%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SEU846^5 : TPTP v6.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n180.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 13:33:16 EDT 2014 % Result : Theorem 3.37s % Output : Proof 3.37s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SEU846^5 : TPTP v6.1.0. Released v4.0.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n180.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 11:36:16 CDT 2014 % % CPUTime : 3.37 % 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 0x219b908>, <kernel.Type object at 0x219b9e0>) of role type named a_type % Using role type % Declaring a:Type % FOF formula (forall (S:(a->Prop)) (T:(a->Prop)) (U:(a->Prop)), (((and ((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))) (forall (Xx:a), ((S Xx)->(T Xx))))->(forall (Xx:a), (((and (U Xx)) ((T Xx)->False))->((and (U Xx)) ((S Xx)->False)))))) of role conjecture named cGAZING_THM11_pme % Conjecture to prove = (forall (S:(a->Prop)) (T:(a->Prop)) (U:(a->Prop)), (((and ((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))) (forall (Xx:a), ((S Xx)->(T Xx))))->(forall (Xx:a), (((and (U Xx)) ((T Xx)->False))->((and (U Xx)) ((S Xx)->False)))))):Prop % Parameter a_DUMMY:a. % We need to prove ['(forall (S:(a->Prop)) (T:(a->Prop)) (U:(a->Prop)), (((and ((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))) (forall (Xx:a), ((S Xx)->(T Xx))))->(forall (Xx:a), (((and (U Xx)) ((T Xx)->False))->((and (U Xx)) ((S Xx)->False))))))'] % Parameter a:Type. % Trying to prove (forall (S:(a->Prop)) (T:(a->Prop)) (U:(a->Prop)), (((and ((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))) (forall (Xx:a), ((S Xx)->(T Xx))))->(forall (Xx:a), (((and (U Xx)) ((T Xx)->False))->((and (U Xx)) ((S Xx)->False)))))) % Found x1:(U Xx) % Found x1 as proof of (U Xx) % Found x1:(U Xx) % Found x1 as proof of (U Xx) % Found x1:(U Xx) % Found (fun (x2:((T Xx)->False))=> x1) as proof of (U Xx) % Found (fun (x1:(U Xx)) (x2:((T Xx)->False))=> x1) as proof of (((T Xx)->False)->(U Xx)) % Found (fun (x1:(U Xx)) (x2:((T Xx)->False))=> x1) as proof of ((U Xx)->(((T Xx)->False)->(U Xx))) % Found (and_rect00 (fun (x1:(U Xx)) (x2:((T Xx)->False))=> x1)) as proof of (U Xx) % Found ((and_rect0 (U Xx)) (fun (x1:(U Xx)) (x2:((T Xx)->False))=> x1)) as proof of (U Xx) % Found (((fun (P:Type) (x1:((U Xx)->(((T Xx)->False)->P)))=> (((((and_rect (U Xx)) ((T Xx)->False)) P) x1) x0)) (U Xx)) (fun (x1:(U Xx)) (x2:((T Xx)->False))=> x1)) as proof of (U Xx) % Found (((fun (P:Type) (x1:((U Xx)->(((T Xx)->False)->P)))=> (((((and_rect (U Xx)) ((T Xx)->False)) P) x1) x0)) (U Xx)) (fun (x1:(U Xx)) (x2:((T Xx)->False))=> x1)) as proof of (U Xx) % Found x3:(U Xx) % Found x3 as proof of (U Xx) % Found x1:(U Xx) % Found x1 as proof of (U Xx) % Found x1:(U Xx) % Found (fun (x2:(not (T Xx)))=> x1) as proof of (U Xx) % Found (fun (x1:(U Xx)) (x2:(not (T Xx)))=> x1) as proof of ((not (T Xx))->(U Xx)) % Found (fun (x1:(U Xx)) (x2:(not (T Xx)))=> x1) as proof of ((U Xx)->((not (T Xx))->(U Xx))) % Found (and_rect00 (fun (x1:(U Xx)) (x2:(not (T Xx)))=> x1)) as proof of (U Xx) % Found ((and_rect0 (U Xx)) (fun (x1:(U Xx)) (x2:(not (T Xx)))=> x1)) as proof of (U Xx) % Found (((fun (P:Type) (x1:((U Xx)->((not (T Xx))->P)))=> (((((and_rect (U Xx)) (not (T Xx))) P) x1) x0)) (U Xx)) (fun (x1:(U Xx)) (x2:(not (T Xx)))=> x1)) as proof of (U Xx) % Found (((fun (P:Type) (x1:((U Xx)->((not (T Xx))->P)))=> (((((and_rect (U Xx)) (not (T Xx))) P) x1) x0)) (U Xx)) (fun (x1:(U Xx)) (x2:(not (T Xx)))=> x1)) as proof of (U Xx) % Found x1:(U Xx) % Found x1 as proof of (U Xx) % Found x3:(U Xx) % Found x3 as proof of (U Xx) % Found x200:=(x20 x5):(T Xx) % Found (x20 x5) as proof of (T Xx) % Found ((x2 Xx) x5) as proof of (T Xx) % Found ((x2 Xx) x5) as proof of (T Xx) % Found (x4 ((x2 Xx) x5)) as proof of False % Found (fun (x5:(S Xx))=> (x4 ((x2 Xx) x5))) as proof of False % Found (fun (x5:(S Xx))=> (x4 ((x2 Xx) x5))) as proof of ((S Xx)->False) % Found ((conj00 x3) (fun (x5:(S Xx))=> (x4 ((x2 Xx) x5)))) as proof of ((and (U Xx)) ((S Xx)->False)) % Found (((conj0 ((S Xx)->False)) x3) (fun (x5:(S Xx))=> (x4 ((x2 Xx) x5)))) as proof of ((and (U Xx)) ((S Xx)->False)) % Found ((((conj (U Xx)) ((S Xx)->False)) x3) (fun (x5:(S Xx))=> (x4 ((x2 Xx) x5)))) as proof of ((and (U Xx)) ((S Xx)->False)) % Found (fun (x4:((T Xx)->False))=> ((((conj (U Xx)) ((S Xx)->False)) x3) (fun (x5:(S Xx))=> (x4 ((x2 Xx) x5))))) as proof of ((and (U Xx)) ((S Xx)->False)) % Found (fun (x3:(U Xx)) (x4:((T Xx)->False))=> ((((conj (U Xx)) ((S Xx)->False)) x3) (fun (x5:(S Xx))=> (x4 ((x2 Xx) x5))))) as proof of (((T Xx)->False)->((and (U Xx)) ((S Xx)->False))) % Found (fun (x3:(U Xx)) (x4:((T Xx)->False))=> ((((conj (U Xx)) ((S Xx)->False)) x3) (fun (x5:(S Xx))=> (x4 ((x2 Xx) x5))))) as proof of ((U Xx)->(((T Xx)->False)->((and (U Xx)) ((S Xx)->False)))) % Found (and_rect10 (fun (x3:(U Xx)) (x4:((T Xx)->False))=> ((((conj (U Xx)) ((S Xx)->False)) x3) (fun (x5:(S Xx))=> (x4 ((x2 Xx) x5)))))) as proof of ((and (U Xx)) ((S Xx)->False)) % Found ((and_rect1 ((and (U Xx)) ((S Xx)->False))) (fun (x3:(U Xx)) (x4:((T Xx)->False))=> ((((conj (U Xx)) ((S Xx)->False)) x3) (fun (x5:(S Xx))=> (x4 ((x2 Xx) x5)))))) as proof of ((and (U Xx)) ((S Xx)->False)) % Found (((fun (P:Type) (x3:((U Xx)->(((T Xx)->False)->P)))=> (((((and_rect (U Xx)) ((T Xx)->False)) P) x3) x0)) ((and (U Xx)) ((S Xx)->False))) (fun (x3:(U Xx)) (x4:((T Xx)->False))=> ((((conj (U Xx)) ((S Xx)->False)) x3) (fun (x5:(S Xx))=> (x4 ((x2 Xx) x5)))))) as proof of ((and (U Xx)) ((S Xx)->False)) % Found (fun (x2:(forall (Xx0:a), ((S Xx0)->(T Xx0))))=> (((fun (P:Type) (x3:((U Xx)->(((T Xx)->False)->P)))=> (((((and_rect (U Xx)) ((T Xx)->False)) P) x3) x0)) ((and (U Xx)) ((S Xx)->False))) (fun (x3:(U Xx)) (x4:((T Xx)->False))=> ((((conj (U Xx)) ((S Xx)->False)) x3) (fun (x5:(S Xx))=> (x4 ((x2 Xx) x5))))))) as proof of ((and (U Xx)) ((S Xx)->False)) % Found (fun (x1:((and (forall (Xx0:a), ((S Xx0)->(U Xx0)))) (forall (Xx0:a), ((T Xx0)->(U Xx0))))) (x2:(forall (Xx0:a), ((S Xx0)->(T Xx0))))=> (((fun (P:Type) (x3:((U Xx)->(((T Xx)->False)->P)))=> (((((and_rect (U Xx)) ((T Xx)->False)) P) x3) x0)) ((and (U Xx)) ((S Xx)->False))) (fun (x3:(U Xx)) (x4:((T Xx)->False))=> ((((conj (U Xx)) ((S Xx)->False)) x3) (fun (x5:(S Xx))=> (x4 ((x2 Xx) x5))))))) as proof of ((forall (Xx0:a), ((S Xx0)->(T Xx0)))->((and (U Xx)) ((S Xx)->False))) % Found (fun (x1:((and (forall (Xx0:a), ((S Xx0)->(U Xx0)))) (forall (Xx0:a), ((T Xx0)->(U Xx0))))) (x2:(forall (Xx0:a), ((S Xx0)->(T Xx0))))=> (((fun (P:Type) (x3:((U Xx)->(((T Xx)->False)->P)))=> (((((and_rect (U Xx)) ((T Xx)->False)) P) x3) x0)) ((and (U Xx)) ((S Xx)->False))) (fun (x3:(U Xx)) (x4:((T Xx)->False))=> ((((conj (U Xx)) ((S Xx)->False)) x3) (fun (x5:(S Xx))=> (x4 ((x2 Xx) x5))))))) as proof of (((and (forall (Xx0:a), ((S Xx0)->(U Xx0)))) (forall (Xx0:a), ((T Xx0)->(U Xx0))))->((forall (Xx0:a), ((S Xx0)->(T Xx0)))->((and (U Xx)) ((S Xx)->False)))) % Found (and_rect00 (fun (x1:((and (forall (Xx0:a), ((S Xx0)->(U Xx0)))) (forall (Xx0:a), ((T Xx0)->(U Xx0))))) (x2:(forall (Xx0:a), ((S Xx0)->(T Xx0))))=> (((fun (P:Type) (x3:((U Xx)->(((T Xx)->False)->P)))=> (((((and_rect (U Xx)) ((T Xx)->False)) P) x3) x0)) ((and (U Xx)) ((S Xx)->False))) (fun (x3:(U Xx)) (x4:((T Xx)->False))=> ((((conj (U Xx)) ((S Xx)->False)) x3) (fun (x5:(S Xx))=> (x4 ((x2 Xx) x5)))))))) as proof of ((and (U Xx)) ((S Xx)->False)) % Found ((and_rect0 ((and (U Xx)) ((S Xx)->False))) (fun (x1:((and (forall (Xx0:a), ((S Xx0)->(U Xx0)))) (forall (Xx0:a), ((T Xx0)->(U Xx0))))) (x2:(forall (Xx0:a), ((S Xx0)->(T Xx0))))=> (((fun (P:Type) (x3:((U Xx)->(((T Xx)->False)->P)))=> (((((and_rect (U Xx)) ((T Xx)->False)) P) x3) x0)) ((and (U Xx)) ((S Xx)->False))) (fun (x3:(U Xx)) (x4:((T Xx)->False))=> ((((conj (U Xx)) ((S Xx)->False)) x3) (fun (x5:(S Xx))=> (x4 ((x2 Xx) x5)))))))) as proof of ((and (U Xx)) ((S Xx)->False)) % Found (((fun (P:Type) (x1:(((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))->((forall (Xx:a), ((S Xx)->(T Xx)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))) (forall (Xx:a), ((S Xx)->(T Xx)))) P) x1) x)) ((and (U Xx)) ((S Xx)->False))) (fun (x1:((and (forall (Xx0:a), ((S Xx0)->(U Xx0)))) (forall (Xx0:a), ((T Xx0)->(U Xx0))))) (x2:(forall (Xx0:a), ((S Xx0)->(T Xx0))))=> (((fun (P:Type) (x3:((U Xx)->(((T Xx)->False)->P)))=> (((((and_rect (U Xx)) ((T Xx)->False)) P) x3) x0)) ((and (U Xx)) ((S Xx)->False))) (fun (x3:(U Xx)) (x4:((T Xx)->False))=> ((((conj (U Xx)) ((S Xx)->False)) x3) (fun (x5:(S Xx))=> (x4 ((x2 Xx) x5)))))))) as proof of ((and (U Xx)) ((S Xx)->False)) % Found (fun (x0:((and (U Xx)) ((T Xx)->False)))=> (((fun (P:Type) (x1:(((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))->((forall (Xx:a), ((S Xx)->(T Xx)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))) (forall (Xx:a), ((S Xx)->(T Xx)))) P) x1) x)) ((and (U Xx)) ((S Xx)->False))) (fun (x1:((and (forall (Xx0:a), ((S Xx0)->(U Xx0)))) (forall (Xx0:a), ((T Xx0)->(U Xx0))))) (x2:(forall (Xx0:a), ((S Xx0)->(T Xx0))))=> (((fun (P:Type) (x3:((U Xx)->(((T Xx)->False)->P)))=> (((((and_rect (U Xx)) ((T Xx)->False)) P) x3) x0)) ((and (U Xx)) ((S Xx)->False))) (fun (x3:(U Xx)) (x4:((T Xx)->False))=> ((((conj (U Xx)) ((S Xx)->False)) x3) (fun (x5:(S Xx))=> (x4 ((x2 Xx) x5))))))))) as proof of ((and (U Xx)) ((S Xx)->False)) % Found (fun (Xx:a) (x0:((and (U Xx)) ((T Xx)->False)))=> (((fun (P:Type) (x1:(((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))->((forall (Xx:a), ((S Xx)->(T Xx)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))) (forall (Xx:a), ((S Xx)->(T Xx)))) P) x1) x)) ((and (U Xx)) ((S Xx)->False))) (fun (x1:((and (forall (Xx0:a), ((S Xx0)->(U Xx0)))) (forall (Xx0:a), ((T Xx0)->(U Xx0))))) (x2:(forall (Xx0:a), ((S Xx0)->(T Xx0))))=> (((fun (P:Type) (x3:((U Xx)->(((T Xx)->False)->P)))=> (((((and_rect (U Xx)) ((T Xx)->False)) P) x3) x0)) ((and (U Xx)) ((S Xx)->False))) (fun (x3:(U Xx)) (x4:((T Xx)->False))=> ((((conj (U Xx)) ((S Xx)->False)) x3) (fun (x5:(S Xx))=> (x4 ((x2 Xx) x5))))))))) as proof of (((and (U Xx)) ((T Xx)->False))->((and (U Xx)) ((S Xx)->False))) % Found (fun (x:((and ((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))) (forall (Xx:a), ((S Xx)->(T Xx))))) (Xx:a) (x0:((and (U Xx)) ((T Xx)->False)))=> (((fun (P:Type) (x1:(((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))->((forall (Xx:a), ((S Xx)->(T Xx)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))) (forall (Xx:a), ((S Xx)->(T Xx)))) P) x1) x)) ((and (U Xx)) ((S Xx)->False))) (fun (x1:((and (forall (Xx0:a), ((S Xx0)->(U Xx0)))) (forall (Xx0:a), ((T Xx0)->(U Xx0))))) (x2:(forall (Xx0:a), ((S Xx0)->(T Xx0))))=> (((fun (P:Type) (x3:((U Xx)->(((T Xx)->False)->P)))=> (((((and_rect (U Xx)) ((T Xx)->False)) P) x3) x0)) ((and (U Xx)) ((S Xx)->False))) (fun (x3:(U Xx)) (x4:((T Xx)->False))=> ((((conj (U Xx)) ((S Xx)->False)) x3) (fun (x5:(S Xx))=> (x4 ((x2 Xx) x5))))))))) as proof of (forall (Xx:a), (((and (U Xx)) ((T Xx)->False))->((and (U Xx)) ((S Xx)->False)))) % Found (fun (U:(a->Prop)) (x:((and ((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))) (forall (Xx:a), ((S Xx)->(T Xx))))) (Xx:a) (x0:((and (U Xx)) ((T Xx)->False)))=> (((fun (P:Type) (x1:(((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))->((forall (Xx:a), ((S Xx)->(T Xx)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))) (forall (Xx:a), ((S Xx)->(T Xx)))) P) x1) x)) ((and (U Xx)) ((S Xx)->False))) (fun (x1:((and (forall (Xx0:a), ((S Xx0)->(U Xx0)))) (forall (Xx0:a), ((T Xx0)->(U Xx0))))) (x2:(forall (Xx0:a), ((S Xx0)->(T Xx0))))=> (((fun (P:Type) (x3:((U Xx)->(((T Xx)->False)->P)))=> (((((and_rect (U Xx)) ((T Xx)->False)) P) x3) x0)) ((and (U Xx)) ((S Xx)->False))) (fun (x3:(U Xx)) (x4:((T Xx)->False))=> ((((conj (U Xx)) ((S Xx)->False)) x3) (fun (x5:(S Xx))=> (x4 ((x2 Xx) x5))))))))) as proof of (((and ((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))) (forall (Xx:a), ((S Xx)->(T Xx))))->(forall (Xx:a), (((and (U Xx)) ((T Xx)->False))->((and (U Xx)) ((S Xx)->False))))) % Found (fun (T:(a->Prop)) (U:(a->Prop)) (x:((and ((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))) (forall (Xx:a), ((S Xx)->(T Xx))))) (Xx:a) (x0:((and (U Xx)) ((T Xx)->False)))=> (((fun (P:Type) (x1:(((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))->((forall (Xx:a), ((S Xx)->(T Xx)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))) (forall (Xx:a), ((S Xx)->(T Xx)))) P) x1) x)) ((and (U Xx)) ((S Xx)->False))) (fun (x1:((and (forall (Xx0:a), ((S Xx0)->(U Xx0)))) (forall (Xx0:a), ((T Xx0)->(U Xx0))))) (x2:(forall (Xx0:a), ((S Xx0)->(T Xx0))))=> (((fun (P:Type) (x3:((U Xx)->(((T Xx)->False)->P)))=> (((((and_rect (U Xx)) ((T Xx)->False)) P) x3) x0)) ((and (U Xx)) ((S Xx)->False))) (fun (x3:(U Xx)) (x4:((T Xx)->False))=> ((((conj (U Xx)) ((S Xx)->False)) x3) (fun (x5:(S Xx))=> (x4 ((x2 Xx) x5))))))))) as proof of (forall (U:(a->Prop)), (((and ((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))) (forall (Xx:a), ((S Xx)->(T Xx))))->(forall (Xx:a), (((and (U Xx)) ((T Xx)->False))->((and (U Xx)) ((S Xx)->False)))))) % Found (fun (S:(a->Prop)) (T:(a->Prop)) (U:(a->Prop)) (x:((and ((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))) (forall (Xx:a), ((S Xx)->(T Xx))))) (Xx:a) (x0:((and (U Xx)) ((T Xx)->False)))=> (((fun (P:Type) (x1:(((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))->((forall (Xx:a), ((S Xx)->(T Xx)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))) (forall (Xx:a), ((S Xx)->(T Xx)))) P) x1) x)) ((and (U Xx)) ((S Xx)->False))) (fun (x1:((and (forall (Xx0:a), ((S Xx0)->(U Xx0)))) (forall (Xx0:a), ((T Xx0)->(U Xx0))))) (x2:(forall (Xx0:a), ((S Xx0)->(T Xx0))))=> (((fun (P:Type) (x3:((U Xx)->(((T Xx)->False)->P)))=> (((((and_rect (U Xx)) ((T Xx)->False)) P) x3) x0)) ((and (U Xx)) ((S Xx)->False))) (fun (x3:(U Xx)) (x4:((T Xx)->False))=> ((((conj (U Xx)) ((S Xx)->False)) x3) (fun (x5:(S Xx))=> (x4 ((x2 Xx) x5))))))))) as proof of (forall (T:(a->Prop)) (U:(a->Prop)), (((and ((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))) (forall (Xx:a), ((S Xx)->(T Xx))))->(forall (Xx:a), (((and (U Xx)) ((T Xx)->False))->((and (U Xx)) ((S Xx)->False)))))) % Found (fun (S:(a->Prop)) (T:(a->Prop)) (U:(a->Prop)) (x:((and ((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))) (forall (Xx:a), ((S Xx)->(T Xx))))) (Xx:a) (x0:((and (U Xx)) ((T Xx)->False)))=> (((fun (P:Type) (x1:(((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))->((forall (Xx:a), ((S Xx)->(T Xx)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))) (forall (Xx:a), ((S Xx)->(T Xx)))) P) x1) x)) ((and (U Xx)) ((S Xx)->False))) (fun (x1:((and (forall (Xx0:a), ((S Xx0)->(U Xx0)))) (forall (Xx0:a), ((T Xx0)->(U Xx0))))) (x2:(forall (Xx0:a), ((S Xx0)->(T Xx0))))=> (((fun (P:Type) (x3:((U Xx)->(((T Xx)->False)->P)))=> (((((and_rect (U Xx)) ((T Xx)->False)) P) x3) x0)) ((and (U Xx)) ((S Xx)->False))) (fun (x3:(U Xx)) (x4:((T Xx)->False))=> ((((conj (U Xx)) ((S Xx)->False)) x3) (fun (x5:(S Xx))=> (x4 ((x2 Xx) x5))))))))) as proof of (forall (S:(a->Prop)) (T:(a->Prop)) (U:(a->Prop)), (((and ((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))) (forall (Xx:a), ((S Xx)->(T Xx))))->(forall (Xx:a), (((and (U Xx)) ((T Xx)->False))->((and (U Xx)) ((S Xx)->False)))))) % Got proof (fun (S:(a->Prop)) (T:(a->Prop)) (U:(a->Prop)) (x:((and ((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))) (forall (Xx:a), ((S Xx)->(T Xx))))) (Xx:a) (x0:((and (U Xx)) ((T Xx)->False)))=> (((fun (P:Type) (x1:(((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))->((forall (Xx:a), ((S Xx)->(T Xx)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))) (forall (Xx:a), ((S Xx)->(T Xx)))) P) x1) x)) ((and (U Xx)) ((S Xx)->False))) (fun (x1:((and (forall (Xx0:a), ((S Xx0)->(U Xx0)))) (forall (Xx0:a), ((T Xx0)->(U Xx0))))) (x2:(forall (Xx0:a), ((S Xx0)->(T Xx0))))=> (((fun (P:Type) (x3:((U Xx)->(((T Xx)->False)->P)))=> (((((and_rect (U Xx)) ((T Xx)->False)) P) x3) x0)) ((and (U Xx)) ((S Xx)->False))) (fun (x3:(U Xx)) (x4:((T Xx)->False))=> ((((conj (U Xx)) ((S Xx)->False)) x3) (fun (x5:(S Xx))=> (x4 ((x2 Xx) x5))))))))) % Time elapsed = 3.006928s % node=717 cost=666.000000 depth=27 % :::::::::::::::::::::: % % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % (fun (S:(a->Prop)) (T:(a->Prop)) (U:(a->Prop)) (x:((and ((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))) (forall (Xx:a), ((S Xx)->(T Xx))))) (Xx:a) (x0:((and (U Xx)) ((T Xx)->False)))=> (((fun (P:Type) (x1:(((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))->((forall (Xx:a), ((S Xx)->(T Xx)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((S Xx)->(U Xx)))) (forall (Xx:a), ((T Xx)->(U Xx))))) (forall (Xx:a), ((S Xx)->(T Xx)))) P) x1) x)) ((and (U Xx)) ((S Xx)->False))) (fun (x1:((and (forall (Xx0:a), ((S Xx0)->(U Xx0)))) (forall (Xx0:a), ((T Xx0)->(U Xx0))))) (x2:(forall (Xx0:a), ((S Xx0)->(T Xx0))))=> (((fun (P:Type) (x3:((U Xx)->(((T Xx)->False)->P)))=> (((((and_rect (U Xx)) ((T Xx)->False)) P) x3) x0)) ((and (U Xx)) ((S Xx)->False))) (fun (x3:(U Xx)) (x4:((T Xx)->False))=> ((((conj (U Xx)) ((S Xx)->False)) x3) (fun (x5:(S Xx))=> (x4 ((x2 Xx) x5))))))))) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF %------------------------------------------------------------------------------