TSTP Solution File: SYO355^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO355^5 : TPTP v7.5.0. Released v4.0.0.
% 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 00:51:14 EDT 2022
% Result : Theorem 0.82s 0.98s
% Output : Proof 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYO355^5 : TPTP v7.5.0. Released v4.0.0.
% 0.06/0.11 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.32 % Computer : n027.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % RAMPerCPU : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % DateTime : Sat Mar 12 06:52:42 EST 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.33 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.33 Python 2.7.5
% 0.82/0.98 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.82/0.98 FOF formula ((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->(forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), (((eq (fofType->fofType)) Xf) Xg))) of role conjecture named cTHM613
% 0.82/0.98 Conjecture to prove = ((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->(forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), (((eq (fofType->fofType)) Xf) Xg))):Prop
% 0.82/0.98 Parameter fofType_DUMMY:fofType.
% 0.82/0.98 We need to prove ['((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->(forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), (((eq (fofType->fofType)) Xf) Xg)))']
% 0.82/0.98 Parameter fofType:Type.
% 0.82/0.98 Trying to prove ((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->(forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), (((eq (fofType->fofType)) Xf) Xg)))
% 0.82/0.98 Found x10:=(x1 (Xg x0)):(((eq fofType) (Xf x0)) (Xg x0))
% 0.82/0.98 Found (x1 (Xg x0)) as proof of (((eq fofType) (Xf x0)) (Xg x0))
% 0.82/0.98 Found ((x (Xf x0)) (Xg x0)) as proof of (((eq fofType) (Xf x0)) (Xg x0))
% 0.82/0.98 Found (fun (x0:fofType)=> ((x (Xf x0)) (Xg x0))) as proof of (((eq fofType) (Xf x0)) (Xg x0))
% 0.82/0.98 Found (fun (x0:fofType)=> ((x (Xf x0)) (Xg x0))) as proof of (forall (x:fofType), (((eq fofType) (Xf x)) (Xg x)))
% 0.82/0.98 Found (functional_extensionality0000 (fun (x0:fofType)=> ((x (Xf x0)) (Xg x0)))) as proof of (((eq (fofType->fofType)) Xf) Xg)
% 0.82/0.98 Found ((functional_extensionality000 Xg) (fun (x0:fofType)=> ((x (Xf x0)) (Xg x0)))) as proof of (((eq (fofType->fofType)) Xf) Xg)
% 0.82/0.98 Found (((functional_extensionality00 Xf) Xg) (fun (x0:fofType)=> ((x (Xf x0)) (Xg x0)))) as proof of (((eq (fofType->fofType)) Xf) Xg)
% 0.82/0.98 Found ((((functional_extensionality0 fofType) Xf) Xg) (fun (x0:fofType)=> ((x (Xf x0)) (Xg x0)))) as proof of (((eq (fofType->fofType)) Xf) Xg)
% 0.82/0.98 Found (((((functional_extensionality fofType) fofType) Xf) Xg) (fun (x0:fofType)=> ((x (Xf x0)) (Xg x0)))) as proof of (((eq (fofType->fofType)) Xf) Xg)
% 0.82/0.98 Found (fun (Xg:(fofType->fofType))=> (((((functional_extensionality fofType) fofType) Xf) Xg) (fun (x0:fofType)=> ((x (Xf x0)) (Xg x0))))) as proof of (((eq (fofType->fofType)) Xf) Xg)
% 0.82/0.98 Found (fun (Xf:(fofType->fofType)) (Xg:(fofType->fofType))=> (((((functional_extensionality fofType) fofType) Xf) Xg) (fun (x0:fofType)=> ((x (Xf x0)) (Xg x0))))) as proof of (forall (Xg:(fofType->fofType)), (((eq (fofType->fofType)) Xf) Xg))
% 0.82/0.98 Found (fun (x:(forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (Xf:(fofType->fofType)) (Xg:(fofType->fofType))=> (((((functional_extensionality fofType) fofType) Xf) Xg) (fun (x0:fofType)=> ((x (Xf x0)) (Xg x0))))) as proof of (forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), (((eq (fofType->fofType)) Xf) Xg))
% 0.82/0.98 Found (fun (x:(forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (Xf:(fofType->fofType)) (Xg:(fofType->fofType))=> (((((functional_extensionality fofType) fofType) Xf) Xg) (fun (x0:fofType)=> ((x (Xf x0)) (Xg x0))))) as proof of ((forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))->(forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), (((eq (fofType->fofType)) Xf) Xg)))
% 0.82/0.98 Got proof (fun (x:(forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (Xf:(fofType->fofType)) (Xg:(fofType->fofType))=> (((((functional_extensionality fofType) fofType) Xf) Xg) (fun (x0:fofType)=> ((x (Xf x0)) (Xg x0)))))
% 0.82/0.98 Time elapsed = 0.378471s
% 0.82/0.98 node=86 cost=10.000000 depth=12
% 0.82/0.98 ::::::::::::::::::::::
% 0.82/0.98 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.82/0.98 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.82/0.98 (fun (x:(forall (Xa:fofType) (Xb:fofType), (((eq fofType) Xa) Xb))) (Xf:(fofType->fofType)) (Xg:(fofType->fofType))=> (((((functional_extensionality fofType) fofType) Xf) Xg) (fun (x0:fofType)=> ((x (Xf x0)) (Xg x0)))))
% 0.82/0.98 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------