%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : NUM680^1 : TPTP v7.0.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n175.star.cs.uiowa.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz % Memory : 32218.625MB % OS : Linux 3.10.0-693.2.2.el7.x86_64 % CPULimit : 300s % DateTime : Mon Jan 8 13:11:25 EST 2018 % Result : Theorem 20.31s % Output : Proof 20.31s % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.04 % Problem : NUM680^1 : TPTP v7.0.0. Released v3.7.0. % 0.00/0.04 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % 0.02/0.23 % Computer : n175.star.cs.uiowa.edu % 0.02/0.23 % Model : x86_64 x86_64 % 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz % 0.02/0.23 % Memory : 32218.625MB % 0.02/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 % 0.02/0.23 % CPULimit : 300 % 0.02/0.23 % DateTime : Fri Jan 5 12:16:18 CST 2018 % 0.02/0.23 % CPUTime : % 0.08/0.27 Python 2.7.13 % 0.79/1.17 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/'] % 0.79/1.17 FOF formula (<kernel.Constant object at 0x2b3955bbd5a8>, <kernel.Type object at 0x2b3955bbd518>) of role type named nat_type % 0.79/1.17 Using role type % 0.79/1.17 Declaring nat:Type % 0.79/1.17 FOF formula (<kernel.Constant object at 0x2b3955bbe5f0>, <kernel.Constant object at 0x2b3955bbd4d0>) of role type named x % 0.79/1.17 Using role type % 0.79/1.17 Declaring x:nat % 0.79/1.17 FOF formula (<kernel.Constant object at 0x2b3955bbe5f0>, <kernel.Constant object at 0x2b3955bbd4d0>) of role type named y % 0.79/1.17 Using role type % 0.79/1.17 Declaring y:nat % 0.79/1.17 FOF formula (<kernel.Constant object at 0x2b3955bbd5a8>, <kernel.Constant object at 0x2b3955bbd4d0>) of role type named z % 0.79/1.17 Using role type % 0.79/1.17 Declaring z:nat % 0.79/1.17 FOF formula (<kernel.Constant object at 0x2b3955bbd3b0>, <kernel.DependentProduct object at 0x2b3955bbd830>) of role type named more % 0.79/1.17 Using role type % 0.79/1.17 Declaring more:(nat->(nat->Prop)) % 0.79/1.17 FOF formula (<kernel.Constant object at 0x2b3955bbd0e0>, <kernel.DependentProduct object at 0x2b3955bbd7e8>) of role type named pl % 0.79/1.17 Using role type % 0.79/1.17 Declaring pl:(nat->(nat->nat)) % 0.79/1.17 FOF formula ((more ((pl x) z)) ((pl y) z)) of role axiom named m % 0.79/1.17 A new axiom: ((more ((pl x) z)) ((pl y) z)) % 0.79/1.17 FOF formula (forall (Xa:Prop), (((Xa->False)->False)->Xa)) of role axiom named et % 0.79/1.17 A new axiom: (forall (Xa:Prop), (((Xa->False)->False)->Xa)) % 0.79/1.17 FOF formula (<kernel.Constant object at 0x2b3955bbdd88>, <kernel.DependentProduct object at 0x2b3955bbdb00>) of role type named less % 0.79/1.17 Using role type % 0.79/1.17 Declaring less:(nat->(nat->Prop)) % 0.79/1.17 FOF formula (forall (Xx:nat) (Xy:nat), ((((((eq nat) Xx) Xy)->(((more Xx) Xy)->False))->((((((more Xx) Xy)->(((less Xx) Xy)->False))->((((less Xx) Xy)->(not (((eq nat) Xx) Xy)))->False))->False)->False))->False)) of role axiom named satz10b % 0.79/1.17 A new axiom: (forall (Xx:nat) (Xy:nat), ((((((eq nat) Xx) Xy)->(((more Xx) Xy)->False))->((((((more Xx) Xy)->(((less Xx) Xy)->False))->((((less Xx) Xy)->(not (((eq nat) Xx) Xy)))->False))->False)->False))->False)) % 0.79/1.17 FOF formula (forall (Xx:nat) (Xy:nat) (Xz:nat), ((((eq nat) Xx) Xy)->(((eq nat) ((pl Xx) Xz)) ((pl Xy) Xz)))) of role axiom named satz19b % 0.79/1.17 A new axiom: (forall (Xx:nat) (Xy:nat) (Xz:nat), ((((eq nat) Xx) Xy)->(((eq nat) ((pl Xx) Xz)) ((pl Xy) Xz)))) % 0.79/1.17 FOF formula (forall (Xx:nat) (Xy:nat) (Xz:nat), (((less Xx) Xy)->((less ((pl Xx) Xz)) ((pl Xy) Xz)))) of role axiom named satz19c % 0.79/1.17 A new axiom: (forall (Xx:nat) (Xy:nat) (Xz:nat), (((less Xx) Xy)->((less ((pl Xx) Xz)) ((pl Xy) Xz)))) % 0.79/1.17 FOF formula (forall (Xx:nat) (Xy:nat), ((not (((eq nat) Xx) Xy))->((((more Xx) Xy)->False)->((less Xx) Xy)))) of role axiom named satz10a % 0.79/1.17 A new axiom: (forall (Xx:nat) (Xy:nat), ((not (((eq nat) Xx) Xy))->((((more Xx) Xy)->False)->((less Xx) Xy)))) % 0.79/1.17 FOF formula ((more x) y) of role conjecture named satz20a % 0.79/1.17 Conjecture to prove = ((more x) y):Prop % 0.79/1.17 We need to prove ['((more x) y)'] % 0.79/1.17 Parameter nat:Type. % 0.79/1.17 Parameter x:nat. % 0.79/1.17 Parameter y:nat. % 0.79/1.17 Parameter z:nat. % 0.79/1.17 Parameter more:(nat->(nat->Prop)). % 0.79/1.17 Parameter pl:(nat->(nat->nat)). % 0.79/1.17 Axiom m:((more ((pl x) z)) ((pl y) z)). % 0.79/1.17 Axiom et:(forall (Xa:Prop), (((Xa->False)->False)->Xa)). % 0.79/1.17 Parameter less:(nat->(nat->Prop)). % 0.79/1.17 Axiom satz10b:(forall (Xx:nat) (Xy:nat), ((((((eq nat) Xx) Xy)->(((more Xx) Xy)->False))->((((((more Xx) Xy)->(((less Xx) Xy)->False))->((((less Xx) Xy)->(not (((eq nat) Xx) Xy)))->False))->False)->False))->False)). % 0.79/1.17 Axiom satz19b:(forall (Xx:nat) (Xy:nat) (Xz:nat), ((((eq nat) Xx) Xy)->(((eq nat) ((pl Xx) Xz)) ((pl Xy) Xz)))). % 0.79/1.17 Axiom satz19c:(forall (Xx:nat) (Xy:nat) (Xz:nat), (((less Xx) Xy)->((less ((pl Xx) Xz)) ((pl Xy) Xz)))). % 0.79/1.17 Axiom satz10a:(forall (Xx:nat) (Xy:nat), ((not (((eq nat) Xx) Xy))->((((more Xx) Xy)->False)->((less Xx) Xy)))). % 0.79/1.17 Trying to prove ((more x) y) % 0.79/1.17 Found m:((more ((pl x) z)) ((pl y) z)) % 0.79/1.17 Instantiate: Xx:=((pl x) z):nat;Xy:=((pl y) z):nat % 0.79/1.17 Found m as proof of ((more Xx) Xy) % 0.79/1.17 Found eq_ref00:=(eq_ref0 Xx):(((eq nat) Xx) Xx) % 0.79/1.17 Found (eq_ref0 Xx) as proof of (((eq nat) Xx) Xy) % 0.79/1.17 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy) % 0.79/1.17 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy) % 0.79/1.17 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy) % 20.06/20.44 Found m:((more ((pl x) z)) ((pl y) z)) % 20.06/20.44 Instantiate: Xx:=((pl x) z):nat;Xy:=((pl y) z):nat % 20.06/20.44 Found m as proof of ((more Xx) Xy) % 20.06/20.44 Found eq_ref00:=(eq_ref0 Xx):(((eq nat) Xx) Xx) % 20.06/20.44 Found (eq_ref0 Xx) as proof of (((eq nat) Xx) Xy) % 20.06/20.44 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy) % 20.06/20.44 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy) % 20.06/20.44 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy) % 20.06/20.44 Found m:((more ((pl x) z)) ((pl y) z)) % 20.06/20.44 Instantiate: Xx:=((pl x) z):nat;Xy:=((pl y) z):nat % 20.06/20.44 Found m as proof of ((more Xx) Xy) % 20.06/20.44 Found eq_ref00:=(eq_ref0 Xx):(((eq nat) Xx) Xx) % 20.06/20.44 Found (eq_ref0 Xx) as proof of (((eq nat) Xx) Xy) % 20.06/20.44 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy) % 20.06/20.44 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy) % 20.06/20.44 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy) % 20.06/20.44 Found x0:(((more x) y)->False) % 20.06/20.44 Instantiate: Xx:=x:nat;Xy:=y:nat % 20.06/20.44 Found x0 as proof of (((more Xx) Xy)->False) % 20.06/20.44 Found x0:(((more x) y)->False) % 20.06/20.44 Instantiate: Xx:=x:nat;Xy:=y:nat % 20.06/20.44 Found x0 as proof of (((more Xx) Xy)->False) % 20.06/20.44 Found m:((more ((pl x) z)) ((pl y) z)) % 20.06/20.44 Instantiate: Xx:=((pl x) z):nat;Xy:=((pl y) z):nat % 20.06/20.44 Found m as proof of ((more Xx) Xy) % 20.06/20.44 Found (x10 m) as proof of False % 20.06/20.44 Found ((x1 x5) m) as proof of False % 20.06/20.44 Found (fun (x5:(((eq nat) Xx) Xy))=> ((x1 x5) m)) as proof of False % 20.06/20.44 Found (fun (x5:(((eq nat) Xx) Xy))=> ((x1 x5) m)) as proof of (not (((eq nat) Xx) Xy)) % 20.06/20.44 Found m:((more ((pl x) z)) ((pl y) z)) % 20.06/20.44 Instantiate: Xx:=((pl x) z):nat;Xy:=((pl y) z):nat % 20.06/20.44 Found m as proof of ((more Xx) Xy) % 20.06/20.44 Found (x10 m) as proof of False % 20.06/20.44 Found ((x1 x5) m) as proof of False % 20.06/20.44 Found (fun (x5:(((eq nat) Xx) Xy))=> ((x1 x5) m)) as proof of False % 20.06/20.44 Found (fun (x5:(((eq nat) Xx) Xy))=> ((x1 x5) m)) as proof of (not (((eq nat) Xx) Xy)) % 20.06/20.44 Found x10:=(fun (x5:(((eq nat) Xx) Xy))=> ((x1 x5) m)):((((eq nat) Xx) Xy)->False) % 20.06/20.44 Found (fun (x5:(((eq nat) Xx) Xy))=> ((x1 x5) m)) as proof of (not (((eq nat) Xx) Xy)) % 20.06/20.44 Found (fun (x5:(((eq nat) Xx) Xy))=> ((x1 x5) m)) as proof of (not (((eq nat) Xx) Xy)) % 20.06/20.44 Found x5:((more Xx) Xy) % 20.06/20.44 Found x5 as proof of ((more Xx) Xy) % 20.06/20.44 Found x5:(((eq nat) Xx) Xy) % 20.06/20.44 Found x5 as proof of (((eq nat) Xx) Xy) % 20.06/20.44 Found x5:(((eq nat) Xx) Xy) % 20.06/20.44 Found x5 as proof of (((eq nat) Xx) Xy) % 20.06/20.44 Found eq_ref00:=(eq_ref0 Xx):(((eq nat) Xx) Xx) % 20.06/20.44 Found (eq_ref0 Xx) as proof of (((eq nat) Xx) Xy) % 20.06/20.44 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy) % 20.06/20.44 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy) % 20.06/20.44 Found (x1 ((eq_ref nat) Xx)) as proof of (((more Xx) Xy)->False) % 20.06/20.44 Found (x1 ((eq_ref nat) Xx)) as proof of (((more Xx) Xy)->False) % 20.06/20.44 Found x5:(((eq nat) Xx) Xy) % 20.06/20.44 Found x5 as proof of (((eq nat) Xx) Xy) % 20.06/20.44 Found x0:(((more x) y)->False) % 20.06/20.44 Found x0 as proof of (((more x) y)->False) % 20.06/20.44 Found m:((more ((pl x) z)) ((pl y) z)) % 20.06/20.44 Found m as proof of ((more Xx) Xy) % 20.06/20.44 Found eq_ref00:=(eq_ref0 Xx):(((eq nat) Xx) Xx) % 20.06/20.44 Found (eq_ref0 Xx) as proof of (((eq nat) Xx) Xy) % 20.06/20.44 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy) % 20.06/20.44 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy) % 20.06/20.44 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy) % 20.06/20.44 Found m:((more ((pl x) z)) ((pl y) z)) % 20.06/20.44 Instantiate: Xx:=((pl x) z):nat;Xy:=((pl y) z):nat % 20.06/20.44 Found m as proof of ((more Xx) Xy) % 20.06/20.44 Found m:((more ((pl x) z)) ((pl y) z)) % 20.06/20.44 Found m as proof of ((more Xx) Xy) % 20.06/20.44 Found x2:(P Xx) % 20.06/20.44 Instantiate: Xy:=Xx:nat % 20.06/20.44 Found (fun (x2:(P Xx))=> x2) as proof of (P Xy) % 20.06/20.44 Found (fun (P:(nat->Prop)) (x2:(P Xx))=> x2) as proof of ((P Xx)->(P Xy)) % 20.06/20.44 Found (fun (P:(nat->Prop)) (x2:(P Xx))=> x2) as proof of (((eq nat) Xx) Xy) % 20.06/20.44 Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx)) % 20.06/20.44 Found (eq_ref00 P) as proof of ((P Xx)->(P Xy)) % 20.06/20.44 Found ((eq_ref0 Xx) P) as proof of ((P Xx)->(P Xy)) % 20.06/20.44 Found (((eq_ref nat) Xx) P) as proof of ((P Xx)->(P Xy)) % 20.06/20.44 Found (((eq_ref nat) Xx) P) as proof of ((P Xx)->(P Xy)) % 20.06/20.44 Found (fun (P:(nat->Prop))=> (((eq_ref nat) Xx) P)) as proof of ((P Xx)->(P Xy)) % 20.06/20.44 Found (fun (P:(nat->Prop))=> (((eq_ref nat) Xx) P)) as proof of (((eq nat) Xx) Xy) % 20.06/20.44 Found eq_ref00:=(eq_ref0 Xx):(((eq nat) Xx) Xx) % 20.06/20.44 Found (eq_ref0 Xx) as proof of (((eq nat) Xx) Xy) % 20.06/20.44 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy) % 20.06/20.44 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy) % 20.06/20.44 Found ((eq_ref nat) Xx) as proof of (((eq nat) Xx) Xy) % 20.06/20.44 Found satz19b0000:=(satz19b000 z):(((eq nat) ((pl x) z)) ((pl y) z)) % 20.16/20.53 Found (satz19b000 z) as proof of (((eq nat) Xx) Xy) % 20.16/20.53 Found ((fun (Xz:nat)=> ((satz19b00 Xz) x00)) z) as proof of (((eq nat) Xx) Xy) % 20.16/20.53 Found ((fun (Xz:nat)=> (((satz19b0 y) Xz) x00)) z) as proof of (((eq nat) Xx) Xy) % 20.16/20.53 Found ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z) as proof of (((eq nat) Xx) Xy) % 20.16/20.53 Found ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z) as proof of (((eq nat) Xx) Xy) % 20.16/20.53 Found ((x1 ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z)) m) as proof of False % 20.16/20.53 Found (fun (x00:(((eq nat) x) y))=> ((x1 ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z)) m)) as proof of False % 20.16/20.53 Found (fun (x00:(((eq nat) x) y))=> ((x1 ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z)) m)) as proof of (not (((eq nat) x) y)) % 20.16/20.53 Found ((satz10a00 (fun (x00:(((eq nat) x) y))=> ((x1 ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z)) m))) x0) as proof of ((less x) y) % 20.16/20.53 Found (((satz10a0 y) (fun (x00:(((eq nat) x) y))=> ((x1 ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z)) m))) x0) as proof of ((less x) y) % 20.16/20.53 Found ((((satz10a x) y) (fun (x00:(((eq nat) x) y))=> ((x1 ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z)) m))) x0) as proof of ((less x) y) % 20.16/20.53 Found ((((satz10a x) y) (fun (x00:(((eq nat) x) y))=> ((x1 ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z)) m))) x0) as proof of ((less x) y) % 20.16/20.53 Found (satz19c000 ((((satz10a x) y) (fun (x00:(((eq nat) x) y))=> ((x1 ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z)) m))) x0)) as proof of ((less Xx) Xy) % 20.16/20.53 Found ((satz19c00 z) ((((satz10a x) y) (fun (x00:(((eq nat) x) y))=> ((x1 ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z)) m))) x0)) as proof of ((less Xx) Xy) % 20.16/20.53 Found (((satz19c0 y) z) ((((satz10a x) y) (fun (x00:(((eq nat) x) y))=> ((x1 ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z)) m))) x0)) as proof of ((less Xx) Xy) % 20.16/20.53 Found ((((satz19c x) y) z) ((((satz10a x) y) (fun (x00:(((eq nat) x) y))=> ((x1 ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z)) m))) x0)) as proof of ((less Xx) Xy) % 20.16/20.53 Found ((((satz19c x) y) z) ((((satz10a x) y) (fun (x00:(((eq nat) x) y))=> ((x1 ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z)) m))) x0)) as proof of ((less Xx) Xy) % 20.16/20.53 Found ((x3 m) ((((satz19c x) y) z) ((((satz10a x) y) (fun (x00:(((eq nat) x) y))=> ((x1 ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z)) m))) x0))) as proof of False % 20.16/20.53 Found (fun (x4:(((less Xx) Xy)->(not (((eq nat) Xx) Xy))))=> ((x3 m) ((((satz19c x) y) z) ((((satz10a x) y) (fun (x00:(((eq nat) x) y))=> ((x1 ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z)) m))) x0)))) as proof of False % 20.16/20.53 Found (fun (x3:(((more Xx) Xy)->(((less Xx) Xy)->False))) (x4:(((less Xx) Xy)->(not (((eq nat) Xx) Xy))))=> ((x3 m) ((((satz19c x) y) z) ((((satz10a x) y) (fun (x00:(((eq nat) x) y))=> ((x1 ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z)) m))) x0)))) as proof of ((((less Xx) Xy)->(not (((eq nat) Xx) Xy)))->False) % 20.16/20.53 Found (fun (x3:(((more Xx) Xy)->(((less Xx) Xy)->False))) (x4:(((less Xx) Xy)->(not (((eq nat) Xx) Xy))))=> ((x3 m) ((((satz19c x) y) z) ((((satz10a x) y) (fun (x00:(((eq nat) x) y))=> ((x1 ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z)) m))) x0)))) as proof of ((((more Xx) Xy)->(((less Xx) Xy)->False))->((((less Xx) Xy)->(not (((eq nat) Xx) Xy)))->False)) % 20.16/20.53 Found (x2 (fun (x3:(((more Xx) Xy)->(((less Xx) Xy)->False))) (x4:(((less Xx) Xy)->(not (((eq nat) Xx) Xy))))=> ((x3 m) ((((satz19c x) y) z) ((((satz10a x) y) (fun (x00:(((eq nat) x) y))=> ((x1 ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z)) m))) x0))))) as proof of False % 20.16/20.53 Found (fun (x2:(((((more Xx) Xy)->(((less Xx) Xy)->False))->((((less Xx) Xy)->(not (((eq nat) Xx) Xy)))->False))->False))=> (x2 (fun (x3:(((more Xx) Xy)->(((less Xx) Xy)->False))) (x4:(((less Xx) Xy)->(not (((eq nat) Xx) Xy))))=> ((x3 m) ((((satz19c x) y) z) ((((satz10a x) y) (fun (x00:(((eq nat) x) y))=> ((x1 ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z)) m))) x0)))))) as proof of False % 20.16/20.53 Found (fun (x1:((((eq nat) Xx) Xy)->(((more Xx) Xy)->False))) (x2:(((((more Xx) Xy)->(((less Xx) Xy)->False))->((((less Xx) Xy)->(not (((eq nat) Xx) Xy)))->False))->False))=> (x2 (fun (x3:(((more Xx) Xy)->(((less Xx) Xy)->False))) (x4:(((less Xx) Xy)->(not (((eq nat) Xx) Xy))))=> ((x3 m) ((((satz19c x) y) z) ((((satz10a x) y) (fun (x00:(((eq nat) x) y))=> ((x1 ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z)) m))) x0)))))) as proof of ((((((more Xx) Xy)->(((less Xx) Xy)->False))->((((less Xx) Xy)->(not (((eq nat) Xx) Xy)))->False))->False)->False) % 20.16/20.54 Found (fun (x1:((((eq nat) Xx) Xy)->(((more Xx) Xy)->False))) (x2:(((((more Xx) Xy)->(((less Xx) Xy)->False))->((((less Xx) Xy)->(not (((eq nat) Xx) Xy)))->False))->False))=> (x2 (fun (x3:(((more Xx) Xy)->(((less Xx) Xy)->False))) (x4:(((less Xx) Xy)->(not (((eq nat) Xx) Xy))))=> ((x3 m) ((((satz19c x) y) z) ((((satz10a x) y) (fun (x00:(((eq nat) x) y))=> ((x1 ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z)) m))) x0)))))) as proof of (((((eq nat) Xx) Xy)->(((more Xx) Xy)->False))->((((((more Xx) Xy)->(((less Xx) Xy)->False))->((((less Xx) Xy)->(not (((eq nat) Xx) Xy)))->False))->False)->False)) % 20.16/20.54 Found (satz10b00 (fun (x1:((((eq nat) Xx) Xy)->(((more Xx) Xy)->False))) (x2:(((((more Xx) Xy)->(((less Xx) Xy)->False))->((((less Xx) Xy)->(not (((eq nat) Xx) Xy)))->False))->False))=> (x2 (fun (x3:(((more Xx) Xy)->(((less Xx) Xy)->False))) (x4:(((less Xx) Xy)->(not (((eq nat) Xx) Xy))))=> ((x3 m) ((((satz19c x) y) z) ((((satz10a x) y) (fun (x00:(((eq nat) x) y))=> ((x1 ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z)) m))) x0))))))) as proof of False % 20.16/20.54 Found ((satz10b0 ((pl y) z)) (fun (x1:((((eq nat) Xx) ((pl y) z))->(((more Xx) ((pl y) z))->False))) (x2:(((((more Xx) ((pl y) z))->(((less Xx) ((pl y) z))->False))->((((less Xx) ((pl y) z))->(not (((eq nat) Xx) ((pl y) z))))->False))->False))=> (x2 (fun (x3:(((more Xx) ((pl y) z))->(((less Xx) ((pl y) z))->False))) (x4:(((less Xx) ((pl y) z))->(not (((eq nat) Xx) ((pl y) z)))))=> ((x3 m) ((((satz19c x) y) z) ((((satz10a x) y) (fun (x00:(((eq nat) x) y))=> ((x1 ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z)) m))) x0))))))) as proof of False % 20.16/20.54 Found (((satz10b ((pl x) z)) ((pl y) z)) (fun (x1:((((eq nat) ((pl x) z)) ((pl y) z))->(((more ((pl x) z)) ((pl y) z))->False))) (x2:(((((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))->((((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z))))->False))->False))=> (x2 (fun (x3:(((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))) (x4:(((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z)))))=> ((x3 m) ((((satz19c x) y) z) ((((satz10a x) y) (fun (x00:(((eq nat) x) y))=> ((x1 ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z)) m))) x0))))))) as proof of False % 20.16/20.54 Found (fun (x0:(((more x) y)->False))=> (((satz10b ((pl x) z)) ((pl y) z)) (fun (x1:((((eq nat) ((pl x) z)) ((pl y) z))->(((more ((pl x) z)) ((pl y) z))->False))) (x2:(((((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))->((((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z))))->False))->False))=> (x2 (fun (x3:(((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))) (x4:(((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z)))))=> ((x3 m) ((((satz19c x) y) z) ((((satz10a x) y) (fun (x00:(((eq nat) x) y))=> ((x1 ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z)) m))) x0)))))))) as proof of False % 20.16/20.54 Found (fun (x0:(((more x) y)->False))=> (((satz10b ((pl x) z)) ((pl y) z)) (fun (x1:((((eq nat) ((pl x) z)) ((pl y) z))->(((more ((pl x) z)) ((pl y) z))->False))) (x2:(((((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))->((((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z))))->False))->False))=> (x2 (fun (x3:(((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))) (x4:(((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z)))))=> ((x3 m) ((((satz19c x) y) z) ((((satz10a x) y) (fun (x00:(((eq nat) x) y))=> ((x1 ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z)) m))) x0)))))))) as proof of ((((more x) y)->False)->False) % 20.16/20.54 Found (et0 (fun (x0:(((more x) y)->False))=> (((satz10b ((pl x) z)) ((pl y) z)) (fun (x1:((((eq nat) ((pl x) z)) ((pl y) z))->(((more ((pl x) z)) ((pl y) z))->False))) (x2:(((((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))->((((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z))))->False))->False))=> (x2 (fun (x3:(((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))) (x4:(((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z)))))=> ((x3 m) ((((satz19c x) y) z) ((((satz10a x) y) (fun (x00:(((eq nat) x) y))=> ((x1 ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z)) m))) x0))))))))) as proof of ((more x) y) % 20.31/20.69 Found ((et ((more x) y)) (fun (x0:(((more x) y)->False))=> (((satz10b ((pl x) z)) ((pl y) z)) (fun (x1:((((eq nat) ((pl x) z)) ((pl y) z))->(((more ((pl x) z)) ((pl y) z))->False))) (x2:(((((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))->((((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z))))->False))->False))=> (x2 (fun (x3:(((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))) (x4:(((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z)))))=> ((x3 m) ((((satz19c x) y) z) ((((satz10a x) y) (fun (x00:(((eq nat) x) y))=> ((x1 ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z)) m))) x0))))))))) as proof of ((more x) y) % 20.31/20.69 Found ((et ((more x) y)) (fun (x0:(((more x) y)->False))=> (((satz10b ((pl x) z)) ((pl y) z)) (fun (x1:((((eq nat) ((pl x) z)) ((pl y) z))->(((more ((pl x) z)) ((pl y) z))->False))) (x2:(((((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))->((((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z))))->False))->False))=> (x2 (fun (x3:(((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))) (x4:(((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z)))))=> ((x3 m) ((((satz19c x) y) z) ((((satz10a x) y) (fun (x00:(((eq nat) x) y))=> ((x1 ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z)) m))) x0))))))))) as proof of ((more x) y) % 20.31/20.69 Got proof ((et ((more x) y)) (fun (x0:(((more x) y)->False))=> (((satz10b ((pl x) z)) ((pl y) z)) (fun (x1:((((eq nat) ((pl x) z)) ((pl y) z))->(((more ((pl x) z)) ((pl y) z))->False))) (x2:(((((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))->((((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z))))->False))->False))=> (x2 (fun (x3:(((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))) (x4:(((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z)))))=> ((x3 m) ((((satz19c x) y) z) ((((satz10a x) y) (fun (x00:(((eq nat) x) y))=> ((x1 ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z)) m))) x0))))))))) % 20.31/20.69 Time elapsed = 19.803860s % 20.31/20.69 node=3778 cost=1359.000000 depth=32 % 20.31/20.69:::::::::::::::::::::: % 20.31/20.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 20.31/20.69 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p % 20.31/20.69 ((et ((more x) y)) (fun (x0:(((more x) y)->False))=> (((satz10b ((pl x) z)) ((pl y) z)) (fun (x1:((((eq nat) ((pl x) z)) ((pl y) z))->(((more ((pl x) z)) ((pl y) z))->False))) (x2:(((((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))->((((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z))))->False))->False))=> (x2 (fun (x3:(((more ((pl x) z)) ((pl y) z))->(((less ((pl x) z)) ((pl y) z))->False))) (x4:(((less ((pl x) z)) ((pl y) z))->(not (((eq nat) ((pl x) z)) ((pl y) z)))))=> ((x3 m) ((((satz19c x) y) z) ((((satz10a x) y) (fun (x00:(((eq nat) x) y))=> ((x1 ((fun (Xz:nat)=> ((((satz19b x) y) Xz) x00)) z)) m))) x0))))))))) % 20.31/20.69 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p %------------------------------------------------------------------------------