TSTP Solution File: SEU541^2 by Duper---1.0
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% File : Duper---1.0
% Problem : SEU541^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n017.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 16:42:36 EDT 2023
% Result : Theorem 3.35s 3.62s
% Output : Proof 3.35s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU541^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : duper %s
% 0.14/0.34 % Computer : n017.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 : Wed Aug 23 20:53:39 EDT 2023
% 0.14/0.34 % CPUTime :
% 3.35/3.62 SZS status Theorem for theBenchmark.p
% 3.35/3.62 SZS output start Proof for theBenchmark.p
% 3.35/3.62 Clause #0 (by assumption #[]): Eq (Eq prop2setI (∀ (Xphi : Prop), Xphi → in emptyset (prop2set Xphi))) True
% 3.35/3.62 Clause #1 (by assumption #[]): Eq (Eq set2prop fun A => in emptyset A) True
% 3.35/3.62 Clause #2 (by assumption #[]): Eq (Not (prop2setI → ∀ (Xphi : Prop), Xphi → set2prop (prop2set Xphi))) True
% 3.35/3.62 Clause #3 (by clausification #[2]): Eq (prop2setI → ∀ (Xphi : Prop), Xphi → set2prop (prop2set Xphi)) False
% 3.35/3.62 Clause #4 (by clausification #[3]): Eq prop2setI True
% 3.35/3.62 Clause #5 (by clausification #[3]): Eq (∀ (Xphi : Prop), Xphi → set2prop (prop2set Xphi)) False
% 3.35/3.62 Clause #6 (by clausification #[5]): ∀ (a : Prop), Eq (Not (skS.0 0 a → set2prop (prop2set (skS.0 0 a)))) True
% 3.35/3.62 Clause #7 (by clausification #[6]): ∀ (a : Prop), Eq (skS.0 0 a → set2prop (prop2set (skS.0 0 a))) False
% 3.35/3.62 Clause #8 (by clausification #[7]): ∀ (a : Prop), Eq (skS.0 0 a) True
% 3.35/3.62 Clause #9 (by clausification #[7]): ∀ (a : Prop), Eq (set2prop (prop2set (skS.0 0 a))) False
% 3.35/3.62 Clause #11 (by identity boolHoist #[8]): ∀ (a : Prop), Or (Eq (skS.0 0 False) True) (Eq a True)
% 3.35/3.62 Clause #14 (by equality factoring #[11]): Or (Ne True True) (Eq (skS.0 0 False) True)
% 3.35/3.62 Clause #16 (by clausification #[0]): Eq prop2setI (∀ (Xphi : Prop), Xphi → in emptyset (prop2set Xphi))
% 3.35/3.62 Clause #17 (by bool simp #[16]): Eq prop2setI (And (True → in emptyset (prop2set True)) (False → in emptyset (prop2set False)))
% 3.35/3.62 Clause #18 (by bool simp #[17]): Eq prop2setI (And (True → in emptyset (prop2set True)) True)
% 3.35/3.62 Clause #19 (by bool simp #[18]): Eq prop2setI (True → in emptyset (prop2set True))
% 3.35/3.62 Clause #20 (by bool simp #[19]): Eq prop2setI (in emptyset (prop2set True))
% 3.35/3.62 Clause #21 (by forward demodulation #[20, 4]): Eq True (in emptyset (prop2set True))
% 3.35/3.62 Clause #25 (by clausification #[14]): Or (Eq (skS.0 0 False) True) (Or (Eq True False) (Eq True False))
% 3.35/3.62 Clause #27 (by clausification #[25]): Or (Eq (skS.0 0 False) True) (Eq True False)
% 3.35/3.62 Clause #28 (by clausification #[27]): Eq (skS.0 0 False) True
% 3.35/3.62 Clause #29 (by identity loobHoist #[9]): ∀ (a : Prop), Or (Eq (set2prop (prop2set True)) False) (Eq (skS.0 0 a) False)
% 3.35/3.62 Clause #32 (by identity boolHoist #[29]): ∀ (a : Prop), Or (Eq (set2prop (prop2set True)) False) (Or (Eq (skS.0 0 False) False) (Eq a True))
% 3.35/3.62 Clause #33 (by betaEtaReduce #[1]): Eq (Eq set2prop (in emptyset)) True
% 3.35/3.62 Clause #34 (by clausification #[33]): Eq set2prop (in emptyset)
% 3.35/3.62 Clause #35 (by argument congruence #[34]): ∀ (a : Iota), Eq (set2prop a) (in emptyset a)
% 3.35/3.62 Clause #40 (by superposition #[35, 21]): Eq True (set2prop (prop2set True))
% 3.35/3.62 Clause #51 (by forward demodulation #[32, 40]): ∀ (a : Prop), Or (Eq True False) (Or (Eq (skS.0 0 False) False) (Eq a True))
% 3.35/3.62 Clause #52 (by clausification #[51]): ∀ (a : Prop), Or (Eq (skS.0 0 False) False) (Eq a True)
% 3.35/3.62 Clause #53 (by superposition #[52, 28]): ∀ (a : Prop), Or (Eq a True) (Eq False True)
% 3.35/3.62 Clause #54 (by clausification #[53]): ∀ (a : Prop), Eq a True
% 3.35/3.62 Clause #57 (by falseElim #[54]): False
% 3.35/3.62 SZS output end Proof for theBenchmark.p
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