%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SYO001^1 : TPTP v7.5.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n027.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 00:50:22 EDT 2022 % Result : Theorem 0.68s 0.86s % Output : Proof 0.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : SYO001^1 : TPTP v7.5.0. Released v3.7.0. % 0.03/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % 0.11/0.33 % Computer : n027.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % RAMPerCPU : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % DateTime : Thu Mar 10 22:54:11 EST 2022 % 0.11/0.33 % CPUTime : % 0.11/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27' % 0.11/0.34 Python 2.7.5 % 0.68/0.86 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/'] % 0.68/0.86 FOF formula (<kernel.Constant object at 0x2b6487497050>, <kernel.DependentProduct object at 0x13a9bd8>) of role type named leibeq_decl % 0.68/0.86 Using role type % 0.68/0.86 Declaring leibeq:(fofType->(fofType->Prop)) % 0.68/0.86 FOF formula (((eq (fofType->(fofType->Prop))) leibeq) (fun (X:fofType) (Y:fofType)=> (forall (P:(fofType->Prop)), ((P X)->(P Y))))) of role definition named leibeq % 0.68/0.86 A new definition: (((eq (fofType->(fofType->Prop))) leibeq) (fun (X:fofType) (Y:fofType)=> (forall (P:(fofType->Prop)), ((P X)->(P Y))))) % 0.68/0.86 Defined: leibeq:=(fun (X:fofType) (Y:fofType)=> (forall (P:(fofType->Prop)), ((P X)->(P Y)))) % 0.68/0.86 FOF formula (forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((leibeq X) Y)) ((leibeq Y) Z))->((leibeq X) Z))) of role conjecture named conj % 0.68/0.86 Conjecture to prove = (forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((leibeq X) Y)) ((leibeq Y) Z))->((leibeq X) Z))):Prop % 0.68/0.86 Parameter fofType_DUMMY:fofType. % 0.68/0.86 We need to prove ['(forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((leibeq X) Y)) ((leibeq Y) Z))->((leibeq X) Z)))'] % 0.68/0.86 Parameter fofType:Type. % 0.68/0.86 Definition leibeq:=(fun (X:fofType) (Y:fofType)=> (forall (P:(fofType->Prop)), ((P X)->(P Y)))):(fofType->(fofType->Prop)). % 0.68/0.86 Trying to prove (forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((leibeq X) Y)) ((leibeq Y) Z))->((leibeq X) Z))) % 0.68/0.86 Found x100:=(x10 x0):((leibeq X) Z) % 0.68/0.86 Found (x10 x0) as proof of ((leibeq X) Z) % 0.68/0.86 Found ((x1 (leibeq X)) x0) as proof of ((leibeq X) Z) % 0.68/0.86 Found (fun (x1:((leibeq Y) Z))=> ((x1 (leibeq X)) x0)) as proof of ((leibeq X) Z) % 0.68/0.86 Found (fun (x0:((leibeq X) Y)) (x1:((leibeq Y) Z))=> ((x1 (leibeq X)) x0)) as proof of (((leibeq Y) Z)->((leibeq X) Z)) % 0.68/0.86 Found (fun (x0:((leibeq X) Y)) (x1:((leibeq Y) Z))=> ((x1 (leibeq X)) x0)) as proof of (((leibeq X) Y)->(((leibeq Y) Z)->((leibeq X) Z))) % 0.68/0.86 Found (and_rect00 (fun (x0:((leibeq X) Y)) (x1:((leibeq Y) Z))=> ((x1 (leibeq X)) x0))) as proof of ((leibeq X) Z) % 0.68/0.86 Found ((and_rect0 ((leibeq X) Z)) (fun (x0:((leibeq X) Y)) (x1:((leibeq Y) Z))=> ((x1 (leibeq X)) x0))) as proof of ((leibeq X) Z) % 0.68/0.86 Found (((fun (P:Type) (x0:(((leibeq X) Y)->(((leibeq Y) Z)->P)))=> (((((and_rect ((leibeq X) Y)) ((leibeq Y) Z)) P) x0) x)) ((leibeq X) Z)) (fun (x0:((leibeq X) Y)) (x1:((leibeq Y) Z))=> ((x1 (leibeq X)) x0))) as proof of ((leibeq X) Z) % 0.68/0.86 Found (fun (x:((and ((leibeq X) Y)) ((leibeq Y) Z)))=> (((fun (P:Type) (x0:(((leibeq X) Y)->(((leibeq Y) Z)->P)))=> (((((and_rect ((leibeq X) Y)) ((leibeq Y) Z)) P) x0) x)) ((leibeq X) Z)) (fun (x0:((leibeq X) Y)) (x1:((leibeq Y) Z))=> ((x1 (leibeq X)) x0)))) as proof of ((leibeq X) Z) % 0.68/0.86 Found (fun (Z:fofType) (x:((and ((leibeq X) Y)) ((leibeq Y) Z)))=> (((fun (P:Type) (x0:(((leibeq X) Y)->(((leibeq Y) Z)->P)))=> (((((and_rect ((leibeq X) Y)) ((leibeq Y) Z)) P) x0) x)) ((leibeq X) Z)) (fun (x0:((leibeq X) Y)) (x1:((leibeq Y) Z))=> ((x1 (leibeq X)) x0)))) as proof of (((and ((leibeq X) Y)) ((leibeq Y) Z))->((leibeq X) Z)) % 0.68/0.86 Found (fun (Y:fofType) (Z:fofType) (x:((and ((leibeq X) Y)) ((leibeq Y) Z)))=> (((fun (P:Type) (x0:(((leibeq X) Y)->(((leibeq Y) Z)->P)))=> (((((and_rect ((leibeq X) Y)) ((leibeq Y) Z)) P) x0) x)) ((leibeq X) Z)) (fun (x0:((leibeq X) Y)) (x1:((leibeq Y) Z))=> ((x1 (leibeq X)) x0)))) as proof of (forall (Z:fofType), (((and ((leibeq X) Y)) ((leibeq Y) Z))->((leibeq X) Z))) % 0.68/0.86 Found (fun (X:fofType) (Y:fofType) (Z:fofType) (x:((and ((leibeq X) Y)) ((leibeq Y) Z)))=> (((fun (P:Type) (x0:(((leibeq X) Y)->(((leibeq Y) Z)->P)))=> (((((and_rect ((leibeq X) Y)) ((leibeq Y) Z)) P) x0) x)) ((leibeq X) Z)) (fun (x0:((leibeq X) Y)) (x1:((leibeq Y) Z))=> ((x1 (leibeq X)) x0)))) as proof of (forall (Y:fofType) (Z:fofType), (((and ((leibeq X) Y)) ((leibeq Y) Z))->((leibeq X) Z))) % 0.68/0.86 Found (fun (X:fofType) (Y:fofType) (Z:fofType) (x:((and ((leibeq X) Y)) ((leibeq Y) Z)))=> (((fun (P:Type) (x0:(((leibeq X) Y)->(((leibeq Y) Z)->P)))=> (((((and_rect ((leibeq X) Y)) ((leibeq Y) Z)) P) x0) x)) ((leibeq X) Z)) (fun (x0:((leibeq X) Y)) (x1:((leibeq Y) Z))=> ((x1 (leibeq X)) x0)))) as proof of (forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((leibeq X) Y)) ((leibeq Y) Z))->((leibeq X) Z))) % 0.68/0.86 Got proof (fun (X:fofType) (Y:fofType) (Z:fofType) (x:((and ((leibeq X) Y)) ((leibeq Y) Z)))=> (((fun (P:Type) (x0:(((leibeq X) Y)->(((leibeq Y) Z)->P)))=> (((((and_rect ((leibeq X) Y)) ((leibeq Y) Z)) P) x0) x)) ((leibeq X) Z)) (fun (x0:((leibeq X) Y)) (x1:((leibeq Y) Z))=> ((x1 (leibeq X)) x0)))) % 0.68/0.86 Time elapsed = 0.253425s % 0.68/0.86 node=40 cost=148.000000 depth=12 % 0.68/0.86 :::::::::::::::::::::: % 0.68/0.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 0.68/0.86 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % 0.68/0.86 (fun (X:fofType) (Y:fofType) (Z:fofType) (x:((and ((leibeq X) Y)) ((leibeq Y) Z)))=> (((fun (P:Type) (x0:(((leibeq X) Y)->(((leibeq Y) Z)->P)))=> (((((and_rect ((leibeq X) Y)) ((leibeq Y) Z)) P) x0) x)) ((leibeq X) Z)) (fun (x0:((leibeq X) Y)) (x1:((leibeq Y) Z))=> ((x1 (leibeq X)) x0)))) % 0.68/0.86 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p %------------------------------------------------------------------------------