%------------------------------------------------------------------------------
% File     : Duper---1.0
% Problem  : SEU808^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : duper %s

% Computer : n018.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  : 300s
% DateTime : Thu Aug 31 16:43:59 EDT 2023

% Result   : Theorem 3.52s 3.76s
% Output   : Proof 3.52s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU808^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13  % Command    : duper %s
% 0.13/0.34  % Computer : n018.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Wed Aug 23 19:44:42 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 3.52/3.76  SZS status Theorem for theBenchmark.p
% 3.52/3.76  SZS output start Proof for theBenchmark.p
% 3.52/3.76  Clause #0 (by assumption #[]): Eq (Eq omegaSAx (∀ (Xx : Iota), in Xx omega → in (setadjoin Xx Xx) omega)) True
% 3.52/3.76  Clause #1 (by assumption #[]): Eq (Eq omegaS fun Xx => setadjoin Xx Xx) True
% 3.52/3.76  Clause #2 (by assumption #[]): Eq (Not (omegaSAx → ∀ (Xx : Iota), in Xx omega → in (omegaS Xx) omega)) True
% 3.52/3.76  Clause #3 (by clausification #[2]): Eq (omegaSAx → ∀ (Xx : Iota), in Xx omega → in (omegaS Xx) omega) False
% 3.52/3.76  Clause #4 (by clausification #[3]): Eq omegaSAx True
% 3.52/3.76  Clause #5 (by clausification #[3]): Eq (∀ (Xx : Iota), in Xx omega → in (omegaS Xx) omega) False
% 3.52/3.76  Clause #6 (by clausification #[5]): ∀ (a : Iota), Eq (Not (in (skS.0 0 a) omega → in (omegaS (skS.0 0 a)) omega)) True
% 3.52/3.76  Clause #7 (by clausification #[6]): ∀ (a : Iota), Eq (in (skS.0 0 a) omega → in (omegaS (skS.0 0 a)) omega) False
% 3.52/3.76  Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (in (skS.0 0 a) omega) True
% 3.52/3.76  Clause #9 (by clausification #[7]): ∀ (a : Iota), Eq (in (omegaS (skS.0 0 a)) omega) False
% 3.52/3.76  Clause #10 (by clausification #[1]): Eq omegaS fun Xx => setadjoin Xx Xx
% 3.52/3.76  Clause #11 (by argument congruence #[10]): ∀ (a : Iota), Eq (omegaS a) ((fun Xx => setadjoin Xx Xx) a)
% 3.52/3.76  Clause #12 (by betaEtaReduce #[11]): ∀ (a : Iota), Eq (omegaS a) (setadjoin a a)
% 3.52/3.76  Clause #13 (by clausification #[0]): Eq omegaSAx (∀ (Xx : Iota), in Xx omega → in (setadjoin Xx Xx) omega)
% 3.52/3.76  Clause #14 (by forward demodulation #[13, 4]): Eq True (∀ (Xx : Iota), in Xx omega → in (setadjoin Xx Xx) omega)
% 3.52/3.76  Clause #15 (by clausification #[14]): ∀ (a : Iota), Eq (in a omega → in (setadjoin a a) omega) True
% 3.52/3.76  Clause #16 (by clausification #[15]): ∀ (a : Iota), Or (Eq (in a omega) False) (Eq (in (setadjoin a a) omega) True)
% 3.52/3.76  Clause #17 (by forward demodulation #[16, 12]): ∀ (a : Iota), Or (Eq (in a omega) False) (Eq (in (omegaS a) omega) True)
% 3.52/3.76  Clause #18 (by superposition #[17, 8]): ∀ (a : Iota), Or (Eq (in (omegaS (skS.0 0 a)) omega) True) (Eq False True)
% 3.52/3.76  Clause #19 (by clausification #[18]): ∀ (a : Iota), Eq (in (omegaS (skS.0 0 a)) omega) True
% 3.52/3.76  Clause #20 (by superposition #[19, 9]): Eq True False
% 3.52/3.76  Clause #22 (by clausification #[20]): False
% 3.52/3.76  SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------