%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SYN382^5 : TPTP v6.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n092.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 13:38:18 EDT 2014 % Result : Theorem 2.13s % Output : Proof 2.13s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----ERROR: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SYN382^5 : TPTP v6.1.0. Released v4.0.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n092.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 09:32:56 CDT 2014 % % CPUTime: 2.13 % 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 0x25ba248>, <kernel.DependentProduct object at 0x2635d88>) of role type named cQ % Using role type % Declaring cQ:(fofType->(fofType->Prop)) % FOF formula (<kernel.Constant object at 0x20cbc20>, <kernel.DependentProduct object at 0x2635e60>) of role type named cP % Using role type % Declaring cP:(fofType->(fofType->Prop)) % FOF formula ((forall (Xz:fofType), ((ex fofType) (fun (Xx:fofType)=> ((or (forall (Xy:fofType), ((cP Xx) Xy))) ((cQ Xx) Xz)))))->(forall (Xy:fofType), ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))))) of role conjecture named cX2134 % Conjecture to prove = ((forall (Xz:fofType), ((ex fofType) (fun (Xx:fofType)=> ((or (forall (Xy:fofType), ((cP Xx) Xy))) ((cQ Xx) Xz)))))->(forall (Xy:fofType), ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))))):Prop % Parameter fofType_DUMMY:fofType. % We need to prove ['((forall (Xz:fofType), ((ex fofType) (fun (Xx:fofType)=> ((or (forall (Xy:fofType), ((cP Xx) Xy))) ((cQ Xx) Xz)))))->(forall (Xy:fofType), ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))))'] % Parameter fofType:Type. % Parameter cQ:(fofType->(fofType->Prop)). % Parameter cP:(fofType->(fofType->Prop)). % Trying to prove ((forall (Xz:fofType), ((ex fofType) (fun (Xx:fofType)=> ((or (forall (Xy:fofType), ((cP Xx) Xy))) ((cQ Xx) Xz)))))->(forall (Xy:fofType), ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))))) % Found or_intror00:=(or_intror0 ((cQ x1) Xz)):(((cQ x1) Xz)->((or ((cP x3) Xy)) ((cQ x1) Xz))) % Found (or_intror0 ((cQ x1) Xz)) as proof of (((cQ x1) Xz)->((or ((cP x3) Xy)) ((cQ x3) Xy))) % Found ((or_intror ((cP x3) Xy)) ((cQ x1) Xz)) as proof of (((cQ x1) Xz)->((or ((cP x3) Xy)) ((cQ x3) Xy))) % Found ((or_intror ((cP x3) Xy)) ((cQ x1) Xz)) as proof of (((cQ x1) Xz)->((or ((cP x3) Xy)) ((cQ x3) Xy))) % Found ((or_intror ((cP x3) Xy)) ((cQ x1) Xz)) as proof of (((cQ x1) Xz)->((or ((cP x3) Xy)) ((cQ x3) Xy))) % Found ((or_intror ((cP x3) Xy)) ((cQ x1) Xz)) as proof of (((cQ x1) Xz)->((or ((cP x3) Xy)) ((cQ x3) Xy))) % Found or_intror00:=(or_intror0 ((cQ x2) Xz)):(((cQ x2) Xz)->((or ((cP x0) Xy)) ((cQ x2) Xz))) % Found (or_intror0 ((cQ x2) Xz)) as proof of (((cQ x2) Xz)->((or ((cP x0) Xy)) ((cQ x0) Xy))) % Found ((or_intror ((cP x0) Xy)) ((cQ x2) Xz)) as proof of (((cQ x2) Xz)->((or ((cP x0) Xy)) ((cQ x0) Xy))) % Found ((or_intror ((cP x0) Xy)) ((cQ x2) Xz)) as proof of (((cQ x2) Xz)->((or ((cP x0) Xy)) ((cQ x0) Xy))) % Found ((or_intror ((cP x0) Xy)) ((cQ x2) Xz)) as proof of (((cQ x2) Xz)->((or ((cP x0) Xy)) ((cQ x0) Xy))) % Found ((or_intror ((cP x0) Xy)) ((cQ x2) Xz)) as proof of (((cQ x2) Xz)->((or ((cP x0) Xy)) ((cQ x0) Xy))) % Found x40:=(x4 Xy):((cP x1) Xy) % Found (x4 Xy) as proof of ((cP x3) Xy) % Found (x4 Xy) as proof of ((cP x3) Xy) % Found (or_introl00 (x4 Xy)) as proof of ((or ((cP x3) Xy)) ((cQ x3) Xy)) % Found ((or_introl0 ((cQ x3) Xy)) (x4 Xy)) as proof of ((or ((cP x3) Xy)) ((cQ x3) Xy)) % Found (((or_introl ((cP x3) Xy)) ((cQ x3) Xy)) (x4 Xy)) as proof of ((or ((cP x3) Xy)) ((cQ x3) Xy)) % Found (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x3) Xy)) ((cQ x3) Xy)) (x4 Xy))) as proof of ((or ((cP x3) Xy)) ((cQ x3) Xy)) % Found (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x3) Xy)) ((cQ x3) Xy)) (x4 Xy))) as proof of ((forall (Xy0:fofType), ((cP x1) Xy0))->((or ((cP x3) Xy)) ((cQ x3) Xy))) % Found ((or_ind00 (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x3) Xy)) ((cQ x3) Xy)) (x4 Xy)))) ((or_intror ((cP x3) Xy)) ((cQ x1) Xz))) as proof of ((or ((cP x3) Xy)) ((cQ x3) Xy)) % Found (((or_ind0 ((or ((cP x3) Xy)) ((cQ x3) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x3) Xy)) ((cQ x3) Xy)) (x4 Xy)))) ((or_intror ((cP x3) Xy)) ((cQ x1) Xz))) as proof of ((or ((cP x3) Xy)) ((cQ x3) Xy)) % Found ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xz)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)) P) x4) x5) x2)) ((or ((cP x3) Xy)) ((cQ x3) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x3) Xy)) ((cQ x3) Xy)) (x4 Xy)))) ((or_intror ((cP x3) Xy)) ((cQ x1) Xz))) as proof of ((or ((cP x3) Xy)) ((cQ x3) Xy)) % Found ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xz)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)) P) x4) x5) x2)) ((or ((cP x3) Xy)) ((cQ x3) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x3) Xy)) ((cQ x3) Xy)) (x4 Xy)))) ((or_intror ((cP x3) Xy)) ((cQ x1) Xz))) as proof of ((or ((cP x3) Xy)) ((cQ x3) Xy)) % Found (ex_intro000 ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xz)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)) P) x4) x5) x2)) ((or ((cP x3) Xy)) ((cQ x3) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x3) Xy)) ((cQ x3) Xy)) (x4 Xy)))) ((or_intror ((cP x3) Xy)) ((cQ x1) Xz)))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) % Found ((ex_intro00 x1) ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xz)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)) P) x4) x5) x2)) ((or ((cP x1) Xy)) ((cQ x1) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x1) Xy)) ((cQ x1) Xy)) (x4 Xy)))) ((or_intror ((cP x1) Xy)) ((cQ x1) Xz)))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) % Found (((ex_intro0 (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) x1) ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xz)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)) P) x4) x5) x2)) ((or ((cP x1) Xy)) ((cQ x1) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x1) Xy)) ((cQ x1) Xy)) (x4 Xy)))) ((or_intror ((cP x1) Xy)) ((cQ x1) Xz)))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) % Found ((((ex_intro fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) x1) ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xz)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)) P) x4) x5) x2)) ((or ((cP x1) Xy)) ((cQ x1) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x1) Xy)) ((cQ x1) Xy)) (x4 Xy)))) ((or_intror ((cP x1) Xy)) ((cQ x1) Xz)))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) % Found (fun (x2:((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) x1) ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xz)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)) P) x4) x5) x2)) ((or ((cP x1) Xy)) ((cQ x1) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x1) Xy)) ((cQ x1) Xy)) (x4 Xy)))) ((or_intror ((cP x1) Xy)) ((cQ x1) Xz))))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) % Found (fun (x1:fofType) (x2:((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) x1) ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xz)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)) P) x4) x5) x2)) ((or ((cP x1) Xy)) ((cQ x1) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x1) Xy)) ((cQ x1) Xy)) (x4 Xy)))) ((or_intror ((cP x1) Xy)) ((cQ x1) Xz))))) as proof of (((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz))->((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))) % Found (fun (x1:fofType) (x2:((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) x1) ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xz)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)) P) x4) x5) x2)) ((or ((cP x1) Xy)) ((cQ x1) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x1) Xy)) ((cQ x1) Xy)) (x4 Xy)))) ((or_intror ((cP x1) Xy)) ((cQ x1) Xz))))) as proof of (forall (x:fofType), (((or (forall (Xy0:fofType), ((cP x) Xy0))) ((cQ x) Xz))->((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))))) % Found (ex_ind00 (fun (x1:fofType) (x2:((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) x1) ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xz)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)) P) x4) x5) x2)) ((or ((cP x1) Xy)) ((cQ x1) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x1) Xy)) ((cQ x1) Xy)) (x4 Xy)))) ((or_intror ((cP x1) Xy)) ((cQ x1) Xz)))))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) % Found ((ex_ind0 ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))) (fun (x1:fofType) (x2:((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) x1) ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xz)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)) P) x4) x5) x2)) ((or ((cP x1) Xy)) ((cQ x1) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x1) Xy)) ((cQ x1) Xy)) (x4 Xy)))) ((or_intror ((cP x1) Xy)) ((cQ x1) Xz)))))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) % Found (((fun (P:Prop) (x1:(forall (x:fofType), (((or (forall (Xy:fofType), ((cP x) Xy))) ((cQ x) Xz))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((or (forall (Xy:fofType), ((cP Xx) Xy))) ((cQ Xx) Xz)))) P) x1) x0)) ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))) (fun (x1:fofType) (x2:((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) x1) ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xz)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xz)) P) x4) x5) x2)) ((or ((cP x1) Xy)) ((cQ x1) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x1) Xy)) ((cQ x1) Xy)) (x4 Xy)))) ((or_intror ((cP x1) Xy)) ((cQ x1) Xz)))))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) % Found (((fun (P:Prop) (x1:(forall (x1:fofType), (((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((or (forall (Xy0:fofType), ((cP Xx) Xy0))) ((cQ Xx) Xy)))) P) x1) (x Xy))) ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))) (fun (x1:fofType) (x2:((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy)))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) x1) ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xy)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy)) P) x4) x5) x2)) ((or ((cP x1) Xy)) ((cQ x1) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x1) Xy)) ((cQ x1) Xy)) (x4 Xy)))) ((or_intror ((cP x1) Xy)) ((cQ x1) Xy)))))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) % Found (fun (Xy:fofType)=> (((fun (P:Prop) (x1:(forall (x1:fofType), (((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((or (forall (Xy0:fofType), ((cP Xx) Xy0))) ((cQ Xx) Xy)))) P) x1) (x Xy))) ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))) (fun (x1:fofType) (x2:((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy)))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) x1) ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xy)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy)) P) x4) x5) x2)) ((or ((cP x1) Xy)) ((cQ x1) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x1) Xy)) ((cQ x1) Xy)) (x4 Xy)))) ((or_intror ((cP x1) Xy)) ((cQ x1) Xy))))))) as proof of ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) % Found (fun (x:(forall (Xz:fofType), ((ex fofType) (fun (Xx:fofType)=> ((or (forall (Xy:fofType), ((cP Xx) Xy))) ((cQ Xx) Xz)))))) (Xy:fofType)=> (((fun (P:Prop) (x1:(forall (x1:fofType), (((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((or (forall (Xy0:fofType), ((cP Xx) Xy0))) ((cQ Xx) Xy)))) P) x1) (x Xy))) ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))) (fun (x1:fofType) (x2:((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy)))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) x1) ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xy)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy)) P) x4) x5) x2)) ((or ((cP x1) Xy)) ((cQ x1) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x1) Xy)) ((cQ x1) Xy)) (x4 Xy)))) ((or_intror ((cP x1) Xy)) ((cQ x1) Xy))))))) as proof of (forall (Xy:fofType), ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))) % Found (fun (x:(forall (Xz:fofType), ((ex fofType) (fun (Xx:fofType)=> ((or (forall (Xy:fofType), ((cP Xx) Xy))) ((cQ Xx) Xz)))))) (Xy:fofType)=> (((fun (P:Prop) (x1:(forall (x1:fofType), (((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((or (forall (Xy0:fofType), ((cP Xx) Xy0))) ((cQ Xx) Xy)))) P) x1) (x Xy))) ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))) (fun (x1:fofType) (x2:((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy)))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) x1) ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xy)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy)) P) x4) x5) x2)) ((or ((cP x1) Xy)) ((cQ x1) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x1) Xy)) ((cQ x1) Xy)) (x4 Xy)))) ((or_intror ((cP x1) Xy)) ((cQ x1) Xy))))))) as proof of ((forall (Xz:fofType), ((ex fofType) (fun (Xx:fofType)=> ((or (forall (Xy:fofType), ((cP Xx) Xy))) ((cQ Xx) Xz)))))->(forall (Xy:fofType), ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))))) % Got proof (fun (x:(forall (Xz:fofType), ((ex fofType) (fun (Xx:fofType)=> ((or (forall (Xy:fofType), ((cP Xx) Xy))) ((cQ Xx) Xz)))))) (Xy:fofType)=> (((fun (P:Prop) (x1:(forall (x1:fofType), (((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((or (forall (Xy0:fofType), ((cP Xx) Xy0))) ((cQ Xx) Xy)))) P) x1) (x Xy))) ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))) (fun (x1:fofType) (x2:((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy)))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) x1) ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xy)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy)) P) x4) x5) x2)) ((or ((cP x1) Xy)) ((cQ x1) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x1) Xy)) ((cQ x1) Xy)) (x4 Xy)))) ((or_intror ((cP x1) Xy)) ((cQ x1) Xy))))))) % Time elapsed = 1.794600s % node=356 cost=1246.000000 depth=24 % :::::::::::::::::::::: % % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % (fun (x:(forall (Xz:fofType), ((ex fofType) (fun (Xx:fofType)=> ((or (forall (Xy:fofType), ((cP Xx) Xy))) ((cQ Xx) Xz)))))) (Xy:fofType)=> (((fun (P:Prop) (x1:(forall (x1:fofType), (((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy))->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> ((or (forall (Xy0:fofType), ((cP Xx) Xy0))) ((cQ Xx) Xy)))) P) x1) (x Xy))) ((ex fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy))))) (fun (x1:fofType) (x2:((or (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy)))=> ((((ex_intro fofType) (fun (Xx:fofType)=> ((or ((cP Xx) Xy)) ((cQ Xx) Xy)))) x1) ((((fun (P:Prop) (x4:((forall (Xy0:fofType), ((cP x1) Xy0))->P)) (x5:(((cQ x1) Xy)->P))=> ((((((or_ind (forall (Xy0:fofType), ((cP x1) Xy0))) ((cQ x1) Xy)) P) x4) x5) x2)) ((or ((cP x1) Xy)) ((cQ x1) Xy))) (fun (x4:(forall (Xy0:fofType), ((cP x1) Xy0)))=> (((or_introl ((cP x1) Xy)) ((cQ x1) Xy)) (x4 Xy)))) ((or_intror ((cP x1) Xy)) ((cQ x1) Xy))))))) % % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % EOF %------------------------------------------------------------------------------