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Duper---1.0.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : Duper---1.0
% Problem  : ALG201+1 : TPTP v9.2.0. Released v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : duper %s

% Computer : n014.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 Oct  3 07:44:06 PM UTC 2025

% Result   : Theorem 11.87s 12.09s
% Output   : Proof 11.87s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : ALG201+1 : TPTP v9.2.0. Released v2.7.0.
% 0.07/0.13  % Command    : duper %s
% 0.13/0.34  % Computer : n014.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   : Fri Oct  3 09:29:38 EDT 2025
% 0.13/0.34  % CPUTime    : 
% 11.87/12.09  SZS status Theorem for theBenchmark.p
% 11.87/12.09  SZS output start Proof for theBenchmark.p
% 11.87/12.09  Clause #2 (by assumption #[]): Eq (∀ (U : Iota), sorti1 U → Ne (op1 U U) U) True
% 11.87/12.09  Clause #3 (by assumption #[]): Eq (Not (∀ (U : Iota), sorti2 U → Ne (op2 U U) U)) True
% 11.87/12.09  Clause #4 (by assumption #[]): Eq
% 11.87/12.09    (Not
% 11.87/12.09      (And (∀ (U : Iota), sorti1 U → sorti2 (h U)) (∀ (V : Iota), sorti2 V → sorti1 (j V)) →
% 11.87/12.09        Not
% 11.87/12.09          (And
% 11.87/12.09            (And
% 11.87/12.09              (And (∀ (W : Iota), sorti1 W → ∀ (X : Iota), sorti1 X → Eq (h (op1 W X)) (op2 (h W) (h X)))
% 11.87/12.09                (∀ (Y : Iota), sorti2 Y → ∀ (Z : Iota), sorti2 Z → Eq (j (op2 Y Z)) (op1 (j Y) (j Z))))
% 11.87/12.09              (∀ (X1 : Iota), sorti2 X1 → Eq (h (j X1)) X1))
% 11.87/12.09            (∀ (X2 : Iota), sorti1 X2 → Eq (j (h X2)) X2))))
% 11.87/12.09    True
% 11.87/12.09  Clause #5 (by clausification #[2]): ∀ (a : Iota), Eq (sorti1 a → Ne (op1 a a) a) True
% 11.87/12.09  Clause #6 (by clausification #[5]): ∀ (a : Iota), Or (Eq (sorti1 a) False) (Eq (Ne (op1 a a) a) True)
% 11.87/12.09  Clause #7 (by clausification #[6]): ∀ (a : Iota), Or (Eq (sorti1 a) False) (Ne (op1 a a) a)
% 11.87/12.09  Clause #16 (by clausification #[3]): Eq (∀ (U : Iota), sorti2 U → Ne (op2 U U) U) False
% 11.87/12.09  Clause #17 (by clausification #[16]): ∀ (a : Iota), Eq (Not (sorti2 (skS.0 0 a) → Ne (op2 (skS.0 0 a) (skS.0 0 a)) (skS.0 0 a))) True
% 11.87/12.09  Clause #18 (by clausification #[17]): ∀ (a : Iota), Eq (sorti2 (skS.0 0 a) → Ne (op2 (skS.0 0 a) (skS.0 0 a)) (skS.0 0 a)) False
% 11.87/12.09  Clause #19 (by clausification #[18]): ∀ (a : Iota), Eq (sorti2 (skS.0 0 a)) True
% 11.87/12.09  Clause #20 (by clausification #[18]): ∀ (a : Iota), Eq (Ne (op2 (skS.0 0 a) (skS.0 0 a)) (skS.0 0 a)) False
% 11.87/12.09  Clause #24 (by clausification #[4]): Eq
% 11.87/12.09    (And (∀ (U : Iota), sorti1 U → sorti2 (h U)) (∀ (V : Iota), sorti2 V → sorti1 (j V)) →
% 11.87/12.09      Not
% 11.87/12.09        (And
% 11.87/12.09          (And
% 11.87/12.09            (And (∀ (W : Iota), sorti1 W → ∀ (X : Iota), sorti1 X → Eq (h (op1 W X)) (op2 (h W) (h X)))
% 11.87/12.09              (∀ (Y : Iota), sorti2 Y → ∀ (Z : Iota), sorti2 Z → Eq (j (op2 Y Z)) (op1 (j Y) (j Z))))
% 11.87/12.09            (∀ (X1 : Iota), sorti2 X1 → Eq (h (j X1)) X1))
% 11.87/12.09          (∀ (X2 : Iota), sorti1 X2 → Eq (j (h X2)) X2)))
% 11.87/12.09    False
% 11.87/12.09  Clause #25 (by clausification #[24]): Eq (And (∀ (U : Iota), sorti1 U → sorti2 (h U)) (∀ (V : Iota), sorti2 V → sorti1 (j V))) True
% 11.87/12.09  Clause #26 (by clausification #[24]): Eq
% 11.87/12.09    (Not
% 11.87/12.09      (And
% 11.87/12.09        (And
% 11.87/12.09          (And (∀ (W : Iota), sorti1 W → ∀ (X : Iota), sorti1 X → Eq (h (op1 W X)) (op2 (h W) (h X)))
% 11.87/12.09            (∀ (Y : Iota), sorti2 Y → ∀ (Z : Iota), sorti2 Z → Eq (j (op2 Y Z)) (op1 (j Y) (j Z))))
% 11.87/12.09          (∀ (X1 : Iota), sorti2 X1 → Eq (h (j X1)) X1))
% 11.87/12.09        (∀ (X2 : Iota), sorti1 X2 → Eq (j (h X2)) X2)))
% 11.87/12.09    False
% 11.87/12.09  Clause #27 (by clausification #[25]): Eq (∀ (V : Iota), sorti2 V → sorti1 (j V)) True
% 11.87/12.09  Clause #29 (by clausification #[27]): ∀ (a : Iota), Eq (sorti2 a → sorti1 (j a)) True
% 11.87/12.09  Clause #30 (by clausification #[29]): ∀ (a : Iota), Or (Eq (sorti2 a) False) (Eq (sorti1 (j a)) True)
% 11.87/12.09  Clause #31 (by superposition #[30, 19]): ∀ (a : Iota), Or (Eq (sorti1 (j (skS.0 0 a))) True) (Eq False True)
% 11.87/12.09  Clause #34 (by clausification #[31]): ∀ (a : Iota), Eq (sorti1 (j (skS.0 0 a))) True
% 11.87/12.09  Clause #35 (by superposition #[34, 7]): ∀ (a : Iota), Or (Eq True False) (Ne (op1 (j (skS.0 0 a)) (j (skS.0 0 a))) (j (skS.0 0 a)))
% 11.87/12.09  Clause #50 (by clausification #[20]): ∀ (a : Iota), Eq (op2 (skS.0 0 a) (skS.0 0 a)) (skS.0 0 a)
% 11.87/12.09  Clause #72 (by clausification #[26]): Eq
% 11.87/12.09    (And
% 11.87/12.09      (And
% 11.87/12.09        (And (∀ (W : Iota), sorti1 W → ∀ (X : Iota), sorti1 X → Eq (h (op1 W X)) (op2 (h W) (h X)))
% 11.87/12.09          (∀ (Y : Iota), sorti2 Y → ∀ (Z : Iota), sorti2 Z → Eq (j (op2 Y Z)) (op1 (j Y) (j Z))))
% 11.87/12.09        (∀ (X1 : Iota), sorti2 X1 → Eq (h (j X1)) X1))
% 11.87/12.09      (∀ (X2 : Iota), sorti1 X2 → Eq (j (h X2)) X2))
% 11.87/12.09    True
% 11.87/12.09  Clause #74 (by clausification #[72]): Eq
% 11.87/12.09    (And
% 11.87/12.09      (And (∀ (W : Iota), sorti1 W → ∀ (X : Iota), sorti1 X → Eq (h (op1 W X)) (op2 (h W) (h X)))
% 11.87/12.09        (∀ (Y : Iota), sorti2 Y → ∀ (Z : Iota), sorti2 Z → Eq (j (op2 Y Z)) (op1 (j Y) (j Z))))
% 11.87/12.09      (∀ (X1 : Iota), sorti2 X1 → Eq (h (j X1)) X1))
% 11.87/12.12    True
% 11.87/12.12  Clause #106 (by clausification #[35]): ∀ (a : Iota), Ne (op1 (j (skS.0 0 a)) (j (skS.0 0 a))) (j (skS.0 0 a))
% 11.87/12.12  Clause #409 (by clausification #[74]): Eq
% 11.87/12.12    (And (∀ (W : Iota), sorti1 W → ∀ (X : Iota), sorti1 X → Eq (h (op1 W X)) (op2 (h W) (h X)))
% 11.87/12.12      (∀ (Y : Iota), sorti2 Y → ∀ (Z : Iota), sorti2 Z → Eq (j (op2 Y Z)) (op1 (j Y) (j Z))))
% 11.87/12.12    True
% 11.87/12.12  Clause #1825 (by clausification #[409]): Eq (∀ (Y : Iota), sorti2 Y → ∀ (Z : Iota), sorti2 Z → Eq (j (op2 Y Z)) (op1 (j Y) (j Z))) True
% 11.87/12.12  Clause #1827 (by clausification #[1825]): ∀ (a : Iota), Eq (sorti2 a → ∀ (Z : Iota), sorti2 Z → Eq (j (op2 a Z)) (op1 (j a) (j Z))) True
% 11.87/12.12  Clause #1828 (by clausification #[1827]): ∀ (a : Iota), Or (Eq (sorti2 a) False) (Eq (∀ (Z : Iota), sorti2 Z → Eq (j (op2 a Z)) (op1 (j a) (j Z))) True)
% 11.87/12.12  Clause #1829 (by clausification #[1828]): ∀ (a a_1 : Iota), Or (Eq (sorti2 a) False) (Eq (sorti2 a_1 → Eq (j (op2 a a_1)) (op1 (j a) (j a_1))) True)
% 11.87/12.12  Clause #1830 (by clausification #[1829]): ∀ (a a_1 : Iota),
% 11.87/12.12    Or (Eq (sorti2 a) False) (Or (Eq (sorti2 a_1) False) (Eq (Eq (j (op2 a a_1)) (op1 (j a) (j a_1))) True))
% 11.87/12.12  Clause #1831 (by clausification #[1830]): ∀ (a a_1 : Iota), Or (Eq (sorti2 a) False) (Or (Eq (sorti2 a_1) False) (Eq (j (op2 a a_1)) (op1 (j a) (j a_1))))
% 11.87/12.12  Clause #1832 (by superposition #[1831, 19]): ∀ (a a_1 : Iota),
% 11.87/12.12    Or (Eq (sorti2 a) False) (Or (Eq (j (op2 (skS.0 0 a_1) a)) (op1 (j (skS.0 0 a_1)) (j a))) (Eq False True))
% 11.87/12.12  Clause #1909 (by clausification #[1832]): ∀ (a a_1 : Iota), Or (Eq (sorti2 a) False) (Eq (j (op2 (skS.0 0 a_1) a)) (op1 (j (skS.0 0 a_1)) (j a)))
% 11.87/12.12  Clause #1910 (by superposition #[1909, 19]): ∀ (a a_1 : Iota), Or (Eq (j (op2 (skS.0 0 a) (skS.0 0 a_1))) (op1 (j (skS.0 0 a)) (j (skS.0 0 a_1)))) (Eq False True)
% 11.87/12.12  Clause #1985 (by clausification #[1910]): ∀ (a a_1 : Iota), Eq (j (op2 (skS.0 0 a) (skS.0 0 a_1))) (op1 (j (skS.0 0 a)) (j (skS.0 0 a_1)))
% 11.87/12.12  Clause #1986 (by backward demodulation #[1985, 106]): ∀ (a : Iota), Ne (j (op2 (skS.0 0 a) (skS.0 0 a))) (j (skS.0 0 a))
% 11.87/12.12  Clause #1989 (by forward demodulation #[1986, 50]): ∀ (a : Iota), Ne (j (skS.0 0 a)) (j (skS.0 0 a))
% 11.87/12.12  Clause #1990 (by eliminate resolved literals #[1989]): False
% 11.87/12.12  SZS output end Proof for theBenchmark.p
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