%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SEU695^2 : TPTP v6.1.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n185.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 13:32:50 EDT 2014 % Result : Theorem 4.10s % Output : Proof 4.10s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SEU695^2 : TPTP v6.1.0. Released v3.7.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n185.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 11:13:46 CDT 2014 % % CPUTime : 4.10 % 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 0x1696128>, <kernel.DependentProduct object at 0x16764d0>) of role type named in_type % Using role type % Declaring in:(fofType->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x16965a8>, <kernel.DependentProduct object at 0x16764d0>) of role type named kpair_type % Using role type % Declaring kpair:(fofType->(fofType->fofType)) % FOF formula (<kernel.Constant object at 0x18ed7e8>, <kernel.DependentProduct object at 0x1676170>) of role type named dpsetconstr_type % Using role type % Declaring dpsetconstr:(fofType->(fofType->((fofType->(fofType->Prop))->fofType))) % FOF formula (<kernel.Constant object at 0x16965a8>, <kernel.Sort object at 0x1379f38>) of role type named dpsetconstrI_type % Using role type % Declaring dpsetconstrI:Prop % FOF formula (((eq Prop) dpsetconstrI) (forall (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop))) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((Xphi Xx) Xy)->((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)))))))))) of role definition named dpsetconstrI % A new definition: (((eq Prop) dpsetconstrI) (forall (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop))) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((Xphi Xx) Xy)->((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu)))))))))) % Defined: dpsetconstrI:=(forall (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop))) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((Xphi Xx) Xy)->((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu))))))))) % FOF formula (<kernel.Constant object at 0x137df80>, <kernel.DependentProduct object at 0x1676050>) of role type named func_type % Using role type % Declaring func:(fofType->(fofType->(fofType->Prop))) % FOF formula (<kernel.Constant object at 0x1676248>, <kernel.DependentProduct object at 0x16761b8>) of role type named ap_type % Using role type % Declaring ap:(fofType->(fofType->(fofType->(fofType->fofType)))) % FOF formula (<kernel.Constant object at 0x1676170>, <kernel.DependentProduct object at 0x1676488>) of role type named lam_type % Using role type % Declaring lam:(fofType->(fofType->((fofType->fofType)->fofType))) % FOF formula (((eq (fofType->(fofType->((fofType->fofType)->fofType)))) lam) (fun (A:fofType) (B:fofType) (Xf:(fofType->fofType))=> (((dpsetconstr A) B) (fun (Xx:fofType) (Xy:fofType)=> (((eq fofType) (Xf Xx)) Xy))))) of role definition named lam % A new definition: (((eq (fofType->(fofType->((fofType->fofType)->fofType)))) lam) (fun (A:fofType) (B:fofType) (Xf:(fofType->fofType))=> (((dpsetconstr A) B) (fun (Xx:fofType) (Xy:fofType)=> (((eq fofType) (Xf Xx)) Xy))))) % Defined: lam:=(fun (A:fofType) (B:fofType) (Xf:(fofType->fofType))=> (((dpsetconstr A) B) (fun (Xx:fofType) (Xy:fofType)=> (((eq fofType) (Xf Xx)) Xy)))) % FOF formula (<kernel.Constant object at 0x16761b8>, <kernel.Sort object at 0x1379f38>) of role type named lamp_type % Using role type % Declaring lamp:Prop % FOF formula (((eq Prop) lamp) (forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(((func A) B) (((lam A) B) (fun (Xx:fofType)=> (Xf Xx))))))) of role definition named lamp % A new definition: (((eq Prop) lamp) (forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(((func A) B) (((lam A) B) (fun (Xx:fofType)=> (Xf Xx))))))) % Defined: lamp:=(forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(((func A) B) (((lam A) B) (fun (Xx:fofType)=> (Xf Xx)))))) % FOF formula (<kernel.Constant object at 0x1381680>, <kernel.Sort object at 0x1379f38>) of role type named funcGraphProp2_type % Using role type % Declaring funcGraphProp2:Prop % FOF formula (((eq Prop) funcGraphProp2) (forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy))))))))) of role definition named funcGraphProp2 % A new definition: (((eq Prop) funcGraphProp2) (forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy))))))))) % Defined: funcGraphProp2:=(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy)))))))) % FOF formula (dpsetconstrI->(lamp->(funcGraphProp2->(forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx))))))))) of role conjecture named beta1 % Conjecture to prove = (dpsetconstrI->(lamp->(funcGraphProp2->(forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx))))))))):Prop % Parameter fofType_DUMMY:fofType. % We need to prove ['(dpsetconstrI->(lamp->(funcGraphProp2->(forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx)))))))))'] % Parameter fofType:Type. % Parameter in:(fofType->(fofType->Prop)). % Parameter kpair:(fofType->(fofType->fofType)). % Parameter dpsetconstr:(fofType->(fofType->((fofType->(fofType->Prop))->fofType))). % Definition dpsetconstrI:=(forall (A:fofType) (B:fofType) (Xphi:(fofType->(fofType->Prop))) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((Xphi Xx) Xy)->((in ((kpair Xx) Xy)) (((dpsetconstr A) B) (fun (Xz:fofType) (Xu:fofType)=> ((Xphi Xz) Xu))))))))):Prop. % Parameter func:(fofType->(fofType->(fofType->Prop))). % Parameter ap:(fofType->(fofType->(fofType->(fofType->fofType)))). % Definition lam:=(fun (A:fofType) (B:fofType) (Xf:(fofType->fofType))=> (((dpsetconstr A) B) (fun (Xx:fofType) (Xy:fofType)=> (((eq fofType) (Xf Xx)) Xy)))):(fofType->(fofType->((fofType->fofType)->fofType))). % Definition lamp:=(forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(((func A) B) (((lam A) B) (fun (Xx:fofType)=> (Xf Xx)))))):Prop. % Definition funcGraphProp2:=(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->(((in ((kpair Xx) Xy)) Xf)->(((eq fofType) ((((ap A) B) Xf) Xx)) Xy)))))))):Prop. % Trying to prove (dpsetconstrI->(lamp->(funcGraphProp2->(forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx))))))))) % Found x40:(P ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) % Found (fun (x40:(P ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)))=> x40) as proof of (P ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) % Found (fun (x40:(P ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)))=> x40) as proof of (P0 ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) % Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b) % Found (eq_ref0 b) as proof of (((eq fofType) b) (Xf Xx)) % Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xf Xx)) % Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xf Xx)) % Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xf Xx)) % Found eq_ref00:=(eq_ref0 ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)):(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) % Found (eq_ref0 ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) as proof of (((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) b) % Found ((eq_ref fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) as proof of (((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) b) % Found ((eq_ref fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) as proof of (((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) b) % Found ((eq_ref fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) as proof of (((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) b) % Found x3:((in Xx) A) % Found x3 as proof of ((in Xx) A) % Found x200:=(x20 x3):((in (Xf Xx)) B) % Found (x20 x3) as proof of ((in (Xf Xx)) B) % Found ((x2 Xx) x3) as proof of ((in (Xf Xx)) B) % Found ((x2 Xx) x3) as proof of ((in (Xf Xx)) B) % Found x00000:=(x0000 x2):(((func A) B) (((lam A) B) (fun (Xx:fofType)=> (Xf Xx)))) % Found (x0000 x2) as proof of (((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) % Found ((x000 Xf) x2) as proof of (((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) % Found (((x00 B) Xf) x2) as proof of (((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) % Found ((((x0 A) B) Xf) x2) as proof of (((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) % Found ((((x0 A) B) Xf) x2) as proof of (((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) % Found eq_ref00:=(eq_ref0 (Xf Xx)):(((eq fofType) (Xf Xx)) (Xf Xx)) % Found (eq_ref0 (Xf Xx)) as proof of (((eq fofType) (Xf Xx)) (Xf Xx)) % Found ((eq_ref fofType) (Xf Xx)) as proof of (((eq fofType) (Xf Xx)) (Xf Xx)) % Found ((eq_ref fofType) (Xf Xx)) as proof of (((eq fofType) (Xf Xx)) (Xf Xx)) % Found x200:=(x20 x3):((in (Xf Xx)) B) % Found (x20 x3) as proof of ((in (Xf Xx)) B) % Found ((x2 Xx) x3) as proof of ((in (Xf Xx)) B) % Found ((x2 Xx) x3) as proof of ((in (Xf Xx)) B) % Found ((x400000 ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))) as proof of ((in ((kpair Xx) (Xf Xx))) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) % Found (((x40000 (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))) as proof of ((in ((kpair Xx) (Xf Xx))) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) % Found ((((x4000 x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))) as proof of ((in ((kpair Xx) (Xf Xx))) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) % Found (((((x400 Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))) as proof of ((in ((kpair Xx) (Xf Xx))) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) % Found ((((((x40 (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))) as proof of ((in ((kpair Xx) (Xf Xx))) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) % Found (((((((x4 B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))) as proof of ((in ((kpair Xx) (Xf Xx))) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) % Found ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))) as proof of ((in ((kpair Xx) (Xf Xx))) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) % Found ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))) as proof of ((in ((kpair Xx) (Xf Xx))) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) % Found ((((x100000 ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx)))) as proof of (((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx)) % Found (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> (((x10000 x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx)))) as proof of (((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx)) % Found (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> ((x1000 x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx)))) as proof of (((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx)) % Found (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> (((x100 (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx)))) as proof of (((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx)) % Found (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> ((((x10 B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx)))) as proof of (((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx)) % Found (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> (((((x1 A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx)))) as proof of (((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx)) % Found (fun (x3:((in Xx) A))=> (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> (((((x1 A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))))) as proof of (((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx)) % Found (fun (Xx:fofType) (x3:((in Xx) A))=> (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> (((((x1 A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))))) as proof of (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx))) % Found (fun (x2:(forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))) (Xx:fofType) (x3:((in Xx) A))=> (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> (((((x1 A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))))) as proof of (forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx)))) % Found (fun (Xf:(fofType->fofType)) (x2:(forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))) (Xx:fofType) (x3:((in Xx) A))=> (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> (((((x1 A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))))) as proof of ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx))))) % Found (fun (B:fofType) (Xf:(fofType->fofType)) (x2:(forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))) (Xx:fofType) (x3:((in Xx) A))=> (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> (((((x1 A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))))) as proof of (forall (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx)))))) % Found (fun (A:fofType) (B:fofType) (Xf:(fofType->fofType)) (x2:(forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))) (Xx:fofType) (x3:((in Xx) A))=> (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> (((((x1 A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))))) as proof of (forall (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx)))))) % Found (fun (x1:funcGraphProp2) (A:fofType) (B:fofType) (Xf:(fofType->fofType)) (x2:(forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))) (Xx:fofType) (x3:((in Xx) A))=> (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> (((((x1 A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))))) as proof of (forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx)))))) % Found (fun (x0:lamp) (x1:funcGraphProp2) (A:fofType) (B:fofType) (Xf:(fofType->fofType)) (x2:(forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))) (Xx:fofType) (x3:((in Xx) A))=> (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> (((((x1 A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))))) as proof of (funcGraphProp2->(forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx))))))) % Found (fun (x:dpsetconstrI) (x0:lamp) (x1:funcGraphProp2) (A:fofType) (B:fofType) (Xf:(fofType->fofType)) (x2:(forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))) (Xx:fofType) (x3:((in Xx) A))=> (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> (((((x1 A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))))) as proof of (lamp->(funcGraphProp2->(forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx)))))))) % Found (fun (x:dpsetconstrI) (x0:lamp) (x1:funcGraphProp2) (A:fofType) (B:fofType) (Xf:(fofType->fofType)) (x2:(forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))) (Xx:fofType) (x3:((in Xx) A))=> (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> (((((x1 A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))))) as proof of (dpsetconstrI->(lamp->(funcGraphProp2->(forall (A:fofType) (B:fofType) (Xf:(fofType->fofType)), ((forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))->(forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) Xx)) (Xf Xx))))))))) % Got proof (fun (x:dpsetconstrI) (x0:lamp) (x1:funcGraphProp2) (A:fofType) (B:fofType) (Xf:(fofType->fofType)) (x2:(forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))) (Xx:fofType) (x3:((in Xx) A))=> (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> (((((x1 A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))))) % Time elapsed = 3.730936s % node=517 cost=716.000000 depth=26 % :::::::::::::::::::::: % % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % (fun (x:dpsetconstrI) (x0:lamp) (x1:funcGraphProp2) (A:fofType) (B:fofType) (Xf:(fofType->fofType)) (x2:(forall (Xx:fofType), (((in Xx) A)->((in (Xf Xx)) B)))) (Xx:fofType) (x3:((in Xx) A))=> (((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy))))) (x5:((in Xx) A))=> ((((fun (x4:(((func A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))))=> (((((x1 A) B) (((lam A) B) (fun (Xy:fofType)=> (Xf Xy)))) x4) Xx)) x4) x5) (Xf Xx))) ((((x0 A) B) Xf) x2)) x3) ((x2 Xx) x3)) ((((((((x A) B) (fun (x12:fofType)=> ((eq fofType) (Xf x12)))) Xx) x3) (Xf Xx)) ((x2 Xx) x3)) ((eq_ref fofType) (Xf Xx))))) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF %------------------------------------------------------------------------------