TSTP Solution File: SEU620^2 by Duper---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Duper---1.0
% Problem  : SEU620^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : duper %s

% Computer : n026.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 16:43:02 EDT 2023

% Result   : Theorem 3.78s 3.97s
% Output   : Proof 3.78s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU620^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13  % Command    : duper %s
% 0.13/0.35  % Computer : n026.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Wed Aug 23 21:46:47 EDT 2023
% 0.13/0.35  % CPUTime    : 
% 3.78/3.97  SZS status Theorem for theBenchmark.p
% 3.78/3.97  SZS output start Proof for theBenchmark.p
% 3.78/3.97  Clause #1 (by assumption #[]): Eq
% 3.78/3.97    (Eq kpairiskpair
% 3.78/3.97      (∀ (Xx Xy : Iota),
% 3.78/3.97        iskpair (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))))
% 3.78/3.97    True
% 3.78/3.97  Clause #2 (by assumption #[]): Eq (Eq kpair fun Xx Xy => setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))
% 3.78/3.97    True
% 3.78/3.97  Clause #3 (by assumption #[]): Eq (Not (kpairiskpair → ∀ (Xx Xy : Iota), iskpair (kpair Xx Xy))) True
% 3.78/3.97  Clause #4 (by clausification #[3]): Eq (kpairiskpair → ∀ (Xx Xy : Iota), iskpair (kpair Xx Xy)) False
% 3.78/3.97  Clause #5 (by clausification #[4]): Eq kpairiskpair True
% 3.78/3.97  Clause #6 (by clausification #[4]): Eq (∀ (Xx Xy : Iota), iskpair (kpair Xx Xy)) False
% 3.78/3.97  Clause #7 (by clausification #[6]): ∀ (a : Iota), Eq (Not (∀ (Xy : Iota), iskpair (kpair (skS.0 0 a) Xy))) True
% 3.78/3.97  Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (Xy : Iota), iskpair (kpair (skS.0 0 a) Xy)) False
% 3.78/3.97  Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (Not (iskpair (kpair (skS.0 0 a) (skS.0 1 a a_1)))) True
% 3.78/3.97  Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (iskpair (kpair (skS.0 0 a) (skS.0 1 a a_1))) False
% 3.78/3.97  Clause #11 (by clausification #[1]): Eq kpairiskpair
% 3.78/3.97    (∀ (Xx Xy : Iota),
% 3.78/3.97      iskpair (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)))
% 3.78/3.97  Clause #12 (by forward demodulation #[11, 5]): Eq True
% 3.78/3.97    (∀ (Xx Xy : Iota),
% 3.78/3.97      iskpair (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)))
% 3.78/3.97  Clause #13 (by clausification #[12]): ∀ (a : Iota),
% 3.78/3.97    Eq
% 3.78/3.97      (∀ (Xy : Iota),
% 3.78/3.97        iskpair (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin Xy emptyset)) emptyset)))
% 3.78/3.97      True
% 3.78/3.97  Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota),
% 3.78/3.97    Eq (iskpair (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset))) True
% 3.78/3.97  Clause #15 (by clausification #[2]): Eq kpair fun Xx Xy => setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)
% 3.78/3.97  Clause #16 (by argument congruence #[15]): ∀ (a : Iota),
% 3.78/3.97    Eq (kpair a)
% 3.78/3.97      ((fun Xx Xy => setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)) a)
% 3.78/3.97  Clause #18 (by betaEtaReduce #[16]): ∀ (a : Iota),
% 3.78/3.97    Eq (kpair a) fun Xy => setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin Xy emptyset)) emptyset)
% 3.78/3.97  Clause #19 (by argument congruence #[18]): ∀ (a a_1 : Iota),
% 3.78/3.97    Eq (kpair a a_1)
% 3.78/3.97      ((fun Xy => setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin Xy emptyset)) emptyset)) a_1)
% 3.78/3.97  Clause #24 (by betaEtaReduce #[19]): ∀ (a a_1 : Iota),
% 3.78/3.97    Eq (kpair a a_1) (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset))
% 3.78/3.97  Clause #25 (by backward demodulation #[24, 14]): ∀ (a a_1 : Iota), Eq (iskpair (kpair a a_1)) True
% 3.78/3.97  Clause #28 (by superposition #[25, 10]): Eq True False
% 3.78/3.97  Clause #31 (by clausification #[28]): False
% 3.78/3.97  SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------