%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SYO104^5 : TPTP v7.5.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n025.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 0s % DateTime : Tue Mar 29 00:50:40 EDT 2022 % Result : Theorem 0.85s 1.05s % Output : Proof 0.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SYO104^5 : TPTP v7.5.0. Released v4.0.0. % 0.00/0.11 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % 0.11/0.32 % Computer : n025.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % RAMPerCPU : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % DateTime : Fri Mar 11 15:18:01 EST 2022 % 0.11/0.32 % CPUTime : % 0.18/0.33 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27' % 0.18/0.33 Python 2.7.5 % 0.78/0.98 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/'] % 0.78/0.98 FOF formula (<kernel.Constant object at 0x2ae777e45290>, <kernel.Constant object at 0x2ae777e45320>) of role type named y % 0.78/0.98 Using role type % 0.78/0.98 Declaring y:fofType % 0.78/0.98 FOF formula (<kernel.Constant object at 0x1b58d88>, <kernel.DependentProduct object at 0x2ae777e45320>) of role type named cQ % 0.78/0.98 Using role type % 0.78/0.98 Declaring cQ:(fofType->(fofType->Prop)) % 0.78/0.98 FOF formula (<kernel.Constant object at 0x2ae777e458c0>, <kernel.DependentProduct object at 0x2ae777e45d88>) of role type named cP % 0.78/0.98 Using role type % 0.78/0.98 Declaring cP:(fofType->(fofType->Prop)) % 0.78/0.98 FOF formula ((iff (forall (Xx:fofType), ((and ((cP Xx) y)) ((cQ Xx) y)))) ((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y)))) of role conjecture named cTTTP2129 % 0.78/0.98 Conjecture to prove = ((iff (forall (Xx:fofType), ((and ((cP Xx) y)) ((cQ Xx) y)))) ((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y)))):Prop % 0.78/0.98 We need to prove ['((iff (forall (Xx:fofType), ((and ((cP Xx) y)) ((cQ Xx) y)))) ((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y))))'] % 0.78/0.98 Parameter fofType:Type. % 0.78/0.98 Parameter y:fofType. % 0.78/0.98 Parameter cQ:(fofType->(fofType->Prop)). % 0.78/0.98 Parameter cP:(fofType->(fofType->Prop)). % 0.78/0.98 Trying to prove ((iff (forall (Xx:fofType), ((and ((cP Xx) y)) ((cQ Xx) y)))) ((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y)))) % 0.78/0.98 Found x00:=(x0 Xx):((cP Xx) y) % 0.78/0.98 Found (x0 Xx) as proof of ((cP Xx) y) % 0.78/0.98 Found (x0 Xx) as proof of ((cP Xx) y) % 0.78/0.98 Found x10:=(x1 Xx):((cQ Xx) y) % 0.78/0.98 Found (x1 Xx) as proof of ((cQ Xx) y) % 0.78/0.98 Found (x1 Xx) as proof of ((cQ Xx) y) % 0.78/0.98 Found ((conj10 (x0 Xx)) (x1 Xx)) as proof of ((and ((cP Xx) y)) ((cQ Xx) y)) % 0.78/0.98 Found (((conj1 ((cQ Xx) y)) (x0 Xx)) (x1 Xx)) as proof of ((and ((cP Xx) y)) ((cQ Xx) y)) % 0.78/0.98 Found ((((conj ((cP Xx) y)) ((cQ Xx) y)) (x0 Xx)) (x1 Xx)) as proof of ((and ((cP Xx) y)) ((cQ Xx) y)) % 0.78/0.98 Found (fun (x1:(forall (Xx0:fofType), ((cQ Xx0) y)))=> ((((conj ((cP Xx) y)) ((cQ Xx) y)) (x0 Xx)) (x1 Xx))) as proof of ((and ((cP Xx) y)) ((cQ Xx) y)) % 0.78/0.98 Found (fun (x0:(forall (Xx0:fofType), ((cP Xx0) y))) (x1:(forall (Xx0:fofType), ((cQ Xx0) y)))=> ((((conj ((cP Xx) y)) ((cQ Xx) y)) (x0 Xx)) (x1 Xx))) as proof of ((forall (Xx0:fofType), ((cQ Xx0) y))->((and ((cP Xx) y)) ((cQ Xx) y))) % 0.78/0.98 Found (fun (x0:(forall (Xx0:fofType), ((cP Xx0) y))) (x1:(forall (Xx0:fofType), ((cQ Xx0) y)))=> ((((conj ((cP Xx) y)) ((cQ Xx) y)) (x0 Xx)) (x1 Xx))) as proof of ((forall (Xx0:fofType), ((cP Xx0) y))->((forall (Xx0:fofType), ((cQ Xx0) y))->((and ((cP Xx) y)) ((cQ Xx) y)))) % 0.78/0.98 Found (and_rect00 (fun (x0:(forall (Xx0:fofType), ((cP Xx0) y))) (x1:(forall (Xx0:fofType), ((cQ Xx0) y)))=> ((((conj ((cP Xx) y)) ((cQ Xx) y)) (x0 Xx)) (x1 Xx)))) as proof of ((and ((cP Xx) y)) ((cQ Xx) y)) % 0.78/0.98 Found ((and_rect0 ((and ((cP Xx) y)) ((cQ Xx) y))) (fun (x0:(forall (Xx0:fofType), ((cP Xx0) y))) (x1:(forall (Xx0:fofType), ((cQ Xx0) y)))=> ((((conj ((cP Xx) y)) ((cQ Xx) y)) (x0 Xx)) (x1 Xx)))) as proof of ((and ((cP Xx) y)) ((cQ Xx) y)) % 0.78/0.98 Found (((fun (P:Type) (x0:((forall (Xx:fofType), ((cP Xx) y))->((forall (Xx:fofType), ((cQ Xx) y))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y))) P) x0) x)) ((and ((cP Xx) y)) ((cQ Xx) y))) (fun (x0:(forall (Xx0:fofType), ((cP Xx0) y))) (x1:(forall (Xx0:fofType), ((cQ Xx0) y)))=> ((((conj ((cP Xx) y)) ((cQ Xx) y)) (x0 Xx)) (x1 Xx)))) as proof of ((and ((cP Xx) y)) ((cQ Xx) y)) % 0.78/0.98 Found (fun (Xx:fofType)=> (((fun (P:Type) (x0:((forall (Xx:fofType), ((cP Xx) y))->((forall (Xx:fofType), ((cQ Xx) y))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y))) P) x0) x)) ((and ((cP Xx) y)) ((cQ Xx) y))) (fun (x0:(forall (Xx0:fofType), ((cP Xx0) y))) (x1:(forall (Xx0:fofType), ((cQ Xx0) y)))=> ((((conj ((cP Xx) y)) ((cQ Xx) y)) (x0 Xx)) (x1 Xx))))) as proof of ((and ((cP Xx) y)) ((cQ Xx) y)) % 0.78/0.98 Found (fun (x:((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y)))) (Xx:fofType)=> (((fun (P:Type) (x0:((forall (Xx:fofType), ((cP Xx) y))->((forall (Xx:fofType), ((cQ Xx) y))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y))) P) x0) x)) ((and ((cP Xx) y)) ((cQ Xx) y))) (fun (x0:(forall (Xx0:fofType), ((cP Xx0) y))) (x1:(forall (Xx0:fofType), ((cQ Xx0) y)))=> ((((conj ((cP Xx) y)) ((cQ Xx) y)) (x0 Xx)) (x1 Xx))))) as proof of (forall (Xx:fofType), ((and ((cP Xx) y)) ((cQ Xx) y))) % 0.85/1.04 Found (fun (x:((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y)))) (Xx:fofType)=> (((fun (P:Type) (x0:((forall (Xx:fofType), ((cP Xx) y))->((forall (Xx:fofType), ((cQ Xx) y))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y))) P) x0) x)) ((and ((cP Xx) y)) ((cQ Xx) y))) (fun (x0:(forall (Xx0:fofType), ((cP Xx0) y))) (x1:(forall (Xx0:fofType), ((cQ Xx0) y)))=> ((((conj ((cP Xx) y)) ((cQ Xx) y)) (x0 Xx)) (x1 Xx))))) as proof of (((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y)))->(forall (Xx:fofType), ((and ((cP Xx) y)) ((cQ Xx) y)))) % 0.85/1.04 Found x2:((cQ Xx0) y) % 0.85/1.04 Instantiate: Xx0:=Xx:fofType % 0.85/1.04 Found (fun (x2:((cQ Xx0) y))=> x2) as proof of ((cQ Xx) y) % 0.85/1.04 Found (fun (x1:((cP Xx0) y)) (x2:((cQ Xx0) y))=> x2) as proof of (((cQ Xx0) y)->((cQ Xx) y)) % 0.85/1.04 Found (fun (x1:((cP Xx0) y)) (x2:((cQ Xx0) y))=> x2) as proof of (((cP Xx0) y)->(((cQ Xx0) y)->((cQ Xx) y))) % 0.85/1.04 Found (and_rect00 (fun (x1:((cP Xx0) y)) (x2:((cQ Xx0) y))=> x2)) as proof of ((cQ Xx) y) % 0.85/1.04 Found ((and_rect0 ((cQ Xx) y)) (fun (x1:((cP Xx0) y)) (x2:((cQ Xx0) y))=> x2)) as proof of ((cQ Xx) y) % 0.85/1.04 Found (((fun (P:Type) (x1:(((cP Xx0) y)->(((cQ Xx0) y)->P)))=> (((((and_rect ((cP Xx0) y)) ((cQ Xx0) y)) P) x1) x0)) ((cQ Xx) y)) (fun (x1:((cP Xx0) y)) (x2:((cQ Xx0) y))=> x2)) as proof of ((cQ Xx) y) % 0.85/1.04 Found (((fun (P:Type) (x1:(((cP Xx) y)->(((cQ Xx) y)->P)))=> (((((and_rect ((cP Xx) y)) ((cQ Xx) y)) P) x1) (x Xx))) ((cQ Xx) y)) (fun (x1:((cP Xx) y)) (x2:((cQ Xx) y))=> x2)) as proof of ((cQ Xx) y) % 0.85/1.04 Found (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cP Xx) y)->(((cQ Xx) y)->P)))=> (((((and_rect ((cP Xx) y)) ((cQ Xx) y)) P) x1) (x Xx))) ((cQ Xx) y)) (fun (x1:((cP Xx) y)) (x2:((cQ Xx) y))=> x2))) as proof of ((cQ Xx) y) % 0.85/1.04 Found (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cP Xx) y)->(((cQ Xx) y)->P)))=> (((((and_rect ((cP Xx) y)) ((cQ Xx) y)) P) x1) (x Xx))) ((cQ Xx) y)) (fun (x1:((cP Xx) y)) (x2:((cQ Xx) y))=> x2))) as proof of (forall (Xx:fofType), ((cQ Xx) y)) % 0.85/1.04 Found x1:((cP Xx0) y) % 0.85/1.04 Instantiate: Xx0:=Xx:fofType % 0.85/1.04 Found (fun (x2:((cQ Xx0) y))=> x1) as proof of ((cP Xx) y) % 0.85/1.04 Found (fun (x1:((cP Xx0) y)) (x2:((cQ Xx0) y))=> x1) as proof of (((cQ Xx0) y)->((cP Xx) y)) % 0.85/1.04 Found (fun (x1:((cP Xx0) y)) (x2:((cQ Xx0) y))=> x1) as proof of (((cP Xx0) y)->(((cQ Xx0) y)->((cP Xx) y))) % 0.85/1.04 Found (and_rect00 (fun (x1:((cP Xx0) y)) (x2:((cQ Xx0) y))=> x1)) as proof of ((cP Xx) y) % 0.85/1.04 Found ((and_rect0 ((cP Xx) y)) (fun (x1:((cP Xx0) y)) (x2:((cQ Xx0) y))=> x1)) as proof of ((cP Xx) y) % 0.85/1.04 Found (((fun (P:Type) (x1:(((cP Xx0) y)->(((cQ Xx0) y)->P)))=> (((((and_rect ((cP Xx0) y)) ((cQ Xx0) y)) P) x1) x0)) ((cP Xx) y)) (fun (x1:((cP Xx0) y)) (x2:((cQ Xx0) y))=> x1)) as proof of ((cP Xx) y) % 0.85/1.04 Found (((fun (P:Type) (x1:(((cP Xx) y)->(((cQ Xx) y)->P)))=> (((((and_rect ((cP Xx) y)) ((cQ Xx) y)) P) x1) (x Xx))) ((cP Xx) y)) (fun (x1:((cP Xx) y)) (x2:((cQ Xx) y))=> x1)) as proof of ((cP Xx) y) % 0.85/1.04 Found (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cP Xx) y)->(((cQ Xx) y)->P)))=> (((((and_rect ((cP Xx) y)) ((cQ Xx) y)) P) x1) (x Xx))) ((cP Xx) y)) (fun (x1:((cP Xx) y)) (x2:((cQ Xx) y))=> x1))) as proof of ((cP Xx) y) % 0.85/1.04 Found (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cP Xx) y)->(((cQ Xx) y)->P)))=> (((((and_rect ((cP Xx) y)) ((cQ Xx) y)) P) x1) (x Xx))) ((cP Xx) y)) (fun (x1:((cP Xx) y)) (x2:((cQ Xx) y))=> x1))) as proof of (forall (Xx:fofType), ((cP Xx) y)) % 0.85/1.04 Found ((conj10 (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cP Xx) y)->(((cQ Xx) y)->P)))=> (((((and_rect ((cP Xx) y)) ((cQ Xx) y)) P) x1) (x Xx))) ((cP Xx) y)) (fun (x1:((cP Xx) y)) (x2:((cQ Xx) y))=> x1)))) (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cP Xx) y)->(((cQ Xx) y)->P)))=> (((((and_rect ((cP Xx) y)) ((cQ Xx) y)) P) x1) (x Xx))) ((cQ Xx) y)) (fun (x1:((cP Xx) y)) (x2:((cQ Xx) y))=> x2)))) as proof of ((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y))) % 0.85/1.04 Found (((conj1 (forall (Xx:fofType), ((cQ Xx) y))) (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cP Xx) y)->(((cQ Xx) y)->P)))=> (((((and_rect ((cP Xx) y)) ((cQ Xx) y)) P) x1) (x Xx))) ((cP Xx) y)) (fun (x1:((cP Xx) y)) (x2:((cQ Xx) y))=> x1)))) (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cP Xx) y)->(((cQ Xx) y)->P)))=> (((((and_rect ((cP Xx) y)) ((cQ Xx) y)) P) x1) (x Xx))) ((cQ Xx) y)) (fun (x1:((cP Xx) y)) (x2:((cQ Xx) y))=> x2)))) as proof of ((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y))) % 0.85/1.04 Found ((((conj (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y))) (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cP Xx) y)->(((cQ Xx) y)->P)))=> (((((and_rect ((cP Xx) y)) ((cQ Xx) y)) P) x1) (x Xx))) ((cP Xx) y)) (fun (x1:((cP Xx) y)) (x2:((cQ Xx) y))=> x1)))) (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cP Xx) y)->(((cQ Xx) y)->P)))=> (((((and_rect ((cP Xx) y)) ((cQ Xx) y)) P) x1) (x Xx))) ((cQ Xx) y)) (fun (x1:((cP Xx) y)) (x2:((cQ Xx) y))=> x2)))) as proof of ((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y))) % 0.85/1.04 Found (fun (x:(forall (Xx:fofType), ((and ((cP Xx) y)) ((cQ Xx) y))))=> ((((conj (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y))) (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cP Xx) y)->(((cQ Xx) y)->P)))=> (((((and_rect ((cP Xx) y)) ((cQ Xx) y)) P) x1) (x Xx))) ((cP Xx) y)) (fun (x1:((cP Xx) y)) (x2:((cQ Xx) y))=> x1)))) (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cP Xx) y)->(((cQ Xx) y)->P)))=> (((((and_rect ((cP Xx) y)) ((cQ Xx) y)) P) x1) (x Xx))) ((cQ Xx) y)) (fun (x1:((cP Xx) y)) (x2:((cQ Xx) y))=> x2))))) as proof of ((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y))) % 0.85/1.04 Found (fun (x:(forall (Xx:fofType), ((and ((cP Xx) y)) ((cQ Xx) y))))=> ((((conj (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y))) (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cP Xx) y)->(((cQ Xx) y)->P)))=> (((((and_rect ((cP Xx) y)) ((cQ Xx) y)) P) x1) (x Xx))) ((cP Xx) y)) (fun (x1:((cP Xx) y)) (x2:((cQ Xx) y))=> x1)))) (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cP Xx) y)->(((cQ Xx) y)->P)))=> (((((and_rect ((cP Xx) y)) ((cQ Xx) y)) P) x1) (x Xx))) ((cQ Xx) y)) (fun (x1:((cP Xx) y)) (x2:((cQ Xx) y))=> x2))))) as proof of ((forall (Xx:fofType), ((and ((cP Xx) y)) ((cQ Xx) y)))->((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y)))) % 0.85/1.04 Found ((conj00 (fun (x:(forall (Xx:fofType), ((and ((cP Xx) y)) ((cQ Xx) y))))=> ((((conj (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y))) (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cP Xx) y)->(((cQ Xx) y)->P)))=> (((((and_rect ((cP Xx) y)) ((cQ Xx) y)) P) x1) (x Xx))) ((cP Xx) y)) (fun (x1:((cP Xx) y)) (x2:((cQ Xx) y))=> x1)))) (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cP Xx) y)->(((cQ Xx) y)->P)))=> (((((and_rect ((cP Xx) y)) ((cQ Xx) y)) P) x1) (x Xx))) ((cQ Xx) y)) (fun (x1:((cP Xx) y)) (x2:((cQ Xx) y))=> x2)))))) (fun (x:((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y)))) (Xx:fofType)=> (((fun (P:Type) (x0:((forall (Xx:fofType), ((cP Xx) y))->((forall (Xx:fofType), ((cQ Xx) y))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y))) P) x0) x)) ((and ((cP Xx) y)) ((cQ Xx) y))) (fun (x0:(forall (Xx0:fofType), ((cP Xx0) y))) (x1:(forall (Xx0:fofType), ((cQ Xx0) y)))=> ((((conj ((cP Xx) y)) ((cQ Xx) y)) (x0 Xx)) (x1 Xx)))))) as proof of ((iff (forall (Xx:fofType), ((and ((cP Xx) y)) ((cQ Xx) y)))) ((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y)))) % 0.85/1.05 Found (((conj0 (((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y)))->(forall (Xx:fofType), ((and ((cP Xx) y)) ((cQ Xx) y))))) (fun (x:(forall (Xx:fofType), ((and ((cP Xx) y)) ((cQ Xx) y))))=> ((((conj (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y))) (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cP Xx) y)->(((cQ Xx) y)->P)))=> (((((and_rect ((cP Xx) y)) ((cQ Xx) y)) P) x1) (x Xx))) ((cP Xx) y)) (fun (x1:((cP Xx) y)) (x2:((cQ Xx) y))=> x1)))) (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cP Xx) y)->(((cQ Xx) y)->P)))=> (((((and_rect ((cP Xx) y)) ((cQ Xx) y)) P) x1) (x Xx))) ((cQ Xx) y)) (fun (x1:((cP Xx) y)) (x2:((cQ Xx) y))=> x2)))))) (fun (x:((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y)))) (Xx:fofType)=> (((fun (P:Type) (x0:((forall (Xx:fofType), ((cP Xx) y))->((forall (Xx:fofType), ((cQ Xx) y))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y))) P) x0) x)) ((and ((cP Xx) y)) ((cQ Xx) y))) (fun (x0:(forall (Xx0:fofType), ((cP Xx0) y))) (x1:(forall (Xx0:fofType), ((cQ Xx0) y)))=> ((((conj ((cP Xx) y)) ((cQ Xx) y)) (x0 Xx)) (x1 Xx)))))) as proof of ((iff (forall (Xx:fofType), ((and ((cP Xx) y)) ((cQ Xx) y)))) ((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y)))) % 0.85/1.05 Found ((((conj ((forall (Xx:fofType), ((and ((cP Xx) y)) ((cQ Xx) y)))->((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y))))) (((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y)))->(forall (Xx:fofType), ((and ((cP Xx) y)) ((cQ Xx) y))))) (fun (x:(forall (Xx:fofType), ((and ((cP Xx) y)) ((cQ Xx) y))))=> ((((conj (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y))) (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cP Xx) y)->(((cQ Xx) y)->P)))=> (((((and_rect ((cP Xx) y)) ((cQ Xx) y)) P) x1) (x Xx))) ((cP Xx) y)) (fun (x1:((cP Xx) y)) (x2:((cQ Xx) y))=> x1)))) (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cP Xx) y)->(((cQ Xx) y)->P)))=> (((((and_rect ((cP Xx) y)) ((cQ Xx) y)) P) x1) (x Xx))) ((cQ Xx) y)) (fun (x1:((cP Xx) y)) (x2:((cQ Xx) y))=> x2)))))) (fun (x:((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y)))) (Xx:fofType)=> (((fun (P:Type) (x0:((forall (Xx:fofType), ((cP Xx) y))->((forall (Xx:fofType), ((cQ Xx) y))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y))) P) x0) x)) ((and ((cP Xx) y)) ((cQ Xx) y))) (fun (x0:(forall (Xx0:fofType), ((cP Xx0) y))) (x1:(forall (Xx0:fofType), ((cQ Xx0) y)))=> ((((conj ((cP Xx) y)) ((cQ Xx) y)) (x0 Xx)) (x1 Xx)))))) as proof of ((iff (forall (Xx:fofType), ((and ((cP Xx) y)) ((cQ Xx) y)))) ((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y)))) % 0.85/1.05 Found ((((conj ((forall (Xx:fofType), ((and ((cP Xx) y)) ((cQ Xx) y)))->((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y))))) (((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y)))->(forall (Xx:fofType), ((and ((cP Xx) y)) ((cQ Xx) y))))) (fun (x:(forall (Xx:fofType), ((and ((cP Xx) y)) ((cQ Xx) y))))=> ((((conj (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y))) (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cP Xx) y)->(((cQ Xx) y)->P)))=> (((((and_rect ((cP Xx) y)) ((cQ Xx) y)) P) x1) (x Xx))) ((cP Xx) y)) (fun (x1:((cP Xx) y)) (x2:((cQ Xx) y))=> x1)))) (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cP Xx) y)->(((cQ Xx) y)->P)))=> (((((and_rect ((cP Xx) y)) ((cQ Xx) y)) P) x1) (x Xx))) ((cQ Xx) y)) (fun (x1:((cP Xx) y)) (x2:((cQ Xx) y))=> x2)))))) (fun (x:((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y)))) (Xx:fofType)=> (((fun (P:Type) (x0:((forall (Xx:fofType), ((cP Xx) y))->((forall (Xx:fofType), ((cQ Xx) y))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y))) P) x0) x)) ((and ((cP Xx) y)) ((cQ Xx) y))) (fun (x0:(forall (Xx0:fofType), ((cP Xx0) y))) (x1:(forall (Xx0:fofType), ((cQ Xx0) y)))=> ((((conj ((cP Xx) y)) ((cQ Xx) y)) (x0 Xx)) (x1 Xx)))))) as proof of ((iff (forall (Xx:fofType), ((and ((cP Xx) y)) ((cQ Xx) y)))) ((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y)))) % 0.85/1.05 Got proof ((((conj ((forall (Xx:fofType), ((and ((cP Xx) y)) ((cQ Xx) y)))->((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y))))) (((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y)))->(forall (Xx:fofType), ((and ((cP Xx) y)) ((cQ Xx) y))))) (fun (x:(forall (Xx:fofType), ((and ((cP Xx) y)) ((cQ Xx) y))))=> ((((conj (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y))) (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cP Xx) y)->(((cQ Xx) y)->P)))=> (((((and_rect ((cP Xx) y)) ((cQ Xx) y)) P) x1) (x Xx))) ((cP Xx) y)) (fun (x1:((cP Xx) y)) (x2:((cQ Xx) y))=> x1)))) (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cP Xx) y)->(((cQ Xx) y)->P)))=> (((((and_rect ((cP Xx) y)) ((cQ Xx) y)) P) x1) (x Xx))) ((cQ Xx) y)) (fun (x1:((cP Xx) y)) (x2:((cQ Xx) y))=> x2)))))) (fun (x:((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y)))) (Xx:fofType)=> (((fun (P:Type) (x0:((forall (Xx:fofType), ((cP Xx) y))->((forall (Xx:fofType), ((cQ Xx) y))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y))) P) x0) x)) ((and ((cP Xx) y)) ((cQ Xx) y))) (fun (x0:(forall (Xx0:fofType), ((cP Xx0) y))) (x1:(forall (Xx0:fofType), ((cQ Xx0) y)))=> ((((conj ((cP Xx) y)) ((cQ Xx) y)) (x0 Xx)) (x1 Xx)))))) % 0.85/1.05 Time elapsed = 0.423784s % 0.85/1.05 node=121 cost=569.000000 depth=17 % 0.85/1.05 :::::::::::::::::::::: % 0.85/1.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 0.85/1.05 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % 0.85/1.05 ((((conj ((forall (Xx:fofType), ((and ((cP Xx) y)) ((cQ Xx) y)))->((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y))))) (((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y)))->(forall (Xx:fofType), ((and ((cP Xx) y)) ((cQ Xx) y))))) (fun (x:(forall (Xx:fofType), ((and ((cP Xx) y)) ((cQ Xx) y))))=> ((((conj (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y))) (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cP Xx) y)->(((cQ Xx) y)->P)))=> (((((and_rect ((cP Xx) y)) ((cQ Xx) y)) P) x1) (x Xx))) ((cP Xx) y)) (fun (x1:((cP Xx) y)) (x2:((cQ Xx) y))=> x1)))) (fun (Xx:fofType)=> (((fun (P:Type) (x1:(((cP Xx) y)->(((cQ Xx) y)->P)))=> (((((and_rect ((cP Xx) y)) ((cQ Xx) y)) P) x1) (x Xx))) ((cQ Xx) y)) (fun (x1:((cP Xx) y)) (x2:((cQ Xx) y))=> x2)))))) (fun (x:((and (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y)))) (Xx:fofType)=> (((fun (P:Type) (x0:((forall (Xx:fofType), ((cP Xx) y))->((forall (Xx:fofType), ((cQ Xx) y))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx) y))) (forall (Xx:fofType), ((cQ Xx) y))) P) x0) x)) ((and ((cP Xx) y)) ((cQ Xx) y))) (fun (x0:(forall (Xx0:fofType), ((cP Xx0) y))) (x1:(forall (Xx0:fofType), ((cQ Xx0) y)))=> ((((conj ((cP Xx) y)) ((cQ Xx) y)) (x0 Xx)) (x1 Xx)))))) % 0.85/1.05 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p %------------------------------------------------------------------------------