%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SEU677^2 : TPTP v6.1.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n099.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 13:32:47 EDT 2014 % Result : Theorem 0.90s % Output : Proof 0.90s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SEU677^2 : TPTP v6.1.0. Released v3.7.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n099.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 11:08:31 CDT 2014 % % CPUTime : 0.90 % 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 0x14a5710>, <kernel.DependentProduct object at 0x14a5b90>) of role type named in_type % Using role type % Declaring in:(fofType->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x14a5c20>, <kernel.Single object at 0x14a5cf8>) of role type named emptyset_type % Using role type % Declaring emptyset:fofType % FOF formula (<kernel.Constant object at 0x14a5b90>, <kernel.DependentProduct object at 0x14a5ea8>) of role type named setadjoin_type % Using role type % Declaring setadjoin:(fofType->(fofType->fofType)) % FOF formula (<kernel.Constant object at 0x14a55f0>, <kernel.DependentProduct object at 0x14a5830>) of role type named powerset_type % Using role type % Declaring powerset:(fofType->fofType) % FOF formula (<kernel.Constant object at 0x14a5518>, <kernel.DependentProduct object at 0x14a5488>) of role type named dsetconstr_type % Using role type % Declaring dsetconstr:(fofType->((fofType->Prop)->fofType)) % FOF formula (<kernel.Constant object at 0x14a5560>, <kernel.Sort object at 0x1385bd8>) of role type named dsetconstrI_type % Using role type % Declaring dsetconstrI:Prop % FOF formula (((eq Prop) dsetconstrI) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))) of role definition named dsetconstrI % A new definition: (((eq Prop) dsetconstrI) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))) % Defined: dsetconstrI:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))) % FOF formula (<kernel.Constant object at 0x18f1b00>, <kernel.DependentProduct object at 0x14a5b90>) of role type named subset_type % Using role type % Declaring subset:(fofType->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x18f1b00>, <kernel.Sort object at 0x1385bd8>) of role type named powersetI1_type % Using role type % Declaring powersetI1:Prop % FOF formula (((eq Prop) powersetI1) (forall (A:fofType) (B:fofType), (((subset B) A)->((in B) (powerset A))))) of role definition named powersetI1 % A new definition: (((eq Prop) powersetI1) (forall (A:fofType) (B:fofType), (((subset B) A)->((in B) (powerset A))))) % Defined: powersetI1:=(forall (A:fofType) (B:fofType), (((subset B) A)->((in B) (powerset A)))) % FOF formula (<kernel.Constant object at 0x14a5488>, <kernel.DependentProduct object at 0x14a5830>) of role type named kpair_type % Using role type % Declaring kpair:(fofType->(fofType->fofType)) % FOF formula (<kernel.Constant object at 0x14a5cb0>, <kernel.DependentProduct object at 0x14a57a0>) of role type named cartprod_type % Using role type % Declaring cartprod:(fofType->(fofType->fofType)) % FOF formula (<kernel.Constant object at 0x14a5f80>, <kernel.DependentProduct object at 0x14a54d0>) of role type named singleton_type % Using role type % Declaring singleton:(fofType->Prop) % FOF formula (((eq (fofType->Prop)) singleton) (fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset))))))) of role definition named singleton % A new definition: (((eq (fofType->Prop)) singleton) (fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset))))))) % Defined: singleton:=(fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset)))))) % FOF formula (<kernel.Constant object at 0x14a55f0>, <kernel.DependentProduct object at 0x14a5440>) of role type named ex1_type % Using role type % Declaring ex1:(fofType->((fofType->Prop)->Prop)) % FOF formula (((eq (fofType->((fofType->Prop)->Prop))) ex1) (fun (A:fofType) (Xphi:(fofType->Prop))=> (singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))) of role definition named ex1 % A new definition: (((eq (fofType->((fofType->Prop)->Prop))) ex1) (fun (A:fofType) (Xphi:(fofType->Prop))=> (singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))) % Defined: ex1:=(fun (A:fofType) (Xphi:(fofType->Prop))=> (singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) % FOF formula (<kernel.Constant object at 0x14a5440>, <kernel.DependentProduct object at 0x14a5f80>) of role type named breln_type % Using role type % Declaring breln:(fofType->(fofType->(fofType->Prop))) % FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) breln) (fun (A:fofType) (B:fofType) (C:fofType)=> ((subset C) ((cartprod A) B)))) of role definition named breln % A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) breln) (fun (A:fofType) (B:fofType) (C:fofType)=> ((subset C) ((cartprod A) B)))) % Defined: breln:=(fun (A:fofType) (B:fofType) (C:fofType)=> ((subset C) ((cartprod A) B))) % FOF formula (<kernel.Constant object at 0x14a5dd0>, <kernel.DependentProduct object at 0x14a55f0>) of role type named func_type % Using role type % Declaring func:(fofType->(fofType->(fofType->Prop))) % FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) func) (fun (A:fofType) (B:fofType) (R:fofType)=> ((and (((breln A) B) R)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) R)))))))) of role definition named func % A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) func) (fun (A:fofType) (B:fofType) (R:fofType)=> ((and (((breln A) B) R)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) R)))))))) % Defined: func:=(fun (A:fofType) (B:fofType) (R:fofType)=> ((and (((breln A) B) R)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) R))))))) % FOF formula (<kernel.Constant object at 0x14a57a0>, <kernel.DependentProduct object at 0x16b2e60>) of role type named funcSet_type % Using role type % Declaring funcSet:(fofType->(fofType->fofType)) % FOF formula (((eq (fofType->(fofType->fofType))) funcSet) (fun (A:fofType) (B:fofType)=> ((dsetconstr (powerset ((cartprod A) B))) (fun (Xf:fofType)=> (((func A) B) Xf))))) of role definition named funcSet % A new definition: (((eq (fofType->(fofType->fofType))) funcSet) (fun (A:fofType) (B:fofType)=> ((dsetconstr (powerset ((cartprod A) B))) (fun (Xf:fofType)=> (((func A) B) Xf))))) % Defined: funcSet:=(fun (A:fofType) (B:fofType)=> ((dsetconstr (powerset ((cartprod A) B))) (fun (Xf:fofType)=> (((func A) B) Xf)))) % FOF formula (dsetconstrI->(powersetI1->(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->((in Xf) ((funcSet A) B)))))) of role conjecture named funcinfuncset % Conjecture to prove = (dsetconstrI->(powersetI1->(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->((in Xf) ((funcSet A) B)))))):Prop % We need to prove ['(dsetconstrI->(powersetI1->(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->((in Xf) ((funcSet A) B))))))'] % Parameter fofType:Type. % Parameter in:(fofType->(fofType->Prop)). % Parameter emptyset:fofType. % Parameter setadjoin:(fofType->(fofType->fofType)). % Parameter powerset:(fofType->fofType). % Parameter dsetconstr:(fofType->((fofType->Prop)->fofType)). % Definition dsetconstrI:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))):Prop. % Parameter subset:(fofType->(fofType->Prop)). % Definition powersetI1:=(forall (A:fofType) (B:fofType), (((subset B) A)->((in B) (powerset A)))):Prop. % Parameter kpair:(fofType->(fofType->fofType)). % Parameter cartprod:(fofType->(fofType->fofType)). % Definition singleton:=(fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset)))))):(fofType->Prop). % Definition ex1:=(fun (A:fofType) (Xphi:(fofType->Prop))=> (singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))):(fofType->((fofType->Prop)->Prop)). % Definition breln:=(fun (A:fofType) (B:fofType) (C:fofType)=> ((subset C) ((cartprod A) B))):(fofType->(fofType->(fofType->Prop))). % Definition func:=(fun (A:fofType) (B:fofType) (R:fofType)=> ((and (((breln A) B) R)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) R))))))):(fofType->(fofType->(fofType->Prop))). % Definition funcSet:=(fun (A:fofType) (B:fofType)=> ((dsetconstr (powerset ((cartprod A) B))) (fun (Xf:fofType)=> (((func A) B) Xf)))):(fofType->(fofType->fofType)). % Trying to prove (dsetconstrI->(powersetI1->(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->((in Xf) ((funcSet A) B)))))) % Found x1:(((func A) B) Xf) % Found x1 as proof of (((func A) B) Xf) % Found x1:(((func A) B) Xf) % Found x1 as proof of (((func A) B) Xf) % Found x0000:=(x000 x2):((in Xf) (powerset ((cartprod A) B))) % Found (x000 x2) as proof of ((in Xf) (powerset ((cartprod A) B))) % Found ((x00 Xf) x2) as proof of ((in Xf) (powerset ((cartprod A) B))) % Found (((x0 ((cartprod A) B)) Xf) x2) as proof of ((in Xf) (powerset ((cartprod A) B))) % Found (((x0 ((cartprod A) B)) Xf) x2) as proof of ((in Xf) (powerset ((cartprod A) B))) % Found ((x400 (((x0 ((cartprod A) B)) Xf) x2)) x1) as proof of ((in Xf) ((funcSet A) B)) % Found (((x40 Xf) (((x0 ((cartprod A) B)) Xf) x2)) x1) as proof of ((in Xf) ((funcSet A) B)) % Found ((((x4 ((func A) B)) Xf) (((x0 ((cartprod A) B)) Xf) x2)) x1) as proof of ((in Xf) ((funcSet A) B)) % Found (((((x (powerset ((cartprod A) B))) ((func A) B)) Xf) (((x0 ((cartprod A) B)) Xf) x2)) x1) as proof of ((in Xf) ((funcSet A) B)) % Found (fun (x3:(forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))=> (((((x (powerset ((cartprod A) B))) ((func A) B)) Xf) (((x0 ((cartprod A) B)) Xf) x2)) x1)) as proof of ((in Xf) ((funcSet A) B)) % Found (fun (x2:(((breln A) B) Xf)) (x3:(forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))=> (((((x (powerset ((cartprod A) B))) ((func A) B)) Xf) (((x0 ((cartprod A) B)) Xf) x2)) x1)) as proof of ((forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))->((in Xf) ((funcSet A) B))) % Found (fun (x2:(((breln A) B) Xf)) (x3:(forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))=> (((((x (powerset ((cartprod A) B))) ((func A) B)) Xf) (((x0 ((cartprod A) B)) Xf) x2)) x1)) as proof of ((((breln A) B) Xf)->((forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))->((in Xf) ((funcSet A) B)))) % Found (and_rect00 (fun (x2:(((breln A) B) Xf)) (x3:(forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))=> (((((x (powerset ((cartprod A) B))) ((func A) B)) Xf) (((x0 ((cartprod A) B)) Xf) x2)) x1))) as proof of ((in Xf) ((funcSet A) B)) % Found ((and_rect0 ((in Xf) ((funcSet A) B))) (fun (x2:(((breln A) B) Xf)) (x3:(forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))=> (((((x (powerset ((cartprod A) B))) ((func A) B)) Xf) (((x0 ((cartprod A) B)) Xf) x2)) x1))) as proof of ((in Xf) ((funcSet A) B)) % Found (((fun (P:Type) (x2:((((breln A) B) Xf)->((forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))->P)))=> (((((and_rect (((breln A) B) Xf)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))) P) x2) x1)) ((in Xf) ((funcSet A) B))) (fun (x2:(((breln A) B) Xf)) (x3:(forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))=> (((((x (powerset ((cartprod A) B))) ((func A) B)) Xf) (((x0 ((cartprod A) B)) Xf) x2)) x1))) as proof of ((in Xf) ((funcSet A) B)) % Found (fun (x1:(((func A) B) Xf))=> (((fun (P:Type) (x2:((((breln A) B) Xf)->((forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))->P)))=> (((((and_rect (((breln A) B) Xf)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))) P) x2) x1)) ((in Xf) ((funcSet A) B))) (fun (x2:(((breln A) B) Xf)) (x3:(forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))=> (((((x (powerset ((cartprod A) B))) ((func A) B)) Xf) (((x0 ((cartprod A) B)) Xf) x2)) x1)))) as proof of ((in Xf) ((funcSet A) B)) % Found (fun (Xf:fofType) (x1:(((func A) B) Xf))=> (((fun (P:Type) (x2:((((breln A) B) Xf)->((forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))->P)))=> (((((and_rect (((breln A) B) Xf)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))) P) x2) x1)) ((in Xf) ((funcSet A) B))) (fun (x2:(((breln A) B) Xf)) (x3:(forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))=> (((((x (powerset ((cartprod A) B))) ((func A) B)) Xf) (((x0 ((cartprod A) B)) Xf) x2)) x1)))) as proof of ((((func A) B) Xf)->((in Xf) ((funcSet A) B))) % Found (fun (B:fofType) (Xf:fofType) (x1:(((func A) B) Xf))=> (((fun (P:Type) (x2:((((breln A) B) Xf)->((forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))->P)))=> (((((and_rect (((breln A) B) Xf)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))) P) x2) x1)) ((in Xf) ((funcSet A) B))) (fun (x2:(((breln A) B) Xf)) (x3:(forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))=> (((((x (powerset ((cartprod A) B))) ((func A) B)) Xf) (((x0 ((cartprod A) B)) Xf) x2)) x1)))) as proof of (forall (Xf:fofType), ((((func A) B) Xf)->((in Xf) ((funcSet A) B)))) % Found (fun (A:fofType) (B:fofType) (Xf:fofType) (x1:(((func A) B) Xf))=> (((fun (P:Type) (x2:((((breln A) B) Xf)->((forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))->P)))=> (((((and_rect (((breln A) B) Xf)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))) P) x2) x1)) ((in Xf) ((funcSet A) B))) (fun (x2:(((breln A) B) Xf)) (x3:(forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))=> (((((x (powerset ((cartprod A) B))) ((func A) B)) Xf) (((x0 ((cartprod A) B)) Xf) x2)) x1)))) as proof of (forall (B:fofType) (Xf:fofType), ((((func A) B) Xf)->((in Xf) ((funcSet A) B)))) % Found (fun (x0:powersetI1) (A:fofType) (B:fofType) (Xf:fofType) (x1:(((func A) B) Xf))=> (((fun (P:Type) (x2:((((breln A) B) Xf)->((forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))->P)))=> (((((and_rect (((breln A) B) Xf)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))) P) x2) x1)) ((in Xf) ((funcSet A) B))) (fun (x2:(((breln A) B) Xf)) (x3:(forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))=> (((((x (powerset ((cartprod A) B))) ((func A) B)) Xf) (((x0 ((cartprod A) B)) Xf) x2)) x1)))) as proof of (forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->((in Xf) ((funcSet A) B)))) % Found (fun (x:dsetconstrI) (x0:powersetI1) (A:fofType) (B:fofType) (Xf:fofType) (x1:(((func A) B) Xf))=> (((fun (P:Type) (x2:((((breln A) B) Xf)->((forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))->P)))=> (((((and_rect (((breln A) B) Xf)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))) P) x2) x1)) ((in Xf) ((funcSet A) B))) (fun (x2:(((breln A) B) Xf)) (x3:(forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))=> (((((x (powerset ((cartprod A) B))) ((func A) B)) Xf) (((x0 ((cartprod A) B)) Xf) x2)) x1)))) as proof of (powersetI1->(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->((in Xf) ((funcSet A) B))))) % Found (fun (x:dsetconstrI) (x0:powersetI1) (A:fofType) (B:fofType) (Xf:fofType) (x1:(((func A) B) Xf))=> (((fun (P:Type) (x2:((((breln A) B) Xf)->((forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))->P)))=> (((((and_rect (((breln A) B) Xf)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))) P) x2) x1)) ((in Xf) ((funcSet A) B))) (fun (x2:(((breln A) B) Xf)) (x3:(forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))=> (((((x (powerset ((cartprod A) B))) ((func A) B)) Xf) (((x0 ((cartprod A) B)) Xf) x2)) x1)))) as proof of (dsetconstrI->(powersetI1->(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->((in Xf) ((funcSet A) B)))))) % Got proof (fun (x:dsetconstrI) (x0:powersetI1) (A:fofType) (B:fofType) (Xf:fofType) (x1:(((func A) B) Xf))=> (((fun (P:Type) (x2:((((breln A) B) Xf)->((forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))->P)))=> (((((and_rect (((breln A) B) Xf)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))) P) x2) x1)) ((in Xf) ((funcSet A) B))) (fun (x2:(((breln A) B) Xf)) (x3:(forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))=> (((((x (powerset ((cartprod A) B))) ((func A) B)) Xf) (((x0 ((cartprod A) B)) Xf) x2)) x1)))) % Time elapsed = 0.529349s % node=66 cost=335.000000 depth=20 % :::::::::::::::::::::: % % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % (fun (x:dsetconstrI) (x0:powersetI1) (A:fofType) (B:fofType) (Xf:fofType) (x1:(((func A) B) Xf))=> (((fun (P:Type) (x2:((((breln A) B) Xf)->((forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))->P)))=> (((((and_rect (((breln A) B) Xf)) (forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf)))))) P) x2) x1)) ((in Xf) ((funcSet A) B))) (fun (x2:(((breln A) B) Xf)) (x3:(forall (Xx:fofType), (((in Xx) A)->((ex1 B) (fun (Xy:fofType)=> ((in ((kpair Xx) Xy)) Xf))))))=> (((((x (powerset ((cartprod A) B))) ((func A) B)) Xf) (((x0 ((cartprod A) B)) Xf) x2)) x1)))) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF %------------------------------------------------------------------------------