TSTP Solution File: SYO125^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO125^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n029.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 00:50:42 EDT 2022
% Result : Theorem 2.18s 2.34s
% Output : Proof 2.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYO125^5 : TPTP v7.5.0. Released v4.0.0.
% 0.07/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.32 % Computer : n029.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 : Fri Mar 11 15:54:30 EST 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34 Python 2.7.5
% 2.14/2.31 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 2.14/2.31 FOF formula (<kernel.Constant object at 0x1e72368>, <kernel.Sort object at 0x2af69e953638>) of role type named cR
% 2.14/2.31 Using role type
% 2.14/2.31 Declaring cR:Prop
% 2.14/2.31 FOF formula (<kernel.Constant object at 0x1e72248>, <kernel.Sort object at 0x2af69e953638>) of role type named cP
% 2.14/2.31 Using role type
% 2.14/2.31 Declaring cP:Prop
% 2.14/2.31 FOF formula (<kernel.Constant object at 0x1e723f8>, <kernel.Sort object at 0x2af69e953638>) of role type named cQ
% 2.14/2.31 Using role type
% 2.14/2.31 Declaring cQ:Prop
% 2.14/2.31 FOF formula (((and ((iff cP) cQ)) ((iff cQ) cR))->((iff cP) cR)) of role conjecture named cTRIV4
% 2.14/2.31 Conjecture to prove = (((and ((iff cP) cQ)) ((iff cQ) cR))->((iff cP) cR)):Prop
% 2.14/2.31 We need to prove ['(((and ((iff cP) cQ)) ((iff cQ) cR))->((iff cP) cR))']
% 2.14/2.31 Parameter cR:Prop.
% 2.14/2.31 Parameter cP:Prop.
% 2.14/2.31 Parameter cQ:Prop.
% 2.14/2.31 Trying to prove (((and ((iff cP) cQ)) ((iff cQ) cR))->((iff cP) cR))
% 2.14/2.31 Found x40:=(x4 x6):cQ
% 2.14/2.31 Found (x4 x6) as proof of cQ
% 2.14/2.31 Found (x4 x6) as proof of cQ
% 2.14/2.31 Found (x2 (x4 x6)) as proof of cR
% 2.14/2.31 Found (fun (x6:cP)=> (x2 (x4 x6))) as proof of cR
% 2.14/2.31 Found (fun (x6:cP)=> (x2 (x4 x6))) as proof of (cP->cR)
% 2.14/2.31 Found x30:=(x3 x6):cQ
% 2.14/2.31 Found (x3 x6) as proof of cQ
% 2.14/2.31 Found (x3 x6) as proof of cQ
% 2.14/2.31 Found (x5 (x3 x6)) as proof of cP
% 2.14/2.31 Found (fun (x6:cR)=> (x5 (x3 x6))) as proof of cP
% 2.14/2.31 Found (fun (x6:cR)=> (x5 (x3 x6))) as proof of (cR->cP)
% 2.14/2.31 Found ((conj00 (fun (x6:cP)=> (x2 (x4 x6)))) (fun (x6:cR)=> (x5 (x3 x6)))) as proof of ((iff cP) cR)
% 2.14/2.31 Found (((conj0 (cR->cP)) (fun (x6:cP)=> (x2 (x4 x6)))) (fun (x6:cR)=> (x5 (x3 x6)))) as proof of ((iff cP) cR)
% 2.14/2.31 Found ((((conj (cP->cR)) (cR->cP)) (fun (x6:cP)=> (x2 (x4 x6)))) (fun (x6:cR)=> (x5 (x3 x6)))) as proof of ((iff cP) cR)
% 2.14/2.31 Found (fun (x5:(cQ->cP))=> ((((conj (cP->cR)) (cR->cP)) (fun (x6:cP)=> (x2 (x4 x6)))) (fun (x6:cR)=> (x5 (x3 x6))))) as proof of ((iff cP) cR)
% 2.14/2.31 Found (fun (x4:(cP->cQ)) (x5:(cQ->cP))=> ((((conj (cP->cR)) (cR->cP)) (fun (x6:cP)=> (x2 (x4 x6)))) (fun (x6:cR)=> (x5 (x3 x6))))) as proof of ((cQ->cP)->((iff cP) cR))
% 2.14/2.31 Found (fun (x4:(cP->cQ)) (x5:(cQ->cP))=> ((((conj (cP->cR)) (cR->cP)) (fun (x6:cP)=> (x2 (x4 x6)))) (fun (x6:cR)=> (x5 (x3 x6))))) as proof of ((cP->cQ)->((cQ->cP)->((iff cP) cR)))
% 2.14/2.31 Found (and_rect20 (fun (x4:(cP->cQ)) (x5:(cQ->cP))=> ((((conj (cP->cR)) (cR->cP)) (fun (x6:cP)=> (x2 (x4 x6)))) (fun (x6:cR)=> (x5 (x3 x6)))))) as proof of ((iff cP) cR)
% 2.14/2.31 Found ((and_rect2 ((iff cP) cR)) (fun (x4:(cP->cQ)) (x5:(cQ->cP))=> ((((conj (cP->cR)) (cR->cP)) (fun (x6:cP)=> (x2 (x4 x6)))) (fun (x6:cR)=> (x5 (x3 x6)))))) as proof of ((iff cP) cR)
% 2.14/2.31 Found (((fun (P:Type) (x4:((cP->cQ)->((cQ->cP)->P)))=> (((((and_rect (cP->cQ)) (cQ->cP)) P) x4) x0)) ((iff cP) cR)) (fun (x4:(cP->cQ)) (x5:(cQ->cP))=> ((((conj (cP->cR)) (cR->cP)) (fun (x6:cP)=> (x2 (x4 x6)))) (fun (x6:cR)=> (x5 (x3 x6)))))) as proof of ((iff cP) cR)
% 2.14/2.31 Found (fun (x3:(cR->cQ))=> (((fun (P:Type) (x4:((cP->cQ)->((cQ->cP)->P)))=> (((((and_rect (cP->cQ)) (cQ->cP)) P) x4) x0)) ((iff cP) cR)) (fun (x4:(cP->cQ)) (x5:(cQ->cP))=> ((((conj (cP->cR)) (cR->cP)) (fun (x6:cP)=> (x2 (x4 x6)))) (fun (x6:cR)=> (x5 (x3 x6))))))) as proof of ((iff cP) cR)
% 2.14/2.31 Found (fun (x2:(cQ->cR)) (x3:(cR->cQ))=> (((fun (P:Type) (x4:((cP->cQ)->((cQ->cP)->P)))=> (((((and_rect (cP->cQ)) (cQ->cP)) P) x4) x0)) ((iff cP) cR)) (fun (x4:(cP->cQ)) (x5:(cQ->cP))=> ((((conj (cP->cR)) (cR->cP)) (fun (x6:cP)=> (x2 (x4 x6)))) (fun (x6:cR)=> (x5 (x3 x6))))))) as proof of ((cR->cQ)->((iff cP) cR))
% 2.14/2.31 Found (fun (x2:(cQ->cR)) (x3:(cR->cQ))=> (((fun (P:Type) (x4:((cP->cQ)->((cQ->cP)->P)))=> (((((and_rect (cP->cQ)) (cQ->cP)) P) x4) x0)) ((iff cP) cR)) (fun (x4:(cP->cQ)) (x5:(cQ->cP))=> ((((conj (cP->cR)) (cR->cP)) (fun (x6:cP)=> (x2 (x4 x6)))) (fun (x6:cR)=> (x5 (x3 x6))))))) as proof of ((cQ->cR)->((cR->cQ)->((iff cP) cR)))
% 2.14/2.31 Found (and_rect10 (fun (x2:(cQ->cR)) (x3:(cR->cQ))=> (((fun (P:Type) (x4:((cP->cQ)->((cQ->cP)->P)))=> (((((and_rect (cP->cQ)) (cQ->cP)) P) x4) x0)) ((iff cP) cR)) (fun (x4:(cP->cQ)) (x5:(cQ->cP))=> ((((conj (cP->cR)) (cR->cP)) (fun (x6:cP)=> (x2 (x4 x6)))) (fun (x6:cR)=> (x5 (x3 x6)))))))) as proof of ((iff cP) cR)
% 2.14/2.31 Found ((and_rect1 ((iff cP) cR)) (fun (x2:(cQ->cR)) (x3:(cR->cQ))=> (((fun (P:Type) (x4:((cP->cQ)->((cQ->cP)->P)))=> (((((and_rect (cP->cQ)) (cQ->cP)) P) x4) x0)) ((iff cP) cR)) (fun (x4:(cP->cQ)) (x5:(cQ->cP))=> ((((conj (cP->cR)) (cR->cP)) (fun (x6:cP)=> (x2 (x4 x6)))) (fun (x6:cR)=> (x5 (x3 x6)))))))) as proof of ((iff cP) cR)
% 2.14/2.32 Found (((fun (P:Type) (x2:((cQ->cR)->((cR->cQ)->P)))=> (((((and_rect (cQ->cR)) (cR->cQ)) P) x2) x1)) ((iff cP) cR)) (fun (x2:(cQ->cR)) (x3:(cR->cQ))=> (((fun (P:Type) (x4:((cP->cQ)->((cQ->cP)->P)))=> (((((and_rect (cP->cQ)) (cQ->cP)) P) x4) x0)) ((iff cP) cR)) (fun (x4:(cP->cQ)) (x5:(cQ->cP))=> ((((conj (cP->cR)) (cR->cP)) (fun (x6:cP)=> (x2 (x4 x6)))) (fun (x6:cR)=> (x5 (x3 x6)))))))) as proof of ((iff cP) cR)
% 2.14/2.32 Found (fun (x1:((iff cQ) cR))=> (((fun (P:Type) (x2:((cQ->cR)->((cR->cQ)->P)))=> (((((and_rect (cQ->cR)) (cR->cQ)) P) x2) x1)) ((iff cP) cR)) (fun (x2:(cQ->cR)) (x3:(cR->cQ))=> (((fun (P:Type) (x4:((cP->cQ)->((cQ->cP)->P)))=> (((((and_rect (cP->cQ)) (cQ->cP)) P) x4) x0)) ((iff cP) cR)) (fun (x4:(cP->cQ)) (x5:(cQ->cP))=> ((((conj (cP->cR)) (cR->cP)) (fun (x6:cP)=> (x2 (x4 x6)))) (fun (x6:cR)=> (x5 (x3 x6))))))))) as proof of ((iff cP) cR)
% 2.14/2.32 Found (fun (x0:((iff cP) cQ)) (x1:((iff cQ) cR))=> (((fun (P:Type) (x2:((cQ->cR)->((cR->cQ)->P)))=> (((((and_rect (cQ->cR)) (cR->cQ)) P) x2) x1)) ((iff cP) cR)) (fun (x2:(cQ->cR)) (x3:(cR->cQ))=> (((fun (P:Type) (x4:((cP->cQ)->((cQ->cP)->P)))=> (((((and_rect (cP->cQ)) (cQ->cP)) P) x4) x0)) ((iff cP) cR)) (fun (x4:(cP->cQ)) (x5:(cQ->cP))=> ((((conj (cP->cR)) (cR->cP)) (fun (x6:cP)=> (x2 (x4 x6)))) (fun (x6:cR)=> (x5 (x3 x6))))))))) as proof of (((iff cQ) cR)->((iff cP) cR))
% 2.14/2.32 Found (fun (x0:((iff cP) cQ)) (x1:((iff cQ) cR))=> (((fun (P:Type) (x2:((cQ->cR)->((cR->cQ)->P)))=> (((((and_rect (cQ->cR)) (cR->cQ)) P) x2) x1)) ((iff cP) cR)) (fun (x2:(cQ->cR)) (x3:(cR->cQ))=> (((fun (P:Type) (x4:((cP->cQ)->((cQ->cP)->P)))=> (((((and_rect (cP->cQ)) (cQ->cP)) P) x4) x0)) ((iff cP) cR)) (fun (x4:(cP->cQ)) (x5:(cQ->cP))=> ((((conj (cP->cR)) (cR->cP)) (fun (x6:cP)=> (x2 (x4 x6)))) (fun (x6:cR)=> (x5 (x3 x6))))))))) as proof of (((iff cP) cQ)->(((iff cQ) cR)->((iff cP) cR)))
% 2.14/2.32 Found (and_rect00 (fun (x0:((iff cP) cQ)) (x1:((iff cQ) cR))=> (((fun (P:Type) (x2:((cQ->cR)->((cR->cQ)->P)))=> (((((and_rect (cQ->cR)) (cR->cQ)) P) x2) x1)) ((iff cP) cR)) (fun (x2:(cQ->cR)) (x3:(cR->cQ))=> (((fun (P:Type) (x4:((cP->cQ)->((cQ->cP)->P)))=> (((((and_rect (cP->cQ)) (cQ->cP)) P) x4) x0)) ((iff cP) cR)) (fun (x4:(cP->cQ)) (x5:(cQ->cP))=> ((((conj (cP->cR)) (cR->cP)) (fun (x6:cP)=> (x2 (x4 x6)))) (fun (x6:cR)=> (x5 (x3 x6)))))))))) as proof of ((iff cP) cR)
% 2.14/2.32 Found ((and_rect0 ((iff cP) cR)) (fun (x0:((iff cP) cQ)) (x1:((iff cQ) cR))=> (((fun (P:Type) (x2:((cQ->cR)->((cR->cQ)->P)))=> (((((and_rect (cQ->cR)) (cR->cQ)) P) x2) x1)) ((iff cP) cR)) (fun (x2:(cQ->cR)) (x3:(cR->cQ))=> (((fun (P:Type) (x4:((cP->cQ)->((cQ->cP)->P)))=> (((((and_rect (cP->cQ)) (cQ->cP)) P) x4) x0)) ((iff cP) cR)) (fun (x4:(cP->cQ)) (x5:(cQ->cP))=> ((((conj (cP->cR)) (cR->cP)) (fun (x6:cP)=> (x2 (x4 x6)))) (fun (x6:cR)=> (x5 (x3 x6)))))))))) as proof of ((iff cP) cR)
% 2.14/2.32 Found (((fun (P:Type) (x0:(((iff cP) cQ)->(((iff cQ) cR)->P)))=> (((((and_rect ((iff cP) cQ)) ((iff cQ) cR)) P) x0) x)) ((iff cP) cR)) (fun (x0:((iff cP) cQ)) (x1:((iff cQ) cR))=> (((fun (P:Type) (x2:((cQ->cR)->((cR->cQ)->P)))=> (((((and_rect (cQ->cR)) (cR->cQ)) P) x2) x1)) ((iff cP) cR)) (fun (x2:(cQ->cR)) (x3:(cR->cQ))=> (((fun (P:Type) (x4:((cP->cQ)->((cQ->cP)->P)))=> (((((and_rect (cP->cQ)) (cQ->cP)) P) x4) x0)) ((iff cP) cR)) (fun (x4:(cP->cQ)) (x5:(cQ->cP))=> ((((conj (cP->cR)) (cR->cP)) (fun (x6:cP)=> (x2 (x4 x6)))) (fun (x6:cR)=> (x5 (x3 x6)))))))))) as proof of ((iff cP) cR)
% 2.14/2.32 Found (fun (x:((and ((iff cP) cQ)) ((iff cQ) cR)))=> (((fun (P:Type) (x0:(((iff cP) cQ)->(((iff cQ) cR)->P)))=> (((((and_rect ((iff cP) cQ)) ((iff cQ) cR)) P) x0) x)) ((iff cP) cR)) (fun (x0:((iff cP) cQ)) (x1:((iff cQ) cR))=> (((fun (P:Type) (x2:((cQ->cR)->((cR->cQ)->P)))=> (((((and_rect (cQ->cR)) (cR->cQ)) P) x2) x1)) ((iff cP) cR)) (fun (x2:(cQ->cR)) (x3:(cR->cQ))=> (((fun (P:Type) (x4:((cP->cQ)->((cQ->cP)->P)))=> (((((and_rect (cP->cQ)) (cQ->cP)) P) x4) x0)) ((iff cP) cR)) (fun (x4:(cP->cQ)) (x5:(cQ->cP))=> ((((conj (cP->cR)) (cR->cP)) (fun (x6:cP)=> (x2 (x4 x6)))) (fun (x6:cR)=> (x5 (x3 x6))))))))))) as proof of ((iff cP) cR)
% 2.18/2.34 Found (fun (x:((and ((iff cP) cQ)) ((iff cQ) cR)))=> (((fun (P:Type) (x0:(((iff cP) cQ)->(((iff cQ) cR)->P)))=> (((((and_rect ((iff cP) cQ)) ((iff cQ) cR)) P) x0) x)) ((iff cP) cR)) (fun (x0:((iff cP) cQ)) (x1:((iff cQ) cR))=> (((fun (P:Type) (x2:((cQ->cR)->((cR->cQ)->P)))=> (((((and_rect (cQ->cR)) (cR->cQ)) P) x2) x1)) ((iff cP) cR)) (fun (x2:(cQ->cR)) (x3:(cR->cQ))=> (((fun (P:Type) (x4:((cP->cQ)->((cQ->cP)->P)))=> (((((and_rect (cP->cQ)) (cQ->cP)) P) x4) x0)) ((iff cP) cR)) (fun (x4:(cP->cQ)) (x5:(cQ->cP))=> ((((conj (cP->cR)) (cR->cP)) (fun (x6:cP)=> (x2 (x4 x6)))) (fun (x6:cR)=> (x5 (x3 x6))))))))))) as proof of (((and ((iff cP) cQ)) ((iff cQ) cR))->((iff cP) cR))
% 2.18/2.34 Got proof (fun (x:((and ((iff cP) cQ)) ((iff cQ) cR)))=> (((fun (P:Type) (x0:(((iff cP) cQ)->(((iff cQ) cR)->P)))=> (((((and_rect ((iff cP) cQ)) ((iff cQ) cR)) P) x0) x)) ((iff cP) cR)) (fun (x0:((iff cP) cQ)) (x1:((iff cQ) cR))=> (((fun (P:Type) (x2:((cQ->cR)->((cR->cQ)->P)))=> (((((and_rect (cQ->cR)) (cR->cQ)) P) x2) x1)) ((iff cP) cR)) (fun (x2:(cQ->cR)) (x3:(cR->cQ))=> (((fun (P:Type) (x4:((cP->cQ)->((cQ->cP)->P)))=> (((((and_rect (cP->cQ)) (cQ->cP)) P) x4) x0)) ((iff cP) cR)) (fun (x4:(cP->cQ)) (x5:(cQ->cP))=> ((((conj (cP->cR)) (cR->cP)) (fun (x6:cP)=> (x2 (x4 x6)))) (fun (x6:cR)=> (x5 (x3 x6)))))))))))
% 2.18/2.34 Time elapsed = 1.714851s
% 2.18/2.34 node=771 cost=679.000000 depth=27
% 2.18/2.34 ::::::::::::::::::::::
% 2.18/2.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.18/2.34 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.18/2.34 (fun (x:((and ((iff cP) cQ)) ((iff cQ) cR)))=> (((fun (P:Type) (x0:(((iff cP) cQ)->(((iff cQ) cR)->P)))=> (((((and_rect ((iff cP) cQ)) ((iff cQ) cR)) P) x0) x)) ((iff cP) cR)) (fun (x0:((iff cP) cQ)) (x1:((iff cQ) cR))=> (((fun (P:Type) (x2:((cQ->cR)->((cR->cQ)->P)))=> (((((and_rect (cQ->cR)) (cR->cQ)) P) x2) x1)) ((iff cP) cR)) (fun (x2:(cQ->cR)) (x3:(cR->cQ))=> (((fun (P:Type) (x4:((cP->cQ)->((cQ->cP)->P)))=> (((((and_rect (cP->cQ)) (cQ->cP)) P) x4) x0)) ((iff cP) cR)) (fun (x4:(cP->cQ)) (x5:(cQ->cP))=> ((((conj (cP->cR)) (cR->cP)) (fun (x6:cP)=> (x2 (x4 x6)))) (fun (x6:cR)=> (x5 (x3 x6)))))))))))
% 2.18/2.34 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------