0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s 0.12/0.34 % Computer : n024.cluster.edu 0.12/0.34 % Model : x86_64 x86_64 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.34 % Memory : 8042.1875MB 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.34 % CPULimit : 960 0.12/0.34 % WCLimit : 120 0.12/0.34 % DateTime : Tue Aug 9 06:31:22 EDT 2022 0.12/0.34 % CPUTime : 0.12/0.36 0.12/0.36 No.of.Axioms: 32 0.12/0.36 0.12/0.36 Length.of.Defs: 5293 0.12/0.36 0.12/0.36 Contains.Choice.Funs: false 0.12/0.39 (rf:0,axioms:32,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:34,loop_count:0,foatp_calls:0,translation:fof_full).............................. 0.46/0.70 0.46/0.70 ******************************** 0.46/0.70 * All subproblems solved! * 0.46/0.70 ******************************** 0.46/0.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:32,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:532,loop_count:0,foatp_calls:1,translation:fof_full) 0.62/0.81 0.62/0.81 %**** Beginning of derivation protocol **** 0.62/0.81 % SZS output start CNFRefutation 0.62/0.81 thf(tp_mu,type,(mu: $tType)). 0.62/0.81 thf(tp_a,type,(a: ($i>($i>$o)))). 0.62/0.81 thf(tp_b,type,(b: ($i>($i>$o)))). 0.62/0.81 thf(tp_c,type,(c: ($i>($i>$o)))). 0.62/0.81 thf(tp_fool,type,(fool: ($i>($i>$o)))). 0.62/0.81 thf(tp_mand,type,(mand: (($i>$o)>(($i>$o)>($i>$o))))). 0.62/0.81 thf(tp_mbox,type,(mbox: (($i>($i>$o))>(($i>$o)>($i>$o))))). 0.62/0.81 thf(tp_mcountersatisfiable,type,(mcountersatisfiable: (($i>$o)>$o))). 0.62/0.81 thf(tp_mdia,type,(mdia: (($i>($i>$o))>(($i>$o)>($i>$o))))). 0.62/0.81 thf(tp_meq_ind,type,(meq_ind: (mu>(mu>($i>$o))))). 0.62/0.81 thf(tp_meq_prop,type,(meq_prop: (($i>$o)>(($i>$o)>($i>$o))))). 0.62/0.81 thf(tp_mequiv,type,(mequiv: (($i>$o)>(($i>$o)>($i>$o))))). 0.62/0.81 thf(tp_meuclidean,type,(meuclidean: (($i>($i>$o))>$o))). 0.62/0.81 thf(tp_mexists_ind,type,(mexists_ind: ((mu>($i>$o))>($i>$o)))). 0.62/0.81 thf(tp_mexists_prop,type,(mexists_prop: ((($i>$o)>($i>$o))>($i>$o)))). 0.62/0.81 thf(tp_mfalse,type,(mfalse: ($i>$o))). 0.62/0.81 thf(tp_mforall_ind,type,(mforall_ind: ((mu>($i>$o))>($i>$o)))). 0.62/0.81 thf(tp_mforall_prop,type,(mforall_prop: ((($i>$o)>($i>$o))>($i>$o)))). 0.62/0.81 thf(tp_mfunctional,type,(mfunctional: (($i>($i>$o))>$o))). 0.62/0.81 thf(tp_mimplied,type,(mimplied: (($i>$o)>(($i>$o)>($i>$o))))). 0.62/0.81 thf(tp_mimplies,type,(mimplies: (($i>$o)>(($i>$o)>($i>$o))))). 0.62/0.81 thf(tp_minvalid,type,(minvalid: (($i>$o)>$o))). 0.62/0.81 thf(tp_mnot,type,(mnot: (($i>$o)>($i>$o)))). 0.62/0.81 thf(tp_mor,type,(mor: (($i>$o)>(($i>$o)>($i>$o))))). 0.62/0.81 thf(tp_mpartially_functional,type,(mpartially_functional: (($i>($i>$o))>$o))). 0.62/0.81 thf(tp_mreflexive,type,(mreflexive: (($i>($i>$o))>$o))). 0.62/0.81 thf(tp_msatisfiable,type,(msatisfiable: (($i>$o)>$o))). 0.62/0.81 thf(tp_mserial,type,(mserial: (($i>($i>$o))>$o))). 0.62/0.81 thf(tp_msymmetric,type,(msymmetric: (($i>($i>$o))>$o))). 0.62/0.81 thf(tp_mtransitive,type,(mtransitive: (($i>($i>$o))>$o))). 0.62/0.81 thf(tp_mtrue,type,(mtrue: ($i>$o))). 0.62/0.81 thf(tp_mvalid,type,(mvalid: (($i>$o)>$o))). 0.62/0.81 thf(tp_mweakly_connected,type,(mweakly_connected: (($i>($i>$o))>$o))). 0.62/0.81 thf(tp_mweakly_dense,type,(mweakly_dense: (($i>($i>$o))>$o))). 0.62/0.81 thf(tp_mweakly_directed,type,(mweakly_directed: (($i>($i>$o))>$o))). 0.62/0.81 thf(tp_mxor,type,(mxor: (($i>$o)>(($i>$o)>($i>$o))))). 0.62/0.81 thf(tp_sK10_SY108,type,(sK10_SY108: (($i>$o)>($i>$i)))). 0.62/0.81 thf(tp_sK11_SY118,type,(sK11_SY118: (($i>$o)>($i>$i)))). 0.62/0.81 thf(tp_sK12_SY127,type,(sK12_SY127: (($i>$o)>($i>$i)))). 0.62/0.81 thf(tp_sK13_SY131,type,(sK13_SY131: (($i>$o)>($i>$i)))). 0.62/0.81 thf(tp_sK14_SY134,type,(sK14_SY134: (($i>$o)>($i>$i)))). 0.62/0.81 thf(tp_sK15_SY143,type,(sK15_SY143: (($i>$o)>($i>$i)))). 0.62/0.81 thf(tp_sK16_SY163,type,(sK16_SY163: ($i>($i>(($i>$o)>($i>$i)))))). 0.62/0.81 thf(tp_sK17_SY164,type,(sK17_SY164: ($i>($i>(($i>$o)>($i>$i)))))). 0.62/0.81 thf(tp_sK18_SY165,type,(sK18_SY165: ($i>($i>(($i>$o)>($i>$i)))))). 0.62/0.81 thf(tp_sK19_SY166,type,(sK19_SY166: ($i>($i>(($i>$o)>($i>$i)))))). 0.62/0.81 thf(tp_sK1_SX0,type,(sK1_SX0: $i)). 0.62/0.81 thf(tp_sK20_SY167,type,(sK20_SY167: ($i>($i>(($i>$o)>($i>$i)))))). 0.62/0.81 thf(tp_sK21_SY168,type,(sK21_SY168: ($i>($i>(($i>$o)>($i>$i)))))). 0.62/0.81 thf(tp_sK2_SY24,type,(sK2_SY24: ($i>$i))). 0.62/0.81 thf(tp_sK3_SY130,type,(sK3_SY130: $i)). 0.62/0.81 thf(tp_sK4_SY64,type,(sK4_SY64: ($i>$i))). 0.62/0.81 thf(tp_sK5_SY92,type,(sK5_SY92: (($i>$o)>($i>$i)))). 0.62/0.81 thf(tp_sK6_SY97,type,(sK6_SY97: (($i>$o)>($i>$i)))). 0.62/0.81 thf(tp_sK7_SY100,type,(sK7_SY100: (($i>$o)>($i>$i)))). 0.62/0.81 thf(tp_sK8_SY105,type,(sK8_SY105: (($i>$o)>($i>$i)))). 0.62/0.81 thf(tp_sK9_SY107,type,(sK9_SY107: (($i>$o)>($i>$i)))). 0.62/0.81 thf(tp_ws,type,(ws: (($i>($i>$o))>($i>$o)))). 0.62/0.81 thf(mand,definition,(mand = (^[Phi:($i>$o),Psi:($i>$o)]: (mnot@((mor@(mnot@Phi))@(mnot@Psi))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)). 0.62/0.81 thf(mbox,definition,(mbox = (^[R:($i>($i>$o)),Phi:($i>$o),W:$i]: (![V:$i]: ((~ ((R@W)@V)) | (Phi@V))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox)). 0.62/0.81 thf(mcountersatisfiable,definition,(mcountersatisfiable = (^[Phi:($i>$o)]: (?[W:$i]: (~ (Phi@W))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',mcountersatisfiable)). 0.62/0.81 thf(mdia,definition,(mdia = (^[R:($i>($i>$o)),Phi:($i>$o)]: (mnot@((mbox@R)@(mnot@Phi))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia)). 0.62/0.81 thf(meq_ind,definition,(meq_ind = (^[X:mu,Y:mu,W:$i]: (X = Y))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',meq_ind)). 0.62/0.81 thf(meq_prop,definition,(meq_prop = (^[X:($i>$o),Y:($i>$o),W:$i]: ((X@W) = (Y@W)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',meq_prop)). 0.62/0.81 thf(mequiv,definition,(mequiv = (^[Phi:($i>$o),Psi:($i>$o)]: ((mand@((mimplies@Phi)@Psi))@((mimplies@Psi)@Phi)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv)). 0.62/0.81 thf(meuclidean,definition,(meuclidean = (^[R:($i>($i>$o))]: (![S:$i,T:$i,U:$i]: ((((R@S)@T) & ((R@S)@U)) => ((R@T)@U))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',meuclidean)). 0.62/0.81 thf(mexists_ind,definition,(mexists_ind = (^[Phi:(mu>($i>$o))]: (mnot@(mforall_ind@(^[X:mu]: (mnot@(Phi@X))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_ind)). 0.62/0.81 thf(mexists_prop,definition,(mexists_prop = (^[Phi:(($i>$o)>($i>$o))]: (mnot@(mforall_prop@(^[P:($i>$o)]: (mnot@(Phi@P))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_prop)). 0.62/0.81 thf(mfalse,definition,(mfalse = (mnot@mtrue)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',mfalse)). 0.62/0.81 thf(mforall_ind,definition,(mforall_ind = (^[Phi:(mu>($i>$o)),W:$i]: (![X:mu]: ((Phi@X)@W)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_ind)). 0.62/0.81 thf(mforall_prop,definition,(mforall_prop = (^[Phi:(($i>$o)>($i>$o)),W:$i]: (![P:($i>$o)]: ((Phi@P)@W)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_prop)). 0.62/0.81 thf(mfunctional,definition,(mfunctional = (^[R:($i>($i>$o))]: (![S:$i]: (?[T:$i]: (((R@S)@T) & (![U:$i]: (((R@S)@U) => (T = U)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',mfunctional)). 0.62/0.81 thf(mimplied,definition,(mimplied = (^[Phi:($i>$o),Psi:($i>$o)]: ((mor@(mnot@Psi))@Phi))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplied)). 0.62/0.81 thf(mimplies,definition,(mimplies = (^[Phi:($i>$o),Psi:($i>$o)]: ((mor@(mnot@Phi))@Psi))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)). 0.62/0.81 thf(minvalid,definition,(minvalid = (^[Phi:($i>$o)]: (![W:$i]: (~ (Phi@W))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',minvalid)). 0.62/0.81 thf(mnot,definition,(mnot = (^[Phi:($i>$o),W:$i]: (~ (Phi@W)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)). 0.62/0.81 thf(mor,definition,(mor = (^[Phi:($i>$o),Psi:($i>$o),W:$i]: ((Phi@W) | (Psi@W)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)). 0.62/0.81 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/sandbox/benchmark/theBenchmark.p',mpartially_functional)). 0.62/0.81 thf(mreflexive,definition,(mreflexive = (^[R:($i>($i>$o))]: (![S:$i]: ((R@S)@S)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',mreflexive)). 0.62/0.81 thf(msatisfiable,definition,(msatisfiable = (^[Phi:($i>$o)]: (?[W:$i]: (Phi@W)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',msatisfiable)). 0.62/0.81 thf(mserial,definition,(mserial = (^[R:($i>($i>$o))]: (![S:$i]: (?[T:$i]: ((R@S)@T))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',mserial)). 0.62/0.81 thf(msymmetric,definition,(msymmetric = (^[R:($i>($i>$o))]: (![S:$i,T:$i]: (((R@S)@T) => ((R@T)@S))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',msymmetric)). 0.62/0.81 thf(mtransitive,definition,(mtransitive = (^[R:($i>($i>$o))]: (![S:$i,T:$i,U:$i]: ((((R@S)@T) & ((R@T)@U)) => ((R@S)@U))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtransitive)). 0.62/0.81 thf(mtrue,definition,(mtrue = (^[W:$i]: $true)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtrue)). 0.62/0.81 thf(mvalid,definition,(mvalid = (^[Phi:($i>$o)]: (![W:$i]: (Phi@W)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)). 0.62/0.81 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/sandbox/benchmark/theBenchmark.p',mweakly_connected)). 0.62/0.81 thf(mweakly_dense,definition,(mweakly_dense = (^[R:($i>($i>$o))]: (![S:$i,T:$i,U:$i]: (((R@S)@T) => (?[U:$i]: (((R@S)@U) & ((R@U)@T))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',mweakly_dense)). 0.62/0.81 thf(mweakly_directed,definition,(mweakly_directed = (^[R:($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/sandbox/benchmark/theBenchmark.p',mweakly_directed)). 0.62/0.81 thf(mxor,definition,(mxor = (^[Phi:($i>$o),Psi:($i>$o)]: (mnot@((mequiv@Phi)@Psi)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',mxor)). 0.62/0.81 thf(1,axiom,(mvalid@(mforall_prop@(^[Phi:($i>$o)]: ((mimplies@(mnot@((mbox@c)@Phi)))@((mbox@b)@(mnot@((mbox@c)@Phi))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6_axiom_for_fool_c_b)). 0.62/0.81 thf(2,axiom,(mvalid@((mbox@fool)@((mimplies@(ws@a))@((mbox@b)@(ws@a))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2_a_b)). 0.62/0.81 thf(3,axiom,(mvalid@(mforall_prop@(^[Phi:($i>$o)]: ((mimplies@((mbox@fool)@Phi))@((mbox@b)@Phi))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_axiom_for_fool_b)). 0.62/0.81 thf(4,axiom,(mvalid@((mbox@fool)@((mimplies@(ws@c))@((mbox@a)@(ws@c))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2_c_a)). 0.62/0.81 thf(5,axiom,(mvalid@((mbox@fool)@((mimplies@(mnot@(ws@a)))@((mbox@b)@(mnot@(ws@a)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3_a_b)). 0.62/0.81 thf(6,axiom,(mvalid@(mforall_prop@(^[Phi:($i>$o)]: ((mimplies@(mnot@((mbox@b)@Phi)))@((mbox@c)@(mnot@((mbox@b)@Phi))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6_axiom_for_fool_b_c)). 0.62/0.81 thf(7,axiom,(mvalid@((mbox@fool)@((mimplies@(ws@b))@((mbox@c)@(ws@b))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2_b_c)). 0.62/0.81 thf(8,axiom,(mvalid@(mforall_prop@(^[Phi:($i>$o)]: ((mimplies@(mnot@((mbox@a)@Phi)))@((mbox@c)@(mnot@((mbox@a)@Phi))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6_axiom_for_fool_a_c)). 0.62/0.81 thf(9,axiom,(mvalid@((mbox@fool)@((mimplies@(ws@c))@((mbox@b)@(ws@c))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2_c_b)). 0.62/0.81 thf(10,axiom,(mvalid@((mbox@fool)@((mimplies@(mnot@(ws@b)))@((mbox@a)@(mnot@(ws@b)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3_b_a)). 0.62/0.81 thf(11,axiom,(mvalid@(mforall_prop@(^[Phi:($i>$o)]: ((mimplies@((mbox@b)@Phi))@((mbox@c)@((mbox@b)@Phi)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',a7_axiom_for_fool_b_c)). 0.62/0.81 thf(12,axiom,(mvalid@(mforall_prop@(^[Phi:($i>$o)]: ((mimplies@((mbox@c)@Phi))@((mbox@b)@((mbox@c)@Phi)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',a7_axiom_for_fool_c_b)). 0.62/0.81 thf(13,axiom,(mvalid@(mforall_prop@(^[Phi:($i>$o)]: ((mimplies@((mbox@a)@Phi))@((mbox@b)@((mbox@a)@Phi)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',a7_axiom_for_fool_a_b)). 0.62/0.81 thf(14,axiom,(mvalid@(mforall_prop@(^[Phi:($i>$o)]: ((mimplies@((mbox@fool)@Phi))@((mbox@a)@Phi))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_axiom_for_fool_a)). 0.62/0.81 thf(15,axiom,(mvalid@(mforall_prop@(^[A:($i>$o)]: ((mimplies@((mbox@fool)@A))@A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',t_axiom_for_fool)). 0.62/0.81 thf(16,axiom,(mvalid@(mforall_prop@(^[Phi:($i>$o)]: ((mimplies@(mnot@((mbox@b)@Phi)))@((mbox@a)@(mnot@((mbox@b)@Phi))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6_axiom_for_fool_b_a)). 0.62/0.81 thf(17,axiom,(mvalid@((mbox@fool)@((mimplies@(mnot@(ws@c)))@((mbox@a)@(mnot@(ws@c)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3_c_a)). 0.62/0.81 thf(18,axiom,(mvalid@(mforall_prop@(^[Phi:($i>$o)]: ((mimplies@(mnot@((mbox@a)@Phi)))@((mbox@b)@(mnot@((mbox@a)@Phi))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6_axiom_for_fool_a_b)). 0.62/0.81 thf(19,axiom,(mvalid@(mforall_prop@(^[Phi:($i>$o)]: ((mimplies@((mbox@c)@Phi))@((mbox@a)@((mbox@c)@Phi)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',a7_axiom_for_fool_c_a)). 0.62/0.81 thf(20,axiom,(mvalid@(mforall_prop@(^[Phi:($i>$o)]: ((mimplies@((mbox@b)@Phi))@((mbox@a)@((mbox@b)@Phi)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',a7_axiom_for_fool_b_a)). 0.62/0.81 thf(21,axiom,(mvalid@(mnot@((mbox@b)@(ws@b)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5)). 0.62/0.81 thf(22,axiom,(mvalid@(mforall_prop@(^[Phi:($i>$o)]: ((mimplies@(mnot@((mbox@c)@Phi)))@((mbox@a)@(mnot@((mbox@c)@Phi))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6_axiom_for_fool_c_a)). 0.62/0.81 thf(23,axiom,(mvalid@((mbox@fool)@((mimplies@(mnot@(ws@b)))@((mbox@c)@(mnot@(ws@b)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3_b_c)). 0.62/0.81 thf(24,axiom,(mvalid@((mbox@fool)@((mor@(ws@a))@((mor@(ws@b))@(ws@c))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1)). 0.62/0.81 thf(25,axiom,(mvalid@((mbox@fool)@((mimplies@(mnot@(ws@a)))@((mbox@c)@(mnot@(ws@a)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3_a_c)). 0.62/0.81 thf(26,axiom,(mvalid@(mforall_prop@(^[A:($i>$o)]: ((mimplies@((mbox@fool)@A))@((mbox@fool)@((mbox@fool)@A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_axiom_for_fool)). 0.62/0.81 thf(27,axiom,(mvalid@(mforall_prop@(^[Phi:($i>$o)]: ((mimplies@((mbox@a)@Phi))@((mbox@c)@((mbox@a)@Phi)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',a7_axiom_for_fool_a_c)). 0.62/0.81 thf(28,axiom,(mvalid@((mbox@fool)@((mimplies@(ws@a))@((mbox@c)@(ws@a))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2_a_c)). 0.62/0.81 thf(29,axiom,(mvalid@(mforall_prop@(^[Phi:($i>$o)]: ((mimplies@((mbox@fool)@Phi))@((mbox@c)@Phi))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_axiom_for_fool_c)). 0.62/0.81 thf(30,axiom,(mvalid@((mbox@fool)@((mimplies@(ws@b))@((mbox@a)@(ws@b))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2_b_a)). 0.62/0.81 thf(31,axiom,(mvalid@((mbox@fool)@((mimplies@(mnot@(ws@c)))@((mbox@b)@(mnot@(ws@c)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3_c_b)). 0.62/0.81 thf(32,axiom,(mvalid@(mnot@((mbox@a)@(ws@a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4)). 0.62/0.81 thf(33,conjecture,(mvalid@((mbox@c)@(ws@c))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)). 0.62/0.81 thf(34,negated_conjecture,(((mvalid@((mbox@c)@(ws@c)))=$false)),inference(negate_conjecture,[status(cth)],[33])). 0.62/0.81 thf(35,plain,(((~ (mvalid@((mbox@c)@(ws@c))))=$true)),inference(polarity_switch,[status(thm)],[34])). 0.62/0.81 thf(36,plain,(((mvalid@(mnot@((mbox@a)@(ws@a))))=$true)),inference(copy,[status(thm)],[32])). 0.62/0.81 thf(37,plain,(((mvalid@((mbox@fool)@((mimplies@(mnot@(ws@c)))@((mbox@b)@(mnot@(ws@c))))))=$true)),inference(copy,[status(thm)],[31])). 0.62/0.81 thf(38,plain,(((mvalid@((mbox@fool)@((mimplies@(ws@b))@((mbox@a)@(ws@b)))))=$true)),inference(copy,[status(thm)],[30])). 0.62/0.81 thf(39,plain,(((mvalid@(mforall_prop@(^[Phi:($i>$o)]: ((mimplies@((mbox@fool)@Phi))@((mbox@c)@Phi)))))=$true)),inference(copy,[status(thm)],[29])). 0.62/0.81 thf(40,plain,(((mvalid@((mbox@fool)@((mimplies@(ws@a))@((mbox@c)@(ws@a)))))=$true)),inference(copy,[status(thm)],[28])). 0.62/0.81 thf(41,plain,(((mvalid@(mforall_prop@(^[Phi:($i>$o)]: ((mimplies@((mbox@a)@Phi))@((mbox@c)@((mbox@a)@Phi))))))=$true)),inference(copy,[status(thm)],[27])). 0.62/0.81 thf(42,plain,(((mvalid@(mforall_prop@(^[A:($i>$o)]: ((mimplies@((mbox@fool)@A))@((mbox@fool)@((mbox@fool)@A))))))=$true)),inference(copy,[status(thm)],[26])). 0.62/0.81 thf(43,plain,(((mvalid@((mbox@fool)@((mimplies@(mnot@(ws@a)))@((mbox@c)@(mnot@(ws@a))))))=$true)),inference(copy,[status(thm)],[25])). 0.62/0.81 thf(44,plain,(((mvalid@((mbox@fool)@((mor@(ws@a))@((mor@(ws@b))@(ws@c)))))=$true)),inference(copy,[status(thm)],[24])). 0.62/0.81 thf(45,plain,(((mvalid@((mbox@fool)@((mimplies@(mnot@(ws@b)))@((mbox@c)@(mnot@(ws@b))))))=$true)),inference(copy,[status(thm)],[23])). 0.62/0.81 thf(46,plain,(((mvalid@(mforall_prop@(^[Phi:($i>$o)]: ((mimplies@(mnot@((mbox@c)@Phi)))@((mbox@a)@(mnot@((mbox@c)@Phi)))))))=$true)),inference(copy,[status(thm)],[22])). 0.62/0.81 thf(47,plain,(((mvalid@(mnot@((mbox@b)@(ws@b))))=$true)),inference(copy,[status(thm)],[21])). 0.62/0.81 thf(48,plain,(((mvalid@(mforall_prop@(^[Phi:($i>$o)]: ((mimplies@((mbox@b)@Phi))@((mbox@a)@((mbox@b)@Phi))))))=$true)),inference(copy,[status(thm)],[20])). 0.62/0.81 thf(49,plain,(((mvalid@(mforall_prop@(^[Phi:($i>$o)]: ((mimplies@((mbox@c)@Phi))@((mbox@a)@((mbox@c)@Phi))))))=$true)),inference(copy,[status(thm)],[19])). 0.62/0.81 thf(50,plain,(((mvalid@(mforall_prop@(^[Phi:($i>$o)]: ((mimplies@(mnot@((mbox@a)@Phi)))@((mbox@b)@(mnot@((mbox@a)@Phi)))))))=$true)),inference(copy,[status(thm)],[18])). 0.62/0.81 thf(51,plain,(((mvalid@((mbox@fool)@((mimplies@(mnot@(ws@c)))@((mbox@a)@(mnot@(ws@c))))))=$true)),inference(copy,[status(thm)],[17])). 0.62/0.81 thf(52,plain,(((mvalid@(mforall_prop@(^[Phi:($i>$o)]: ((mimplies@(mnot@((mbox@b)@Phi)))@((mbox@a)@(mnot@((mbox@b)@Phi)))))))=$true)),inference(copy,[status(thm)],[16])). 0.62/0.81 thf(53,plain,(((mvalid@(mforall_prop@(^[A:($i>$o)]: ((mimplies@((mbox@fool)@A))@A))))=$true)),inference(copy,[status(thm)],[15])). 0.62/0.81 thf(54,plain,(((mvalid@(mforall_prop@(^[Phi:($i>$o)]: ((mimplies@((mbox@fool)@Phi))@((mbox@a)@Phi)))))=$true)),inference(copy,[status(thm)],[14])). 0.62/0.81 thf(55,plain,(((mvalid@(mforall_prop@(^[Phi:($i>$o)]: ((mimplies@((mbox@a)@Phi))@((mbox@b)@((mbox@a)@Phi))))))=$true)),inference(copy,[status(thm)],[13])). 0.62/0.81 thf(56,plain,(((mvalid@(mforall_prop@(^[Phi:($i>$o)]: ((mimplies@((mbox@c)@Phi))@((mbox@b)@((mbox@c)@Phi))))))=$true)),inference(copy,[status(thm)],[12])). 0.62/0.81 thf(57,plain,(((mvalid@(mforall_prop@(^[Phi:($i>$o)]: ((mimplies@((mbox@b)@Phi))@((mbox@c)@((mbox@b)@Phi))))))=$true)),inference(copy,[status(thm)],[11])). 0.62/0.81 thf(58,plain,(((mvalid@((mbox@fool)@((mimplies@(mnot@(ws@b)))@((mbox@a)@(mnot@(ws@b))))))=$true)),inference(copy,[status(thm)],[10])). 0.62/0.81 thf(59,plain,(((mvalid@((mbox@fool)@((mimplies@(ws@c))@((mbox@b)@(ws@c)))))=$true)),inference(copy,[status(thm)],[9])). 0.62/0.81 thf(60,plain,(((mvalid@(mforall_prop@(^[Phi:($i>$o)]: ((mimplies@(mnot@((mbox@a)@Phi)))@((mbox@c)@(mnot@((mbox@a)@Phi)))))))=$true)),inference(copy,[status(thm)],[8])). 0.62/0.81 thf(61,plain,(((mvalid@((mbox@fool)@((mimplies@(ws@b))@((mbox@c)@(ws@b)))))=$true)),inference(copy,[status(thm)],[7])). 0.62/0.81 thf(62,plain,(((mvalid@(mforall_prop@(^[Phi:($i>$o)]: ((mimplies@(mnot@((mbox@b)@Phi)))@((mbox@c)@(mnot@((mbox@b)@Phi)))))))=$true)),inference(copy,[status(thm)],[6])). 0.62/0.81 thf(63,plain,(((mvalid@((mbox@fool)@((mimplies@(mnot@(ws@a)))@((mbox@b)@(mnot@(ws@a))))))=$true)),inference(copy,[status(thm)],[5])). 0.62/0.81 thf(64,plain,(((mvalid@((mbox@fool)@((mimplies@(ws@c))@((mbox@a)@(ws@c)))))=$true)),inference(copy,[status(thm)],[4])). 0.62/0.81 thf(65,plain,(((mvalid@(mforall_prop@(^[Phi:($i>$o)]: ((mimplies@((mbox@fool)@Phi))@((mbox@b)@Phi)))))=$true)),inference(copy,[status(thm)],[3])). 0.62/0.81 thf(66,plain,(((mvalid@((mbox@fool)@((mimplies@(ws@a))@((mbox@b)@(ws@a)))))=$true)),inference(copy,[status(thm)],[2])). 0.62/0.81 thf(67,plain,(((mvalid@(mforall_prop@(^[Phi:($i>$o)]: ((mimplies@(mnot@((mbox@c)@Phi)))@((mbox@b)@(mnot@((mbox@c)@Phi)))))))=$true)),inference(copy,[status(thm)],[1])). 0.62/0.81 thf(68,plain,(((~ (mvalid@((mbox@c)@(ws@c))))=$true)),inference(copy,[status(thm)],[35])). 0.62/0.81 thf(69,plain,(((![SX0:$i,SX1:$i]: ((~ ((fool@SX0)@SX1)) | ((~ (~ ((ws@a)@SX1))) | (![SX2:$i]: ((~ ((c@SX1)@SX2)) | (~ ((ws@a)@SX2)))))))=$true)),inference(unfold_def,[status(thm)],[43,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor])). 0.62/0.81 thf(70,plain,(((![SX0:$i,SX1:$i]: ((~ ((fool@SX0)@SX1)) | ((~ ((ws@a)@SX1)) | (![SX2:$i]: ((~ ((b@SX1)@SX2)) | ((ws@a)@SX2))))))=$true)),inference(unfold_def,[status(thm)],[66,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor])). 0.62/0.81 thf(71,plain,(((![SX0:$i,SX1:($i>$o)]: ((~ (![SX2:$i]: ((~ ((fool@SX0)@SX2)) | (SX1@SX2)))) | (![SX2:$i]: ((~ ((c@SX0)@SX2)) | (SX1@SX2)))))=$true)),inference(unfold_def,[status(thm)],[39,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor])). 0.62/0.81 thf(72,plain,(((![SX0:$i,SX1:($i>$o)]: ((~ (~ (![SX2:$i]: ((~ ((c@SX0)@SX2)) | (SX1@SX2))))) | (![SX2:$i]: ((~ ((a@SX0)@SX2)) | (~ (![SX3:$i]: ((~ ((c@SX2)@SX3)) | (SX1@SX3))))))))=$true)),inference(unfold_def,[status(thm)],[46,mand,mbox,mcountersatisfiable,mdia,meq_ind,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])). 0.62/0.81 thf(73,plain,(((![SX0:$i,SX1:($i>$o)]: ((~ (![SX2:$i]: ((~ ((fool@SX0)@SX2)) | (SX1@SX2)))) | (![SX2:$i]: ((~ ((fool@SX0)@SX2)) | (![SX3:$i]: ((~ ((fool@SX2)@SX3)) | (SX1@SX3)))))))=$true)),inference(unfold_def,[status(thm)],[42,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor])). 0.62/0.81 thf(74,plain,(((![SX0:$i,SX1:($i>$o)]: ((~ (![SX2:$i]: ((~ ((a@SX0)@SX2)) | (SX1@SX2)))) | (![SX2:$i]: ((~ ((c@SX0)@SX2)) | (![SX3:$i]: ((~ ((a@SX2)@SX3)) | (SX1@SX3)))))))=$true)),inference(unfold_def,[status(thm)],[41,mand,mbox,mcountersatisfiable,mdia,meq_ind,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])). 0.62/0.81 thf(75,plain,(((![SX0:$i,SX1:$i]: ((~ ((fool@SX0)@SX1)) | ((~ ((ws@c)@SX1)) | (![SX2:$i]: ((~ ((a@SX1)@SX2)) | ((ws@c)@SX2))))))=$true)),inference(unfold_def,[status(thm)],[64,mand,mbox,mcountersatisfiable,mdia,meq_ind,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])). 0.62/0.81 thf(76,plain,(((![SX0:$i,SX1:$i]: ((~ ((fool@SX0)@SX1)) | ((~ (~ ((ws@c)@SX1))) | (![SX2:$i]: ((~ ((b@SX1)@SX2)) | (~ ((ws@c)@SX2)))))))=$true)),inference(unfold_def,[status(thm)],[37,mand,mbox,mcountersatisfiable,mdia,meq_ind,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])). 0.62/0.81 thf(77,plain,(((![SX0:$i,SX1:$i]: ((~ ((fool@SX0)@SX1)) | (((ws@a)@SX1) | (((ws@b)@SX1) | ((ws@c)@SX1)))))=$true)),inference(unfold_def,[status(thm)],[44,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor])). 0.62/0.81 thf(78,plain,(((![SX0:$i]: (~ (![SX1:$i]: ((~ ((b@SX0)@SX1)) | ((ws@b)@SX1)))))=$true)),inference(unfold_def,[status(thm)],[47,mand,mbox,mcountersatisfiable,mdia,meq_ind,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])). 0.62/0.81 thf(79,plain,(((![SX0:$i,SX1:($i>$o)]: ((~ (![SX2:$i]: ((~ ((fool@SX0)@SX2)) | (SX1@SX2)))) | (![SX2:$i]: ((~ ((b@SX0)@SX2)) | (SX1@SX2)))))=$true)),inference(unfold_def,[status(thm)],[65,mand,mbox,mcountersatisfiable,mdia,meq_ind,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])). 0.62/0.81 thf(80,plain,(((![SX0:$i,SX1:($i>$o)]: ((~ (![SX2:$i]: ((~ ((fool@SX0)@SX2)) | (SX1@SX2)))) | (SX1@SX0)))=$true)),inference(unfold_def,[status(thm)],[53,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor])). 0.62/0.81 thf(81,plain,(((![SX0:$i,SX1:($i>$o)]: ((~ (![SX2:$i]: ((~ ((b@SX0)@SX2)) | (SX1@SX2)))) | (![SX2:$i]: ((~ ((a@SX0)@SX2)) | (![SX3:$i]: ((~ ((b@SX2)@SX3)) | (SX1@SX3)))))))=$true)),inference(unfold_def,[status(thm)],[48,mand,mbox,mcountersatisfiable,mdia,meq_ind,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])). 0.62/0.81 thf(82,plain,(((![SX0:$i,SX1:$i]: ((~ ((fool@SX0)@SX1)) | ((~ (~ ((ws@b)@SX1))) | (![SX2:$i]: ((~ ((a@SX1)@SX2)) | (~ ((ws@b)@SX2)))))))=$true)),inference(unfold_def,[status(thm)],[58,mand,mbox,mcountersatisfiable,mdia,meq_ind,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])). 0.62/0.81 thf(83,plain,(((![SX0:$i,SX1:$i]: ((~ ((fool@SX0)@SX1)) | ((~ ((ws@b)@SX1)) | (![SX2:$i]: ((~ ((c@SX1)@SX2)) | ((ws@b)@SX2))))))=$true)),inference(unfold_def,[status(thm)],[61,mand,mbox,mcountersatisfiable,mdia,meq_ind,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])). 0.62/0.81 thf(84,plain,(((![SX0:$i,SX1:$i]: ((~ ((fool@SX0)@SX1)) | ((~ ((ws@b)@SX1)) | (![SX2:$i]: ((~ ((a@SX1)@SX2)) | ((ws@b)@SX2))))))=$true)),inference(unfold_def,[status(thm)],[38,mand,mbox,mcountersatisfiable,mdia,meq_ind,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])). 0.62/0.81 thf(85,plain,(((![SX0:$i,SX1:$i]: ((~ ((fool@SX0)@SX1)) | ((~ ((ws@c)@SX1)) | (![SX2:$i]: ((~ ((b@SX1)@SX2)) | ((ws@c)@SX2))))))=$true)),inference(unfold_def,[status(thm)],[59,mand,mbox,mcountersatisfiable,mdia,meq_ind,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])). 0.62/0.81 thf(86,plain,(((![SX0:$i,SX1:($i>$o)]: ((~ (~ (![SX2:$i]: ((~ ((a@SX0)@SX2)) | (SX1@SX2))))) | (![SX2:$i]: ((~ ((c@SX0)@SX2)) | (~ (![SX3:$i]: ((~ ((a@SX2)@SX3)) | (SX1@SX3))))))))=$true)),inference(unfold_def,[status(thm)],[60,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor])). 0.62/0.81 thf(87,plain,(((![SX0:$i,SX1:($i>$o)]: ((~ (![SX2:$i]: ((~ ((a@SX0)@SX2)) | (SX1@SX2)))) | (![SX2:$i]: ((~ ((b@SX0)@SX2)) | (![SX3:$i]: ((~ ((a@SX2)@SX3)) | (SX1@SX3)))))))=$true)),inference(unfold_def,[status(thm)],[55,mand,mbox,mcountersatisfiable,mdia,meq_ind,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])). 0.62/0.81 thf(88,plain,(((![SX0:$i,SX1:($i>$o)]: ((~ (~ (![SX2:$i]: ((~ ((c@SX0)@SX2)) | (SX1@SX2))))) | (![SX2:$i]: ((~ ((b@SX0)@SX2)) | (~ (![SX3:$i]: ((~ ((c@SX2)@SX3)) | (SX1@SX3))))))))=$true)),inference(unfold_def,[status(thm)],[67,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor])). 0.62/0.81 thf(89,plain,(((![SX0:$i,SX1:$i]: ((~ ((fool@SX0)@SX1)) | ((~ ((ws@a)@SX1)) | (![SX2:$i]: ((~ ((c@SX1)@SX2)) | ((ws@a)@SX2))))))=$true)),inference(unfold_def,[status(thm)],[40,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor])). 0.62/0.81 thf(90,plain,(((![SX0:$i,SX1:$i]: ((~ ((fool@SX0)@SX1)) | ((~ (~ ((ws@c)@SX1))) | (![SX2:$i]: ((~ ((a@SX1)@SX2)) | (~ ((ws@c)@SX2)))))))=$true)),inference(unfold_def,[status(thm)],[51,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor])). 0.62/0.81 thf(91,plain,(((![SX0:$i,SX1:$i]: ((~ ((fool@SX0)@SX1)) | ((~ (~ ((ws@a)@SX1))) | (![SX2:$i]: ((~ ((b@SX1)@SX2)) | (~ ((ws@a)@SX2)))))))=$true)),inference(unfold_def,[status(thm)],[63,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor])). 0.62/0.81 thf(92,plain,(((![SX0:$i,SX1:($i>$o)]: ((~ (![SX2:$i]: ((~ ((b@SX0)@SX2)) | (SX1@SX2)))) | (![SX2:$i]: ((~ ((c@SX0)@SX2)) | (![SX3:$i]: ((~ ((b@SX2)@SX3)) | (SX1@SX3)))))))=$true)),inference(unfold_def,[status(thm)],[57,mand,mbox,mcountersatisfiable,mdia,meq_ind,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])). 0.62/0.81 thf(93,plain,(((~ (![SX0:$i,SX1:$i]: ((~ ((c@SX0)@SX1)) | ((ws@c)@SX1))))=$true)),inference(unfold_def,[status(thm)],[68,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor])). 0.62/0.81 thf(94,plain,(((![SX0:$i]: (~ (![SX1:$i]: ((~ ((a@SX0)@SX1)) | ((ws@a)@SX1)))))=$true)),inference(unfold_def,[status(thm)],[36,mand,mbox,mcountersatisfiable,mdia,meq_ind,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])). 0.62/0.81 thf(95,plain,(((![SX0:$i,SX1:($i>$o)]: ((~ (![SX2:$i]: ((~ ((fool@SX0)@SX2)) | (SX1@SX2)))) | (![SX2:$i]: ((~ ((a@SX0)@SX2)) | (SX1@SX2)))))=$true)),inference(unfold_def,[status(thm)],[54,mand,mbox,mcountersatisfiable,mdia,meq_ind,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])). 0.62/0.81 thf(96,plain,(((![SX0:$i,SX1:$i]: ((~ ((fool@SX0)@SX1)) | ((~ (~ ((ws@b)@SX1))) | (![SX2:$i]: ((~ ((c@SX1)@SX2)) | (~ ((ws@b)@SX2)))))))=$true)),inference(unfold_def,[status(thm)],[45,mand,mbox,mcountersatisfiable,mdia,meq_ind,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])). 0.62/0.81 thf(97,plain,(((![SX0:$i,SX1:($i>$o)]: ((~ (![SX2:$i]: ((~ ((c@SX0)@SX2)) | (SX1@SX2)))) | (![SX2:$i]: ((~ ((b@SX0)@SX2)) | (![SX3:$i]: ((~ ((c@SX2)@SX3)) | (SX1@SX3)))))))=$true)),inference(unfold_def,[status(thm)],[56,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor])). 0.62/0.81 thf(98,plain,(((![SX0:$i,SX1:($i>$o)]: ((~ (~ (![SX2:$i]: ((~ ((b@SX0)@SX2)) | (SX1@SX2))))) | (![SX2:$i]: ((~ ((c@SX0)@SX2)) | (~ (![SX3:$i]: ((~ ((b@SX2)@SX3)) | (SX1@SX3))))))))=$true)),inference(unfold_def,[status(thm)],[62,mand,mbox,mcountersatisfiable,mdia,meq_ind,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])). 0.62/0.81 thf(99,plain,(((![SX0:$i,SX1:($i>$o)]: ((~ (~ (![SX2:$i]: ((~ ((b@SX0)@SX2)) | (SX1@SX2))))) | (![SX2:$i]: ((~ ((a@SX0)@SX2)) | (~ (![SX3:$i]: ((~ ((b@SX2)@SX3)) | (SX1@SX3))))))))=$true)),inference(unfold_def,[status(thm)],[52,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor])). 0.62/0.81 thf(100,plain,(((![SX0:$i,SX1:($i>$o)]: 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(SX1@SX3))))))))=$true)),inference(unfold_def,[status(thm)],[50,mand,mbox,mcountersatisfiable,mdia,meq_ind,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor])). 0.62/0.81 thf(102,plain,(![SV1:$i]: (((![SY0:$i]: ((~ ((fool@SV1)@SY0)) | ((~ (~ ((ws@a)@SY0))) | (![SX2:$i]: ((~ ((c@SY0)@SX2)) | (~ ((ws@a)@SX2)))))))=$true))),inference(extcnf_forall_pos,[status(thm)],[69])). 0.62/0.81 thf(103,plain,(![SV2:$i]: (((![SY2:$i]: ((~ ((fool@SV2)@SY2)) | ((~ ((ws@a)@SY2)) | (![SX2:$i]: ((~ ((b@SY2)@SX2)) | ((ws@a)@SX2))))))=$true))),inference(extcnf_forall_pos,[status(thm)],[70])). 0.62/0.81 thf(104,plain,(![SV3:$i]: (((![SY4:($i>$o)]: ((~ (![SY5:$i]: ((~ ((fool@SV3)@SY5)) | (SY4@SY5)))) | (![SY6:$i]: ((~ ((c@SV3)@SY6)) | (SY4@SY6)))))=$true))),inference(extcnf_forall_pos,[status(thm)],[71])). 0.62/0.81 thf(105,plain,(![SV4:$i]: (((![SY7:($i>$o)]: ((~ (~ (![SY8:$i]: ((~ ((c@SV4)@SY8)) | (SY7@SY8))))) | (![SY9:$i]: ((~ ((a@SV4)@SY9)) | (~ (![SX3:$i]: ((~ ((c@SY9)@SX3)) | (SY7@SX3))))))))=$true))),inference(extcnf_forall_pos,[status(thm)],[72])). 0.62/0.81 thf(106,plain,(![SV5:$i]: (((![SY11:($i>$o)]: ((~ (![SY12:$i]: ((~ ((fool@SV5)@SY12)) | (SY11@SY12)))) | (![SY13:$i]: ((~ ((fool@SV5)@SY13)) | (![SX3:$i]: ((~ ((fool@SY13)@SX3)) | (SY11@SX3)))))))=$true))),inference(extcnf_forall_pos,[status(thm)],[73])). 0.62/0.81 thf(107,plain,(![SV6:$i]: (((![SY15:($i>$o)]: ((~ (![SY16:$i]: ((~ ((a@SV6)@SY16)) | (SY15@SY16)))) | (![SY17:$i]: ((~ ((c@SV6)@SY17)) | (![SX3:$i]: ((~ ((a@SY17)@SX3)) | (SY15@SX3)))))))=$true))),inference(extcnf_forall_pos,[status(thm)],[74])). 0.62/0.81 thf(108,plain,(![SV7:$i]: (((![SY19:$i]: ((~ ((fool@SV7)@SY19)) | ((~ ((ws@c)@SY19)) | (![SX2:$i]: ((~ ((a@SY19)@SX2)) | ((ws@c)@SX2))))))=$true))),inference(extcnf_forall_pos,[status(thm)],[75])). 0.62/0.81 thf(109,plain,(![SV8:$i]: (((![SY21:$i]: ((~ ((fool@SV8)@SY21)) | ((~ (~ ((ws@c)@SY21))) | (![SX2:$i]: ((~ ((b@SY21)@SX2)) | (~ ((ws@c)@SX2)))))))=$true))),inference(extcnf_forall_pos,[status(thm)],[76])). 0.62/0.81 thf(110,plain,(![SV9:$i]: (((![SY23:$i]: ((~ ((fool@SV9)@SY23)) | (((ws@a)@SY23) | (((ws@b)@SY23) | ((ws@c)@SY23)))))=$true))),inference(extcnf_forall_pos,[status(thm)],[77])). 0.62/0.81 thf(111,plain,(![SV10:$i]: (((~ (![SY24:$i]: ((~ ((b@SV10)@SY24)) | ((ws@b)@SY24))))=$true))),inference(extcnf_forall_pos,[status(thm)],[78])). 0.62/0.81 thf(112,plain,(![SV11:$i]: (((![SY25:($i>$o)]: ((~ (![SY26:$i]: ((~ ((fool@SV11)@SY26)) | (SY25@SY26)))) | (![SY27:$i]: ((~ ((b@SV11)@SY27)) | (SY25@SY27)))))=$true))),inference(extcnf_forall_pos,[status(thm)],[79])). 0.62/0.81 thf(113,plain,(![SV12:$i]: (((![SY28:($i>$o)]: ((~ (![SY29:$i]: ((~ ((fool@SV12)@SY29)) | (SY28@SY29)))) | (SY28@SV12)))=$true))),inference(extcnf_forall_pos,[status(thm)],[80])). 0.62/0.81 thf(114,plain,(![SV13:$i]: (((![SY30:($i>$o)]: ((~ (![SY31:$i]: ((~ ((b@SV13)@SY31)) | (SY30@SY31)))) | (![SY32:$i]: ((~ ((a@SV13)@SY32)) | (![SX3:$i]: ((~ ((b@SY32)@SX3)) | (SY30@SX3)))))))=$true))),inference(extcnf_forall_pos,[status(thm)],[81])). 0.62/0.81 thf(115,plain,(![SV14:$i]: (((![SY34:$i]: ((~ ((fool@SV14)@SY34)) | ((~ (~ ((ws@b)@SY34))) | (![SX2:$i]: ((~ ((a@SY34)@SX2)) | (~ ((ws@b)@SX2)))))))=$true))),inference(extcnf_forall_pos,[status(thm)],[82])). 0.62/0.81 thf(116,plain,(![SV15:$i]: (((![SY36:$i]: ((~ ((fool@SV15)@SY36)) | ((~ ((ws@b)@SY36)) | (![SX2:$i]: ((~ ((c@SY36)@SX2)) | ((ws@b)@SX2))))))=$true))),inference(extcnf_forall_pos,[status(thm)],[83])). 0.62/0.81 thf(117,plain,(![SV16:$i]: (((![SY38:$i]: ((~ ((fool@SV16)@SY38)) | ((~ ((ws@b)@SY38)) | (![SX2:$i]: ((~ ((a@SY38)@SX2)) | ((ws@b)@SX2))))))=$true))),inference(extcnf_forall_pos,[status(thm)],[84])). 0.62/0.81 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((SV58@((sK14_SY134@SV58)@SV28))=$false))),inference(extcnf_or_pos,[status(thm)],[449])). 0.62/0.81 thf(476,plain,(![SV66:$i,SV59:($i>$o),SV104:$i,SV29:$i]: ((((c@SV29)@SV104)=$false) | ((~ (![SY166:$i]: ((~ ((b@SV104)@SY166)) | (SV59@SY166))))=$true) | ((SV59@SV66)=$true) | (((b@SV29)@SV66)=$false))),inference(extcnf_not_pos,[status(thm)],[450])). 0.62/0.81 thf(477,plain,(![SV67:$i,SV60:($i>$o),SV105:$i,SV30:$i]: ((((a@SV30)@SV105)=$false) | ((~ (![SY167:$i]: ((~ ((b@SV105)@SY167)) | (SV60@SY167))))=$true) | ((SV60@SV67)=$true) | (((b@SV30)@SV67)=$false))),inference(extcnf_not_pos,[status(thm)],[451])). 0.62/0.81 thf(478,plain,(![SV31:$i,SV61:($i>$o),SV120:$i,SV100:$i]: ((((~ ((c@SV100)@SV120)) | (SV61@SV120))=$true) | (((a@SV31)@SV100)=$false) | (((c@SV31)@((sK15_SY143@SV61)@SV31))=$true))),inference(extcnf_forall_pos,[status(thm)],[452])). 0.62/0.81 thf(479,plain,(![SV31:$i,SV61:($i>$o),SV113:$i,SV84:$i]: (((~ ((c@SV84)@SV113))=$true) | ((SV61@SV113)=$true) | (((a@SV31)@SV84)=$false) | ((SV61@((sK15_SY143@SV61)@SV31))=$false))),inference(extcnf_or_pos,[status(thm)],[453])). 0.62/0.81 thf(480,plain,(![SV68:$i,SV62:($i>$o),SV106:$i,SV32:$i]: ((((b@SV32)@SV106)=$false) | ((~ (![SY168:$i]: ((~ ((a@SV106)@SY168)) | (SV62@SY168))))=$true) | ((SV62@SV68)=$true) | (((a@SV32)@SV68)=$false))),inference(extcnf_not_pos,[status(thm)],[454])). 0.62/0.81 thf(481,plain,(![SV63:$i,SV4:$i,SV36:($i>$o),SV101:$i]: (((![SY163:$i]: ((~ ((c@SV101)@SY163)) | (SV36@SY163)))=$false) | (((a@SV4)@SV101)=$false) | ((SV36@SV63)=$true) | (((c@SV4)@SV63)=$false))),inference(extcnf_not_pos,[status(thm)],[456])). 0.62/0.81 thf(482,plain,(![SV5:$i,SV37:($i>$o),SV114:$i,SV87:$i]: (((~ ((fool@SV87)@SV114))=$true) | ((SV37@SV114)=$true) | (((fool@SV5)@SV87)=$false) | (((fool@SV5)@((sK6_SY97@SV37)@SV5))=$true))),inference(extcnf_or_pos,[status(thm)],[457])). 0.62/0.81 thf(483,plain,(![SV5:$i,SV37:($i>$o),SV107:$i,SV71:$i]: ((((fool@SV71)@SV107)=$false) | ((SV37@SV107)=$true) | (((fool@SV5)@SV71)=$false) | ((SV37@((sK6_SY97@SV37)@SV5))=$false))),inference(extcnf_not_pos,[status(thm)],[458])). 0.62/0.81 thf(484,plain,(![SV6:$i,SV38:($i>$o),SV115:$i,SV88:$i]: (((~ ((a@SV88)@SV115))=$true) | ((SV38@SV115)=$true) | (((c@SV6)@SV88)=$false) | (((a@SV6)@((sK7_SY100@SV38)@SV6))=$true))),inference(extcnf_or_pos,[status(thm)],[459])). 0.62/0.81 thf(485,plain,(![SV6:$i,SV38:($i>$o),SV108:$i,SV72:$i]: ((((a@SV72)@SV108)=$false) | ((SV38@SV108)=$true) | (((c@SV6)@SV72)=$false) | ((SV38@((sK7_SY100@SV38)@SV6))=$false))),inference(extcnf_not_pos,[status(thm)],[460])). 0.62/0.81 thf(486,plain,(![SV13:$i,SV44:($i>$o),SV116:$i,SV91:$i]: (((~ ((b@SV91)@SV116))=$true) | ((SV44@SV116)=$true) | (((a@SV13)@SV91)=$false) | (((b@SV13)@((sK10_SY108@SV44)@SV13))=$true))),inference(extcnf_or_pos,[status(thm)],[462])). 0.62/0.81 thf(487,plain,(![SV13:$i,SV44:($i>$o),SV109:$i,SV75:$i]: ((((b@SV75)@SV109)=$false) | ((SV44@SV109)=$true) | (((a@SV13)@SV75)=$false) | ((SV44@((sK10_SY108@SV44)@SV13))=$false))),inference(extcnf_not_pos,[status(thm)],[463])). 0.62/0.81 thf(488,plain,(![SV64:$i,SV18:$i,SV49:($i>$o),SV102:$i]: (((![SY164:$i]: ((~ ((a@SV102)@SY164)) | (SV49@SY164)))=$false) | (((c@SV18)@SV102)=$false) | ((SV49@SV64)=$true) | (((a@SV18)@SV64)=$false))),inference(extcnf_not_pos,[status(thm)],[465])). 0.62/0.81 thf(489,plain,(![SV19:$i,SV50:($i>$o),SV117:$i,SV93:$i]: (((~ ((a@SV93)@SV117))=$true) | ((SV50@SV117)=$true) | (((b@SV19)@SV93)=$false) | (((a@SV19)@((sK11_SY118@SV50)@SV19))=$true))),inference(extcnf_or_pos,[status(thm)],[466])). 0.62/0.81 thf(490,plain,(![SV19:$i,SV50:($i>$o),SV110:$i,SV79:$i]: ((((a@SV79)@SV110)=$false) | ((SV50@SV110)=$true) | (((b@SV19)@SV79)=$false) | ((SV50@((sK11_SY118@SV50)@SV19))=$false))),inference(extcnf_not_pos,[status(thm)],[467])). 0.62/0.81 thf(491,plain,(![SV65:$i,SV20:$i,SV51:($i>$o),SV103:$i]: (((![SY165:$i]: ((~ ((c@SV103)@SY165)) | (SV51@SY165)))=$false) | (((b@SV20)@SV103)=$false) | ((SV51@SV65)=$true) | (((c@SV20)@SV65)=$false))),inference(extcnf_not_pos,[status(thm)],[468])). 0.62/0.81 thf(492,plain,(![SV24:$i,SV55:($i>$o),SV118:$i,SV96:$i]: (((~ ((b@SV96)@SV118))=$true) | ((SV55@SV118)=$true) | (((c@SV24)@SV96)=$false) | (((b@SV24)@((sK12_SY127@SV55)@SV24))=$true))),inference(extcnf_or_pos,[status(thm)],[471])). 0.62/0.81 thf(493,plain,(![SV24:$i,SV55:($i>$o),SV111:$i,SV81:$i]: ((((b@SV81)@SV111)=$false) | ((SV55@SV111)=$true) | (((c@SV24)@SV81)=$false) | ((SV55@((sK12_SY127@SV55)@SV24))=$false))),inference(extcnf_not_pos,[status(thm)],[472])). 0.62/0.81 thf(494,plain,(![SV28:$i,SV58:($i>$o),SV119:$i,SV99:$i]: (((~ ((c@SV99)@SV119))=$true) | ((SV58@SV119)=$true) | (((b@SV28)@SV99)=$false) | (((c@SV28)@((sK14_SY134@SV58)@SV28))=$true))),inference(extcnf_or_pos,[status(thm)],[474])). 0.62/0.81 thf(495,plain,(![SV28:$i,SV58:($i>$o),SV112:$i,SV83:$i]: ((((c@SV83)@SV112)=$false) | ((SV58@SV112)=$true) | (((b@SV28)@SV83)=$false) | ((SV58@((sK14_SY134@SV58)@SV28))=$false))),inference(extcnf_not_pos,[status(thm)],[475])). 0.62/0.81 thf(496,plain,(![SV66:$i,SV29:$i,SV59:($i>$o),SV104:$i]: (((![SY166:$i]: ((~ ((b@SV104)@SY166)) | (SV59@SY166)))=$false) | (((c@SV29)@SV104)=$false) | ((SV59@SV66)=$true) | (((b@SV29)@SV66)=$false))),inference(extcnf_not_pos,[status(thm)],[476])). 0.62/0.81 thf(497,plain,(![SV67:$i,SV30:$i,SV60:($i>$o),SV105:$i]: (((![SY167:$i]: ((~ ((b@SV105)@SY167)) | (SV60@SY167)))=$false) | (((a@SV30)@SV105)=$false) | ((SV60@SV67)=$true) | (((b@SV30)@SV67)=$false))),inference(extcnf_not_pos,[status(thm)],[477])). 0.62/0.81 thf(498,plain,(![SV31:$i,SV61:($i>$o),SV120:$i,SV100:$i]: (((~ ((c@SV100)@SV120))=$true) | ((SV61@SV120)=$true) | (((a@SV31)@SV100)=$false) | (((c@SV31)@((sK15_SY143@SV61)@SV31))=$true))),inference(extcnf_or_pos,[status(thm)],[478])). 0.62/0.81 thf(499,plain,(![SV31:$i,SV61:($i>$o),SV113:$i,SV84:$i]: ((((c@SV84)@SV113)=$false) | ((SV61@SV113)=$true) | (((a@SV31)@SV84)=$false) | ((SV61@((sK15_SY143@SV61)@SV31))=$false))),inference(extcnf_not_pos,[status(thm)],[479])). 0.62/0.81 thf(500,plain,(![SV68:$i,SV32:$i,SV62:($i>$o),SV106:$i]: (((![SY168:$i]: ((~ ((a@SV106)@SY168)) | (SV62@SY168)))=$false) | (((b@SV32)@SV106)=$false) | ((SV62@SV68)=$true) | (((a@SV32)@SV68)=$false))),inference(extcnf_not_pos,[status(thm)],[480])). 0.62/0.81 thf(501,plain,(![SV36:($i>$o),SV4:$i,SV63:$i,SV101:$i]: ((((~ ((c@SV101)@((((sK16_SY163@SV63)@SV4)@SV36)@SV101))) | (SV36@((((sK16_SY163@SV63)@SV4)@SV36)@SV101)))=$false) | (((a@SV4)@SV101)=$false) | ((SV36@SV63)=$true) | (((c@SV4)@SV63)=$false))),inference(extcnf_forall_neg,[status(esa)],[481])). 0.62/0.81 thf(502,plain,(![SV5:$i,SV37:($i>$o),SV114:$i,SV87:$i]: ((((fool@SV87)@SV114)=$false) | ((SV37@SV114)=$true) | (((fool@SV5)@SV87)=$false) | (((fool@SV5)@((sK6_SY97@SV37)@SV5))=$true))),inference(extcnf_not_pos,[status(thm)],[482])). 0.62/0.81 thf(503,plain,(![SV6:$i,SV38:($i>$o),SV115:$i,SV88:$i]: ((((a@SV88)@SV115)=$false) | ((SV38@SV115)=$true) | (((c@SV6)@SV88)=$false) | (((a@SV6)@((sK7_SY100@SV38)@SV6))=$true))),inference(extcnf_not_pos,[status(thm)],[484])). 0.62/0.81 thf(504,plain,(![SV13:$i,SV44:($i>$o),SV116:$i,SV91:$i]: ((((b@SV91)@SV116)=$false) | ((SV44@SV116)=$true) | (((a@SV13)@SV91)=$false) | (((b@SV13)@((sK10_SY108@SV44)@SV13))=$true))),inference(extcnf_not_pos,[status(thm)],[486])). 0.62/0.81 thf(505,plain,(![SV49:($i>$o),SV18:$i,SV64:$i,SV102:$i]: ((((~ ((a@SV102)@((((sK17_SY164@SV64)@SV18)@SV49)@SV102))) | (SV49@((((sK17_SY164@SV64)@SV18)@SV49)@SV102)))=$false) | (((c@SV18)@SV102)=$false) | ((SV49@SV64)=$true) | (((a@SV18)@SV64)=$false))),inference(extcnf_forall_neg,[status(esa)],[488])). 0.62/0.81 thf(506,plain,(![SV19:$i,SV50:($i>$o),SV117:$i,SV93:$i]: ((((a@SV93)@SV117)=$false) | ((SV50@SV117)=$true) | (((b@SV19)@SV93)=$false) | (((a@SV19)@((sK11_SY118@SV50)@SV19))=$true))),inference(extcnf_not_pos,[status(thm)],[489])). 0.62/0.81 thf(507,plain,(![SV51:($i>$o),SV20:$i,SV65:$i,SV103:$i]: ((((~ ((c@SV103)@((((sK18_SY165@SV65)@SV20)@SV51)@SV103))) | (SV51@((((sK18_SY165@SV65)@SV20)@SV51)@SV103)))=$false) | (((b@SV20)@SV103)=$false) | ((SV51@SV65)=$true) | (((c@SV20)@SV65)=$false))),inference(extcnf_forall_neg,[status(esa)],[491])). 0.62/0.81 thf(508,plain,(![SV24:$i,SV55:($i>$o),SV118:$i,SV96:$i]: ((((b@SV96)@SV118)=$false) | ((SV55@SV118)=$true) | (((c@SV24)@SV96)=$false) | (((b@SV24)@((sK12_SY127@SV55)@SV24))=$true))),inference(extcnf_not_pos,[status(thm)],[492])). 0.62/0.81 thf(509,plain,(![SV28:$i,SV58:($i>$o),SV119:$i,SV99:$i]: ((((c@SV99)@SV119)=$false) | ((SV58@SV119)=$true) | (((b@SV28)@SV99)=$false) | (((c@SV28)@((sK14_SY134@SV58)@SV28))=$true))),inference(extcnf_not_pos,[status(thm)],[494])). 0.62/0.81 thf(510,plain,(![SV59:($i>$o),SV29:$i,SV66:$i,SV104:$i]: ((((~ ((b@SV104)@((((sK19_SY166@SV66)@SV29)@SV59)@SV104))) | (SV59@((((sK19_SY166@SV66)@SV29)@SV59)@SV104)))=$false) | (((c@SV29)@SV104)=$false) | ((SV59@SV66)=$true) | (((b@SV29)@SV66)=$false))),inference(extcnf_forall_neg,[status(esa)],[496])). 0.62/0.81 thf(511,plain,(![SV60:($i>$o),SV30:$i,SV67:$i,SV105:$i]: ((((~ ((b@SV105)@((((sK20_SY167@SV67)@SV30)@SV60)@SV105))) | (SV60@((((sK20_SY167@SV67)@SV30)@SV60)@SV105)))=$false) | (((a@SV30)@SV105)=$false) | ((SV60@SV67)=$true) | (((b@SV30)@SV67)=$false))),inference(extcnf_forall_neg,[status(esa)],[497])). 0.62/0.81 thf(512,plain,(![SV31:$i,SV61:($i>$o),SV120:$i,SV100:$i]: ((((c@SV100)@SV120)=$false) | ((SV61@SV120)=$true) | (((a@SV31)@SV100)=$false) | (((c@SV31)@((sK15_SY143@SV61)@SV31))=$true))),inference(extcnf_not_pos,[status(thm)],[498])). 0.62/0.81 thf(513,plain,(![SV62:($i>$o),SV32:$i,SV68:$i,SV106:$i]: ((((~ ((a@SV106)@((((sK21_SY168@SV68)@SV32)@SV62)@SV106))) | (SV62@((((sK21_SY168@SV68)@SV32)@SV62)@SV106)))=$false) | (((b@SV32)@SV106)=$false) | ((SV62@SV68)=$true) | (((a@SV32)@SV68)=$false))),inference(extcnf_forall_neg,[status(esa)],[500])). 0.62/0.81 thf(514,plain,(![SV36:($i>$o),SV4:$i,SV63:$i,SV101:$i]: (((~ ((c@SV101)@((((sK16_SY163@SV63)@SV4)@SV36)@SV101)))=$false) | (((a@SV4)@SV101)=$false) | ((SV36@SV63)=$true) | (((c@SV4)@SV63)=$false))),inference(extcnf_or_neg,[status(thm)],[501])). 0.62/0.81 thf(515,plain,(![SV101:$i,SV4:$i,SV63:$i,SV36:($i>$o)]: (((SV36@((((sK16_SY163@SV63)@SV4)@SV36)@SV101))=$false) | (((a@SV4)@SV101)=$false) | ((SV36@SV63)=$true) | (((c@SV4)@SV63)=$false))),inference(extcnf_or_neg,[status(thm)],[501])). 0.62/0.81 thf(516,plain,(![SV49:($i>$o),SV18:$i,SV64:$i,SV102:$i]: (((~ ((a@SV102)@((((sK17_SY164@SV64)@SV18)@SV49)@SV102)))=$false) | (((c@SV18)@SV102)=$false) | ((SV49@SV64)=$true) | (((a@SV18)@SV64)=$false))),inference(extcnf_or_neg,[status(thm)],[505])). 0.62/0.81 thf(517,plain,(![SV102:$i,SV18:$i,SV64:$i,SV49:($i>$o)]: (((SV49@((((sK17_SY164@SV64)@SV18)@SV49)@SV102))=$false) | (((c@SV18)@SV102)=$false) | ((SV49@SV64)=$true) | (((a@SV18)@SV64)=$false))),inference(extcnf_or_neg,[status(thm)],[505])). 0.62/0.81 thf(518,plain,(![SV51:($i>$o),SV20:$i,SV65:$i,SV103:$i]: (((~ ((c@SV103)@((((sK18_SY165@SV65)@SV20)@SV51)@SV103)))=$false) | (((b@SV20)@SV103)=$false) | ((SV51@SV65)=$true) | (((c@SV20)@SV65)=$false))),inference(extcnf_or_neg,[status(thm)],[507])). 0.62/0.81 thf(519,plain,(![SV103:$i,SV20:$i,SV65:$i,SV51:($i>$o)]: (((SV51@((((sK18_SY165@SV65)@SV20)@SV51)@SV103))=$false) | (((b@SV20)@SV103)=$false) | ((SV51@SV65)=$true) | (((c@SV20)@SV65)=$false))),inference(extcnf_or_neg,[status(thm)],[507])). 0.62/0.81 thf(520,plain,(![SV59:($i>$o),SV29:$i,SV66:$i,SV104:$i]: (((~ ((b@SV104)@((((sK19_SY166@SV66)@SV29)@SV59)@SV104)))=$false) | (((c@SV29)@SV104)=$false) | ((SV59@SV66)=$true) | (((b@SV29)@SV66)=$false))),inference(extcnf_or_neg,[status(thm)],[510])). 0.62/0.81 thf(521,plain,(![SV104:$i,SV29:$i,SV66:$i,SV59:($i>$o)]: (((SV59@((((sK19_SY166@SV66)@SV29)@SV59)@SV104))=$false) | (((c@SV29)@SV104)=$false) | ((SV59@SV66)=$true) | (((b@SV29)@SV66)=$false))),inference(extcnf_or_neg,[status(thm)],[510])). 0.62/0.81 thf(522,plain,(![SV60:($i>$o),SV30:$i,SV67:$i,SV105:$i]: (((~ ((b@SV105)@((((sK20_SY167@SV67)@SV30)@SV60)@SV105)))=$false) | (((a@SV30)@SV105)=$false) | ((SV60@SV67)=$true) | (((b@SV30)@SV67)=$false))),inference(extcnf_or_neg,[status(thm)],[511])). 0.62/0.81 thf(523,plain,(![SV105:$i,SV30:$i,SV67:$i,SV60:($i>$o)]: (((SV60@((((sK20_SY167@SV67)@SV30)@SV60)@SV105))=$false) | (((a@SV30)@SV105)=$false) | ((SV60@SV67)=$true) | (((b@SV30)@SV67)=$false))),inference(extcnf_or_neg,[status(thm)],[511])). 0.62/0.81 thf(524,plain,(![SV62:($i>$o),SV32:$i,SV68:$i,SV106:$i]: (((~ ((a@SV106)@((((sK21_SY168@SV68)@SV32)@SV62)@SV106)))=$false) | (((b@SV32)@SV106)=$false) | ((SV62@SV68)=$true) | (((a@SV32)@SV68)=$false))),inference(extcnf_or_neg,[status(thm)],[513])). 0.62/0.81 thf(525,plain,(![SV106:$i,SV32:$i,SV68:$i,SV62:($i>$o)]: (((SV62@((((sK21_SY168@SV68)@SV32)@SV62)@SV106))=$false) | (((b@SV32)@SV106)=$false) | ((SV62@SV68)=$true) | (((a@SV32)@SV68)=$false))),inference(extcnf_or_neg,[status(thm)],[513])). 0.62/0.81 thf(526,plain,(![SV36:($i>$o),SV4:$i,SV63:$i,SV101:$i]: ((((c@SV101)@((((sK16_SY163@SV63)@SV4)@SV36)@SV101))=$true) | (((a@SV4)@SV101)=$false) | ((SV36@SV63)=$true) | (((c@SV4)@SV63)=$false))),inference(extcnf_not_neg,[status(thm)],[514])). 0.62/0.81 thf(527,plain,(![SV49:($i>$o),SV18:$i,SV64:$i,SV102:$i]: ((((a@SV102)@((((sK17_SY164@SV64)@SV18)@SV49)@SV102))=$true) | (((c@SV18)@SV102)=$false) | ((SV49@SV64)=$true) | (((a@SV18)@SV64)=$false))),inference(extcnf_not_neg,[status(thm)],[516])). 0.62/0.81 thf(528,plain,(![SV51:($i>$o),SV20:$i,SV65:$i,SV103:$i]: ((((c@SV103)@((((sK18_SY165@SV65)@SV20)@SV51)@SV103))=$true) | (((b@SV20)@SV103)=$false) | ((SV51@SV65)=$true) | (((c@SV20)@SV65)=$false))),inference(extcnf_not_neg,[status(thm)],[518])). 0.62/0.81 thf(529,plain,(![SV59:($i>$o),SV29:$i,SV66:$i,SV104:$i]: ((((b@SV104)@((((sK19_SY166@SV66)@SV29)@SV59)@SV104))=$true) | (((c@SV29)@SV104)=$false) | ((SV59@SV66)=$true) | (((b@SV29)@SV66)=$false))),inference(extcnf_not_neg,[status(thm)],[520])). 0.62/0.81 thf(530,plain,(![SV60:($i>$o),SV30:$i,SV67:$i,SV105:$i]: ((((b@SV105)@((((sK20_SY167@SV67)@SV30)@SV60)@SV105))=$true) | (((a@SV30)@SV105)=$false) | ((SV60@SV67)=$true) | (((b@SV30)@SV67)=$false))),inference(extcnf_not_neg,[status(thm)],[522])). 0.62/0.81 thf(531,plain,(![SV62:($i>$o),SV32:$i,SV68:$i,SV106:$i]: ((((a@SV106)@((((sK21_SY168@SV68)@SV32)@SV62)@SV106))=$true) | (((b@SV32)@SV106)=$false) | ((SV62@SV68)=$true) | (((a@SV32)@SV68)=$false))),inference(extcnf_not_neg,[status(thm)],[524])). 0.62/0.81 thf(532,plain,((($false)=$true)),inference(fo_atp_e,[status(thm)],[211,531,530,529,528,527,526,525,523,521,519,517,515,512,509,508,506,504,503,502,499,495,493,490,487,485,483,473,470,469,464,461,455,446,434,427,417,411,406,405,404,400,397,391,389,324,285,281,262,261,246,229,227])). 0.62/0.81 thf(533,plain,($false),inference(solved_all_splits,[solved_all_splits(join,[])],[532])). 0.62/0.81 % SZS output end CNFRefutation 0.62/0.81 0.62/0.81 %**** End of derivation protocol **** 0.62/0.81 %**** no. of clauses in derivation: 533 **** 0.62/0.81 %**** clause counter: 532 **** 0.62/0.81 0.62/0.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:32,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:532,loop_count:0,foatp_calls:1,translation:fof_full) 0.62/0.81 EOF