%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : NUM021^1 : TPTP v7.0.0. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n144.star.cs.uiowa.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz % Memory : 32218.625MB % OS : Linux 3.10.0-693.2.2.el7.x86_64 % CPULimit : 300s % DateTime : Mon Jan 8 13:10:13 EST 2018 % Result : Timeout 290.02s % Output : None % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : NUM021^1 : TPTP v7.0.0. Released v3.6.0. % 0.00/0.04 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % 0.02/0.23 % Computer : n144.star.cs.uiowa.edu % 0.02/0.23 % Model : x86_64 x86_64 % 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz % 0.02/0.23 % Memory : 32218.625MB % 0.02/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 % 0.02/0.23 % CPULimit : 300 % 0.02/0.23 % DateTime : Thu Jan 4 14:50:32 CST 2018 % 0.07/0.23 % CPUTime : % 0.07/0.26 Python 2.7.13 % 0.33/0.76 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/'] % 0.33/0.76 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/NUM006^0.ax, trying next directory % 0.33/0.76 FOF formula (<kernel.Constant object at 0x2aace77adcf8>, <kernel.DependentProduct object at 0x2aace7ecbc20>) of role type named zero % 0.33/0.76 Using role type % 0.33/0.76 Declaring zero:((fofType->fofType)->(fofType->fofType)) % 0.33/0.76 FOF formula (<kernel.Constant object at 0x2aace77ad170>, <kernel.DependentProduct object at 0x2aace77ad368>) of role type named one % 0.33/0.76 Using role type % 0.33/0.76 Declaring one:((fofType->fofType)->(fofType->fofType)) % 0.33/0.76 FOF formula (<kernel.Constant object at 0x2aace7ecbc20>, <kernel.DependentProduct object at 0x2aace77ad368>) of role type named two % 0.33/0.76 Using role type % 0.33/0.76 Declaring two:((fofType->fofType)->(fofType->fofType)) % 0.33/0.76 FOF formula (<kernel.Constant object at 0x2aace77ad5a8>, <kernel.DependentProduct object at 0x2aace744c6c8>) of role type named three % 0.33/0.76 Using role type % 0.33/0.76 Declaring three:((fofType->fofType)->(fofType->fofType)) % 0.33/0.76 FOF formula (<kernel.Constant object at 0x2aace77ad560>, <kernel.DependentProduct object at 0x2aace744cbd8>) of role type named four % 0.33/0.76 Using role type % 0.33/0.76 Declaring four:((fofType->fofType)->(fofType->fofType)) % 0.33/0.76 FOF formula (<kernel.Constant object at 0x2aace77ad368>, <kernel.DependentProduct object at 0x2aace744c368>) of role type named five % 0.33/0.76 Using role type % 0.33/0.76 Declaring five:((fofType->fofType)->(fofType->fofType)) % 0.33/0.76 FOF formula (<kernel.Constant object at 0x2aace77ad560>, <kernel.DependentProduct object at 0x2aace744c4d0>) of role type named six % 0.33/0.76 Using role type % 0.33/0.76 Declaring six:((fofType->fofType)->(fofType->fofType)) % 0.33/0.76 FOF formula (<kernel.Constant object at 0x2aace77ad5a8>, <kernel.DependentProduct object at 0x2aace744cb90>) of role type named seven % 0.33/0.76 Using role type % 0.33/0.76 Declaring seven:((fofType->fofType)->(fofType->fofType)) % 0.33/0.76 FOF formula (<kernel.Constant object at 0x2aace77ad560>, <kernel.DependentProduct object at 0x2aace744c6c8>) of role type named eight % 0.33/0.76 Using role type % 0.33/0.76 Declaring eight:((fofType->fofType)->(fofType->fofType)) % 0.33/0.76 FOF formula (<kernel.Constant object at 0x2aace77ad5a8>, <kernel.DependentProduct object at 0x2aace744cbd8>) of role type named nine % 0.33/0.76 Using role type % 0.33/0.76 Declaring nine:((fofType->fofType)->(fofType->fofType)) % 0.33/0.76 FOF formula (<kernel.Constant object at 0x2aace77ad5a8>, <kernel.DependentProduct object at 0x2aace744c320>) of role type named ten % 0.33/0.76 Using role type % 0.33/0.76 Declaring ten:((fofType->fofType)->(fofType->fofType)) % 0.33/0.76 FOF formula (<kernel.Constant object at 0x2aace7ea4ea8>, <kernel.DependentProduct object at 0x2aace744c320>) of role type named succ % 0.33/0.76 Using role type % 0.33/0.76 Declaring succ:(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))) % 0.33/0.76 FOF formula (<kernel.Constant object at 0x2aace7ea4fc8>, <kernel.DependentProduct object at 0x2aace744cb90>) of role type named plus % 0.33/0.76 Using role type % 0.33/0.76 Declaring plus:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))) % 0.33/0.76 FOF formula (<kernel.Constant object at 0x2aace77fe6c8>, <kernel.DependentProduct object at 0x2aace744cb90>) of role type named mult % 0.33/0.76 Using role type % 0.33/0.76 Declaring mult:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))) % 0.33/0.76 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) zero) (fun (X:(fofType->fofType)) (Y:fofType)=> Y)) of role definition named zero_ax % 0.33/0.76 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) zero) (fun (X:(fofType->fofType)) (Y:fofType)=> Y)) % 0.33/0.76 Defined: zero:=(fun (X:(fofType->fofType)) (Y:fofType)=> Y) % 0.33/0.76 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) one) (fun (X:(fofType->fofType)) (Y:fofType)=> (X Y))) of role definition named one_ax % 0.33/0.76 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) one) (fun (X:(fofType->fofType)) (Y:fofType)=> (X Y))) % 0.33/0.76 Defined: one:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X Y)) % 0.33/0.76 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) two) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X Y)))) of role definition named two_ax % 0.33/0.77 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) two) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X Y)))) % 0.33/0.77 Defined: two:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X Y))) % 0.33/0.77 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) three) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X Y))))) of role definition named three_ax % 0.33/0.77 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) three) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X Y))))) % 0.33/0.77 Defined: three:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X Y)))) % 0.33/0.77 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) four) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X Y)))))) of role definition named four_ax % 0.33/0.77 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) four) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X Y)))))) % 0.33/0.77 Defined: four:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X Y))))) % 0.33/0.77 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) five) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X Y))))))) of role definition named five_ax % 0.33/0.77 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) five) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X Y))))))) % 0.33/0.77 Defined: five:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X Y)))))) % 0.33/0.77 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) six) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X Y)))))))) of role definition named six_ax % 0.33/0.77 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) six) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X Y)))))))) % 0.33/0.77 Defined: six:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X Y))))))) % 0.33/0.77 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) seven) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X Y))))))))) of role definition named seven_ax % 0.33/0.77 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) seven) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X Y))))))))) % 0.33/0.77 Defined: seven:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X Y)))))))) % 0.33/0.77 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) eight) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X Y)))))))))) of role definition named eight_ax % 0.33/0.77 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) eight) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X Y)))))))))) % 0.33/0.77 Defined: eight:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X Y))))))))) % 0.33/0.77 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) nine) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X Y))))))))))) of role definition named nine_ax % 0.33/0.77 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) nine) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X Y))))))))))) % 0.33/0.77 Defined: nine:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X Y)))))))))) % 0.33/0.77 FOF formula (((eq ((fofType->fofType)->(fofType->fofType))) ten) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X (X Y)))))))))))) of role definition named ten_ax % 0.33/0.77 A new definition: (((eq ((fofType->fofType)->(fofType->fofType))) ten) (fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X (X Y)))))))))))) % 0.33/0.77 Defined: ten:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X (X Y))))))))))) % 0.33/0.77 FOF formula (((eq (((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))) succ) (fun (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> (X ((N X) Y)))) of role definition named succ_ax % 0.33/0.77 A new definition: (((eq (((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))) succ) (fun (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> (X ((N X) Y)))) % 0.33/0.77 Defined: succ:=(fun (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> (X ((N X) Y))) % 0.33/0.77 FOF formula (((eq (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) plus) (fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M X) ((N X) Y)))) of role definition named plus_ax % 0.33/0.78 A new definition: (((eq (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) plus) (fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M X) ((N X) Y)))) % 0.33/0.78 Defined: plus:=(fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M X) ((N X) Y))) % 0.33/0.78 FOF formula (((eq (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) mult) (fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M (N X)) Y))) of role definition named mult_ax % 0.33/0.78 A new definition: (((eq (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) mult) (fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M (N X)) Y))) % 0.33/0.78 Defined: mult:=(fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M (N X)) Y)) % 0.33/0.78 FOF formula ((ex (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) of role conjecture named thm % 0.33/0.78 Conjecture to prove = ((ex (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))):Prop % 0.33/0.78 Parameter fofType_DUMMY:fofType. % 0.33/0.78 We need to prove ['((ex (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three))))'] % 0.33/0.78 Parameter fofType:Type. % 0.33/0.78 Definition zero:=(fun (X:(fofType->fofType)) (Y:fofType)=> Y):((fofType->fofType)->(fofType->fofType)). % 0.33/0.78 Definition one:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X Y)):((fofType->fofType)->(fofType->fofType)). % 0.33/0.78 Definition two:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X Y))):((fofType->fofType)->(fofType->fofType)). % 0.33/0.78 Definition three:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X Y)))):((fofType->fofType)->(fofType->fofType)). % 0.33/0.78 Definition four:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X Y))))):((fofType->fofType)->(fofType->fofType)). % 0.33/0.78 Definition five:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X Y)))))):((fofType->fofType)->(fofType->fofType)). % 0.33/0.78 Definition six:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X Y))))))):((fofType->fofType)->(fofType->fofType)). % 0.33/0.78 Definition seven:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X Y)))))))):((fofType->fofType)->(fofType->fofType)). % 0.33/0.78 Definition eight:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X Y))))))))):((fofType->fofType)->(fofType->fofType)). % 0.33/0.78 Definition nine:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X Y)))))))))):((fofType->fofType)->(fofType->fofType)). % 8.16/8.60 Definition ten:=(fun (X:(fofType->fofType)) (Y:fofType)=> (X (X (X (X (X (X (X (X (X (X Y))))))))))):((fofType->fofType)->(fofType->fofType)). % 8.16/8.60 Definition succ:=(fun (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> (X ((N X) Y))):(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))). % 8.16/8.60 Definition plus:=(fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M X) ((N X) Y))):(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))). % 8.16/8.60 Definition mult:=(fun (M:((fofType->fofType)->(fofType->fofType))) (N:((fofType->fofType)->(fofType->fofType))) (X:(fofType->fofType)) (Y:fofType)=> ((M (N X)) Y)):(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))). % 8.16/8.60 Trying to prove ((ex (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) % 8.16/8.60 Found eq_ref00:=(eq_ref0 ((x two) three)):(((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) ((x two) three)) % 8.16/8.60 Found (eq_ref0 ((x two) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) five) % 8.16/8.60 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((x two) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) five) % 8.16/8.60 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((x two) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) five) % 8.16/8.60 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((x two) three)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) five) % 8.16/8.60 Found eq_ref00:=(eq_ref0 ((x one) two)):(((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) ((x one) two)) % 8.16/8.60 Found (eq_ref0 ((x one) two)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three) % 8.16/8.60 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((x one) two)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three) % 8.16/8.60 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((x one) two)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three) % 8.16/8.60 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((x one) two)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three) % 8.16/8.60 Found eta_expansion000:=(eta_expansion00 (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))):(((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) (fun (x:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)))) % 8.16/8.60 Found (eta_expansion00 (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) b) % 8.16/8.61 Found ((eta_expansion0 Prop) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) b) % 8.16/8.61 Found (((eta_expansion (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) Prop) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) b) % 8.16/8.61 Found (((eta_expansion (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) Prop) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) b) % 8.16/8.61 Found (((eta_expansion (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) Prop) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) b) % 21.31/21.76 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x)) % 21.31/21.76 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three))) % 21.31/21.76 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three))) % 21.31/21.76 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three))) % 21.31/21.76 Found (fun (x:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three))) % 21.31/21.76 Found (fun (x:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((eq_ref Prop) (f x))) as proof of (forall (x:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))), (((eq Prop) (f x)) ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)))) % 21.31/21.76 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x)) % 21.31/21.76 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three))) % 21.31/21.76 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three))) % 21.31/21.76 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three))) % 21.31/21.76 Found (fun (x:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three))) % 21.31/21.76 Found (fun (x:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((eq_ref Prop) (f x))) as proof of (forall (x:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))), (((eq Prop) (f x)) ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((x two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)))) % 21.31/21.76 Found x01:(P ((x one) two)) % 21.31/21.76 Found (fun (x01:(P ((x one) two)))=> x01) as proof of (P ((x one) two)) % 21.31/21.76 Found (fun (x01:(P ((x one) two)))=> x01) as proof of (P0 ((x one) two)) % 21.31/21.76 Found x01:(P ((x one) two)) % 21.31/21.76 Found (fun (x01:(P ((x one) two)))=> x01) as proof of (P ((x one) two)) % 21.31/21.76 Found (fun (x01:(P ((x one) two)))=> x01) as proof of (P0 ((x one) two)) % 21.31/21.76 Found x01:(P ((x one) two)) % 21.31/21.76 Found (fun (x01:(P ((x one) two)))=> x01) as proof of (P ((x one) two)) % 21.31/21.76 Found (fun (x01:(P ((x one) two)))=> x01) as proof of (P0 ((x one) two)) % 21.31/21.76 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->(fofType->fofType))) b) b) % 21.31/21.76 Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) three) % 21.31/21.76 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) three) % 21.31/21.76 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) three) % 21.31/21.76 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) three) % 47.72/48.19 Found eq_ref00:=(eq_ref0 ((x one) two)):(((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) ((x one) two)) % 47.72/48.19 Found (eq_ref0 ((x one) two)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) b) % 47.72/48.19 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((x one) two)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) b) % 47.72/48.19 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((x one) two)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) b) % 47.72/48.19 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) ((x one) two)) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) b) % 47.72/48.19 Found x01:(P ((x one) two)) % 47.72/48.19 Found (fun (x01:(P ((x one) two)))=> x01) as proof of (P ((x one) two)) % 47.72/48.19 Found (fun (x01:(P ((x one) two)))=> x01) as proof of (P0 ((x one) two)) % 47.72/48.19 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->(fofType->fofType))) b) b) % 47.72/48.19 Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((x one) two)) % 47.72/48.19 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((x one) two)) % 47.72/48.19 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((x one) two)) % 47.72/48.19 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) b) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) b) ((x one) two)) % 47.72/48.19 Found eq_ref00:=(eq_ref0 three):(((eq ((fofType->fofType)->(fofType->fofType))) three) three) % 47.72/48.19 Found (eq_ref0 three) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) three) b) % 47.72/48.19 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) three) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) three) b) % 47.72/48.19 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) three) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) three) b) % 47.72/48.19 Found ((eq_ref ((fofType->fofType)->(fofType->fofType))) three) as proof of (((eq ((fofType->fofType)->(fofType->fofType))) three) b) % 47.72/48.19 Found x01:(P three) % 47.72/48.19 Found (fun (x01:(P three))=> x01) as proof of (P three) % 47.72/48.19 Found (fun (x01:(P three))=> x01) as proof of (P0 three) % 47.72/48.19 Found x01:(P three) % 47.72/48.19 Found (fun (x01:(P three))=> x01) as proof of (P three) % 47.72/48.19 Found (fun (x01:(P three))=> x01) as proof of (P0 three) % 47.72/48.19 Found x11:(P (((x one) two) x0)) % 47.72/48.19 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P (((x one) two) x0)) % 47.72/48.19 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P0 (((x one) two) x0)) % 47.72/48.19 Found x11:(P (((x one) two) x0)) % 47.72/48.19 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P (((x one) two) x0)) % 47.72/48.19 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P0 (((x one) two) x0)) % 47.72/48.19 Found x01:(P three) % 47.72/48.19 Found (fun (x01:(P three))=> x01) as proof of (P three) % 47.72/48.19 Found (fun (x01:(P three))=> x01) as proof of (P0 three) % 47.72/48.19 Found eta_expansion000:=(eta_expansion00 (((x one) two) x0)):(((eq (fofType->fofType)) (((x one) two) x0)) (fun (x1:fofType)=> ((((x one) two) x0) x1))) % 47.72/48.19 Found (eta_expansion00 (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b) % 47.72/48.19 Found ((eta_expansion0 fofType) (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b) % 47.72/48.19 Found (((eta_expansion fofType) fofType) (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b) % 47.72/48.19 Found (((eta_expansion fofType) fofType) (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b) % 47.72/48.19 Found (((eta_expansion fofType) fofType) (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b) % 47.72/48.19 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x))) % 47.72/48.19 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (three x0)) % 47.72/48.19 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (three x0)) % 47.72/48.19 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (three x0)) % 47.72/48.19 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (three x0)) % 47.72/48.19 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (three x0)) % 100.79/101.29 Found eq_ref00:=(eq_ref0 (((x one) two) x0)):(((eq (fofType->fofType)) (((x one) two) x0)) (((x one) two) x0)) % 100.79/101.29 Found (eq_ref0 (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b) % 100.79/101.29 Found ((eq_ref (fofType->fofType)) (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b) % 100.79/101.29 Found ((eq_ref (fofType->fofType)) (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b) % 100.79/101.29 Found ((eq_ref (fofType->fofType)) (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b) % 100.79/101.29 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x))) % 100.79/101.29 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (three x0)) % 100.79/101.29 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (three x0)) % 100.79/101.29 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (three x0)) % 100.79/101.29 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (three x0)) % 100.79/101.29 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (three x0)) % 100.79/101.29 Found x11:(P (((x one) two) x0)) % 100.79/101.29 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P (((x one) two) x0)) % 100.79/101.29 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P0 (((x one) two) x0)) % 100.79/101.29 Found x11:(P (((x one) two) x0)) % 100.79/101.29 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P (((x one) two) x0)) % 100.79/101.29 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P0 (((x one) two) x0)) % 100.79/101.29 Found x11:(P (((x one) two) x0)) % 100.79/101.29 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P (((x one) two) x0)) % 100.79/101.29 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P0 (((x one) two) x0)) % 100.79/101.29 Found x11:(P (((x one) two) x0)) % 100.79/101.29 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P (((x one) two) x0)) % 100.79/101.29 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P0 (((x one) two) x0)) % 100.79/101.29 Found x11:(P ((((x one) two) x0) y)) % 100.79/101.29 Found (fun (x11:(P ((((x one) two) x0) y)))=> x11) as proof of (P ((((x one) two) x0) y)) % 100.79/101.29 Found (fun (x11:(P ((((x one) two) x0) y)))=> x11) as proof of (P0 ((((x one) two) x0) y)) % 100.79/101.29 Found eq_ref00:=(eq_ref0 ((((x one) two) x0) y)):(((eq fofType) ((((x one) two) x0) y)) ((((x one) two) x0) y)) % 100.79/101.29 Found (eq_ref0 ((((x one) two) x0) y)) as proof of (((eq fofType) ((((x one) two) x0) y)) b) % 100.79/101.29 Found ((eq_ref fofType) ((((x one) two) x0) y)) as proof of (((eq fofType) ((((x one) two) x0) y)) b) % 100.79/101.29 Found ((eq_ref fofType) ((((x one) two) x0) y)) as proof of (((eq fofType) ((((x one) two) x0) y)) b) % 100.79/101.29 Found ((eq_ref fofType) ((((x one) two) x0) y)) as proof of (((eq fofType) ((((x one) two) x0) y)) b) % 100.79/101.29 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 100.79/101.29 Found (eq_ref0 b) as proof of (((eq fofType) b) ((three x0) y)) % 100.79/101.29 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) y)) % 100.79/101.29 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) y)) % 100.79/101.29 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) y)) % 100.79/101.29 Found x11:(P (three x0)) % 100.79/101.29 Found (fun (x11:(P (three x0)))=> x11) as proof of (P (three x0)) % 100.79/101.29 Found (fun (x11:(P (three x0)))=> x11) as proof of (P0 (three x0)) % 100.79/101.29 Found x11:(P (three x0)) % 100.79/101.29 Found (fun (x11:(P (three x0)))=> x11) as proof of (P (three x0)) % 100.79/101.29 Found (fun (x11:(P (three x0)))=> x11) as proof of (P0 (three x0)) % 100.79/101.29 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x))) % 100.79/101.29 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0)) % 100.79/101.29 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0)) % 100.79/101.29 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0)) % 100.79/101.29 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0)) % 100.79/101.29 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0)) % 100.79/101.29 Found eta_expansion000:=(eta_expansion00 (three x0)):(((eq (fofType->fofType)) (three x0)) (fun (x:fofType)=> ((three x0) x))) % 100.79/101.29 Found (eta_expansion00 (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b) % 102.76/103.25 Found ((eta_expansion0 fofType) (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b) % 102.76/103.25 Found (((eta_expansion fofType) fofType) (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b) % 102.76/103.25 Found (((eta_expansion fofType) fofType) (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b) % 102.76/103.25 Found (((eta_expansion fofType) fofType) (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b) % 102.76/103.25 Found eq_ref00:=(eq_ref0 (three x0)):(((eq (fofType->fofType)) (three x0)) (three x0)) % 102.76/103.25 Found (eq_ref0 (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b) % 102.76/103.25 Found ((eq_ref (fofType->fofType)) (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b) % 102.76/103.25 Found ((eq_ref (fofType->fofType)) (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b) % 102.76/103.25 Found ((eq_ref (fofType->fofType)) (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b) % 102.76/103.25 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x))) % 102.76/103.25 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0)) % 102.76/103.25 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0)) % 102.76/103.25 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0)) % 102.76/103.25 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0)) % 102.76/103.25 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0)) % 102.76/103.25 Found eta_expansion000:=(eta_expansion00 (three x0)):(((eq (fofType->fofType)) (three x0)) (fun (x:fofType)=> ((three x0) x))) % 102.76/103.25 Found (eta_expansion00 (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b) % 102.76/103.25 Found ((eta_expansion0 fofType) (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b) % 102.76/103.25 Found (((eta_expansion fofType) fofType) (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b) % 102.76/103.25 Found (((eta_expansion fofType) fofType) (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b) % 102.76/103.25 Found (((eta_expansion fofType) fofType) (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b) % 102.76/103.25 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x))) % 102.76/103.25 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0)) % 102.76/103.25 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0)) % 102.76/103.25 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0)) % 102.76/103.25 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0)) % 102.76/103.25 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0)) % 102.76/103.25 Found eta_expansion_dep000:=(eta_expansion_dep00 (three x0)):(((eq (fofType->fofType)) (three x0)) (fun (x:fofType)=> ((three x0) x))) % 102.76/103.25 Found (eta_expansion_dep00 (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b) % 102.76/103.25 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b) % 102.76/103.25 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b) % 102.76/103.25 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b) % 102.76/103.25 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (three x0)) as proof of (((eq (fofType->fofType)) (three x0)) b) % 102.76/103.25 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x))) % 102.76/103.25 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0)) % 102.76/103.25 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0)) % 102.76/103.25 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0)) % 102.76/103.25 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0)) % 102.76/103.25 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (((x one) two) x0)) % 120.05/120.56 Found x11:(P (three x0)) % 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P (three x0)) % 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P0 (three x0)) % 120.05/120.56 Found x11:(P (three x0)) % 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P (three x0)) % 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P0 (three x0)) % 120.05/120.56 Found x11:(P (three x0)) % 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P (three x0)) % 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P0 (three x0)) % 120.05/120.56 Found x11:(P (three x0)) % 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P (three x0)) % 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P0 (three x0)) % 120.05/120.56 Found x11:(P (three x0)) % 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P (three x0)) % 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P0 (three x0)) % 120.05/120.56 Found x11:(P (three x0)) % 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P (three x0)) % 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P0 (three x0)) % 120.05/120.56 Found x11:(P (three x0)) % 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P (three x0)) % 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P0 (three x0)) % 120.05/120.56 Found x11:(P (three x0)) % 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P (three x0)) % 120.05/120.56 Found (fun (x11:(P (three x0)))=> x11) as proof of (P0 (three x0)) % 120.05/120.56 Found x21:(P ((((x one) two) x0) x1)) % 120.05/120.56 Found (fun (x21:(P ((((x one) two) x0) x1)))=> x21) as proof of (P ((((x one) two) x0) x1)) % 120.05/120.56 Found (fun (x21:(P ((((x one) two) x0) x1)))=> x21) as proof of (P0 ((((x one) two) x0) x1)) % 120.05/120.56 Found x21:(P ((((x one) two) x0) x1)) % 120.05/120.56 Found (fun (x21:(P ((((x one) two) x0) x1)))=> x21) as proof of (P ((((x one) two) x0) x1)) % 120.05/120.56 Found (fun (x21:(P ((((x one) two) x0) x1)))=> x21) as proof of (P0 ((((x one) two) x0) x1)) % 120.05/120.56 Found x21:(P ((((x one) two) x0) x1)) % 120.05/120.56 Found (fun (x21:(P ((((x one) two) x0) x1)))=> x21) as proof of (P ((((x one) two) x0) x1)) % 120.05/120.56 Found (fun (x21:(P ((((x one) two) x0) x1)))=> x21) as proof of (P0 ((((x one) two) x0) x1)) % 120.05/120.56 Found x21:(P ((((x one) two) x0) x1)) % 120.05/120.56 Found (fun (x21:(P ((((x one) two) x0) x1)))=> x21) as proof of (P ((((x one) two) x0) x1)) % 120.05/120.56 Found (fun (x21:(P ((((x one) two) x0) x1)))=> x21) as proof of (P0 ((((x one) two) x0) x1)) % 120.05/120.56 Found x11:(P ((three x0) y)) % 120.05/120.56 Found (fun (x11:(P ((three x0) y)))=> x11) as proof of (P ((three x0) y)) % 120.05/120.56 Found (fun (x11:(P ((three x0) y)))=> x11) as proof of (P0 ((three x0) y)) % 120.05/120.56 Found eq_ref00:=(eq_ref0 ((((x one) two) x0) x1)):(((eq fofType) ((((x one) two) x0) x1)) ((((x one) two) x0) x1)) % 120.05/120.56 Found (eq_ref0 ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b) % 120.05/120.56 Found ((eq_ref fofType) ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b) % 120.05/120.56 Found ((eq_ref fofType) ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b) % 120.05/120.56 Found ((eq_ref fofType) ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b) % 120.05/120.56 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 120.05/120.56 Found (eq_ref0 b) as proof of (((eq fofType) b) ((three x0) x1)) % 120.05/120.56 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) x1)) % 120.05/120.56 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) x1)) % 120.05/120.56 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) x1)) % 120.05/120.56 Found eq_ref00:=(eq_ref0 ((((x one) two) x0) x1)):(((eq fofType) ((((x one) two) x0) x1)) ((((x one) two) x0) x1)) % 120.05/120.56 Found (eq_ref0 ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b) % 120.05/120.56 Found ((eq_ref fofType) ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b) % 120.05/120.56 Found ((eq_ref fofType) ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b) % 120.05/120.56 Found ((eq_ref fofType) ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b) % 120.05/120.56 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 120.05/120.56 Found (eq_ref0 b) as proof of (((eq fofType) b) ((three x0) x1)) % 120.05/120.56 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) x1)) % 120.05/120.56 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) x1)) % 120.05/120.56 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) x1)) % 120.05/120.56 Found eq_ref00:=(eq_ref0 ((((x one) two) x0) x1)):(((eq fofType) ((((x one) two) x0) x1)) ((((x one) two) x0) x1)) % 200.88/201.41 Found (eq_ref0 ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b) % 200.88/201.41 Found ((eq_ref fofType) ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b) % 200.88/201.41 Found ((eq_ref fofType) ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b) % 200.88/201.41 Found ((eq_ref fofType) ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b) % 200.88/201.41 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 200.88/201.41 Found (eq_ref0 b) as proof of (((eq fofType) b) ((three x0) x1)) % 200.88/201.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) x1)) % 200.88/201.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) x1)) % 200.88/201.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) x1)) % 200.88/201.41 Found eq_ref00:=(eq_ref0 ((((x one) two) x0) x1)):(((eq fofType) ((((x one) two) x0) x1)) ((((x one) two) x0) x1)) % 200.88/201.41 Found (eq_ref0 ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b) % 200.88/201.41 Found ((eq_ref fofType) ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b) % 200.88/201.41 Found ((eq_ref fofType) ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b) % 200.88/201.41 Found ((eq_ref fofType) ((((x one) two) x0) x1)) as proof of (((eq fofType) ((((x one) two) x0) x1)) b) % 200.88/201.41 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 200.88/201.41 Found (eq_ref0 b) as proof of (((eq fofType) b) ((three x0) x1)) % 200.88/201.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) x1)) % 200.88/201.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) x1)) % 200.88/201.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) x1)) % 200.88/201.41 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 200.88/201.41 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((x one) two) x0) y)) % 200.88/201.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) y)) % 200.88/201.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) y)) % 200.88/201.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) y)) % 200.88/201.41 Found eq_ref00:=(eq_ref0 ((three x0) y)):(((eq fofType) ((three x0) y)) ((three x0) y)) % 200.88/201.41 Found (eq_ref0 ((three x0) y)) as proof of (((eq fofType) ((three x0) y)) b) % 200.88/201.41 Found ((eq_ref fofType) ((three x0) y)) as proof of (((eq fofType) ((three x0) y)) b) % 200.88/201.41 Found ((eq_ref fofType) ((three x0) y)) as proof of (((eq fofType) ((three x0) y)) b) % 200.88/201.41 Found ((eq_ref fofType) ((three x0) y)) as proof of (((eq fofType) ((three x0) y)) b) % 200.88/201.41 Found eq_ref00:=(eq_ref0 ((three x0) y)):(((eq fofType) ((three x0) y)) ((three x0) y)) % 200.88/201.41 Found (eq_ref0 ((three x0) y)) as proof of (((eq fofType) ((three x0) y)) b) % 200.88/201.41 Found ((eq_ref fofType) ((three x0) y)) as proof of (((eq fofType) ((three x0) y)) b) % 200.88/201.41 Found ((eq_ref fofType) ((three x0) y)) as proof of (((eq fofType) ((three x0) y)) b) % 200.88/201.41 Found ((eq_ref fofType) ((three x0) y)) as proof of (((eq fofType) ((three x0) y)) b) % 200.88/201.41 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 200.88/201.41 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((x one) two) x0) y)) % 200.88/201.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) y)) % 200.88/201.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) y)) % 200.88/201.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) y)) % 200.88/201.41 Found eta_expansion_dep000:=(eta_expansion_dep00 (((x one) two) x0)):(((eq (fofType->fofType)) (((x one) two) x0)) (fun (x1:fofType)=> ((((x one) two) x0) x1))) % 200.88/201.41 Found (eta_expansion_dep00 (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b) % 200.88/201.41 Found ((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b) % 200.88/201.41 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b) % 200.88/201.41 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b) % 200.88/201.41 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b) % 207.35/207.92 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->fofType)) b) (fun (x:fofType)=> (b x))) % 207.35/207.92 Found (eta_expansion00 b) as proof of (((eq (fofType->fofType)) b) (three x0)) % 207.35/207.92 Found ((eta_expansion0 fofType) b) as proof of (((eq (fofType->fofType)) b) (three x0)) % 207.35/207.92 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (three x0)) % 207.35/207.92 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (three x0)) % 207.35/207.92 Found (((eta_expansion fofType) fofType) b) as proof of (((eq (fofType->fofType)) b) (three x0)) % 207.35/207.92 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->fofType)) b) b) % 207.35/207.92 Found (eq_ref0 b) as proof of (((eq (fofType->fofType)) b) (three x0)) % 207.35/207.92 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (three x0)) % 207.35/207.92 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (three x0)) % 207.35/207.92 Found ((eq_ref (fofType->fofType)) b) as proof of (((eq (fofType->fofType)) b) (three x0)) % 207.35/207.92 Found eta_expansion000:=(eta_expansion00 (((x one) two) x0)):(((eq (fofType->fofType)) (((x one) two) x0)) (fun (x1:fofType)=> ((((x one) two) x0) x1))) % 207.35/207.92 Found (eta_expansion00 (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b) % 207.35/207.92 Found ((eta_expansion0 fofType) (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b) % 207.35/207.92 Found (((eta_expansion fofType) fofType) (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b) % 207.35/207.92 Found (((eta_expansion fofType) fofType) (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b) % 207.35/207.92 Found (((eta_expansion fofType) fofType) (((x one) two) x0)) as proof of (((eq (fofType->fofType)) (((x one) two) x0)) b) % 207.35/207.92 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) a) (fun (x:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> (a x))) % 207.35/207.92 Found (eta_expansion_dep00 a) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) a) b) % 207.35/207.92 Found ((eta_expansion_dep0 (fun (x1:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> Prop)) a) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) a) b) % 207.35/207.92 Found (((eta_expansion_dep (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) (fun (x1:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> Prop)) a) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) a) b) % 207.35/207.92 Found (((eta_expansion_dep (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) (fun (x1:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> Prop)) a) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) a) b) % 207.35/207.92 Found (((eta_expansion_dep (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) (fun (x1:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> Prop)) a) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) a) b) % 207.35/207.92 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) b) (fun (x:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> (b x))) % 207.52/208.12 Found (eta_expansion_dep00 b) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) b) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) % 207.52/208.12 Found ((eta_expansion_dep0 (fun (x1:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> Prop)) b) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) b) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) % 207.52/208.12 Found (((eta_expansion_dep (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) (fun (x1:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> Prop)) b) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) b) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) % 207.52/208.12 Found (((eta_expansion_dep (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) (fun (x1:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> Prop)) b) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) b) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) % 207.52/208.12 Found (((eta_expansion_dep (((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))) (fun (x1:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> Prop)) b) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) b) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) % 207.52/208.12 Found eq_ref00:=(eq_ref0 b):(((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) b) b) % 207.52/208.12 Found (eq_ref0 b) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) b) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) % 229.87/230.41 Found ((eq_ref ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) b) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) b) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) % 229.87/230.41 Found ((eq_ref ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) b) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) b) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) % 229.87/230.41 Found ((eq_ref ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) b) as proof of (((eq ((((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType))))->Prop)) b) (fun (Op:(((fofType->fofType)->(fofType->fofType))->(((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))))=> ((and (((eq ((fofType->fofType)->(fofType->fofType))) ((Op two) three)) five)) (((eq ((fofType->fofType)->(fofType->fofType))) ((Op one) two)) three)))) % 229.87/230.41 Found x11:(P (((x one) two) x0)) % 229.87/230.41 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P (((x one) two) x0)) % 229.87/230.41 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P0 (((x one) two) x0)) % 229.87/230.41 Found x11:(P (((x one) two) x0)) % 229.87/230.41 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P (((x one) two) x0)) % 229.87/230.41 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P0 (((x one) two) x0)) % 229.87/230.41 Found x11:(P (((x one) two) x0)) % 229.87/230.41 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P (((x one) two) x0)) % 229.87/230.41 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P0 (((x one) two) x0)) % 229.87/230.41 Found x11:(P (((x one) two) x0)) % 229.87/230.41 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P (((x one) two) x0)) % 229.87/230.41 Found (fun (x11:(P (((x one) two) x0)))=> x11) as proof of (P0 (((x one) two) x0)) % 229.87/230.41 Found eq_ref00:=(eq_ref0 (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)):(((eq Prop) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)) % 229.87/230.41 Found (eq_ref0 (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)) as proof of (((eq Prop) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)) b) % 229.87/230.41 Found ((eq_ref Prop) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)) as proof of (((eq Prop) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)) b) % 229.87/230.41 Found ((eq_ref Prop) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)) as proof of (((eq Prop) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)) b) % 229.87/230.41 Found ((eq_ref Prop) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)) as proof of (((eq Prop) (((eq ((fofType->fofType)->(fofType->fofType))) ((x one) two)) three)) b) % 229.87/230.41 Found x21:(P ((three x0) x1)) % 229.87/230.41 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P ((three x0) x1)) % 229.87/230.41 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P0 ((three x0) x1)) % 229.87/230.41 Found x21:(P ((three x0) x1)) % 229.87/230.41 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P ((three x0) x1)) % 232.93/233.49 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P0 ((three x0) x1)) % 232.93/233.49 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 232.93/233.49 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 232.93/233.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 232.93/233.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 232.93/233.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 232.93/233.49 Found eq_ref00:=(eq_ref0 ((three x0) x1)):(((eq fofType) ((three x0) x1)) ((three x0) x1)) % 232.93/233.49 Found (eq_ref0 ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 232.93/233.49 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 232.93/233.49 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 232.93/233.49 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 232.93/233.49 Found eq_ref00:=(eq_ref0 ((three x0) x1)):(((eq fofType) ((three x0) x1)) ((three x0) x1)) % 232.93/233.49 Found (eq_ref0 ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 232.93/233.49 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 232.93/233.49 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 232.93/233.49 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 232.93/233.49 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 232.93/233.49 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 232.93/233.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 232.93/233.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 232.93/233.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 232.93/233.49 Found eq_ref00:=(eq_ref0 ((three x0) x1)):(((eq fofType) ((three x0) x1)) ((three x0) x1)) % 232.93/233.49 Found (eq_ref0 ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 232.93/233.49 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 232.93/233.49 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 232.93/233.49 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 232.93/233.49 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 232.93/233.49 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 232.93/233.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 232.93/233.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 232.93/233.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 232.93/233.49 Found x21:(P ((three x0) x1)) % 232.93/233.49 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P ((three x0) x1)) % 232.93/233.49 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P0 ((three x0) x1)) % 232.93/233.49 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 232.93/233.49 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 232.93/233.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 232.93/233.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 232.93/233.49 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 232.93/233.49 Found eq_ref00:=(eq_ref0 ((three x0) x1)):(((eq fofType) ((three x0) x1)) ((three x0) x1)) % 232.93/233.49 Found (eq_ref0 ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 232.93/233.49 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 232.93/233.49 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 232.93/233.49 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 232.93/233.49 Found x21:(P ((three x0) x1)) % 232.93/233.49 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P ((three x0) x1)) % 232.93/233.49 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P0 ((three x0) x1)) % 232.93/233.49 Found eq_ref00:=(eq_ref0 ((three x0) x1)):(((eq fofType) ((three x0) x1)) ((three x0) x1)) % 232.93/233.49 Found (eq_ref0 ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 232.93/233.49 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 232.93/233.49 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 232.93/233.49 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 232.93/233.49 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 236.28/236.81 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 236.28/236.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 236.28/236.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 236.28/236.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 236.28/236.81 Found eq_ref00:=(eq_ref0 ((three x0) x1)):(((eq fofType) ((three x0) x1)) ((three x0) x1)) % 236.28/236.81 Found (eq_ref0 ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 236.28/236.81 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 236.28/236.81 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 236.28/236.81 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 236.28/236.81 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 236.28/236.81 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 236.28/236.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 236.28/236.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 236.28/236.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 236.28/236.81 Found eq_ref00:=(eq_ref0 ((three x0) x1)):(((eq fofType) ((three x0) x1)) ((three x0) x1)) % 236.28/236.81 Found (eq_ref0 ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 236.28/236.81 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 236.28/236.81 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 236.28/236.81 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 236.28/236.81 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 236.28/236.81 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 236.28/236.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 236.28/236.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 236.28/236.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 236.28/236.81 Found x21:(P ((three x0) x1)) % 236.28/236.81 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P ((three x0) x1)) % 236.28/236.81 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P0 ((three x0) x1)) % 236.28/236.81 Found x21:(P ((three x0) x1)) % 236.28/236.81 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P ((three x0) x1)) % 236.28/236.81 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P0 ((three x0) x1)) % 236.28/236.81 Found x21:(P ((three x0) x1)) % 236.28/236.81 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P ((three x0) x1)) % 236.28/236.81 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P0 ((three x0) x1)) % 236.28/236.81 Found x21:(P ((three x0) x1)) % 236.28/236.81 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P ((three x0) x1)) % 236.28/236.81 Found (fun (x21:(P ((three x0) x1)))=> x21) as proof of (P0 ((three x0) x1)) % 236.28/236.81 Found eq_ref00:=(eq_ref0 ((three x0) x1)):(((eq fofType) ((three x0) x1)) ((three x0) x1)) % 236.28/236.81 Found (eq_ref0 ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 236.28/236.81 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 236.28/236.81 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 236.28/236.81 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 236.28/236.81 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 236.28/236.81 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 236.28/236.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 236.28/236.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 236.28/236.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 236.28/236.81 Found eq_ref00:=(eq_ref0 ((three x0) x1)):(((eq fofType) ((three x0) x1)) ((three x0) x1)) % 236.28/236.81 Found (eq_ref0 ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 236.28/236.81 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 236.28/236.81 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 236.28/236.81 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 236.28/236.81 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 236.28/236.81 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 236.28/236.81 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 290.02/290.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 290.02/290.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 290.02/290.60 Found eq_ref00:=(eq_ref0 ((three x0) x1)):(((eq fofType) ((three x0) x1)) ((three x0) x1)) % 290.02/290.60 Found (eq_ref0 ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 290.02/290.60 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 290.02/290.60 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 290.02/290.60 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 290.02/290.60 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 290.02/290.60 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 290.02/290.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 290.02/290.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 290.02/290.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 290.02/290.60 Found eq_ref00:=(eq_ref0 ((three x0) x1)):(((eq fofType) ((three x0) x1)) ((three x0) x1)) % 290.02/290.60 Found (eq_ref0 ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 290.02/290.60 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 290.02/290.60 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 290.02/290.60 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 290.02/290.60 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 290.02/290.60 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 290.02/290.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 290.02/290.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 290.02/290.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 290.02/290.60 Found eq_ref00:=(eq_ref0 ((three x0) x1)):(((eq fofType) ((three x0) x1)) ((three x0) x1)) % 290.02/290.60 Found (eq_ref0 ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 290.02/290.60 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 290.02/290.60 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 290.02/290.60 Found ((eq_ref fofType) ((three x0) x1)) as proof of (((eq fofType) ((three x0) x1)) b) % 290.02/290.60 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 290.02/290.60 Found (eq_ref0 b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 290.02/290.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 290.02/290.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 290.02/290.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((((x one) two) x0) x1)) % 290.02/290.60 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % 290.02/290.60 Found (eq_ref0 b) as proof of (((eq fofType) b) ((three x0) y)) % 290.02/290.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) y)) % 290.02/290.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) y)) % 290.02/290.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((three x0) y)) % 290.02/290.60 Found eq_ref00:=(eq_ref0 ((((x one) two) x0) y)):(((eq fofType) ((((x one) two) x0) y)) ((((x one) two) x0) y)) % 290.02/290.60 Found (eq_ref0 ((((x one) two) x0) y)) as proof of (((eq fofType) ((((x one) two) x0) y)) b) % 290.02/290.60 Found ((eq_ref fofType) ((((x one) two) x0) y)) as proof of (((eq fofType) ((((x one) two) x0) y)) b) % 290.02/290.60 Found ((eq_ref fofType) ((((x one) two) x0) y)) as proof of (((eq fofType) ((((x one) two) x0) y)) b) % 290.02/290.60 Found ((eq_ref fofType) ((((x one) two) x0) y)) as proof of (((eq fofType) ((((x one) two) x0) y)) b) % 290.02/290.60 Found x01:(P ((x one) two)) % 290.02/290.60 Found (fun (x01:(P ((x one) two)))=> x01) as proof of (P ((x one) two)) % 290.02/290.60 Found (fun (x01:(P ((x one) two)))=> x01) as proof of (P0 ((x one) two)) % 290.02/290.60 Found x01:(P ((x one) two)) % 290.02/290.60 Found (fun (x01:(P ((x one) two)))=> x01) as proof of (P ((x one) two)) % 290.02/290.60 Found (fun (x01:(P ((x one) two)))=> x01) as proof of (P0 ((x one) two)) % 290.02/290.60 Found x0:(P ((x one) two)) % 290.02/290.60 Instantiate: b:=((x one) two):((fofType->fofType)->(fofType->fofType)) % 290.02/290.60 Found x0 as proof of (P0 b) % 290.02/290.60 Found eta_expansion000:=(eta_expansion00 three):(((eq ((fofType->fofType)->(fofType->fofType))) three) (fun (x:(fofType->fofType))=> (three x))) % 290.02/290.60 Found (eta_expansion00 %------------------------------------------------------------------------------