TSTP Solution File: SET716^4 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SET716^4 : TPTP v6.1.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n189.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 13:31:01 EDT 2014
% Result : Theorem 2.14s
% Output : Proof 2.14s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SET716^4 : TPTP v6.1.0. Released v3.6.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n189.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 10:44:56 CDT 2014
% % CPUTime : 2.14
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/SET008^1.ax, trying next directory
% FOF formula (<kernel.Constant object at 0x26fa950>, <kernel.DependentProduct object at 0x26faef0>) of role type named fun_image_decl
% Using role type
% Declaring fun_image:((fofType->fofType)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->fofType)->((fofType->Prop)->(fofType->Prop)))) fun_image) (fun (F:(fofType->fofType)) (A:(fofType->Prop)) (Y:fofType)=> ((ex fofType) (fun (X:fofType)=> ((and (A X)) (((eq fofType) Y) (F X))))))) of role definition named fun_image
% A new definition: (((eq ((fofType->fofType)->((fofType->Prop)->(fofType->Prop)))) fun_image) (fun (F:(fofType->fofType)) (A:(fofType->Prop)) (Y:fofType)=> ((ex fofType) (fun (X:fofType)=> ((and (A X)) (((eq fofType) Y) (F X)))))))
% Defined: fun_image:=(fun (F:(fofType->fofType)) (A:(fofType->Prop)) (Y:fofType)=> ((ex fofType) (fun (X:fofType)=> ((and (A X)) (((eq fofType) Y) (F X))))))
% FOF formula (<kernel.Constant object at 0x26d8d40>, <kernel.DependentProduct object at 0x26fa320>) of role type named fun_composition_decl
% Using role type
% Declaring fun_composition:((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))
% FOF formula (((eq ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) fun_composition) (fun (F:(fofType->fofType)) (G:(fofType->fofType)) (X:fofType)=> (G (F X)))) of role definition named fun_composition
% A new definition: (((eq ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) fun_composition) (fun (F:(fofType->fofType)) (G:(fofType->fofType)) (X:fofType)=> (G (F X))))
% Defined: fun_composition:=(fun (F:(fofType->fofType)) (G:(fofType->fofType)) (X:fofType)=> (G (F X)))
% FOF formula (<kernel.Constant object at 0x26fa560>, <kernel.DependentProduct object at 0x26faf80>) of role type named fun_inv_image_decl
% Using role type
% Declaring fun_inv_image:((fofType->fofType)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->fofType)->((fofType->Prop)->(fofType->Prop)))) fun_inv_image) (fun (F:(fofType->fofType)) (B:(fofType->Prop)) (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> ((and (B Y)) (((eq fofType) Y) (F X))))))) of role definition named fun_inv_image
% A new definition: (((eq ((fofType->fofType)->((fofType->Prop)->(fofType->Prop)))) fun_inv_image) (fun (F:(fofType->fofType)) (B:(fofType->Prop)) (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> ((and (B Y)) (((eq fofType) Y) (F X)))))))
% Defined: fun_inv_image:=(fun (F:(fofType->fofType)) (B:(fofType->Prop)) (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> ((and (B Y)) (((eq fofType) Y) (F X))))))
% FOF formula (<kernel.Constant object at 0x26faf80>, <kernel.DependentProduct object at 0x26fa170>) of role type named fun_injective_decl
% Using role type
% Declaring fun_injective:((fofType->fofType)->Prop)
% FOF formula (((eq ((fofType->fofType)->Prop)) fun_injective) (fun (F:(fofType->fofType))=> (forall (X:fofType) (Y:fofType), ((((eq fofType) (F X)) (F Y))->(((eq fofType) X) Y))))) of role definition named fun_injective
% A new definition: (((eq ((fofType->fofType)->Prop)) fun_injective) (fun (F:(fofType->fofType))=> (forall (X:fofType) (Y:fofType), ((((eq fofType) (F X)) (F Y))->(((eq fofType) X) Y)))))
% Defined: fun_injective:=(fun (F:(fofType->fofType))=> (forall (X:fofType) (Y:fofType), ((((eq fofType) (F X)) (F Y))->(((eq fofType) X) Y))))
% FOF formula (<kernel.Constant object at 0x26fa050>, <kernel.DependentProduct object at 0x26fad88>) of role type named fun_surjective_decl
% Using role type
% Declaring fun_surjective:((fofType->fofType)->Prop)
% FOF formula (((eq ((fofType->fofType)->Prop)) fun_surjective) (fun (F:(fofType->fofType))=> (forall (Y:fofType), ((ex fofType) (fun (X:fofType)=> (((eq fofType) Y) (F X))))))) of role definition named fun_surjective
% A new definition: (((eq ((fofType->fofType)->Prop)) fun_surjective) (fun (F:(fofType->fofType))=> (forall (Y:fofType), ((ex fofType) (fun (X:fofType)=> (((eq fofType) Y) (F X)))))))
% Defined: fun_surjective:=(fun (F:(fofType->fofType))=> (forall (Y:fofType), ((ex fofType) (fun (X:fofType)=> (((eq fofType) Y) (F X))))))
% FOF formula (<kernel.Constant object at 0x26fa560>, <kernel.DependentProduct object at 0x26faf80>) of role type named fun_bijective_decl
% Using role type
% Declaring fun_bijective:((fofType->fofType)->Prop)
% FOF formula (((eq ((fofType->fofType)->Prop)) fun_bijective) (fun (F:(fofType->fofType))=> ((and (fun_injective F)) (fun_surjective F)))) of role definition named fun_bijective
% A new definition: (((eq ((fofType->fofType)->Prop)) fun_bijective) (fun (F:(fofType->fofType))=> ((and (fun_injective F)) (fun_surjective F))))
% Defined: fun_bijective:=(fun (F:(fofType->fofType))=> ((and (fun_injective F)) (fun_surjective F)))
% FOF formula (<kernel.Constant object at 0x26fad88>, <kernel.DependentProduct object at 0x231ecb0>) of role type named fun_decreasing_decl
% Using role type
% Declaring fun_decreasing:((fofType->fofType)->((fofType->(fofType->Prop))->Prop))
% FOF formula (((eq ((fofType->fofType)->((fofType->(fofType->Prop))->Prop))) fun_decreasing) (fun (F:(fofType->fofType)) (SMALLER:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((SMALLER X) Y)->((SMALLER (F Y)) (F X)))))) of role definition named fun_decreasing
% A new definition: (((eq ((fofType->fofType)->((fofType->(fofType->Prop))->Prop))) fun_decreasing) (fun (F:(fofType->fofType)) (SMALLER:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((SMALLER X) Y)->((SMALLER (F Y)) (F X))))))
% Defined: fun_decreasing:=(fun (F:(fofType->fofType)) (SMALLER:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((SMALLER X) Y)->((SMALLER (F Y)) (F X)))))
% FOF formula (<kernel.Constant object at 0x26fa050>, <kernel.DependentProduct object at 0x231ef80>) of role type named fun_increasing_decl
% Using role type
% Declaring fun_increasing:((fofType->fofType)->((fofType->(fofType->Prop))->Prop))
% FOF formula (((eq ((fofType->fofType)->((fofType->(fofType->Prop))->Prop))) fun_increasing) (fun (F:(fofType->fofType)) (SMALLER:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((SMALLER X) Y)->((SMALLER (F X)) (F Y)))))) of role definition named fun_increasing
% A new definition: (((eq ((fofType->fofType)->((fofType->(fofType->Prop))->Prop))) fun_increasing) (fun (F:(fofType->fofType)) (SMALLER:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((SMALLER X) Y)->((SMALLER (F X)) (F Y))))))
% Defined: fun_increasing:=(fun (F:(fofType->fofType)) (SMALLER:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((SMALLER X) Y)->((SMALLER (F X)) (F Y)))))
% FOF formula (forall (F:(fofType->fofType)) (G:(fofType->fofType)), (((and (fun_injective F)) (fun_injective G))->(fun_injective ((fun_composition F) G)))) of role conjecture named thm
% Conjecture to prove = (forall (F:(fofType->fofType)) (G:(fofType->fofType)), (((and (fun_injective F)) (fun_injective G))->(fun_injective ((fun_composition F) G)))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(forall (F:(fofType->fofType)) (G:(fofType->fofType)), (((and (fun_injective F)) (fun_injective G))->(fun_injective ((fun_composition F) G))))']
% Parameter fofType:Type.
% Definition fun_image:=(fun (F:(fofType->fofType)) (A:(fofType->Prop)) (Y:fofType)=> ((ex fofType) (fun (X:fofType)=> ((and (A X)) (((eq fofType) Y) (F X)))))):((fofType->fofType)->((fofType->Prop)->(fofType->Prop))).
% Definition fun_composition:=(fun (F:(fofType->fofType)) (G:(fofType->fofType)) (X:fofType)=> (G (F X))):((fofType->fofType)->((fofType->fofType)->(fofType->fofType))).
% Definition fun_inv_image:=(fun (F:(fofType->fofType)) (B:(fofType->Prop)) (X:fofType)=> ((ex fofType) (fun (Y:fofType)=> ((and (B Y)) (((eq fofType) Y) (F X)))))):((fofType->fofType)->((fofType->Prop)->(fofType->Prop))).
% Definition fun_injective:=(fun (F:(fofType->fofType))=> (forall (X:fofType) (Y:fofType), ((((eq fofType) (F X)) (F Y))->(((eq fofType) X) Y)))):((fofType->fofType)->Prop).
% Definition fun_surjective:=(fun (F:(fofType->fofType))=> (forall (Y:fofType), ((ex fofType) (fun (X:fofType)=> (((eq fofType) Y) (F X)))))):((fofType->fofType)->Prop).
% Definition fun_bijective:=(fun (F:(fofType->fofType))=> ((and (fun_injective F)) (fun_surjective F))):((fofType->fofType)->Prop).
% Definition fun_decreasing:=(fun (F:(fofType->fofType)) (SMALLER:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((SMALLER X) Y)->((SMALLER (F Y)) (F X))))):((fofType->fofType)->((fofType->(fofType->Prop))->Prop)).
% Definition fun_increasing:=(fun (F:(fofType->fofType)) (SMALLER:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((SMALLER X) Y)->((SMALLER (F X)) (F Y))))):((fofType->fofType)->((fofType->(fofType->Prop))->Prop)).
% Trying to prove (forall (F:(fofType->fofType)) (G:(fofType->fofType)), (((and (fun_injective F)) (fun_injective G))->(fun_injective ((fun_composition F) G))))
% Found x1000:=(x100 x2):(((eq fofType) (F X)) (F Y))
% Found (x100 x2) as proof of (((eq fofType) (F X)) (F Y))
% Found ((x10 (F Y)) x2) as proof of (((eq fofType) (F X)) (F Y))
% Found (((x1 (F X)) (F Y)) x2) as proof of (((eq fofType) (F X)) (F Y))
% Found (((x1 (F X)) (F Y)) x2) as proof of (((eq fofType) (F X)) (F Y))
% Found (x000 (((x1 (F X)) (F Y)) x2)) as proof of (((eq fofType) X) Y)
% Found ((x00 Y) (((x1 (F X)) (F Y)) x2)) as proof of (((eq fofType) X) Y)
% Found (((x0 X) Y) (((x1 (F X)) (F Y)) x2)) as proof of (((eq fofType) X) Y)
% Found (fun (x2:(((eq fofType) (((fun_composition F) G) X)) (((fun_composition F) G) Y)))=> (((x0 X) Y) (((x1 (F X)) (F Y)) x2))) as proof of (((eq fofType) X) Y)
% Found (fun (Y:fofType) (x2:(((eq fofType) (((fun_composition F) G) X)) (((fun_composition F) G) Y)))=> (((x0 X) Y) (((x1 (F X)) (F Y)) x2))) as proof of ((((eq fofType) (((fun_composition F) G) X)) (((fun_composition F) G) Y))->(((eq fofType) X) Y))
% Found (fun (X:fofType) (Y:fofType) (x2:(((eq fofType) (((fun_composition F) G) X)) (((fun_composition F) G) Y)))=> (((x0 X) Y) (((x1 (F X)) (F Y)) x2))) as proof of (forall (Y:fofType), ((((eq fofType) (((fun_composition F) G) X)) (((fun_composition F) G) Y))->(((eq fofType) X) Y)))
% Found (fun (x1:(fun_injective G)) (X:fofType) (Y:fofType) (x2:(((eq fofType) (((fun_composition F) G) X)) (((fun_composition F) G) Y)))=> (((x0 X) Y) (((x1 (F X)) (F Y)) x2))) as proof of (fun_injective ((fun_composition F) G))
% Found (fun (x0:(fun_injective F)) (x1:(fun_injective G)) (X:fofType) (Y:fofType) (x2:(((eq fofType) (((fun_composition F) G) X)) (((fun_composition F) G) Y)))=> (((x0 X) Y) (((x1 (F X)) (F Y)) x2))) as proof of ((fun_injective G)->(fun_injective ((fun_composition F) G)))
% Found (fun (x0:(fun_injective F)) (x1:(fun_injective G)) (X:fofType) (Y:fofType) (x2:(((eq fofType) (((fun_composition F) G) X)) (((fun_composition F) G) Y)))=> (((x0 X) Y) (((x1 (F X)) (F Y)) x2))) as proof of ((fun_injective F)->((fun_injective G)->(fun_injective ((fun_composition F) G))))
% Found (and_rect00 (fun (x0:(fun_injective F)) (x1:(fun_injective G)) (X:fofType) (Y:fofType) (x2:(((eq fofType) (((fun_composition F) G) X)) (((fun_composition F) G) Y)))=> (((x0 X) Y) (((x1 (F X)) (F Y)) x2)))) as proof of (fun_injective ((fun_composition F) G))
% Found ((and_rect0 (fun_injective ((fun_composition F) G))) (fun (x0:(fun_injective F)) (x1:(fun_injective G)) (X:fofType) (Y:fofType) (x2:(((eq fofType) (((fun_composition F) G) X)) (((fun_composition F) G) Y)))=> (((x0 X) Y) (((x1 (F X)) (F Y)) x2)))) as proof of (fun_injective ((fun_composition F) G))
% Found (((fun (P:Type) (x0:((fun_injective F)->((fun_injective G)->P)))=> (((((and_rect (fun_injective F)) (fun_injective G)) P) x0) x)) (fun_injective ((fun_composition F) G))) (fun (x0:(fun_injective F)) (x1:(fun_injective G)) (X:fofType) (Y:fofType) (x2:(((eq fofType) (((fun_composition F) G) X)) (((fun_composition F) G) Y)))=> (((x0 X) Y) (((x1 (F X)) (F Y)) x2)))) as proof of (fun_injective ((fun_composition F) G))
% Found (fun (x:((and (fun_injective F)) (fun_injective G)))=> (((fun (P:Type) (x0:((fun_injective F)->((fun_injective G)->P)))=> (((((and_rect (fun_injective F)) (fun_injective G)) P) x0) x)) (fun_injective ((fun_composition F) G))) (fun (x0:(fun_injective F)) (x1:(fun_injective G)) (X:fofType) (Y:fofType) (x2:(((eq fofType) (((fun_composition F) G) X)) (((fun_composition F) G) Y)))=> (((x0 X) Y) (((x1 (F X)) (F Y)) x2))))) as proof of (fun_injective ((fun_composition F) G))
% Found (fun (G:(fofType->fofType)) (x:((and (fun_injective F)) (fun_injective G)))=> (((fun (P:Type) (x0:((fun_injective F)->((fun_injective G)->P)))=> (((((and_rect (fun_injective F)) (fun_injective G)) P) x0) x)) (fun_injective ((fun_composition F) G))) (fun (x0:(fun_injective F)) (x1:(fun_injective G)) (X:fofType) (Y:fofType) (x2:(((eq fofType) (((fun_composition F) G) X)) (((fun_composition F) G) Y)))=> (((x0 X) Y) (((x1 (F X)) (F Y)) x2))))) as proof of (((and (fun_injective F)) (fun_injective G))->(fun_injective ((fun_composition F) G)))
% Found (fun (F:(fofType->fofType)) (G:(fofType->fofType)) (x:((and (fun_injective F)) (fun_injective G)))=> (((fun (P:Type) (x0:((fun_injective F)->((fun_injective G)->P)))=> (((((and_rect (fun_injective F)) (fun_injective G)) P) x0) x)) (fun_injective ((fun_composition F) G))) (fun (x0:(fun_injective F)) (x1:(fun_injective G)) (X:fofType) (Y:fofType) (x2:(((eq fofType) (((fun_composition F) G) X)) (((fun_composition F) G) Y)))=> (((x0 X) Y) (((x1 (F X)) (F Y)) x2))))) as proof of (forall (G:(fofType->fofType)), (((and (fun_injective F)) (fun_injective G))->(fun_injective ((fun_composition F) G))))
% Found (fun (F:(fofType->fofType)) (G:(fofType->fofType)) (x:((and (fun_injective F)) (fun_injective G)))=> (((fun (P:Type) (x0:((fun_injective F)->((fun_injective G)->P)))=> (((((and_rect (fun_injective F)) (fun_injective G)) P) x0) x)) (fun_injective ((fun_composition F) G))) (fun (x0:(fun_injective F)) (x1:(fun_injective G)) (X:fofType) (Y:fofType) (x2:(((eq fofType) (((fun_composition F) G) X)) (((fun_composition F) G) Y)))=> (((x0 X) Y) (((x1 (F X)) (F Y)) x2))))) as proof of (forall (F:(fofType->fofType)) (G:(fofType->fofType)), (((and (fun_injective F)) (fun_injective G))->(fun_injective ((fun_composition F) G))))
% Got proof (fun (F:(fofType->fofType)) (G:(fofType->fofType)) (x:((and (fun_injective F)) (fun_injective G)))=> (((fun (P:Type) (x0:((fun_injective F)->((fun_injective G)->P)))=> (((((and_rect (fun_injective F)) (fun_injective G)) P) x0) x)) (fun_injective ((fun_composition F) G))) (fun (x0:(fun_injective F)) (x1:(fun_injective G)) (X:fofType) (Y:fofType) (x2:(((eq fofType) (((fun_composition F) G) X)) (((fun_composition F) G) Y)))=> (((x0 X) Y) (((x1 (F X)) (F Y)) x2)))))
% Time elapsed = 1.779414s
% node=213 cost=316.000000 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:(fofType->fofType)) (G:(fofType->fofType)) (x:((and (fun_injective F)) (fun_injective G)))=> (((fun (P:Type) (x0:((fun_injective F)->((fun_injective G)->P)))=> (((((and_rect (fun_injective F)) (fun_injective G)) P) x0) x)) (fun_injective ((fun_composition F) G))) (fun (x0:(fun_injective F)) (x1:(fun_injective G)) (X:fofType) (Y:fofType) (x2:(((eq fofType) (((fun_composition F) G) X)) (((fun_composition F) G) Y)))=> (((x0 X) Y) (((x1 (F X)) (F Y)) x2)))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------