%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SYO149^5 : TPTP v7.5.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n023.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 00:50:45 EDT 2022 % Result : Theorem 0.52s 0.73s % Output : Proof 0.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : SYO149^5 : TPTP v7.5.0. Released v4.0.0. % 0.03/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % 0.12/0.33 % Computer : n023.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 17:40:27 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 % 0.52/0.72 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/'] % 0.52/0.72 FOF formula (<kernel.Constant object at 0x10b51b8>, <kernel.Constant object at 0x10b5dd0>) of role type named a % 0.52/0.72 Using role type % 0.52/0.72 Declaring a:fofType % 0.52/0.72 FOF formula (<kernel.Constant object at 0x10b1368>, <kernel.DependentProduct object at 0x1393a28>) of role type named f % 0.52/0.72 Using role type % 0.52/0.72 Declaring f:(fofType->fofType) % 0.52/0.72 FOF formula (<kernel.Constant object at 0x10ace18>, <kernel.DependentProduct object at 0x1393ea8>) of role type named cP % 0.52/0.72 Using role type % 0.52/0.72 Declaring cP:(fofType->Prop) % 0.52/0.72 FOF formula (<kernel.Constant object at 0x10b5fc8>, <kernel.DependentProduct object at 0x1393fc8>) of role type named cQ % 0.52/0.72 Using role type % 0.52/0.72 Declaring cQ:(fofType->Prop) % 0.52/0.72 FOF formula (((and ((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (cP a))->(cP (f a))) of role conjecture named cSIMPLEPQ % 0.52/0.72 Conjecture to prove = (((and ((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (cP a))->(cP (f a))):Prop % 0.52/0.72 We need to prove ['(((and ((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (cP a))->(cP (f a)))'] % 0.52/0.72 Parameter fofType:Type. % 0.52/0.72 Parameter a:fofType. % 0.52/0.72 Parameter f:(fofType->fofType). % 0.52/0.72 Parameter cP:(fofType->Prop). % 0.52/0.72 Parameter cQ:(fofType->Prop). % 0.52/0.72 Trying to prove (((and ((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (cP a))->(cP (f a))) % 0.52/0.72 Found x200:=(x20 x1):(cQ (f a)) % 0.52/0.72 Found (x20 x1) as proof of (cQ (f a)) % 0.52/0.72 Found ((x2 a) x1) as proof of (cQ (f a)) % 0.52/0.72 Found ((x2 a) x1) as proof of (cQ (f a)) % 0.52/0.72 Found (x30 ((x2 a) x1)) as proof of (cP (f a)) % 0.52/0.72 Found ((x3 (f a)) ((x2 a) x1)) as proof of (cP (f a)) % 0.52/0.72 Found (fun (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1))) as proof of (cP (f a)) % 0.52/0.72 Found (fun (x2:(forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1))) as proof of ((forall (Xy:fofType), ((cQ Xy)->(cP Xy)))->(cP (f a))) % 0.52/0.72 Found (fun (x2:(forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1))) as proof of ((forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))->((forall (Xy:fofType), ((cQ Xy)->(cP Xy)))->(cP (f a)))) % 0.52/0.72 Found (and_rect10 (fun (x2:(forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1)))) as proof of (cP (f a)) % 0.52/0.72 Found ((and_rect1 (cP (f a))) (fun (x2:(forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1)))) as proof of (cP (f a)) % 0.52/0.72 Found (((fun (P:Type) (x2:((forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))->((forall (Xy:fofType), ((cQ Xy)->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy)))) P) x2) x0)) (cP (f a))) (fun (x2:(forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1)))) as proof of (cP (f a)) % 0.52/0.72 Found (fun (x1:(cP a))=> (((fun (P:Type) (x2:((forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))->((forall (Xy:fofType), ((cQ Xy)->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy)))) P) x2) x0)) (cP (f a))) (fun (x2:(forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1))))) as proof of (cP (f a)) % 0.52/0.72 Found (fun (x0:((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (x1:(cP a))=> (((fun (P:Type) (x2:((forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))->((forall (Xy:fofType), ((cQ Xy)->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy)))) P) x2) x0)) (cP (f a))) (fun (x2:(forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1))))) as proof of ((cP a)->(cP (f a))) % 0.52/0.72 Found (fun (x0:((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (x1:(cP a))=> (((fun (P:Type) (x2:((forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))->((forall (Xy:fofType), ((cQ Xy)->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy)))) P) x2) x0)) (cP (f a))) (fun (x2:(forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1))))) as proof of (((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))->((cP a)->(cP (f a)))) % 0.52/0.72 Found (and_rect00 (fun (x0:((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (x1:(cP a))=> (((fun (P:Type) (x2:((forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))->((forall (Xy:fofType), ((cQ Xy)->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy)))) P) x2) x0)) (cP (f a))) (fun (x2:(forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1)))))) as proof of (cP (f a)) % 0.52/0.72 Found ((and_rect0 (cP (f a))) (fun (x0:((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (x1:(cP a))=> (((fun (P:Type) (x2:((forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))->((forall (Xy:fofType), ((cQ Xy)->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy)))) P) x2) x0)) (cP (f a))) (fun (x2:(forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1)))))) as proof of (cP (f a)) % 0.52/0.72 Found (((fun (P:Type) (x0:(((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))->((cP a)->P)))=> (((((and_rect ((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (cP a)) P) x0) x)) (cP (f a))) (fun (x0:((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (x1:(cP a))=> (((fun (P:Type) (x2:((forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))->((forall (Xy:fofType), ((cQ Xy)->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy)))) P) x2) x0)) (cP (f a))) (fun (x2:(forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1)))))) as proof of (cP (f a)) % 0.52/0.72 Found (fun (x:((and ((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (cP a)))=> (((fun (P:Type) (x0:(((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))->((cP a)->P)))=> (((((and_rect ((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (cP a)) P) x0) x)) (cP (f a))) (fun (x0:((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (x1:(cP a))=> (((fun (P:Type) (x2:((forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))->((forall (Xy:fofType), ((cQ Xy)->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy)))) P) x2) x0)) (cP (f a))) (fun (x2:(forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1))))))) as proof of (cP (f a)) % 0.52/0.72 Found (fun (x:((and ((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (cP a)))=> (((fun (P:Type) (x0:(((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))->((cP a)->P)))=> (((((and_rect ((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (cP a)) P) x0) x)) (cP (f a))) (fun (x0:((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (x1:(cP a))=> (((fun (P:Type) (x2:((forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))->((forall (Xy:fofType), ((cQ Xy)->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy)))) P) x2) x0)) (cP (f a))) (fun (x2:(forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1))))))) as proof of (((and ((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (cP a))->(cP (f a))) % 0.52/0.73 Got proof (fun (x:((and ((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (cP a)))=> (((fun (P:Type) (x0:(((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))->((cP a)->P)))=> (((((and_rect ((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (cP a)) P) x0) x)) (cP (f a))) (fun (x0:((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (x1:(cP a))=> (((fun (P:Type) (x2:((forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))->((forall (Xy:fofType), ((cQ Xy)->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy)))) P) x2) x0)) (cP (f a))) (fun (x2:(forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1))))))) % 0.52/0.73 Time elapsed = 0.105628s % 0.52/0.73 node=18 cost=288.000000 depth=18 % 0.52/0.73 :::::::::::::::::::::: % 0.52/0.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 0.52/0.73 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % 0.52/0.73 (fun (x:((and ((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (cP a)))=> (((fun (P:Type) (x0:(((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))->((cP a)->P)))=> (((((and_rect ((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (cP a)) P) x0) x)) (cP (f a))) (fun (x0:((and (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy))))) (x1:(cP a))=> (((fun (P:Type) (x2:((forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))->((forall (Xy:fofType), ((cQ Xy)->(cP Xy)))->P)))=> (((((and_rect (forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (forall (Xy:fofType), ((cQ Xy)->(cP Xy)))) P) x2) x0)) (cP (f a))) (fun (x2:(forall (Xx:fofType), ((cP Xx)->(cQ (f Xx))))) (x3:(forall (Xy:fofType), ((cQ Xy)->(cP Xy))))=> ((x3 (f a)) ((x2 a) x1))))))) % 0.52/0.73 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p %------------------------------------------------------------------------------