TSTP Solution File: SYO175^5 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO175^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 00:50:50 EDT 2022
% Result : Timeout 292.11s 292.47s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYO175^5 : TPTP v7.5.0. Released v4.0.0.
% 0.07/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % RAMPerCPU : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Fri Mar 11 17:08:52 EST 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34 Python 2.7.5
% 0.20/0.61 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.20/0.61 FOF formula (<kernel.Constant object at 0xbc9908>, <kernel.Type object at 0xbc9518>) of role type named p_type
% 0.20/0.61 Using role type
% 0.20/0.61 Declaring p:Type
% 0.20/0.61 FOF formula (<kernel.Constant object at 0xbcddd0>, <kernel.Type object at 0xbc9098>) of role type named a_type
% 0.20/0.61 Using role type
% 0.20/0.61 Declaring a:Type
% 0.20/0.61 FOF formula (<kernel.Constant object at 0xbc9248>, <kernel.Constant object at 0xbc91b8>) of role type named cGRAIN
% 0.20/0.61 Using role type
% 0.20/0.61 Declaring cGRAIN:p
% 0.20/0.61 FOF formula (<kernel.Constant object at 0xbc9518>, <kernel.DependentProduct object at 0xbc9bd8>) of role type named cVEG_EATS
% 0.20/0.61 Using role type
% 0.20/0.61 Declaring cVEG_EATS:(a->(p->Prop))
% 0.20/0.61 FOF formula (<kernel.Constant object at 0xbc95a8>, <kernel.DependentProduct object at 0xbc9248>) of role type named cMEAT_EATS
% 0.20/0.61 Using role type
% 0.20/0.61 Declaring cMEAT_EATS:(a->(a->Prop))
% 0.20/0.61 FOF formula (<kernel.Constant object at 0xbc9638>, <kernel.Constant object at 0xbc9248>) of role type named cSNAIL
% 0.20/0.61 Using role type
% 0.20/0.61 Declaring cSNAIL:a
% 0.20/0.61 FOF formula (<kernel.Constant object at 0xbc9bd8>, <kernel.Constant object at 0xbc9248>) of role type named cCATERPILLAR
% 0.20/0.61 Using role type
% 0.20/0.61 Declaring cCATERPILLAR:a
% 0.20/0.61 FOF formula (<kernel.Constant object at 0xbc9128>, <kernel.Constant object at 0xbc9248>) of role type named cBIRD
% 0.20/0.61 Using role type
% 0.20/0.61 Declaring cBIRD:a
% 0.20/0.61 FOF formula (<kernel.Constant object at 0xbc9638>, <kernel.Constant object at 0xbc91b8>) of role type named cWOLF
% 0.20/0.61 Using role type
% 0.20/0.61 Declaring cWOLF:a
% 0.20/0.61 FOF formula (<kernel.Constant object at 0xbc9bd8>, <kernel.Constant object at 0x2b704204a3f8>) of role type named cFOX
% 0.20/0.61 Using role type
% 0.20/0.61 Declaring cFOX:a
% 0.20/0.61 FOF formula (<kernel.Constant object at 0xbc9638>, <kernel.DependentProduct object at 0xbc91b8>) of role type named cSMALLER
% 0.20/0.61 Using role type
% 0.20/0.61 Declaring cSMALLER:(a->(a->Prop))
% 0.20/0.61 FOF formula (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) ((cMEAT_EATS cBIRD) cCATERPILLAR))) (((cMEAT_EATS cBIRD) cSNAIL)->False))) ((ex p) (fun (Xy:p)=> ((cVEG_EATS cCATERPILLAR) Xy))))) ((ex p) (fun (Xy:p)=> ((cVEG_EATS cSNAIL) Xy))))->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) of role conjecture named cPUZ031_1_HO
% 0.20/0.61 Conjecture to prove = (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) ((cMEAT_EATS cBIRD) cCATERPILLAR))) (((cMEAT_EATS cBIRD) cSNAIL)->False))) ((ex p) (fun (Xy:p)=> ((cVEG_EATS cCATERPILLAR) Xy))))) ((ex p) (fun (Xy:p)=> ((cVEG_EATS cSNAIL) Xy))))->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))):Prop
% 0.20/0.61 We need to prove ['(((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) ((cMEAT_EATS cBIRD) cCATERPILLAR))) (((cMEAT_EATS cBIRD) cSNAIL)->False))) ((ex p) (fun (Xy:p)=> ((cVEG_EATS cCATERPILLAR) Xy))))) ((ex p) (fun (Xy:p)=> ((cVEG_EATS cSNAIL) Xy))))->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))']
% 0.20/0.61 Parameter p:Type.
% 90.04/90.29 Parameter a:Type.
% 90.04/90.29 Parameter cGRAIN:p.
% 90.04/90.29 Parameter cVEG_EATS:(a->(p->Prop)).
% 90.04/90.29 Parameter cMEAT_EATS:(a->(a->Prop)).
% 90.04/90.29 Parameter cSNAIL:a.
% 90.04/90.29 Parameter cCATERPILLAR:a.
% 90.04/90.29 Parameter cBIRD:a.
% 90.04/90.29 Parameter cWOLF:a.
% 90.04/90.29 Parameter cFOX:a.
% 90.04/90.29 Parameter cSMALLER:(a->(a->Prop)).
% 90.04/90.29 Trying to prove (((and ((and ((and ((and ((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) ((cMEAT_EATS cBIRD) cCATERPILLAR))) (((cMEAT_EATS cBIRD) cSNAIL)->False))) ((ex p) (fun (Xy:p)=> ((cVEG_EATS cCATERPILLAR) Xy))))) ((ex p) (fun (Xy:p)=> ((cVEG_EATS cSNAIL) Xy))))->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))
% 90.04/90.29 Found False_rect00:=(False_rect0 ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))):((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 90.04/90.29 Found (False_rect0 ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 90.04/90.29 Found ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 90.04/90.29 Found (fun (x7:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 90.04/90.29 Found (fun (x6:((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) (x7:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))) as proof of (((cMEAT_EATS cBIRD) cCATERPILLAR)->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))
% 90.04/90.29 Found (fun (x6:((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) (x7:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))) as proof of (((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))->(((cMEAT_EATS cBIRD) cCATERPILLAR)->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))
% 90.04/90.29 Found (and_rect30 (fun (x6:((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) (x7:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 90.04/90.29 Found ((and_rect3 ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) (fun (x6:((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) (x7:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 90.04/90.29 Found (((fun (P:Type) (x6:(((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))->(((cMEAT_EATS cBIRD) cCATERPILLAR)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) ((cMEAT_EATS cBIRD) cCATERPILLAR)) P) x6) x4)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) (fun (x6:((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) (x7:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 90.04/90.29 Found (((fun (P:Type) (x6:(((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))->(((cMEAT_EATS cBIRD) cCATERPILLAR)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) ((cMEAT_EATS cBIRD) cCATERPILLAR)) P) x6) x4)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) (fun (x6:((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) (x7:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 214.22/214.52 Found x7:((cMEAT_EATS cBIRD) cCATERPILLAR)
% 214.22/214.52 Instantiate: x8:=cBIRD:a;x9:=cCATERPILLAR:a
% 214.22/214.52 Found x7 as proof of ((cMEAT_EATS x8) x9)
% 214.22/214.52 Found False_rect00:=(False_rect0 ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))):((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 214.22/214.52 Found (False_rect0 ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 214.22/214.52 Found ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 214.22/214.52 Found (fun (x9:(((cVEG_EATS cWOLF) cGRAIN)->False))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 214.22/214.52 Found (fun (x8:((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (x9:(((cVEG_EATS cWOLF) cGRAIN)->False))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))) as proof of ((((cVEG_EATS cWOLF) cGRAIN)->False)->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))
% 214.22/214.52 Found (fun (x8:((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (x9:(((cVEG_EATS cWOLF) cGRAIN)->False))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))) as proof of (((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))->((((cVEG_EATS cWOLF) cGRAIN)->False)->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))
% 214.22/214.52 Found (and_rect40 (fun (x8:((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (x9:(((cVEG_EATS cWOLF) cGRAIN)->False))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 214.22/214.53 Found ((and_rect4 ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) (fun (x8:((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (x9:(((cVEG_EATS cWOLF) cGRAIN)->False))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 214.22/214.53 Found (((fun (P:Type) (x8:(((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))->((((cVEG_EATS cWOLF) cGRAIN)->False)->P)))=> (((((and_rect ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False)) P) x8) x6)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) (fun (x8:((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (x9:(((cVEG_EATS cWOLF) cGRAIN)->False))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 214.22/214.53 Found (((fun (P:Type) (x8:(((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))->((((cVEG_EATS cWOLF) cGRAIN)->False)->P)))=> (((((and_rect ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False)) P) x8) x6)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) (fun (x8:((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (x9:(((cVEG_EATS cWOLF) cGRAIN)->False))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 232.23/232.58 Found False_rect00:=(False_rect0 ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))):((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 232.23/232.58 Found (False_rect0 ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 232.23/232.58 Found ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 232.23/232.58 Found (fun (x9:(((cVEG_EATS cWOLF) cGRAIN)->False))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 232.23/232.58 Found (fun (x8:((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (x9:(((cVEG_EATS cWOLF) cGRAIN)->False))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))) as proof of ((((cVEG_EATS cWOLF) cGRAIN)->False)->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))
% 232.23/232.58 Found (fun (x8:((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (x9:(((cVEG_EATS cWOLF) cGRAIN)->False))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))) as proof of (((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))->((((cVEG_EATS cWOLF) cGRAIN)->False)->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))
% 232.23/232.58 Found (and_rect40 (fun (x8:((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (x9:(((cVEG_EATS cWOLF) cGRAIN)->False))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 232.23/232.58 Found ((and_rect4 ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) (fun (x8:((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (x9:(((cVEG_EATS cWOLF) cGRAIN)->False))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 232.23/232.58 Found (((fun (P:Type) (x8:(((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))->((((cVEG_EATS cWOLF) cGRAIN)->False)->P)))=> (((((and_rect ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False)) P) x8) x6)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) (fun (x8:((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (x9:(((cVEG_EATS cWOLF) cGRAIN)->False))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 232.23/232.58 Found (fun (x7:((cMEAT_EATS cBIRD) cCATERPILLAR))=> (((fun (P:Type) (x8:(((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))->((((cVEG_EATS cWOLF) cGRAIN)->False)->P)))=> (((((and_rect ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False)) P) x8) x6)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) (fun (x8:((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (x9:(((cVEG_EATS cWOLF) cGRAIN)->False))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 232.23/232.58 Found (fun (x7:((cMEAT_EATS cBIRD) cCATERPILLAR))=> (((fun (P:Type) (x8:(((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))->((((cVEG_EATS cWOLF) cGRAIN)->False)->P)))=> (((((and_rect ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False)) P) x8) x6)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) (fun (x8:((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (x9:(((cVEG_EATS cWOLF) cGRAIN)->False))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))))) as proof of (((cMEAT_EATS cBIRD) cCATERPILLAR)->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))
% 239.74/240.08 Found x8:((cMEAT_EATS cBIRD) cCATERPILLAR)
% 239.74/240.08 Instantiate: x0:=cBIRD:a;x9:=cCATERPILLAR:a
% 239.74/240.08 Found x8 as proof of ((cMEAT_EATS x0) x9)
% 239.74/240.08 Found x8:((cMEAT_EATS cBIRD) cCATERPILLAR)
% 239.74/240.08 Instantiate: x2:=cBIRD:a;x9:=cCATERPILLAR:a
% 239.74/240.08 Found x8 as proof of ((cMEAT_EATS x2) x9)
% 239.74/240.08 Found False_rect00:=(False_rect0 ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))):((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 239.74/240.08 Found (False_rect0 ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 239.74/240.08 Found ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 239.74/240.08 Found (fun (x9:(((cVEG_EATS cWOLF) cGRAIN)->False))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 239.74/240.08 Found (fun (x8:((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (x9:(((cVEG_EATS cWOLF) cGRAIN)->False))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))) as proof of ((((cVEG_EATS cWOLF) cGRAIN)->False)->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))
% 239.74/240.08 Found (fun (x8:((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (x9:(((cVEG_EATS cWOLF) cGRAIN)->False))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))) as proof of (((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))->((((cVEG_EATS cWOLF) cGRAIN)->False)->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))
% 239.74/240.08 Found (and_rect40 (fun (x8:((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (x9:(((cVEG_EATS cWOLF) cGRAIN)->False))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 239.74/240.08 Found ((and_rect4 ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) (fun (x8:((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (x9:(((cVEG_EATS cWOLF) cGRAIN)->False))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 239.74/240.08 Found (((fun (P:Type) (x8:(((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))->((((cVEG_EATS cWOLF) cGRAIN)->False)->P)))=> (((((and_rect ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False)) P) x8) x6)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) (fun (x8:((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (x9:(((cVEG_EATS cWOLF) cGRAIN)->False))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 239.74/240.08 Found (fun (x7:((cMEAT_EATS cBIRD) cCATERPILLAR))=> (((fun (P:Type) (x8:(((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))->((((cVEG_EATS cWOLF) cGRAIN)->False)->P)))=> (((((and_rect ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False)) P) x8) x6)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) (fun (x8:((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (x9:(((cVEG_EATS cWOLF) cGRAIN)->False))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 239.74/240.09 Found (fun (x6:((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) (x7:((cMEAT_EATS cBIRD) cCATERPILLAR))=> (((fun (P:Type) (x8:(((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))->((((cVEG_EATS cWOLF) cGRAIN)->False)->P)))=> (((((and_rect ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False)) P) x8) x6)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) (fun (x8:((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (x9:(((cVEG_EATS cWOLF) cGRAIN)->False))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))))) as proof of (((cMEAT_EATS cBIRD) cCATERPILLAR)->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))
% 239.74/240.09 Found (fun (x6:((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) (x7:((cMEAT_EATS cBIRD) cCATERPILLAR))=> (((fun (P:Type) (x8:(((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))->((((cVEG_EATS cWOLF) cGRAIN)->False)->P)))=> (((((and_rect ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False)) P) x8) x6)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) (fun (x8:((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (x9:(((cVEG_EATS cWOLF) cGRAIN)->False))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))))) as proof of (((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))->(((cMEAT_EATS cBIRD) cCATERPILLAR)->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))
% 242.84/243.15 Found x8:((cMEAT_EATS cBIRD) cCATERPILLAR)
% 242.84/243.15 Instantiate: x9:=cCATERPILLAR:a;x4:=cBIRD:a
% 242.84/243.15 Found x8 as proof of ((cMEAT_EATS x4) x9)
% 242.84/243.15 Found x8:((cMEAT_EATS cBIRD) cCATERPILLAR)
% 242.84/243.15 Instantiate: x9:=cCATERPILLAR:a;x6:=cBIRD:a
% 242.84/243.15 Found x8 as proof of ((cMEAT_EATS x6) x9)
% 242.84/243.15 Found False_rect00:=(False_rect0 ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))):((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 242.84/243.15 Found (False_rect0 ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 242.84/243.15 Found ((fun (P:Type)=> ((False_rect P) x70)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 242.84/243.15 Found (fun (x9:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x70)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 242.84/243.15 Found (fun (x8:((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) (x9:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x70)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))) as proof of (((cMEAT_EATS cBIRD) cCATERPILLAR)->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))
% 242.84/243.15 Found (fun (x8:((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) (x9:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x70)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))) as proof of (((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))->(((cMEAT_EATS cBIRD) cCATERPILLAR)->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))
% 242.84/243.15 Found (and_rect30 (fun (x8:((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) (x9:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x70)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 242.84/243.15 Found ((and_rect3 ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) (fun (x8:((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) (x9:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x70)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 242.84/243.15 Found (((fun (P:Type) (x8:(((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))->(((cMEAT_EATS cBIRD) cCATERPILLAR)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) ((cMEAT_EATS cBIRD) cCATERPILLAR)) P) x8) x6)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) (fun (x8:((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) (x9:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x70)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 242.84/243.15 Found (((fun (P:Type) (x8:(((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))->(((cMEAT_EATS cBIRD) cCATERPILLAR)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) ((cMEAT_EATS cBIRD) cCATERPILLAR)) P) x8) x6)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) (fun (x8:((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) (x9:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x70)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 245.71/246.06 Found False_rect00:=(False_rect0 ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))):((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 245.71/246.06 Found (False_rect0 ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 245.71/246.06 Found ((fun (P:Type)=> ((False_rect P) x70)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 245.71/246.06 Found (fun (x9:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x70)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 245.71/246.06 Found (fun (x8:((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) (x9:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x70)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))) as proof of (((cMEAT_EATS cBIRD) cCATERPILLAR)->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))
% 245.71/246.06 Found (fun (x8:((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) (x9:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x70)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))) as proof of (((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))->(((cMEAT_EATS cBIRD) cCATERPILLAR)->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))
% 245.71/246.06 Found (and_rect30 (fun (x8:((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) (x9:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x70)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 245.71/246.06 Found ((and_rect3 ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) (fun (x8:((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) (x9:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x70)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 245.71/246.06 Found (((fun (P:Type) (x8:(((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))->(((cMEAT_EATS cBIRD) cCATERPILLAR)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) ((cMEAT_EATS cBIRD) cCATERPILLAR)) P) x8) x6)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) (fun (x8:((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) (x9:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x70)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 245.71/246.06 Found (((fun (P:Type) (x8:(((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))->(((cMEAT_EATS cBIRD) cCATERPILLAR)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) ((cMEAT_EATS cBIRD) cCATERPILLAR)) P) x8) x6)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) (fun (x8:((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) (x9:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x70)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 292.11/292.47 Found x7:((cMEAT_EATS cBIRD) cCATERPILLAR)
% 292.11/292.47 Instantiate: x8:=cBIRD:a;x9:=cCATERPILLAR:a
% 292.11/292.47 Found x7 as proof of ((cMEAT_EATS x8) x9)
% 292.11/292.47 Found x9:((cMEAT_EATS cBIRD) cCATERPILLAR)
% 292.11/292.47 Instantiate: x0:=cBIRD:a;x1:=cCATERPILLAR:a
% 292.11/292.47 Found x9 as proof of ((cMEAT_EATS x0) x1)
% 292.11/292.47 Found x9:((cMEAT_EATS cBIRD) cCATERPILLAR)
% 292.11/292.47 Instantiate: x3:=cCATERPILLAR:a;x0:=cBIRD:a
% 292.11/292.47 Found x9 as proof of ((cMEAT_EATS x0) x3)
% 292.11/292.47 Found x9:((cMEAT_EATS cBIRD) cCATERPILLAR)
% 292.11/292.47 Instantiate: x2:=cBIRD:a;x3:=cCATERPILLAR:a
% 292.11/292.47 Found x9 as proof of ((cMEAT_EATS x2) x3)
% 292.11/292.47 Found x9:((cMEAT_EATS cBIRD) cCATERPILLAR)
% 292.11/292.47 Instantiate: x0:=cBIRD:a;x5:=cCATERPILLAR:a
% 292.11/292.47 Found x9 as proof of ((cMEAT_EATS x0) x5)
% 292.11/292.47 Found x9:((cMEAT_EATS cBIRD) cCATERPILLAR)
% 292.11/292.47 Instantiate: x0:=cBIRD:a;x7:=cCATERPILLAR:a
% 292.11/292.47 Found x9 as proof of ((cMEAT_EATS x0) x7)
% 292.11/292.47 Found x9:((cMEAT_EATS cBIRD) cCATERPILLAR)
% 292.11/292.47 Instantiate: x2:=cBIRD:a;x5:=cCATERPILLAR:a
% 292.11/292.47 Found x9 as proof of ((cMEAT_EATS x2) x5)
% 292.11/292.47 Found x9:((cMEAT_EATS cBIRD) cCATERPILLAR)
% 292.11/292.47 Instantiate: x2:=cBIRD:a;x7:=cCATERPILLAR:a
% 292.11/292.47 Found x9 as proof of ((cMEAT_EATS x2) x7)
% 292.11/292.47 Found x9:((cMEAT_EATS cBIRD) cCATERPILLAR)
% 292.11/292.47 Instantiate: x4:=cBIRD:a;x5:=cCATERPILLAR:a
% 292.11/292.47 Found x9 as proof of ((cMEAT_EATS x4) x5)
% 292.11/292.47 Found x9:((cMEAT_EATS cBIRD) cCATERPILLAR)
% 292.11/292.47 Instantiate: x7:=cCATERPILLAR:a;x4:=cBIRD:a
% 292.11/292.47 Found x9 as proof of ((cMEAT_EATS x4) x7)
% 292.11/292.47 Found x9:((cMEAT_EATS cBIRD) cCATERPILLAR)
% 292.11/292.47 Instantiate: x6:=cBIRD:a;x7:=cCATERPILLAR:a
% 292.11/292.47 Found x9 as proof of ((cMEAT_EATS x6) x7)
% 292.11/292.47 Found False_rect00:=(False_rect0 ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS x8) Xy)) ((cVEG_EATS Xy) cGRAIN))))):((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS x8) Xy)) ((cVEG_EATS Xy) cGRAIN))))
% 292.11/292.47 Found (False_rect0 ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS x8) Xy)) ((cVEG_EATS Xy) cGRAIN))))) as proof of ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS x8) Xy)) ((cVEG_EATS Xy) cGRAIN))))
% 292.11/292.47 Found ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS x8) Xy)) ((cVEG_EATS Xy) cGRAIN))))) as proof of ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS x8) Xy)) ((cVEG_EATS Xy) cGRAIN))))
% 292.11/292.47 Found ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS x8) Xy)) ((cVEG_EATS Xy) cGRAIN))))) as proof of ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS x8) Xy)) ((cVEG_EATS Xy) cGRAIN))))
% 292.11/292.47 Found (ex_intro000 ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS x8) Xy)) ((cVEG_EATS Xy) cGRAIN)))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 292.11/292.47 Found False_rect00:=(False_rect0 ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))):((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 292.11/292.47 Found (False_rect0 ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 292.11/292.47 Found ((fun (P:Type)=> ((False_rect P) x70)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 292.11/292.47 Found (fun (x9:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x70)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 292.11/292.47 Found (fun (x8:((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) (x9:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x70)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))) as proof of (((cMEAT_EATS cBIRD) cCATERPILLAR)->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))
% 292.11/292.47 Found (fun (x8:((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) (x9:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x70)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))) as proof of (((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))->(((cMEAT_EATS cBIRD) cCATERPILLAR)->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))
% 292.11/292.47 Found (and_rect30 (fun (x8:((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) (x9:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x70)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 292.11/292.47 Found ((and_rect3 ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) (fun (x8:((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) (x9:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x70)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 292.11/292.47 Found (((fun (P:Type) (x8:(((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))->(((cMEAT_EATS cBIRD) cCATERPILLAR)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) ((cMEAT_EATS cBIRD) cCATERPILLAR)) P) x8) x6)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) (fun (x8:((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) (x9:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x70)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 295.07/295.45 Found (((fun (P:Type) (x8:(((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))->(((cMEAT_EATS cBIRD) cCATERPILLAR)->P)))=> (((((and_rect ((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) ((cMEAT_EATS cBIRD) cCATERPILLAR)) P) x8) x6)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) (fun (x8:((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) (x9:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x70)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 295.07/295.45 Found False_rect00:=(False_rect0 ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))):((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 295.07/295.45 Found (False_rect0 ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 295.07/295.45 Found ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 295.07/295.45 Found (fun (x9:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 295.07/295.45 Found (fun (x8:((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) (x9:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))) as proof of (((cMEAT_EATS cBIRD) cCATERPILLAR)->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))
% 295.07/295.45 Found (fun (x8:((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) (x9:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN)))))))) as proof of (((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))->(((cMEAT_EATS cBIRD) cCATERPILLAR)->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))
% 295.07/295.45 Found (and_rect30 (fun (x8:((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) (x9:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 295.07/295.45 Found ((and_rect3 ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))) (fun (x8:((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_EATS cWOLF) cGRAIN)->False))) (x9:((cMEAT_EATS cBIRD) cCATERPILLAR))=> ((fun (P:Type)=> ((False_rect P) x50)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((and ((cMEAT_EATS Xx) Xy)) ((cVEG_EATS Xy) cGRAIN))))))
% 295.07/295.45 Found (((fun (P:Type) (x8:(((and ((and ((and ((and ((and ((and (forall (Xx:a), ((or (forall (Xy:p), ((cVEG_EATS Xx) Xy))) (forall (Xz:a), (((and ((cSMALLER Xz) Xx)) ((ex p) (fun (Xw:p)=> ((cVEG_EATS Xz) Xw))))->((cMEAT_EATS Xx) Xz)))))) ((cSMALLER cCATERPILLAR) cBIRD))) ((cSMALLER cSNAIL) cBIRD))) ((cSMALLER cBIRD) cFOX))) ((cSMALLER cFOX) cWOLF))) (((cMEAT_EATS cWOLF) cFOX)->False))) (((cVEG_
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