TSTP Solution File: SYO011^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO011^1 : TPTP v7.5.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Mar 29 00:50:23 EDT 2022
% Result : Theorem 2.01s 2.21s
% Output : Proof 2.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYO011^1 : TPTP v7.5.0. Released v3.7.0.
% 0.06/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.32 % Computer : n001.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % RAMPerCPU : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % DateTime : Fri Mar 11 00:38:54 EST 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34 Python 2.7.5
% 2.01/2.19 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 2.01/2.19 FOF formula (<kernel.Constant object at 0x210e560>, <kernel.DependentProduct object at 0x210e248>) of role type named leibeq_type
% 2.01/2.19 Using role type
% 2.01/2.19 Declaring leibeq:(fofType->(fofType->Prop))
% 2.01/2.19 FOF formula (((eq (fofType->(fofType->Prop))) leibeq) (fun (U:fofType) (V:fofType)=> (forall (Q:(fofType->Prop)), ((Q U)->(Q V))))) of role definition named leibeq
% 2.01/2.19 A new definition: (((eq (fofType->(fofType->Prop))) leibeq) (fun (U:fofType) (V:fofType)=> (forall (Q:(fofType->Prop)), ((Q U)->(Q V)))))
% 2.01/2.19 Defined: leibeq:=(fun (U:fofType) (V:fofType)=> (forall (Q:(fofType->Prop)), ((Q U)->(Q V))))
% 2.01/2.19 FOF formula (<kernel.Constant object at 0x20ecb00>, <kernel.DependentProduct object at 0x20ecab8>) of role type named p_type
% 2.01/2.19 Using role type
% 2.01/2.19 Declaring p:((fofType->fofType)->Prop)
% 2.01/2.19 FOF formula (<kernel.Constant object at 0x20eca70>, <kernel.DependentProduct object at 0x20ec638>) of role type named f_type
% 2.01/2.19 Using role type
% 2.01/2.19 Declaring f:(fofType->fofType)
% 2.01/2.19 FOF formula (((and (forall (X:fofType), ((leibeq (f X)) X))) (p (fun (X:fofType)=> X)))->(p f)) of role conjecture named conj
% 2.01/2.19 Conjecture to prove = (((and (forall (X:fofType), ((leibeq (f X)) X))) (p (fun (X:fofType)=> X)))->(p f)):Prop
% 2.01/2.19 Parameter fofType_DUMMY:fofType.
% 2.01/2.19 We need to prove ['(((and (forall (X:fofType), ((leibeq (f X)) X))) (p (fun (X:fofType)=> X)))->(p f))']
% 2.01/2.19 Parameter fofType:Type.
% 2.01/2.19 Definition leibeq:=(fun (U:fofType) (V:fofType)=> (forall (Q:(fofType->Prop)), ((Q U)->(Q V)))):(fofType->(fofType->Prop)).
% 2.01/2.19 Parameter p:((fofType->fofType)->Prop).
% 2.01/2.19 Parameter f:(fofType->fofType).
% 2.01/2.19 Trying to prove (((and (forall (X:fofType), ((leibeq (f X)) X))) (p (fun (X:fofType)=> X)))->(p f))
% 2.01/2.19 Found eq_ref000:=(eq_ref00 p):((p (fun (X:fofType)=> X))->(p (fun (X:fofType)=> X)))
% 2.01/2.19 Found (eq_ref00 p) as proof of (P (fun (X:fofType)=> X))
% 2.01/2.19 Found ((eq_ref0 (fun (X:fofType)=> X)) p) as proof of (P (fun (X:fofType)=> X))
% 2.01/2.19 Found (((eq_ref (fofType->fofType)) (fun (X:fofType)=> X)) p) as proof of (P (fun (X:fofType)=> X))
% 2.01/2.19 Found (((eq_ref (fofType->fofType)) (fun (X:fofType)=> X)) p) as proof of (P (fun (X:fofType)=> X))
% 2.01/2.19 Found eta_expansion_dep0000:=(eta_expansion_dep000 p):((p (fun (X:fofType)=> X))->(p (fun (x:fofType)=> x)))
% 2.01/2.19 Found (eta_expansion_dep000 p) as proof of (P (fun (X:fofType)=> X))
% 2.01/2.19 Found ((eta_expansion_dep00 (fun (X:fofType)=> X)) p) as proof of (P (fun (X:fofType)=> X))
% 2.01/2.19 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (X:fofType)=> X)) p) as proof of (P (fun (X:fofType)=> X))
% 2.01/2.19 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (X:fofType)=> X)) p) as proof of (P (fun (X:fofType)=> X))
% 2.01/2.19 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (X:fofType)=> X)) p) as proof of (P (fun (X:fofType)=> X))
% 2.01/2.19 Found eta_expansion_dep0000:=(eta_expansion_dep000 p):((p (fun (X:fofType)=> X))->(p (fun (x:fofType)=> x)))
% 2.01/2.19 Found (eta_expansion_dep000 p) as proof of (P (fun (X:fofType)=> X))
% 2.01/2.19 Found ((eta_expansion_dep00 (fun (X:fofType)=> X)) p) as proof of (P (fun (X:fofType)=> X))
% 2.01/2.19 Found (((eta_expansion_dep0 (fun (x2:fofType)=> fofType)) (fun (X:fofType)=> X)) p) as proof of (P (fun (X:fofType)=> X))
% 2.01/2.19 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (X:fofType)=> X)) p) as proof of (P (fun (X:fofType)=> X))
% 2.01/2.19 Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> fofType)) (fun (X:fofType)=> X)) p) as proof of (P (fun (X:fofType)=> X))
% 2.01/2.19 Found functional_extensionality00000:=(functional_extensionality0000 x0):(((eq (fofType->fofType)) f) (fun (X:fofType)=> X))
% 2.01/2.19 Found (functional_extensionality0000 x0) as proof of (((eq (fofType->fofType)) f) (fun (X:fofType)=> X))
% 2.01/2.19 Found ((functional_extensionality000 (fun (X:fofType)=> X)) x0) as proof of (((eq (fofType->fofType)) f) (fun (X:fofType)=> X))
% 2.01/2.19 Found (((functional_extensionality00 f) (fun (X:fofType)=> X)) x0) as proof of (((eq (fofType->fofType)) f) (fun (X:fofType)=> X))
% 2.01/2.19 Found ((((functional_extensionality0 fofType) f) (fun (X:fofType)=> X)) x0) as proof of (((eq (fofType->fofType)) f) (fun (X:fofType)=> X))
% 2.01/2.20 Found (((((functional_extensionality fofType) fofType) f) (fun (X:fofType)=> X)) x0) as proof of (((eq (fofType->fofType)) f) (fun (X:fofType)=> X))
% 2.01/2.20 Found (((((functional_extensionality fofType) fofType) f) (fun (X:fofType)=> X)) x0) as proof of (((eq (fofType->fofType)) f) (fun (X:fofType)=> X))
% 2.01/2.20 Found (eq_sym0000 (((((functional_extensionality fofType) fofType) f) (fun (X:fofType)=> X)) x0)) as proof of ((p (fun (X:fofType)=> X))->(p f))
% 2.01/2.20 Found (eq_sym0000 (((((functional_extensionality fofType) fofType) f) (fun (X:fofType)=> X)) x0)) as proof of ((p (fun (X:fofType)=> X))->(p f))
% 2.01/2.20 Found ((fun (x1:(((eq (fofType->fofType)) f) (fun (X:fofType)=> X)))=> ((eq_sym000 x1) p)) (((((functional_extensionality fofType) fofType) f) (fun (X:fofType)=> X)) x0)) as proof of ((p (fun (X:fofType)=> X))->(p f))
% 2.01/2.20 Found ((fun (x1:(((eq (fofType->fofType)) f) (fun (X:fofType)=> X)))=> (((eq_sym00 (fun (X:fofType)=> X)) x1) p)) (((((functional_extensionality fofType) fofType) f) (fun (X:fofType)=> X)) x0)) as proof of ((p (fun (X:fofType)=> X))->(p f))
% 2.01/2.20 Found ((fun (x1:(((eq (fofType->fofType)) f) (fun (X:fofType)=> X)))=> ((((eq_sym0 f) (fun (X:fofType)=> X)) x1) p)) (((((functional_extensionality fofType) fofType) f) (fun (X:fofType)=> X)) x0)) as proof of ((p (fun (X:fofType)=> X))->(p f))
% 2.01/2.20 Found ((fun (x1:(((eq (fofType->fofType)) f) (fun (X:fofType)=> X)))=> (((((eq_sym (fofType->fofType)) f) (fun (X:fofType)=> X)) x1) p)) (((((functional_extensionality fofType) fofType) f) (fun (X:fofType)=> X)) x0)) as proof of ((p (fun (X:fofType)=> X))->(p f))
% 2.01/2.20 Found (fun (x0:(forall (X:fofType), (((eq fofType) (f X)) X)))=> ((fun (x1:(((eq (fofType->fofType)) f) (fun (X:fofType)=> X)))=> (((((eq_sym (fofType->fofType)) f) (fun (X:fofType)=> X)) x1) p)) (((((functional_extensionality fofType) fofType) f) (fun (X:fofType)=> X)) x0))) as proof of ((p (fun (X:fofType)=> X))->(p f))
% 2.01/2.20 Found (fun (x0:(forall (X:fofType), (((eq fofType) (f X)) X)))=> ((fun (x1:(((eq (fofType->fofType)) f) (fun (X:fofType)=> X)))=> (((((eq_sym (fofType->fofType)) f) (fun (X:fofType)=> X)) x1) p)) (((((functional_extensionality fofType) fofType) f) (fun (X:fofType)=> X)) x0))) as proof of ((forall (X:fofType), (((eq fofType) (f X)) X))->((p (fun (X:fofType)=> X))->(p f)))
% 2.01/2.20 Found (and_rect00 (fun (x0:(forall (X:fofType), (((eq fofType) (f X)) X)))=> ((fun (x1:(((eq (fofType->fofType)) f) (fun (X:fofType)=> X)))=> (((((eq_sym (fofType->fofType)) f) (fun (X:fofType)=> X)) x1) p)) (((((functional_extensionality fofType) fofType) f) (fun (X:fofType)=> X)) x0)))) as proof of (p f)
% 2.01/2.20 Found ((and_rect0 (p f)) (fun (x0:(forall (X:fofType), (((eq fofType) (f X)) X)))=> ((fun (x1:(((eq (fofType->fofType)) f) (fun (X:fofType)=> X)))=> (((((eq_sym (fofType->fofType)) f) (fun (X:fofType)=> X)) x1) p)) (((((functional_extensionality fofType) fofType) f) (fun (X:fofType)=> X)) x0)))) as proof of (p f)
% 2.01/2.20 Found (((fun (P:Type) (x0:((forall (X:fofType), (((eq fofType) (f X)) X))->((p (fun (X:fofType)=> X))->P)))=> (((((and_rect (forall (X:fofType), (((eq fofType) (f X)) X))) (p (fun (X:fofType)=> X))) P) x0) x)) (p f)) (fun (x0:(forall (X:fofType), (((eq fofType) (f X)) X)))=> ((fun (x1:(((eq (fofType->fofType)) f) (fun (X:fofType)=> X)))=> (((((eq_sym (fofType->fofType)) f) (fun (X:fofType)=> X)) x1) p)) (((((functional_extensionality fofType) fofType) f) (fun (X:fofType)=> X)) x0)))) as proof of (p f)
% 2.01/2.20 Found (fun (x:((and (forall (X:fofType), (((eq fofType) (f X)) X))) (p (fun (X:fofType)=> X))))=> (((fun (P:Type) (x0:((forall (X:fofType), (((eq fofType) (f X)) X))->((p (fun (X:fofType)=> X))->P)))=> (((((and_rect (forall (X:fofType), (((eq fofType) (f X)) X))) (p (fun (X:fofType)=> X))) P) x0) x)) (p f)) (fun (x0:(forall (X:fofType), (((eq fofType) (f X)) X)))=> ((fun (x1:(((eq (fofType->fofType)) f) (fun (X:fofType)=> X)))=> (((((eq_sym (fofType->fofType)) f) (fun (X:fofType)=> X)) x1) p)) (((((functional_extensionality fofType) fofType) f) (fun (X:fofType)=> X)) x0))))) as proof of (p f)
% 2.01/2.20 Found (fun (x:((and (forall (X:fofType), (((eq fofType) (f X)) X))) (p (fun (X:fofType)=> X))))=> (((fun (P:Type) (x0:((forall (X:fofType), (((eq fofType) (f X)) X))->((p (fun (X:fofType)=> X))->P)))=> (((((and_rect (forall (X:fofType), (((eq fofType) (f X)) X))) (p (fun (X:fofType)=> X))) P) x0) x)) (p f)) (fun (x0:(forall (X:fofType), (((eq fofType) (f X)) X)))=> ((fun (x1:(((eq (fofType->fofType)) f) (fun (X:fofType)=> X)))=> (((((eq_sym (fofType->fofType)) f) (fun (X:fofType)=> X)) x1) p)) (((((functional_extensionality fofType) fofType) f) (fun (X:fofType)=> X)) x0))))) as proof of (((and (forall (X:fofType), (((eq fofType) (f X)) X))) (p (fun (X:fofType)=> X)))->(p f))
% 2.01/2.21 Found (fun (x:((and (forall (X:fofType), (((eq fofType) (f X)) X))) (p (fun (X:fofType)=> X))))=> (((fun (P:Type) (x0:((forall (X:fofType), (((eq fofType) (f X)) X))->((p (fun (X:fofType)=> X))->P)))=> (((((and_rect (forall (X:fofType), (((eq fofType) (f X)) X))) (p (fun (X:fofType)=> X))) P) x0) x)) (p f)) (fun (x0:(forall (X:fofType), (((eq fofType) (f X)) X)))=> ((fun (x1:(((eq (fofType->fofType)) f) (fun (X:fofType)=> X)))=> (((((eq_sym (fofType->fofType)) f) (fun (X:fofType)=> X)) x1) p)) (((((functional_extensionality fofType) fofType) f) (fun (X:fofType)=> X)) x0))))) as proof of (((and (forall (X:fofType), ((leibeq (f X)) X))) (p (fun (X:fofType)=> X)))->(p f))
% 2.01/2.21 Got proof (fun (x:((and (forall (X:fofType), (((eq fofType) (f X)) X))) (p (fun (X:fofType)=> X))))=> (((fun (P:Type) (x0:((forall (X:fofType), (((eq fofType) (f X)) X))->((p (fun (X:fofType)=> X))->P)))=> (((((and_rect (forall (X:fofType), (((eq fofType) (f X)) X))) (p (fun (X:fofType)=> X))) P) x0) x)) (p f)) (fun (x0:(forall (X:fofType), (((eq fofType) (f X)) X)))=> ((fun (x1:(((eq (fofType->fofType)) f) (fun (X:fofType)=> X)))=> (((((eq_sym (fofType->fofType)) f) (fun (X:fofType)=> X)) x1) p)) (((((functional_extensionality fofType) fofType) f) (fun (X:fofType)=> X)) x0)))))
% 2.01/2.21 Time elapsed = 1.589829s
% 2.01/2.21 node=384 cost=637.000000 depth=19
% 2.01/2.21 ::::::::::::::::::::::
% 2.01/2.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.01/2.21 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.01/2.21 (fun (x:((and (forall (X:fofType), (((eq fofType) (f X)) X))) (p (fun (X:fofType)=> X))))=> (((fun (P:Type) (x0:((forall (X:fofType), (((eq fofType) (f X)) X))->((p (fun (X:fofType)=> X))->P)))=> (((((and_rect (forall (X:fofType), (((eq fofType) (f X)) X))) (p (fun (X:fofType)=> X))) P) x0) x)) (p f)) (fun (x0:(forall (X:fofType), (((eq fofType) (f X)) X)))=> ((fun (x1:(((eq (fofType->fofType)) f) (fun (X:fofType)=> X)))=> (((((eq_sym (fofType->fofType)) f) (fun (X:fofType)=> X)) x1) p)) (((((functional_extensionality fofType) fofType) f) (fun (X:fofType)=> X)) x0)))))
% 2.01/2.21 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------