%------------------------------------------------------------------------------
% File     : Duper---1.0
% Problem  : SYO143^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : duper %s

% Computer : n019.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 : Fri Sep  1 04:21:38 EDT 2023

% Result   : Theorem 3.48s 3.74s
% Output   : Proof 3.48s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SYO143^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : duper %s
% 0.14/0.34  % Computer : n019.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Sat Aug 26 00:35:13 EDT 2023
% 0.14/0.34  % CPUTime    : 
% 3.48/3.74  SZS status Theorem for theBenchmark.p
% 3.48/3.74  SZS output start Proof for theBenchmark.p
% 3.48/3.74  Clause #0 (by assumption #[]): Eq (Not (Or (Not (Exists fun Xy => ∀ (Xx : Iota), cP Xy → cP Xx)) (Exists fun Xz => cQ Xz) → Exists fun Xz => cQ Xz))
% 3.48/3.74    True
% 3.48/3.74  Clause #1 (by betaEtaReduce #[0]): Eq (Not (Or (Not (Exists fun Xy => ∀ (Xx : Iota), cP Xy → cP Xx)) (Exists cQ) → Exists cQ)) True
% 3.48/3.74  Clause #2 (by clausification #[1]): Eq (Or (Not (Exists fun Xy => ∀ (Xx : Iota), cP Xy → cP Xx)) (Exists cQ) → Exists cQ) False
% 3.48/3.74  Clause #3 (by clausification #[2]): Eq (Or (Not (Exists fun Xy => ∀ (Xx : Iota), cP Xy → cP Xx)) (Exists cQ)) True
% 3.48/3.74  Clause #4 (by clausification #[2]): Eq (Exists cQ) False
% 3.48/3.74  Clause #5 (by clausification #[3]): Or (Eq (Not (Exists fun Xy => ∀ (Xx : Iota), cP Xy → cP Xx)) True) (Eq (Exists cQ) True)
% 3.48/3.74  Clause #6 (by clausification #[5]): Or (Eq (Exists cQ) True) (Eq (Exists fun Xy => ∀ (Xx : Iota), cP Xy → cP Xx) False)
% 3.48/3.74  Clause #7 (by clausification #[6]): ∀ (a : Iota), Or (Eq (Exists fun Xy => ∀ (Xx : Iota), cP Xy → cP Xx) False) (Eq (cQ (skS.0 0 a)) True)
% 3.48/3.74  Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 0 a)) True) (Eq (∀ (Xx : Iota), cP a_1 → cP Xx) False)
% 3.48/3.74  Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), Or (Eq (cQ (skS.0 0 a)) True) (Eq (Not (cP a_1 → cP (skS.0 1 a_1 a_2))) True)
% 3.48/3.74  Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), Or (Eq (cQ (skS.0 0 a)) True) (Eq (cP a_1 → cP (skS.0 1 a_1 a_2)) False)
% 3.48/3.74  Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 0 a)) True) (Eq (cP a_1) True)
% 3.48/3.74  Clause #12 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Or (Eq (cQ (skS.0 0 a)) True) (Eq (cP (skS.0 1 a_1 a_2)) False)
% 3.48/3.74  Clause #13 (by clausification #[4]): ∀ (a : Iota), Eq (cQ a) False
% 3.48/3.74  Clause #14 (by superposition #[13, 11]): ∀ (a : Iota), Or (Eq False True) (Eq (cP a) True)
% 3.48/3.74  Clause #15 (by clausification #[14]): ∀ (a : Iota), Eq (cP a) True
% 3.48/3.74  Clause #16 (by superposition #[12, 15]): ∀ (a : Iota), Or (Eq (cQ (skS.0 0 a)) True) (Eq True False)
% 3.48/3.74  Clause #17 (by clausification #[16]): ∀ (a : Iota), Eq (cQ (skS.0 0 a)) True
% 3.48/3.74  Clause #18 (by superposition #[17, 13]): Eq True False
% 3.48/3.74  Clause #19 (by clausification #[18]): False
% 3.48/3.74  SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------