TSTP Solution File: SYO277^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO277^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n032.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 00:51:04 EDT 2022
% Result : Theorem 1.06s 1.24s
% Output : Proof 1.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.09 % Problem : SYO277^5 : TPTP v7.5.0. Released v4.0.0.
% 0.06/0.10 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % RAMPerCPU : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % DateTime : Sat Mar 12 00:13:17 EST 2022
% 0.09/0.29 % CPUTime :
% 0.09/0.30 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.09/0.30 Python 2.7.5
% 1.06/1.23 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 1.06/1.23 FOF formula (forall (X:fofType) (Y:fofType), ((iff (forall (Xq:(fofType->Prop)), ((Xq X)->(Xq Y)))) (forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y))))) of role conjecture named cTHM47D
% 1.06/1.23 Conjecture to prove = (forall (X:fofType) (Y:fofType), ((iff (forall (Xq:(fofType->Prop)), ((Xq X)->(Xq Y)))) (forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y))))):Prop
% 1.06/1.23 Parameter fofType_DUMMY:fofType.
% 1.06/1.23 We need to prove ['(forall (X:fofType) (Y:fofType), ((iff (forall (Xq:(fofType->Prop)), ((Xq X)->(Xq Y)))) (forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y)))))']
% 1.06/1.23 Parameter fofType:Type.
% 1.06/1.23 Trying to prove (forall (X:fofType) (Y:fofType), ((iff (forall (Xq:(fofType->Prop)), ((Xq X)->(Xq Y)))) (forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y)))))
% 1.06/1.23 Found eq_ref0:=(eq_ref fofType):(forall (a:fofType), (((eq fofType) a) a))
% 1.06/1.23 Found (eq_ref fofType) as proof of (forall (Z:fofType), (((eq fofType) Z) Z))
% 1.06/1.23 Found (eq_ref fofType) as proof of (forall (Z:fofType), (((eq fofType) Z) Z))
% 1.06/1.23 Found (x0 (eq_ref fofType)) as proof of (((eq fofType) X) Y)
% 1.06/1.23 Found ((x (eq fofType)) (eq_ref fofType)) as proof of (((eq fofType) X) Y)
% 1.06/1.23 Found (fun (x:(forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y))))=> ((x (eq fofType)) (eq_ref fofType))) as proof of (((eq fofType) X) Y)
% 1.06/1.23 Found (fun (x:(forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y))))=> ((x (eq fofType)) (eq_ref fofType))) as proof of ((forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y)))->(((eq fofType) X) Y))
% 1.06/1.23 Found x000:=(x00 X):((R X) X)
% 1.06/1.23 Found (x00 X) as proof of ((R X) X)
% 1.06/1.23 Found (fun (x00:(forall (Z:fofType), ((R Z) Z)))=> (x00 X)) as proof of ((R X) X)
% 1.06/1.23 Found (fun (R:(fofType->(fofType->Prop))) (x00:(forall (Z:fofType), ((R Z) Z)))=> (x00 X)) as proof of ((forall (Z:fofType), ((R Z) Z))->((R X) X))
% 1.06/1.23 Found (fun (R:(fofType->(fofType->Prop))) (x00:(forall (Z:fofType), ((R Z) Z)))=> (x00 X)) as proof of (forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) X)))
% 1.06/1.23 Found (x0 (fun (R:(fofType->(fofType->Prop))) (x00:(forall (Z:fofType), ((R Z) Z)))=> (x00 X))) as proof of (forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y)))
% 1.06/1.23 Found ((x (fun (x1:fofType)=> (forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) x1))))) (fun (R:(fofType->(fofType->Prop))) (x00:(forall (Z:fofType), ((R Z) Z)))=> (x00 X))) as proof of (forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y)))
% 1.06/1.23 Found (fun (x:(((eq fofType) X) Y))=> ((x (fun (x1:fofType)=> (forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) x1))))) (fun (R:(fofType->(fofType->Prop))) (x00:(forall (Z:fofType), ((R Z) Z)))=> (x00 X)))) as proof of (forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y)))
% 1.06/1.23 Found (fun (x:(((eq fofType) X) Y))=> ((x (fun (x1:fofType)=> (forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) x1))))) (fun (R:(fofType->(fofType->Prop))) (x00:(forall (Z:fofType), ((R Z) Z)))=> (x00 X)))) as proof of ((((eq fofType) X) Y)->(forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y))))
% 1.06/1.23 Found ((conj00 (fun (x:(((eq fofType) X) Y))=> ((x (fun (x1:fofType)=> (forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) x1))))) (fun (R:(fofType->(fofType->Prop))) (x00:(forall (Z:fofType), ((R Z) Z)))=> (x00 X))))) (fun (x:(forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y))))=> ((x (eq fofType)) (eq_ref fofType)))) as proof of ((and ((((eq fofType) X) Y)->(forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y))))) ((forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y)))->(((eq fofType) X) Y)))
% 1.06/1.23 Found (((conj0 ((forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y)))->(((eq fofType) X) Y))) (fun (x:(((eq fofType) X) Y))=> ((x (fun (x1:fofType)=> (forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) x1))))) (fun (R:(fofType->(fofType->Prop))) (x00:(forall (Z:fofType), ((R Z) Z)))=> (x00 X))))) (fun (x:(forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y))))=> ((x (eq fofType)) (eq_ref fofType)))) as proof of ((and ((((eq fofType) X) Y)->(forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y))))) ((forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y)))->(((eq fofType) X) Y)))
% 1.06/1.23 Found ((((conj ((((eq fofType) X) Y)->(forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y))))) ((forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y)))->(((eq fofType) X) Y))) (fun (x:(((eq fofType) X) Y))=> ((x (fun (x1:fofType)=> (forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) x1))))) (fun (R:(fofType->(fofType->Prop))) (x00:(forall (Z:fofType), ((R Z) Z)))=> (x00 X))))) (fun (x:(forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y))))=> ((x (eq fofType)) (eq_ref fofType)))) as proof of ((and ((((eq fofType) X) Y)->(forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y))))) ((forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y)))->(((eq fofType) X) Y)))
% 1.06/1.23 Found ((((conj ((((eq fofType) X) Y)->(forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y))))) ((forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y)))->(((eq fofType) X) Y))) (fun (x:(((eq fofType) X) Y))=> ((x (fun (x1:fofType)=> (forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) x1))))) (fun (R:(fofType->(fofType->Prop))) (x00:(forall (Z:fofType), ((R Z) Z)))=> (x00 X))))) (fun (x:(forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y))))=> ((x (eq fofType)) (eq_ref fofType)))) as proof of ((and ((((eq fofType) X) Y)->(forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y))))) ((forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y)))->(((eq fofType) X) Y)))
% 1.06/1.23 Found (fun (Y:fofType)=> ((((conj ((((eq fofType) X) Y)->(forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y))))) ((forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y)))->(((eq fofType) X) Y))) (fun (x:(((eq fofType) X) Y))=> ((x (fun (x1:fofType)=> (forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) x1))))) (fun (R:(fofType->(fofType->Prop))) (x00:(forall (Z:fofType), ((R Z) Z)))=> (x00 X))))) (fun (x:(forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y))))=> ((x (eq fofType)) (eq_ref fofType))))) as proof of ((iff (((eq fofType) X) Y)) (forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y))))
% 1.06/1.23 Found (fun (X:fofType) (Y:fofType)=> ((((conj ((((eq fofType) X) Y)->(forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y))))) ((forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y)))->(((eq fofType) X) Y))) (fun (x:(((eq fofType) X) Y))=> ((x (fun (x1:fofType)=> (forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) x1))))) (fun (R:(fofType->(fofType->Prop))) (x00:(forall (Z:fofType), ((R Z) Z)))=> (x00 X))))) (fun (x:(forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y))))=> ((x (eq fofType)) (eq_ref fofType))))) as proof of (forall (Y:fofType), ((iff (((eq fofType) X) Y)) (forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y)))))
% 1.06/1.23 Found (fun (X:fofType) (Y:fofType)=> ((((conj ((((eq fofType) X) Y)->(forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y))))) ((forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y)))->(((eq fofType) X) Y))) (fun (x:(((eq fofType) X) Y))=> ((x (fun (x1:fofType)=> (forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) x1))))) (fun (R:(fofType->(fofType->Prop))) (x00:(forall (Z:fofType), ((R Z) Z)))=> (x00 X))))) (fun (x:(forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y))))=> ((x (eq fofType)) (eq_ref fofType))))) as proof of (forall (X:fofType) (Y:fofType), ((iff (((eq fofType) X) Y)) (forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y)))))
% 1.06/1.24 Found (fun (X:fofType) (Y:fofType)=> ((((conj ((((eq fofType) X) Y)->(forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y))))) ((forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y)))->(((eq fofType) X) Y))) (fun (x:(((eq fofType) X) Y))=> ((x (fun (x1:fofType)=> (forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) x1))))) (fun (R:(fofType->(fofType->Prop))) (x00:(forall (Z:fofType), ((R Z) Z)))=> (x00 X))))) (fun (x:(forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y))))=> ((x (eq fofType)) (eq_ref fofType))))) as proof of (forall (X:fofType) (Y:fofType), ((iff (forall (Xq:(fofType->Prop)), ((Xq X)->(Xq Y)))) (forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y)))))
% 1.06/1.24 Got proof (fun (X:fofType) (Y:fofType)=> ((((conj ((((eq fofType) X) Y)->(forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y))))) ((forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y)))->(((eq fofType) X) Y))) (fun (x:(((eq fofType) X) Y))=> ((x (fun (x1:fofType)=> (forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) x1))))) (fun (R:(fofType->(fofType->Prop))) (x00:(forall (Z:fofType), ((R Z) Z)))=> (x00 X))))) (fun (x:(forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y))))=> ((x (eq fofType)) (eq_ref fofType)))))
% 1.06/1.24 Time elapsed = 0.697396s
% 1.06/1.24 node=145 cost=3369.000000 depth=15
% 1.06/1.24 ::::::::::::::::::::::
% 1.06/1.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.06/1.24 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.06/1.24 (fun (X:fofType) (Y:fofType)=> ((((conj ((((eq fofType) X) Y)->(forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y))))) ((forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y)))->(((eq fofType) X) Y))) (fun (x:(((eq fofType) X) Y))=> ((x (fun (x1:fofType)=> (forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) x1))))) (fun (R:(fofType->(fofType->Prop))) (x00:(forall (Z:fofType), ((R Z) Z)))=> (x00 X))))) (fun (x:(forall (R:(fofType->(fofType->Prop))), ((forall (Z:fofType), ((R Z) Z))->((R X) Y))))=> ((x (eq fofType)) (eq_ref fofType)))))
% 1.06/1.24 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------