0))=$true)),inference(unfold_def,[status(thm)],[12,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor])).
0.17/0.41	 thf(17,plain,(((![SX0:$i,SX1:$i,SX2:$i]: ((~ (~ ((~ ((rel_s4@SX0)@SX1)) | (~ ((rel_s4@SX1)@SX2))))) | ((rel_s4@SX0)@SX2)))=$true)),inference(unfold_def,[status(thm)],[11,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor])).
0.17/0.41	 thf(18,plain,(![SV1:$i]: ((((exists_in_world@(sK1_X@SV1))@SV1)=$true))),inference(extcnf_forall_pos,[status(thm)],[10])).
0.17/0.41	 thf(19,plain,(![SV2:mu]: (((![SY0:$i,SY1:$i]: (((~ ((exists_in_world@SV2)@SY0)) | (~ ((rel_s4@SY0)@SY1))) | ((exists_in_world@SV2)@SY1)))=$true))),inference(extcnf_forall_pos,[status(thm)],[13])).
0.17/0.41	 thf(20,plain,(((![SX0:$i]: ((~ (~ (![SX1:$i]: ((~ ((rel_s4@SX0)@SX1)) | (~ ((~ (p@SX1)) | (![SX2:$i]: ((~ ((rel_s4@SX1)@SX2)) | (q@SX2))))))))) | ((~ (![SX1:$i]: ((~ ((rel_s4@SX0)@SX1)) | (p@SX1)))) | (~ (![SX1:$i]: ((~ ((rel_s4@SX0)@SX1)) | (~ (q@SX1))))))))=$false)),inference(extcnf_not_pos,[status(thm)],[15])).
0.17/0.41	 thf(21,plain,(![SV3:$i]: ((((rel_s4@SV3)@SV3)=$true))),inference(extcnf_forall_pos,[status(thm)],[16])).
0.17/0.41	 thf(22,plain,(![SV4:$i]: (((![SY2:$i,SY3:$i]: ((~ (~ ((~ ((rel_s4@SV4)@SY2)) | (~ ((rel_s4@SY2)@SY3))))) | ((rel_s4@SV4)@SY3)))=$true))),inference(extcnf_forall_pos,[status(thm)],[17])).
0.17/0.41	 thf(23,plain,(![SV5:$i,SV2:mu]: (((![SY4:$i]: (((~ ((exists_in_world@SV2)@SV5)) | (~ ((rel_s4@SV5)@SY4))) | ((exists_in_world@SV2)@SY4)))=$true))),inference(extcnf_forall_pos,[status(thm)],[19])).
0.17/0.41	 thf(24,plain,((((~ (~ (![SY5:$i]: ((~ ((rel_s4@sK2_SX0)@SY5)) | (~ ((~ (p@SY5)) | (![SX2:$i]: ((~ ((rel_s4@SY5)@SX2)) | (q@SX2))))))))) | ((~ (![SY7:$i]: ((~ ((rel_s4@sK2_SX0)@SY7)) | (p@SY7)))) | (~ (![SY8:$i]: ((~ ((rel_s4@sK2_SX0)@SY8)) | (~ (q@SY8)))))))=$false)),inference(extcnf_forall_neg,[status(esa)],[20])).
0.17/0.41	 thf(25,plain,(![SV6:$i,SV4:$i]: (((![SY9:$i]: ((~ (~ ((~ ((rel_s4@SV4)@SV6)) | (~ ((rel_s4@SV6)@SY9))))) | ((rel_s4@SV4)@SY9)))=$true))),inference(extcnf_forall_pos,[status(thm)],[22])).
0.17/0.41	 thf(26,plain,(![SV7:$i,SV5:$i,SV2:mu]: (((((~ ((exists_in_world@SV2)@SV5)) | (~ ((rel_s4@SV5)@SV7))) | ((exists_in_world@SV2)@SV7))=$true))),inference(extcnf_forall_pos,[status(thm)],[23])).
0.17/0.41	 thf(27,plain,(((~ (~ (![SY5:$i]: ((~ ((rel_s4@sK2_SX0)@SY5)) | (~ ((~ (p@SY5)) | (![SX2:$i]: ((~ ((rel_s4@SY5)@SX2)) | (q@SX2)))))))))=$false)),inference(extcnf_or_neg,[status(thm)],[24])).
0.17/0.41	 thf(28,plain,((((~ (![SY7:$i]: ((~ ((rel_s4@sK2_SX0)@SY7)) | (p@SY7)))) | (~ (![SY8:$i]: ((~ ((rel_s4@sK2_SX0)@SY8)) | (~ (q@SY8))))))=$false)),inference(extcnf_or_neg,[status(thm)],[24])).
0.17/0.41	 thf(29,plain,(![SV8:$i,SV6:$i,SV4:$i]: ((((~ (~ ((~ ((rel_s4@SV4)@SV6)) | (~ ((rel_s4@SV6)@SV8))))) | ((rel_s4@SV4)@SV8))=$true))),inference(extcnf_forall_pos,[status(thm)],[25])).
0.17/0.41	 thf(30,plain,(![SV7:$i,SV5:$i,SV2:mu]: ((((~ ((exists_in_world@SV2)@SV5)) | (~ ((rel_s4@SV5)@SV7)))=$true) | (((exists_in_world@SV2)@SV7)=$true))),inference(extcnf_or_pos,[status(thm)],[26])).
0.17/0.41	 thf(31,plain,(((~ (![SY5:$i]: ((~ ((rel_s4@sK2_SX0)@SY5)) | (~ ((~ (p@SY5)) | (![SX2:$i]: ((~ ((rel_s4@SY5)@SX2)) | (q@SX2))))))))=$true)),inference(extcnf_not_neg,[status(thm)],[27])).
0.17/0.41	 thf(32,plain,(((~ (![SY7:$i]: ((~ ((rel_s4@sK2_SX0)@SY7)) | (p@SY7))))=$false)),inference(extcnf_or_neg,[status(thm)],[28])).
0.17/0.41	 thf(33,plain,(((~ (![SY8:$i]: ((~ ((rel_s4@sK2_SX0)@SY8)) | (~ (q@SY8)))))=$false)),inference(extcnf_or_neg,[status(thm)],[28])).
0.17/0.41	 thf(34,plain,(![SV8:$i,SV6:$i,SV4:$i]: (((~ (~ ((~ ((rel_s4@SV4)@SV6)) | (~ ((rel_s4@SV6)@SV8)))))=$true) | (((rel_s4@SV4)@SV8)=$true))),inference(extcnf_or_pos,[status(thm)],[29])).
0.17/0.41	 thf(35,plain,(![SV7:$i,SV5:$i,SV2:mu]: (((~ ((exists_in_world@SV2)@SV5))=$true) | ((~ ((rel_s4@SV5)@SV7))=$true) | (((exists_in_world@SV2)@SV7)=$true))),inference(extcnf_or_pos,[status(thm)],[30])).
0.17/0.41	 thf(36,plain,(((![SY5:$i]: ((~ ((rel_s4@sK2_SX0)@SY5)) | (~ ((~ (p@SY5)) | (![SX2:$i]: ((~ ((rel_s4@SY5)@SX2)) | (q@SX2)))))))=$false)),inference(extcnf_not_pos,[status(thm)],[31])).
0.17/0.41	 thf(37,plain,(((![SY7:$i]: ((~ ((rel_s4@sK2_SX0)@SY7)) | (p@SY7)))=$true)),inference(extcnf_not_neg,[status(thm)],[32])).
0.17/0.41	 thf(38,plain,(((![SY8:$i]: ((~ ((rel_s4@sK2_SX0)@SY8)) | (~ (q@SY8))))=$true)),inference(extcnf_not_neg,[status(thm)],[33])).
0.17/0.41	 thf(39,plain,(![SV8:$i,SV6:$i,SV4:$i]: (((~ ((~ ((rel_s4@SV4)@SV6)) | (~ ((rel_s4@SV6)@SV8))))=$false) | (((rel_s4@SV4)@SV8)=$true))),inference(extcnf_not_pos,[status(thm)],[34])).
0.17/0.41	 thf(40,plain,(![SV7:$i,SV5:$i,SV2:mu]: ((((exists_in_world@SV2)@SV5)=$false) | ((~ ((rel_s4@SV5)@SV7))=$true) | (((exists_in_world@SV2)@SV7)=$true))),inference(extcnf_not_pos,[status(thm)],[35])).
0.17/0.41	 thf(41,plain,((((~ ((rel_s4@sK2_SX0)@sK3_SY5)) | (~ ((~ (p@sK3_SY5)) | (![SY10:$i]: ((~ ((rel_s4@sK3_SY5)@SY10)) | (q@SY10))))))=$false)),inference(extcnf_forall_neg,[status(esa)],[36])).
0.17/0.41	 thf(42,plain,(![SV9:$i]: ((((~ ((rel_s4@sK2_SX0)@SV9)) | (p@SV9))=$true))),inference(extcnf_forall_pos,[status(thm)],[37])).
0.17/0.41	 thf(43,plain,(![SV10:$i]: ((((~ ((rel_s4@sK2_SX0)@SV10)) | (~ (q@SV10)))=$true))),inference(extcnf_forall_pos,[status(thm)],[38])).
0.17/0.41	 thf(44,plain,(![SV8:$i,SV6:$i,SV4:$i]: ((((~ ((rel_s4@SV4)@SV6)) | (~ ((rel_s4@SV6)@SV8)))=$true) | (((rel_s4@SV4)@SV8)=$true))),inference(extcnf_not_neg,[status(thm)],[39])).
0.17/0.41	 thf(45,plain,(![SV2:mu,SV7:$i,SV5:$i]: ((((rel_s4@SV5)@SV7)=$false) | (((exists_in_world@SV2)@SV5)=$false) | (((exists_in_world@SV2)@SV7)=$true))),inference(extcnf_not_pos,[status(thm)],[40])).
0.17/0.41	 thf(46,plain,(((~ ((rel_s4@sK2_SX0)@sK3_SY5))=$false)),inference(extcnf_or_neg,[status(thm)],[41])).
0.17/0.41	 thf(47,plain,(((~ ((~ (p@sK3_SY5)) | (![SY10:$i]: ((~ ((rel_s4@sK3_SY5)@SY10)) | (q@SY10)))))=$false)),inference(extcnf_or_neg,[status(thm)],[41])).
0.17/0.41	 thf(48,plain,(![SV9:$i]: (((~ ((rel_s4@sK2_SX0)@SV9))=$true) | ((p@SV9)=$true))),inference(extcnf_or_pos,[status(thm)],[42])).
0.17/0.41	 thf(49,plain,(![SV10:$i]: (((~ ((rel_s4@sK2_SX0)@SV10))=$true) | ((~ (q@SV10))=$true))),inference(extcnf_or_pos,[status(thm)],[43])).
0.17/0.41	 thf(50,plain,(![SV8:$i,SV6:$i,SV4:$i]: (((~ ((rel_s4@SV4)@SV6))=$true) | ((~ ((rel_s4@SV6)@SV8))=$true) | (((rel_s4@SV4)@SV8)=$true))),inference(extcnf_or_pos,[status(thm)],[44])).
0.17/0.41	 thf(51,plain,((((rel_s4@sK2_SX0)@sK3_SY5)=$true)),inference(extcnf_not_neg,[status(thm)],[46])).
0.17/0.41	 thf(52,plain,((((~ (p@sK3_SY5)) | (![SY10:$i]: ((~ ((rel_s4@sK3_SY5)@SY10)) | (q@SY10))))=$true)),inference(extcnf_not_neg,[status(thm)],[47])).
0.17/0.41	 thf(53,plain,(![SV9:$i]: ((((rel_s4@sK2_SX0)@SV9)=$false) | ((p@SV9)=$true))),inference(extcnf_not_pos,[status(thm)],[48])).
0.17/0.41	 thf(54,plain,(![SV10:$i]: ((((rel_s4@sK2_SX0)@SV10)=$false) | ((~ (q@SV10))=$true))),inference(extcnf_not_pos,[status(thm)],[49])).
0.17/0.41	 thf(55,plain,(![SV8:$i,SV6:$i,SV4:$i]: ((((rel_s4@SV4)@SV6)=$false) | ((~ ((rel_s4@SV6)@SV8))=$true) | (((rel_s4@SV4)@SV8)=$true))),inference(extcnf_not_pos,[status(thm)],[50])).
0.17/0.41	 thf(56,plain,(((~ (p@sK3_SY5))=$true) | ((![SY10:$i]: ((~ ((rel_s4@sK3_SY5)@SY10)) | (q@SY10)))=$true)),inference(extcnf_or_pos,[status(thm)],[52])).
0.17/0.41	 thf(57,plain,(![SV10:$i]: (((q@SV10)=$false) | (((rel_s4@sK2_SX0)@SV10)=$false))),inference(extcnf_not_pos,[status(thm)],[54])).
0.17/0.41	 thf(58,plain,(![SV4:$i,SV8:$i,SV6:$i]: ((((rel_s4@SV6)@SV8)=$false) | (((rel_s4@SV4)@SV6)=$false) | (((rel_s4@SV4)@SV8)=$true))),inference(extcnf_not_pos,[status(thm)],[55])).
0.17/0.41	 thf(59,plain,(((p@sK3_SY5)=$false) | ((![SY10:$i]: ((~ ((rel_s4@sK3_SY5)@SY10)) | (q@SY10)))=$true)),inference(extcnf_not_pos,[status(thm)],[56])).
0.17/0.41	 thf(60,plain,(![SV11:$i]: ((((~ ((rel_s4@sK3_SY5)@SV11)) | (q@SV11))=$true) | ((p@sK3_SY5)=$false))),inference(extcnf_forall_pos,[status(thm)],[59])).
0.17/0.41	 thf(61,plain,(![SV11:$i]: (((~ ((rel_s4@sK3_SY5)@SV11))=$true) | ((q@SV11)=$true) | ((p@sK3_SY5)=$false))),inference(extcnf_or_pos,[status(thm)],[60])).
0.17/0.41	 thf(62,plain,(![SV11:$i]: ((((rel_s4@sK3_SY5)@SV11)=$false) | ((q@SV11)=$true) | ((p@sK3_SY5)=$false))),inference(extcnf_not_pos,[status(thm)],[61])).
0.17/0.41	 thf(63,plain,((($false)=$true)),inference(fo_atp_e,[status(thm)],[18,62,58,57,53,51,45,21])).
0.17/0.41	 thf(64,plain,($false),inference(solved_all_splits,[solved_all_splits(join,[])],[63])).
0.17/0.41	% SZS output end CNFRefutation
0.17/0.41	
0.17/0.41	%**** End of derivation protocol ****
0.17/0.41	%**** no. of clauses in derivation: 64 ****
0.17/0.41	%**** clause counter: 63 ****
0.17/0.41	
0.17/0.41	% SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:63,loop_count:0,foatp_calls:1,translation:fof_full)
0.17/0.41	EOF