%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SEU941^5 : TPTP v6.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n109.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 13:33:24 EDT 2014 % Result : Theorem 1.86s % Output : Proof 1.86s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SEU941^5 : TPTP v6.1.0. Released v4.0.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n109.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 11:44:26 CDT 2014 % % CPUTime : 1.86 % 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 0x11c3e18>, <kernel.Type object at 0x11c3128>) of role type named a_type % Using role type % Declaring a:Type % FOF formula (<kernel.Constant object at 0x11c35a8>, <kernel.Type object at 0xde7998>) of role type named b_type % Using role type % Declaring b:Type % FOF formula (<kernel.Constant object at 0xde79e0>, <kernel.Type object at 0x11c3128>) of role type named c_type % Using role type % Declaring c:Type % FOF formula (forall (F:(a->b)) (G:(b->c)), (((and (forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))) (forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy))))->(forall (Xx:a) (Xy:a), ((((eq c) (G (F Xx))) (G (F Xy)))->(((eq a) Xx) Xy))))) of role conjecture named cFN_THM_1_pme % Conjecture to prove = (forall (F:(a->b)) (G:(b->c)), (((and (forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))) (forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy))))->(forall (Xx:a) (Xy:a), ((((eq c) (G (F Xx))) (G (F Xy)))->(((eq a) Xx) Xy))))):Prop % Parameter a_DUMMY:a. % Parameter b_DUMMY:b. % Parameter c_DUMMY:c. % We need to prove ['(forall (F:(a->b)) (G:(b->c)), (((and (forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))) (forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy))))->(forall (Xx:a) (Xy:a), ((((eq c) (G (F Xx))) (G (F Xy)))->(((eq a) Xx) Xy)))))'] % Parameter a:Type. % Parameter b:Type. % Parameter c:Type. % Trying to prove (forall (F:(a->b)) (G:(b->c)), (((and (forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))) (forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy))))->(forall (Xx:a) (Xy:a), ((((eq c) (G (F Xx))) (G (F Xy)))->(((eq a) Xx) Xy))))) % Found x2000:=(x200 x0):(((eq b) (F Xx)) (F Xy)) % Found (x200 x0) as proof of (((eq b) (F Xx)) (F Xy)) % Found ((x20 (F Xy)) x0) as proof of (((eq b) (F Xx)) (F Xy)) % Found (((x2 (F Xx)) (F Xy)) x0) as proof of (((eq b) (F Xx)) (F Xy)) % Found (((x2 (F Xx)) (F Xy)) x0) as proof of (((eq b) (F Xx)) (F Xy)) % Found (x100 (((x2 (F Xx)) (F Xy)) x0)) as proof of (((eq a) Xx) Xy) % Found ((x10 Xy) (((x2 (F Xx)) (F Xy)) x0)) as proof of (((eq a) Xx) Xy) % Found (((x1 Xx) Xy) (((x2 (F Xx)) (F Xy)) x0)) as proof of (((eq a) Xx) Xy) % Found (fun (x2:(forall (Xx0:b) (Xy0:b), ((((eq c) (G Xx0)) (G Xy0))->(((eq b) Xx0) Xy0))))=> (((x1 Xx) Xy) (((x2 (F Xx)) (F Xy)) x0))) as proof of (((eq a) Xx) Xy) % Found (fun (x1:(forall (Xx0:a) (Xy0:a), ((((eq b) (F Xx0)) (F Xy0))->(((eq a) Xx0) Xy0)))) (x2:(forall (Xx0:b) (Xy0:b), ((((eq c) (G Xx0)) (G Xy0))->(((eq b) Xx0) Xy0))))=> (((x1 Xx) Xy) (((x2 (F Xx)) (F Xy)) x0))) as proof of ((forall (Xx0:b) (Xy0:b), ((((eq c) (G Xx0)) (G Xy0))->(((eq b) Xx0) Xy0)))->(((eq a) Xx) Xy)) % Found (fun (x1:(forall (Xx0:a) (Xy0:a), ((((eq b) (F Xx0)) (F Xy0))->(((eq a) Xx0) Xy0)))) (x2:(forall (Xx0:b) (Xy0:b), ((((eq c) (G Xx0)) (G Xy0))->(((eq b) Xx0) Xy0))))=> (((x1 Xx) Xy) (((x2 (F Xx)) (F Xy)) x0))) as proof of ((forall (Xx0:a) (Xy0:a), ((((eq b) (F Xx0)) (F Xy0))->(((eq a) Xx0) Xy0)))->((forall (Xx0:b) (Xy0:b), ((((eq c) (G Xx0)) (G Xy0))->(((eq b) Xx0) Xy0)))->(((eq a) Xx) Xy))) % Found (and_rect00 (fun (x1:(forall (Xx0:a) (Xy0:a), ((((eq b) (F Xx0)) (F Xy0))->(((eq a) Xx0) Xy0)))) (x2:(forall (Xx0:b) (Xy0:b), ((((eq c) (G Xx0)) (G Xy0))->(((eq b) Xx0) Xy0))))=> (((x1 Xx) Xy) (((x2 (F Xx)) (F Xy)) x0)))) as proof of (((eq a) Xx) Xy) % Found ((and_rect0 (((eq a) Xx) Xy)) (fun (x1:(forall (Xx0:a) (Xy0:a), ((((eq b) (F Xx0)) (F Xy0))->(((eq a) Xx0) Xy0)))) (x2:(forall (Xx0:b) (Xy0:b), ((((eq c) (G Xx0)) (G Xy0))->(((eq b) Xx0) Xy0))))=> (((x1 Xx) Xy) (((x2 (F Xx)) (F Xy)) x0)))) as proof of (((eq a) Xx) Xy) % Found (((fun (P:Type) (x1:((forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))->((forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy)))->P)))=> (((((and_rect (forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))) (forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy)))) P) x1) x)) (((eq a) Xx) Xy)) (fun (x1:(forall (Xx0:a) (Xy0:a), ((((eq b) (F Xx0)) (F Xy0))->(((eq a) Xx0) Xy0)))) (x2:(forall (Xx0:b) (Xy0:b), ((((eq c) (G Xx0)) (G Xy0))->(((eq b) Xx0) Xy0))))=> (((x1 Xx) Xy) (((x2 (F Xx)) (F Xy)) x0)))) as proof of (((eq a) Xx) Xy) % Found (fun (x0:(((eq c) (G (F Xx))) (G (F Xy))))=> (((fun (P:Type) (x1:((forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))->((forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy)))->P)))=> (((((and_rect (forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))) (forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy)))) P) x1) x)) (((eq a) Xx) Xy)) (fun (x1:(forall (Xx0:a) (Xy0:a), ((((eq b) (F Xx0)) (F Xy0))->(((eq a) Xx0) Xy0)))) (x2:(forall (Xx0:b) (Xy0:b), ((((eq c) (G Xx0)) (G Xy0))->(((eq b) Xx0) Xy0))))=> (((x1 Xx) Xy) (((x2 (F Xx)) (F Xy)) x0))))) as proof of (((eq a) Xx) Xy) % Found (fun (Xy:a) (x0:(((eq c) (G (F Xx))) (G (F Xy))))=> (((fun (P:Type) (x1:((forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))->((forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy)))->P)))=> (((((and_rect (forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))) (forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy)))) P) x1) x)) (((eq a) Xx) Xy)) (fun (x1:(forall (Xx0:a) (Xy0:a), ((((eq b) (F Xx0)) (F Xy0))->(((eq a) Xx0) Xy0)))) (x2:(forall (Xx0:b) (Xy0:b), ((((eq c) (G Xx0)) (G Xy0))->(((eq b) Xx0) Xy0))))=> (((x1 Xx) Xy) (((x2 (F Xx)) (F Xy)) x0))))) as proof of ((((eq c) (G (F Xx))) (G (F Xy)))->(((eq a) Xx) Xy)) % Found (fun (Xx:a) (Xy:a) (x0:(((eq c) (G (F Xx))) (G (F Xy))))=> (((fun (P:Type) (x1:((forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))->((forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy)))->P)))=> (((((and_rect (forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))) (forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy)))) P) x1) x)) (((eq a) Xx) Xy)) (fun (x1:(forall (Xx0:a) (Xy0:a), ((((eq b) (F Xx0)) (F Xy0))->(((eq a) Xx0) Xy0)))) (x2:(forall (Xx0:b) (Xy0:b), ((((eq c) (G Xx0)) (G Xy0))->(((eq b) Xx0) Xy0))))=> (((x1 Xx) Xy) (((x2 (F Xx)) (F Xy)) x0))))) as proof of (forall (Xy:a), ((((eq c) (G (F Xx))) (G (F Xy)))->(((eq a) Xx) Xy))) % Found (fun (x:((and (forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))) (forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy))))) (Xx:a) (Xy:a) (x0:(((eq c) (G (F Xx))) (G (F Xy))))=> (((fun (P:Type) (x1:((forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))->((forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy)))->P)))=> (((((and_rect (forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))) (forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy)))) P) x1) x)) (((eq a) Xx) Xy)) (fun (x1:(forall (Xx0:a) (Xy0:a), ((((eq b) (F Xx0)) (F Xy0))->(((eq a) Xx0) Xy0)))) (x2:(forall (Xx0:b) (Xy0:b), ((((eq c) (G Xx0)) (G Xy0))->(((eq b) Xx0) Xy0))))=> (((x1 Xx) Xy) (((x2 (F Xx)) (F Xy)) x0))))) as proof of (forall (Xx:a) (Xy:a), ((((eq c) (G (F Xx))) (G (F Xy)))->(((eq a) Xx) Xy))) % Found (fun (G:(b->c)) (x:((and (forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))) (forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy))))) (Xx:a) (Xy:a) (x0:(((eq c) (G (F Xx))) (G (F Xy))))=> (((fun (P:Type) (x1:((forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))->((forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy)))->P)))=> (((((and_rect (forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))) (forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy)))) P) x1) x)) (((eq a) Xx) Xy)) (fun (x1:(forall (Xx0:a) (Xy0:a), ((((eq b) (F Xx0)) (F Xy0))->(((eq a) Xx0) Xy0)))) (x2:(forall (Xx0:b) (Xy0:b), ((((eq c) (G Xx0)) (G Xy0))->(((eq b) Xx0) Xy0))))=> (((x1 Xx) Xy) (((x2 (F Xx)) (F Xy)) x0))))) as proof of (((and (forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))) (forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy))))->(forall (Xx:a) (Xy:a), ((((eq c) (G (F Xx))) (G (F Xy)))->(((eq a) Xx) Xy)))) % Found (fun (F:(a->b)) (G:(b->c)) (x:((and (forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))) (forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy))))) (Xx:a) (Xy:a) (x0:(((eq c) (G (F Xx))) (G (F Xy))))=> (((fun (P:Type) (x1:((forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))->((forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy)))->P)))=> (((((and_rect (forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))) (forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy)))) P) x1) x)) (((eq a) Xx) Xy)) (fun (x1:(forall (Xx0:a) (Xy0:a), ((((eq b) (F Xx0)) (F Xy0))->(((eq a) Xx0) Xy0)))) (x2:(forall (Xx0:b) (Xy0:b), ((((eq c) (G Xx0)) (G Xy0))->(((eq b) Xx0) Xy0))))=> (((x1 Xx) Xy) (((x2 (F Xx)) (F Xy)) x0))))) as proof of (forall (G:(b->c)), (((and (forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))) (forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy))))->(forall (Xx:a) (Xy:a), ((((eq c) (G (F Xx))) (G (F Xy)))->(((eq a) Xx) Xy))))) % Found (fun (F:(a->b)) (G:(b->c)) (x:((and (forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))) (forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy))))) (Xx:a) (Xy:a) (x0:(((eq c) (G (F Xx))) (G (F Xy))))=> (((fun (P:Type) (x1:((forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))->((forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy)))->P)))=> (((((and_rect (forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))) (forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy)))) P) x1) x)) (((eq a) Xx) Xy)) (fun (x1:(forall (Xx0:a) (Xy0:a), ((((eq b) (F Xx0)) (F Xy0))->(((eq a) Xx0) Xy0)))) (x2:(forall (Xx0:b) (Xy0:b), ((((eq c) (G Xx0)) (G Xy0))->(((eq b) Xx0) Xy0))))=> (((x1 Xx) Xy) (((x2 (F Xx)) (F Xy)) x0))))) as proof of (forall (F:(a->b)) (G:(b->c)), (((and (forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))) (forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy))))->(forall (Xx:a) (Xy:a), ((((eq c) (G (F Xx))) (G (F Xy)))->(((eq a) Xx) Xy))))) % Got proof (fun (F:(a->b)) (G:(b->c)) (x:((and (forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))) (forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy))))) (Xx:a) (Xy:a) (x0:(((eq c) (G (F Xx))) (G (F Xy))))=> (((fun (P:Type) (x1:((forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))->((forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy)))->P)))=> (((((and_rect (forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))) (forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy)))) P) x1) x)) (((eq a) Xx) Xy)) (fun (x1:(forall (Xx0:a) (Xy0:a), ((((eq b) (F Xx0)) (F Xy0))->(((eq a) Xx0) Xy0)))) (x2:(forall (Xx0:b) (Xy0:b), ((((eq c) (G Xx0)) (G Xy0))->(((eq b) Xx0) Xy0))))=> (((x1 Xx) Xy) (((x2 (F Xx)) (F Xy)) x0))))) % Time elapsed = 1.539745s % node=176 cost=349.000000 depth=19 % :::::::::::::::::::::: % % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % (fun (F:(a->b)) (G:(b->c)) (x:((and (forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))) (forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy))))) (Xx:a) (Xy:a) (x0:(((eq c) (G (F Xx))) (G (F Xy))))=> (((fun (P:Type) (x1:((forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))->((forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy)))->P)))=> (((((and_rect (forall (Xx:a) (Xy:a), ((((eq b) (F Xx)) (F Xy))->(((eq a) Xx) Xy)))) (forall (Xx:b) (Xy:b), ((((eq c) (G Xx)) (G Xy))->(((eq b) Xx) Xy)))) P) x1) x)) (((eq a) Xx) Xy)) (fun (x1:(forall (Xx0:a) (Xy0:a), ((((eq b) (F Xx0)) (F Xy0))->(((eq a) Xx0) Xy0)))) (x2:(forall (Xx0:b) (Xy0:b), ((((eq c) (G Xx0)) (G Xy0))->(((eq b) Xx0) Xy0))))=> (((x1 Xx) Xy) (((x2 (F Xx)) (F Xy)) x0))))) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF %------------------------------------------------------------------------------