%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SYN358^5 : TPTP v6.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n113.star.cs.uiowa.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz % Memory : 32286.75MB % OS : Linux 2.6.32-431.20.3.el6.x86_64 % CPULimit : 300s % DateTime : Thu Jul 17 13:38:16 EDT 2014 % Result : Theorem 3.17s % Output : Proof 3.17s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SYN358^5 : TPTP v6.1.0. Released v4.0.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n113.star.cs.uiowa.edu % % Model : x86_64 x86_64 % % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz % % Memory : 32286.75MB % % OS : Linux 2.6.32-431.20.3.el6.x86_64 % % CPULimit : 300 % % DateTime : Thu Jul 17 09:25:56 CDT 2014 % % CPUTime: 3.17 % Python 2.7.5 % Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/'] % FOF formula (<kernel.Constant object at 0x251bbd8>, <kernel.DependentProduct object at 0x26f2d40>) of role type named cQ % Using role type % Declaring cQ:(fofType->Prop) % FOF formula (<kernel.Constant object at 0x26f4ab8>, <kernel.Sort object at 0x23e5ea8>) of role type named p % Using role type % Declaring p:Prop % FOF formula ((iff ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) of role conjecture named cX2109 % Conjecture to prove = ((iff ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))):Prop % Parameter fofType_DUMMY:fofType. % We need to prove ['((iff ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))'] % Parameter fofType:Type. % Parameter cQ:(fofType->Prop). % Parameter p:Prop. % Trying to prove ((iff ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) % Found x2:p % Found x2 as proof of p % Found x0:p % Found x0 as proof of p % Found x1:p % Found x1 as proof of p % Found x2:p % Found x2 as proof of p % Found x2:p % Found (fun (x3:(cQ x0))=> x2) as proof of p % Found (fun (x2:p) (x3:(cQ x0))=> x2) as proof of ((cQ x0)->p) % Found (fun (x2:p) (x3:(cQ x0))=> x2) as proof of (p->((cQ x0)->p)) % Found (and_rect00 (fun (x2:p) (x3:(cQ x0))=> x2)) as proof of p % Found ((and_rect0 p) (fun (x2:p) (x3:(cQ x0))=> x2)) as proof of p % Found (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) p) (fun (x2:p) (x3:(cQ x0))=> x2)) as proof of p % Found (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) p) (fun (x2:p) (x3:(cQ x0))=> x2)) as proof of p % Found x0:p % Found x0 as proof of p % Found conj100:=(conj10 (cQ x3)):((cQ x3)->((and p) (cQ x3))) % Found (conj10 (cQ x3)) as proof of ((cQ x3)->((and p) (cQ x0))) % Found ((fun (B:Prop)=> ((conj1 B) x1)) (cQ x3)) as proof of ((cQ x3)->((and p) (cQ x0))) % Found ((fun (B:Prop)=> (((conj p) B) x1)) (cQ x3)) as proof of ((cQ x3)->((and p) (cQ x0))) % Found ((fun (B:Prop)=> (((conj p) B) x1)) (cQ x3)) as proof of ((cQ x3)->((and p) (cQ x0))) % Found conj100:=(conj10 (cQ x3)):((cQ x3)->((and p) (cQ x3))) % Found (conj10 (cQ x3)) as proof of ((cQ x3)->((and p) (cQ x2))) % Found ((fun (B:Prop)=> ((conj1 B) x0)) (cQ x3)) as proof of ((cQ x3)->((and p) (cQ x2))) % Found ((fun (B:Prop)=> (((conj p) B) x0)) (cQ x3)) as proof of ((cQ x3)->((and p) (cQ x2))) % Found ((fun (B:Prop)=> (((conj p) B) x0)) (cQ x3)) as proof of ((cQ x3)->((and p) (cQ x2))) % Found x1:p % Found x1 as proof of p % Found x1:p % Found (fun (x2:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> x1) as proof of p % Found (fun (x1:p) (x2:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> x1) as proof of (((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->p) % Found (fun (x1:p) (x2:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> x1) as proof of (p->(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->p)) % Found (and_rect00 (fun (x1:p) (x2:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> x1)) as proof of p % Found ((and_rect0 p) (fun (x1:p) (x2:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> x1)) as proof of p % Found (((fun (P:Type) (x1:(p->(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->P)))=> (((((and_rect p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) P) x1) x)) p) (fun (x1:p) (x2:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> x1)) as proof of p % Found (((fun (P:Type) (x1:(p->(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->P)))=> (((((and_rect p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) P) x1) x)) p) (fun (x1:p) (x2:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> x1)) as proof of p % Found x2:p % Found (fun (x3:(cQ x0))=> x2) as proof of p % Found (fun (x2:p) (x3:(cQ x0))=> x2) as proof of ((cQ x0)->p) % Found (fun (x2:p) (x3:(cQ x0))=> x2) as proof of (p->((cQ x0)->p)) % Found (and_rect00 (fun (x2:p) (x3:(cQ x0))=> x2)) as proof of p % Found ((and_rect0 p) (fun (x2:p) (x3:(cQ x0))=> x2)) as proof of p % Found (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) p) (fun (x2:p) (x3:(cQ x0))=> x2)) as proof of p % Found (fun (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) p) (fun (x2:p) (x3:(cQ x0))=> x2))) as proof of p % Found (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) p) (fun (x2:p) (x3:(cQ x0))=> x2))) as proof of (((and p) (cQ x0))->p) % Found (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) p) (fun (x2:p) (x3:(cQ x0))=> x2))) as proof of (forall (x:fofType), (((and p) (cQ x))->p)) % Found (ex_ind00 (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) p) (fun (x2:p) (x3:(cQ x0))=> x2)))) as proof of p % Found ((ex_ind0 p) (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) p) (fun (x2:p) (x3:(cQ x0))=> x2)))) as proof of p % Found (((fun (P:Prop) (x0:(forall (x:fofType), (((and p) (cQ x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) P) x0) x)) p) (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) p) (fun (x2:p) (x3:(cQ x0))=> x2)))) as proof of p % Found (((fun (P:Prop) (x0:(forall (x:fofType), (((and p) (cQ x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) P) x0) x)) p) (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) p) (fun (x2:p) (x3:(cQ x0))=> x2)))) as proof of p % Found x2:p % Found (fun (x3:(cQ x0))=> x2) as proof of p % Found (fun (x2:p) (x3:(cQ x0))=> x2) as proof of ((cQ x0)->p) % Found (fun (x2:p) (x3:(cQ x0))=> x2) as proof of (p->((cQ x0)->p)) % Found (and_rect00 (fun (x2:p) (x3:(cQ x0))=> x2)) as proof of p % Found ((and_rect0 p) (fun (x2:p) (x3:(cQ x0))=> x2)) as proof of p % Found (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) p) (fun (x2:p) (x3:(cQ x0))=> x2)) as proof of p % Found (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) p) (fun (x2:p) (x3:(cQ x0))=> x2)) as proof of p % Found conj100:=(conj10 x0):((cQ x3)->((and p) (cQ x3))) % Found (conj10 x0) as proof of ((cQ x3)->((and p) (cQ x2))) % Found ((conj1 (cQ x3)) x0) as proof of ((cQ x3)->((and p) (cQ x2))) % Found (((conj p) (cQ x3)) x0) as proof of ((cQ x3)->((and p) (cQ x2))) % Found (((conj p) (cQ x3)) x0) as proof of ((cQ x3)->((and p) (cQ x2))) % Found conj100:=(conj10 x1):((cQ x3)->((and p) (cQ x3))) % Found (conj10 x1) as proof of ((cQ x3)->((and p) (cQ x0))) % Found ((conj1 (cQ x3)) x1) as proof of ((cQ x3)->((and p) (cQ x0))) % Found (((conj p) (cQ x3)) x1) as proof of ((cQ x3)->((and p) (cQ x0))) % Found (((conj p) (cQ x3)) x1) as proof of ((cQ x3)->((and p) (cQ x0))) % Found x0:p % Found x0 as proof of p % Found (conj10 x0) as proof of ((cQ x3)->((and p) (cQ x2))) % Found ((conj1 (cQ x3)) x0) as proof of ((cQ x3)->((and p) (cQ x2))) % Found (((conj p) (cQ x3)) x0) as proof of ((cQ x3)->((and p) (cQ x2))) % Found (((conj p) (cQ x3)) x0) as proof of ((cQ x3)->((and p) (cQ x2))) % Found x1:p % Found x1 as proof of p % Found (conj10 x1) as proof of ((cQ x3)->((and p) (cQ x0))) % Found ((conj1 (cQ x3)) x1) as proof of ((cQ x3)->((and p) (cQ x0))) % Found (((conj p) (cQ x3)) x1) as proof of ((cQ x3)->((and p) (cQ x0))) % Found (((conj p) (cQ x3)) x1) as proof of ((cQ x3)->((and p) (cQ x0))) % Found ex_intro0000:=(ex_intro000 x3):((ex fofType) (fun (Xx:fofType)=> (cQ Xx))) % Found (ex_intro000 x3) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))) % Found ((ex_intro00 x0) x3) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))) % Found (((ex_intro0 (fun (Xx:fofType)=> (cQ Xx))) x0) x3) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))) % Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))) % Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))) % Found ((conj10 x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3)) as proof of ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) % Found (((conj1 ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3)) as proof of ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) % Found ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3)) as proof of ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) % Found (fun (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3))) as proof of ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) % Found (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3))) as proof of ((cQ x0)->((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) % Found (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3))) as proof of (p->((cQ x0)->((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))) % Found (and_rect00 (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3)))) as proof of ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) % Found ((and_rect0 ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3)))) as proof of ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) % Found (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3)))) as proof of ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) % Found (fun (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3))))) as proof of ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) % Found (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3))))) as proof of (((and p) (cQ x0))->((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) % Found (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3))))) as proof of (forall (x:fofType), (((and p) (cQ x))->((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))) % Found (ex_ind00 (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3)))))) as proof of ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) % Found ((ex_ind0 ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3)))))) as proof of ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) % Found (((fun (P:Prop) (x0:(forall (x:fofType), (((and p) (cQ x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) P) x0) x)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3)))))) as proof of ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) % Found (fun (x:((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))=> (((fun (P:Prop) (x0:(forall (x:fofType), (((and p) (cQ x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) P) x0) x)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3))))))) as proof of ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) % Found (fun (x:((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))=> (((fun (P:Prop) (x0:(forall (x:fofType), (((and p) (cQ x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) P) x0) x)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3))))))) as proof of (((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))->((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) % Found x3:(cQ x2) % Instantiate: x4:=x2:fofType % Found x3 as proof of (cQ x4) % Found (conj100 x3) as proof of ((and p) (cQ x4)) % Found ((conj10 (cQ x4)) x3) as proof of ((and p) (cQ x4)) % Found (((fun (B:Prop)=> ((conj1 B) x0)) (cQ x4)) x3) as proof of ((and p) (cQ x4)) % Found (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x4)) x3) as proof of ((and p) (cQ x4)) % Found (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x4)) x3) as proof of ((and p) (cQ x4)) % Found (ex_intro000 (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x4)) x3)) as proof of ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) % Found ((ex_intro00 x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3)) as proof of ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) % Found (((ex_intro0 (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3)) as proof of ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) % Found ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3)) as proof of ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) % Found (fun (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) % Found (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3))) as proof of ((cQ x2)->((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) % Found (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3))) as proof of (forall (x:fofType), ((cQ x)->((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))) % Found (ex_ind00 (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3)))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) % Found ((ex_ind0 ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3)))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) % Found (((fun (P:Prop) (x2:(forall (x:fofType), ((cQ x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cQ Xx))) P) x2) x1)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3)))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) % Found (fun (x1:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> (((fun (P:Prop) (x2:(forall (x:fofType), ((cQ x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cQ Xx))) P) x2) x1)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3))))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) % Found (fun (x0:p) (x1:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> (((fun (P:Prop) (x2:(forall (x:fofType), ((cQ x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cQ Xx))) P) x2) x1)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3))))) as proof of (((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) % Found (fun (x0:p) (x1:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> (((fun (P:Prop) (x2:(forall (x:fofType), ((cQ x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cQ Xx))) P) x2) x1)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3))))) as proof of (p->(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))) % Found (and_rect00 (fun (x0:p) (x1:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> (((fun (P:Prop) (x2:(forall (x:fofType), ((cQ x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cQ Xx))) P) x2) x1)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3)))))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) % Found ((and_rect0 ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x0:p) (x1:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> (((fun (P:Prop) (x2:(forall (x:fofType), ((cQ x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cQ Xx))) P) x2) x1)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3)))))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) % Found (((fun (P:Type) (x0:(p->(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->P)))=> (((((and_rect p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) P) x0) x)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x0:p) (x1:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> (((fun (P:Prop) (x2:(forall (x0:fofType), ((cQ x0)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cQ Xx))) P) x2) x1)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3)))))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) % Found (fun (x:((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))=> (((fun (P:Type) (x0:(p->(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->P)))=> (((((and_rect p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) P) x0) x)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x0:p) (x1:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> (((fun (P:Prop) (x2:(forall (x0:fofType), ((cQ x0)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cQ Xx))) P) x2) x1)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3))))))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) % Found (fun (x:((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))=> (((fun (P:Type) (x0:(p->(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->P)))=> (((((and_rect p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) P) x0) x)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x0:p) (x1:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> (((fun (P:Prop) (x2:(forall (x0:fofType), ((cQ x0)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cQ Xx))) P) x2) x1)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3))))))) as proof of (((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))->((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) % Found ((conj00 (fun (x:((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))=> (((fun (P:Prop) (x0:(forall (x:fofType), (((and p) (cQ x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) P) x0) x)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3)))))))) (fun (x:((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))=> (((fun (P:Type) (x0:(p->(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->P)))=> (((((and_rect p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) P) x0) x)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x0:p) (x1:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> (((fun (P:Prop) (x2:(forall (x0:fofType), ((cQ x0)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cQ Xx))) P) x2) x1)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3)))))))) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) % Found (((conj0 (((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))->((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))) (fun (x:((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))=> (((fun (P:Prop) (x0:(forall (x:fofType), (((and p) (cQ x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) P) x0) x)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3)))))))) (fun (x:((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))=> (((fun (P:Type) (x0:(p->(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->P)))=> (((((and_rect p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) P) x0) x)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x0:p) (x1:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> (((fun (P:Prop) (x2:(forall (x0:fofType), ((cQ x0)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cQ Xx))) P) x2) x1)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3)))))))) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) % Found ((((conj (((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))->((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))) (((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))->((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))) (fun (x:((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))=> (((fun (P:Prop) (x0:(forall (x:fofType), (((and p) (cQ x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) P) x0) x)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3)))))))) (fun (x:((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))=> (((fun (P:Type) (x0:(p->(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->P)))=> (((((and_rect p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) P) x0) x)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x0:p) (x1:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> (((fun (P:Prop) (x2:(forall (x0:fofType), ((cQ x0)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cQ Xx))) P) x2) x1)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3)))))))) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) % Found ((((conj (((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))->((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))) (((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))->((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))) (fun (x:((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))=> (((fun (P:Prop) (x0:(forall (x:fofType), (((and p) (cQ x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) P) x0) x)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3)))))))) (fun (x:((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))=> (((fun (P:Type) (x0:(p->(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->P)))=> (((((and_rect p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) P) x0) x)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x0:p) (x1:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> (((fun (P:Prop) (x2:(forall (x0:fofType), ((cQ x0)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cQ Xx))) P) x2) x1)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3)))))))) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) % Got proof ((((conj (((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))->((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))) (((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))->((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))) (fun (x:((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))=> (((fun (P:Prop) (x0:(forall (x:fofType), (((and p) (cQ x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) P) x0) x)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3)))))))) (fun (x:((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))=> (((fun (P:Type) (x0:(p->(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->P)))=> (((((and_rect p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) P) x0) x)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x0:p) (x1:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> (((fun (P:Prop) (x2:(forall (x0:fofType), ((cQ x0)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cQ Xx))) P) x2) x1)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3)))))))) % Time elapsed = 2.831967s % node=551 cost=830.000000 depth=27 % :::::::::::::::::::::: % % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % ((((conj (((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))->((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))) (((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))->((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))) (fun (x:((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))))=> (((fun (P:Prop) (x0:(forall (x:fofType), (((and p) (cQ x))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) P) x0) x)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x0:fofType) (x1:((and p) (cQ x0)))=> (((fun (P:Type) (x2:(p->((cQ x0)->P)))=> (((((and_rect p) (cQ x0)) P) x2) x1)) ((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (fun (x2:p) (x3:(cQ x0))=> ((((conj p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) x2) ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) x0) x3)))))))) (fun (x:((and p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))=> (((fun (P:Type) (x0:(p->(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->P)))=> (((((and_rect p) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) P) x0) x)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x0:p) (x1:((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))=> (((fun (P:Prop) (x2:(forall (x0:fofType), ((cQ x0)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cQ Xx))) P) x2) x1)) ((ex fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx))))) (fun (x2:fofType) (x3:(cQ x2))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((and p) (cQ Xx)))) x2) (((fun (B:Prop)=> (((conj p) B) x0)) (cQ x2)) x3)))))))) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF %------------------------------------------------------------------------------